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I want a summary of each article. Brief key points and explanation!
These article are about Mutual Funds, Equities, International investingt,property and behavioural biases.
12/05/2012
International Investing
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International Investing
There are different ways you can invest internationally: through mutual
funds, American Depositary Receipts, exchange-traded funds, U.S.-traded
foreign stocks, or direct investments in foreign markets. This online brochure
explains the basic facts about international investing and how you can learn
more about foreign companies and markets. Although this brochure covers
foreign stocks, much of it also applies to foreign bonds.
Why should investors read this brochure?
As investors have learned recently, the market value of investments can
change suddenly. This is true in the U. S. securities markets, but the
changes may be even more dramatic in markets outside the United States.
The world’s economies are becoming more interrelated, and dramatic
changes in stock value in one market can spread quickly to other markets.
Keep in mind that even if you only invest in stocks of U.S. companies you
already may have some international exposure in your investment portfolio.
Many of the factors that affect foreign companies also affect the foreign
business operations of U.S. companies. The fear that economic problems
around the globe will hurt the operations of U.S. companies can cause
dramatic changes in U.S. stock prices.
Sudden changes in market value are only one important consideration in
international investing. Changes in foreign currency exchange rates will
affect all international investments, and there are other special risks you
should consider before deciding whether to invest. The degree of risk may
vary, depending on the type of investment and the market. For example,
international mutual funds may be less risky than direct investments in
foreign markets, and investing in developed economies may avoid some of
the risks of investing in emerging markets.
Why do many Americans invest in foreign markets?
Two of the chief reasons why people invest internationally are:
Diversification — spreading your investment risk among foreign
companies and markets that are different than the U.S. economy, and
Growth — taking advantage of the potential for growth in some foreign
economies, particularly in emerging markets.
By including exposure to both domestic and foreign stocks in your portfolio,
you’ll reduce the risk that you’ll lose money and your portfolio’s overall
investment returns will have a smoother ride. That’s because international
investment returns sometimes move in a different direction than U.S. market
returns. Even when international and U.S. investments move in the same
direction the degree of change may be very different. When you compare
the returns from emerging international markets with U.S. market returns you
may see even wider swings in value.
Of course, you have to balance these considerations against the possibility
of higher costs, sudden changes in value, and the special risks of
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international investing.
What are the special risks in international investing?
Although you take risks when you invest in any stock, international investing
has some special risks:
Changes in currency exchange rates. When the exchange rate
between the foreign currency of an international investment and the
U.S. dollar changes, it can increase or reduce your investment return.
How does this work? Foreign companies trade and pay dividends in the
currency of their local market. When you receive dividends or sell your
international investment, you will need to convert the cash you
receive into U.S. dollars. During a period when the foreign currency is
strong compared to the U.S. dollar, this strength increases your
investment return because your foreign earnings translate into more
dollars. If the foreign currency weakens compared to the U.S. dollar,
this weakness reduces your investment return because your earnings
translate into fewer dollars. In addition to exchange rates, you should
be aware that some countries may impose foreign currency controls
that restrict or delay you from moving currency out of a country.
Investor Tidbit: What is an index? An index is a group of stocks
representing a particular segment of a market, or in some cases the entire
market. For example, the Standard & Poor’s 500 index represents a specific
segment of the U.S. capital markets. Foreign stock markets also may be
represented by an index, such as the MSCI EAFE index, a well-known index
in more developed foreign markets, the Nikkei index of large Japanese
companies, or the CAC 40 index of large French companies. The
components of an index can change over time, as new stocks are added
and old ones are dropped.
Dramatic changes in market value. Foreign markets, like all markets,
can experience dramatic changes in market value. One way to reduce
the impact of these price changes is to invest for the long term and
try to ride out sharp upswings and downturns in the market.
Individual investors frequently lose money when they try to “time” the
market in the United States and are even less likely to succeed in a
foreign market. When you “time” the market you have to make two
astute decisions — deciding when to get out before prices fall and
when to get back in before prices rise again.
Political, economic and social events. It is difficult for investors to
understand all the political, economic, and social factors that influence
foreign markets. These factors provide diversification, but they also
contribute to the risk of international investing.
Lack of liquidity. Foreign markets may have lower trading volumes and
fewer listed companies. They may only be open a few hours a day.
Some countries restrict the amount or type of stocks that foreign
investors may purchase. You may have to pay premium prices to buy a
foreign security and have difficulty finding a buyer when you want to
sell.
Less information. Many foreign companies do not provide investors
with the same type of information as U.S. public companies. It may be
difficult to locate up-to-date information, and the information the
company publishes my not be in English.
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Reliance on foreign legal remedies. If you have a problem with your
investment, you may not be able to sue the company in the United
States. Even if you sue successfully in a U.S. court, you may not be
able to collect on a U.S. judgment against a foreign company. You
may have to rely on whatever legal remedies are available in the
company’s home country.
Different market operations. Foreign markets often operate differently
from the major U.S. trading markets. For example, there may be
different periods for clearance and settlement of securities
transactions. Some foreign markets may not report stock trades as
quickly as U.S. markets. Rules providing for the safekeeping of shares
held by custodian banks or depositories may not be as well developed
in some foreign markets, with the risk that your shares may not be
protected if the custodian has credit problems or fails.
What are the costs of international investments?
International investing can be more expensive than investing in U.S.
companies. In smaller markets, you may have to pay a premium to purchase
shares of popular companies. In some countries there may be unexpected
taxes, such as withholding taxes on dividends. Transaction costs such as
fees, broker’s commissions, and taxes often are higher than in U.S. markets.
Mutual funds that invest abroad often have higher fees and expenses than
funds that invest in U.S. stocks, in part because of the extra expense of
trading in foreign markets.
What are the different ways to invest internationally?
Mutual funds. One way to invest internationally is through mutual funds.
There are different kinds of funds that invest in foreign stocks.
Global funds invest primarily in foreign companies, but may also invest
in U.S. companies.
International funds generally limit their investments to companies
outside the United States.
Regional or country funds invest principally in companies located in a
particular geographical region (such as Europe or Latin America) or in a
single country. Some funds invest only in emerging markets, while
others concentrate on more developed markets.
International index funds try to track the results of a particular foreign
market index. Index funds differ from actively managed funds, whose
managers pick stocks based on research about the companies.
International investing through mutual funds can reduce some of the risks
mentioned earlier. Mutual funds provide more diversification than most
investors could achieve on their own. The fund manager also should be
familiar with international investing and have the resources to research
foreign companies. The fund will handle currency conversions and pay any
foreign taxes, and is likely to understand the different operations of foreign
markets.
Like other international investments, mutual funds that invest internationally
probably will have higher costs than funds that invest only in U.S. stocks. If
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you want to learn more about investing in mutual funds, information is
available in our brochure, Invest Wisely – An Introduction to Mutual Funds.
Exchange-Traded Funds. An exchange-traded fund is a type of investment
company whose investment objective is to achieve the same return as a
particular market index. Increasingly popular with investors, ETFs are listed
on stock exchanges and, like stocks (and in contrast to mutual funds), trade
throughout the trading day. A share in an ETF that tracks an international
index gives an exposure to the performance of the underlying stock or bond
portfolio along with the ability to trade that share like any other security.
American Depositary Receipts. The stocks of most foreign companies that
trade in the U.S. markets are traded as American Depositary Receipts (ADRs)
issued by U.S. depositary banks.
Investor Tidbit: ADRs or ADSs? Sometimes the terms “ADR” and “ADS”
(American Depositary Share) are used interchangeably. An ADR is actually
the negotiable physical certificate that evidences ADSs (in much the same
way a stock certificate evidences shares of stock), and an ADS is the
security that represents an ownership interest in deposited securities (in
much the same way a share of stock represents an ownership interest in
the corporation). ADRs are the instruments actually traded in the market.
Each ADR represents one or more shares of a foreign stock or a fraction of a
share. If you own an ADR you have the right to obtain the foreign stock it
represents, but U.S. investors usually find it more convenient to own the
ADR. The price of an ADR corresponds to the price of the foreign stock in its
home market, adjusted for the ratio of ADRs to foreign company shares.
Owning ADRs has some advantages compared to owning foreign shares
directly:
When you buy and sell ADRs you are trading in the U.S. market. Your
trade will clear and settle in U.S. dollars.
The depositary bank will convert any dividends or other cash payments
into U.S. dollars before sending them to you.
The depositary bank may arrange to vote your shares for you as you
instruct.
On the other hand, there are some disadvantages:
It may take a long time for you to receive information from the
company because it must pass through an extra pair of hands. You
may receive information about shareholder meetings only a few days
before the meeting, well past the time when you could vote your
shares.
Depositary banks charge fees for their services and will deduct these
fees from the dividends and other distributions on your shares. The
depositary bank also will incur expenses, such as for converting foreign
currency into U.S. dollars, and usually will pass those expenses on to
you.
U.S. Traded Foreign Stocks
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Although most foreign stocks trade in the U.S. markets as ADRs, some
foreign stocks trade here in the same form as in their local market. For
example, Canadian stocks trade in the same form in the United States as
they do in the Canadian markets, rather than as ADRs. You can purchase
ADRs and other foreign stocks that trade in the United States through your
broker. There are different trading markets in the United States, and the
information available about an ADR or foreign stock will depend on where it
trades.
Stocks Trading on Foreign Markets
If you want to buy or sell stock in a company that only trades on a foreign
stock market, your broker may be able to process your order for you. These
foreign companies do not file reports with the SEC, however, so you will
need to do additional research to get the information you need to make an
investment decision. Always make sure any broker you deal with is
registered with the SEC. It is against the law for unregistered foreign
brokers to call you and solicit your investment.
What should I do if I want to invest?
Like any other investment, you should learn as much as you can about a
company before you invest. Try to learn about the political, economic, and
social conditions in the company’s home country, so you will understand
better the factors that affect the company’s financial results and stock
price. If you invest internationally through mutual funds, make sure you
know the countries where the fund invests and understand the kinds of
investments it makes.
Here are some sources of information:
SEC reports. Many foreign companies file reports with the SEC. The
SEC requires foreign companies to file electronically, so their reports
usually are available through the SEC’s web site at
www.sec.gov/edgar.shtml at no charge. You can get paper copies for
a fee from the SEC’s Public Reference Branch by calling (202) 551-
8090 or sending a request to:
Public Reference Branch
U.S. Securities and Exchange Commission
100 F Street, N.E.
Washington, DC 20549
International Regulators. You might be able to learn more about a
particular company by contacting the securities regulator that
oversees the markets in which that company’s securities trade. Many
international securities regulators post issuer information on their
websites, including audited financial statements. You’ll find a list of
international securities regulators on the website of the International
Organization of Securities Commissions (IOSCO) at www.iosco.org.
Mutual fund firms. You can get the prospectus for a particular mutual
fund directly from the mutual fund firm. Many firms also have websites
that provide helpful information about international investing.
The company. Foreign companies often prepare annual reports, and
some companies also publish an English language version of their
annual report. Ask your broker for copies of the company’s reports or
check to see if they are available from the SEC. Some foreign
companies post their annual reports and other financial information on
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their websites.
Broker-dealers. Your broker may have research reports on particular
foreign companies, individual countries, or geographic regions. Ask
whether updated reports are available on a regular basis. Your broker
also may be able to get copies of SEC reports and other information
for you.
Publications. Many financial publications and international business
newspapers provide extensive news coverage of foreign companies
and markets.
Internet Resources. Various government, commercial, and media
websites offer information about foreign companies and markets.
However, as with any investment opportunity, you should be
extremely wary of “hot tips,” overblown statements, and information
posted on the Internet from unfamiliar sources. For tips on how to
spot and avoid Internet fraud, please visit the “Investor Information”
section of our website at www.sec.gov/investor.shtml.
Investor Tidbit: International Stock Scams
Whether it’s foreign currency trading, “prime European bank” securities or
fictitious coconut plantations in Costa Rica, you should be skeptical about
exotic-sounding international investment “opportunities” offering returns
that sound too good to be true. They usually are. In the past, con artists
have used the names of well-known European banks or the International
Chamber of Commerce — without their knowledge or permission — to
convince unsophisticated investors to part with their money.
Some promoters based in the United States try to make their investment
schemes sound more enticing by giving them an international flavor. Other
promoters actually operate from outside the United States and use the
Internet to reach potential investors around the globe. Remember that
when you invest abroad and something goes wrong, it’s more difficult to
find out what happened and locate your money. As with any investment
opportunity that promises quick profits or a high rate of return, you should
stop, ask questions, and investigate before you invest.
Tracking down information on international investments requires some extra
effort, but it will make you a more informed investor. One of the most
important things to remember is to read and understand the information
before you invest.
If you have more questions or if you have a problem with your international
investment, please contact us right away. To submit your complaint
electronically, please visit our online Complaint Center at
www.sec.gov/complaint.shtml. You also may send us a letter at the
following address:
Office of Investor Education and Advocacy
U.S. Securities and Exchange Commission
100 F Street, N.E.
Washington, DC 20549-0213
http://www.sec.gov/investor/pubs/ininvest.htm
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Home | Previous Page Modified: 08/01/2007
S&P INDICES| Research Insights January 2010
Do Past Mutual Fund Winners Repeat?
The
S&P Persistence Scorecard
Thought Leadership by Global
Research & Design
www.indexresearch.standardandpoors.com
Srikant Dash, CFA, FRM
(212) 438 3012
srikant_dash@sandp.com
The phrase “past performance is not an indicator of future outcomes” is a
common fine print line found in all mutual fund literature. Yet due to either
force of habit or conviction, both investors and advisors consider past
performance and related metrics to be important factors in fund selection.
Does past performance really matter? The semi-annual S&P Persistence
Scorecard seeks to track the consistency of top performers over three- and
five-consecutive year periods, and measure performance persistence
through transition matrices for three- and five-year non-overlapping holding
periods. As in our widely followed Standard & Poor’s Indices Versus Active
Funds (SPIVATM) Scorecards, the University of Chicago’s CRSP
Survivorship Bias Free Mutual Fund Database underlies our analysis.
Very few funds manage to consistently repeat top-half or top-quartile
performance. Over the five years ending September 2009, only 4.27%
large-cap funds, 3.98% mid-cap funds, and 9.13% small-cap funds
maintained a top-half ranking over the five consecutive 12-month periods.
No large- or mid-cap funds, and only one small-cap fund maintained a top-
quartile ranking over the same period.
Looking at longer term performance, 24.32% of large-cap funds with a top-
quartile ranking over the five years ending September 2004 maintained a
top-quartile ranking over the next five years. Only 16.39% of mid-cap funds
and 27.06% of small-cap funds maintained a top-quartile performance over
the same period. Random expectations would suggest a repeat rate of
25%.
Our research suggests that screening for top-quartile funds may be
inappropriate. A healthy plurality of future top-quartile funds comes from the
prior period’s second, third and even fourth quartiles. Screening out bottom
quartile funds may be appropriate, however, since they have a very high
probability of being merged or liquidated.
S&P Persistence Scorecard
S&P INDICES | Research Insights
Introduction
“Past performance is not an indicator of future outcomes” is a phrase found in the fine
print of all mutual fund related literature. However, investors and advisors alike consider
past performance and related metrics to be crucial to the fund selection process.
Does past performance really matter? To answer this question on an ongoing basis, we
are reintroducing the semi-annual S&P Persistence Scorecard. The scorecard seeks to
track the consistency of top performers over consecutive year periods, as well as
measure performance persistence through transition matrices. As in our widely followed
SPIVA reports, the University of Chicago’s CRSP Survivorship Bias Free Mutual Fund
Database serves as our underlying data source.
Listed below are the key features of the S&P Persistence Scorecard:
Historical Rankings without Survivorship bias: For anyone making an
investment decision at the beginning of a time period, all funds available at that
time are part of the initial opportunity set. However, many funds might liquidate
or merge during a period of study. Often analysts use a finite set of funds that
cover the complete historical time period, in essence, ranking the survivors. By
using the University of Chicago’s Center for Research in Security Prices (CRSP)
Survivorship Bias Free Mutual fund Database, the S&P Persistence Scorecard
ranks all funds available at each point in time, and tracks the top-quartile and
top-half performers throughout the time period.
Clean Universe: The mutual fund universe used in these reports comprises
actively managed domestic U.S. equity funds. Index funds, sector funds, and
index-based dynamic (bull/bear) funds are excluded from the sample. To avoid
double counting of multiple share classes, only the largest share class of a fund
is used.
Transition Matrices: Transition matrices show the movements between
quartiles and halves for two non-overlapping three- and five-year periods. They
also track the percentage of funds that have merged or liquidated. Additionally,
we monitor movements between capitalization levels; for example, if some
large-cap funds have become mid- or small-cap funds.
Tracking reports of top performers: The tracking reports show the
percentages of funds that remain in the top-quartile or top-half rankings for three
and five-consecutive year periods.
Standard & Poor’s Persistence Scorecard is the only comprehensive, periodic and
publicly available source of such data. The semi-annual reports can be found online at
Uwww.spiva.standardandpoors.comU.
S&P Persistence Scorecard
S&P INDICES | Research Insights
Very Few Funds Consistently Stay in the Top-Quartile or Top-Half
Reports 1 and 2, found at the end of this paper, show very few funds managing to
consistently repeat top-half or top-quartile performance. Over the five years ending
September 2009, only 15 (4.27%) large-cap funds, 7 (3.98%) mid-cap funds, and 21
(9.13%) small-cap funds maintained a top-half ranking over five consecutive 12-month
periods. No large- or mid-cap funds, and only one small-cap fund, maintained a top-
quartile ranking over the same period. While low in absolute terms, these percentages
are best understood in a probabilistic context. If fund returns are random and
independent of prior returns, one would expect the top-half repeat rate to be 6.25% and
the top-quartile repeat rate to be 0.39%.
Looking at longer term performance, 24.32% of large-cap funds with a top-quartile
ranking over five years ending September 2004 maintained a top-quartile ranking over
the next five years. Only 16.39% of mid-cap funds and 27.06% of small-cap funds
maintained a top-quartile performance over the same period. Again, these percentages
should be put in context of random expectations. If one were to pick a fund randomly,
the chance of choosing a fund that will occupy the top-quartile during the next five years
would be 25%.
Therefore, using the past five years’ annual returns as well as cumulative five-year
historical returns to find futures winners is roughly equivalent to, and for cases like
small-cap funds, slightly superior to, rolling the dice.
Is Quartile Based Screening for Funds Appropriate?
In this scorecard, we reference random expectations because they set a benchmark for
the usefulness of screening funds based on past returns. The fact that in many cases
the repeat rates are higher than random expectations suggests that past performance
should not be dismissed as completely irrelevant. However, we believe the common
practice of screening for funds based on current top-quartile rankings may be
inappropriate for the following reasons:
The low absolute counts of repeat top performers suggest that past performance
cannot be the sole or most important criteria in fund selection.
Furthermore, the transition matrices of Report 3 and 4, found at the end of the paper,
suggest that a healthy percentage of current top-quartile funds come from prior
period second or third quartiles. This is illustrated in the charts found on the next
page. Therefore, advisors and consultants who use granular rankings such as
quartiles, or even quintiles and deciles, may be missing out on funds that should
belong to their initial selection set.
There does seem to be some logic in deeply scrutinizing or even screening out bottom-
quartile funds. Many of the bottom quartile funds are subsequently merged or liquidated.
Clearly, asset management companies do not want to have laggards in their advertised
line-ups.
S&P Persistence Scorecard
S&P INDICES | Research Insights
Source: Standard & Poors, CRSP. Breakdown of top-quartile performers from 10/2004 to 9/2009 based
upon their quartile ranking from 10/1999 to 2/2004.
Where did the top-quartile small-cap
funds for the last five years come from?
3rd Quartile
in Previous
5 Years
16%
4th Quartile
in Previous
5 Years
27%
1
st Quartile
in Previous
5 Years
36%
2nd Quartile in
Previous 5 Years
21%
Where did the top-quartile large-cap
funds for the last five years come from?
3rd Quartile
in Previous
5 Years
19%
4th Quartile
in Previous
5 Years
18% 1
st Quartile
in Previous
5 Years
43%
2nd Quartile in
Previous 5 Years
20%
S&P Persistence Scorecard
S&P INDICES | Research Insights
Report 1: Performance Persistence over Three Consecutive 12-Month Periods
Fund Count at
Start
Percentage Remaining in Top
Quartile
Mutual Fund Category
Sep-07 Sep-08 Sep-09
Top Quartile
All Domestic Funds 570 14.91 3.86
Large-Cap Funds 172 17.44 5.81
Mid-Cap Funds 97 12.37 2.06
Small-Cap Funds 133 14.29 3.01
Multi-Cap Funds 168 14.29 3.57
Fund Count at
Start
Percentage Remaining in Top
Half
Sep-07 Sep-08 Sep-09
Top Half
All Domestic Funds 1139 41.53 20.11
Large-Cap Funds 344 46.22 24.71
Mid-Cap Funds 194 38.14 16.49
Small-Cap Funds 266 40.6 20.3
Multi-Cap Funds 335 39.4 17.31
Source: Standard & Poor’s. For Periods Ending September 30, 2009
Report 2: Performance Persistence over Five Consecutive 12-Month Periods
Fund Count at
Start Percentage Remaining in Top Quartile
Mutual Fund Category
Sep-05 Sep-06 Sep-07 Sep-08 Sep-09
Top Quartile
All Domestic Funds 524 25.19 7.25 1.34 0.38
Large-Cap Funds 176 25 4.55 1.7 0
Mid-Cap Funds 88 26.14 9.09 2.27 0
Small-Cap Funds 115 26.09 6.96 0.87 0.87
Multi-Cap Funds 145 24.14 9.66 0.69 0.69
Fund Count at
Start Percentage Remaining in Top Half
Sep-05 Sep-06 Sep-07 Sep-08 Sep-09
Top Half
All Domestic Funds 1046 50.38 25.14 12.05 5.54
Large-Cap Funds 351 48.15 20.51 10.26 4.27
Mid-Cap Funds 176 47.16 23.3 12.5 3.98
Small-Cap Funds 230 55.22 30 15.65 9.13
Multi-Cap Funds 289 51.21 28.03 11.07 5.19
Source: Standard & Poor’s. For Periods Ending September 30, 2009
S&P Persistence Scorecard
S&P INDICES | Research Insights
Report 3: Three-Year Transition Matrix
(Performance over Two Non-Overlapping Three-Year Periods)
Based On Quartiles
Three-Year Percentages at End
No of Funds at
Start
1st Quartile
(%)
2nd Quartile
(%)
3rd Quartile
(%)
4th Quartile
(%)
Merged/
Liquidated
(%)
Style
Changed (%) Total (%)
Sep-06
All Domestic Funds
1st Quartile 481 23.28 19.33 23.49 24.74 9.15 0 100
2nd Quartile 482 19.09 18.88 20.54 26.14 15.35 0 100
3rd Quartile 481 20.79 21 21.62 17.46 19.13 0 100
4th Quartile 481 17.26 21.41 14.76 12.06 34.51 0 100
Large-Cap Funds
1st Quartile 164 13.41 15.85 26.83 33.54 8.54 1.83 100
2nd Quartile 164 14.02 14.63 21.34 21.95 19.51 8.54 100
3rd Quartile 163 21.47 20.25 14.11 10.43 23.31 10.43 100
4th Quartile 164 21.95 20.12 7.93 4.88 39.02 6.1 100
Mid-Cap Funds
1st Quartile 81 20.99 16.05 25.93 18.52 8.64 9.88 100
2nd Quartile 81 17.28 16.05 19.75 22.22 12.35 12.35 100
3rd Quartile 81 11.11 27.16 8.64 18.52 19.75 14.81 100
4th Quartile 81 20.99 11.11 16.05 11.11 24.69 16.05 100
Small-Cap Funds
1st Quartile 109 26.61 20.18 20.18 24.77 8.26 0 100
2nd Quartile 108 16.67 25.93 20.37 19.44 15.74 1.85 100
3rd Quartile 109 23.85 21.1 23.85 17.43 13.76 0 100
4th Quartile 108 13.89 12.96 16.67 18.52 32.41 5.56 100
Multi-Cap Funds
1st Quartile 128 15.63 11.72 21.09 18.75 7.81 25 100
2nd Quartile 128 10.16 17.97 10.94 19.53 20.31 21.09 100
3rd Quartile 128 17.97 17.97 19.53 9.38 17.19 17.97 100
4th Quartile 128 15.63 10.94 7.81 10.94 32.03 22.66 100
Based On Halves
Three-Year Percentages at End
No of funds at
Start
Top Half
(%)
Bottom Half
(%)
Merged/
Liquidated
(%)
Style
Changed (%) Total (%)
All Domestic Funds
Top Half 963 40.29 47.46 12.25 0 100
Bottom Half 962 40.23 32.95 26.82 0 100
Large-Cap Funds
Top Half 328 28.96 51.83 14.02 5.18 100
Bottom Half 327 41.9 18.65 31.19 8.26 100
Mid-Cap Funds
Top Half 162 35.19 43.21 10.49 11.11 100
Bottom Half 162 35.19 27.16 22.22 15.43 100
Small-Cap Funds
Top Half 217 44.7 42.4 11.98 0.92 100
Bottom Half 217 35.94 38.25 23.04 2.76 100
Multi-Cap Funds
Top Half 256 27.73 35.16 14.06 23.05 100
Bottom Half 256 31.25 23.83 24.61 20.31 100
Source: Standard & Poor’s. For Periods Ending September 30, 2009
S&P Persistence Scorecard
S&P INDICES | Research Insights
Report 4: Five-Year Transition Matrix
(Performance over Two Non-Overlapping Five-Year Periods)
Based On Quartiles
Five-Year Percentages at End
No of Funds at
Start
1st Quartile
(%)
2nd Quartile
(%)
3rd Quartile
(%)
4th Quartile
(%)
Merged/
Liquidated
(%)
Style
Changed (%) Total (%)
Sep-04
All Domestic Funds
1st Quartile 384 29.95 20.83 16.15 20.31 12.76 0 100
2nd Quartile 384 17.71 24.48 19.01 18.49 20.31 0 100
3rd Quartile 384 12.76 14.32 24.48 16.93 31.51 0 100
4th Quartile 384 12.24 13.02 12.76 16.93 45.05 0 100
Large-Cap Funds
1st Quartile 148 24.32 17.57 12.16 22.3 18.92 4.73 100
2nd Quartile 147 11.56 14.97 19.05 13.61 31.29 9.52 100
3rd Quartile 148 10.81 10.14 16.22 12.84 40.54 9.46 100
4th Quartile 147 10.2 14.29 8.84 8.16 49.66 8.84 100
Mid-Cap Funds
1st Quartile 61 16.39 22.95 18.03 14.75 3.28 24.59 100
2nd Quartile 60 13.33 13.33 15 16.67 26.67 15 100
3rd Quartile 61 18.03 18.03 21.31 14.75 19.67 8.2 100
4th Quartile 60 15 6.67 8.33 15 40 15 100
Small-Cap Funds
1st Quartile 85 27.06 27.06 12.94 23.53 7.06 2.35 100
2nd Quartile 85 15.29 20 23.53 21.18 16.47 3.53 100
3rd Quartile 85 11.76 14.12 28.24 15.29 27.06 3.53 100
4th Quartile 85 20 12.94 9.41 14.12 40 3.53 100
Multi-Cap Funds
1st Quartile 91 14.29 12.09 16.48 16.48 14.29 26.37 100
2nd Quartile 91 12.09 19.78 8.79 9.89 15.38 34.07 100
3rd Quartile 91 7.69 12.09 14.29 12.09 23.08 30.77 100
4th Quartile 91 15.38 5.49 8.79 10.99 38.46 20.88 100
Based On Halves
Five-Year Percentages at End
No of funds at
Start
Top Half
(%)
Bottom Half
(%)
Merged/
Liquidated
(%)
Style
Changed (%) Total (%)
All Domestic Funds
Top Half 768 46.48 36.98 16.54 0 100
Bottom Half 768 26.17 35.55 38.28 0 100
Large-Cap Funds
Top Half 295 34.24 33.56 25.08 7.12 100
Bottom Half 295 22.71 23.05 45.08 9.15 100
Mid-Cap Funds
Top Half 121 33.06 32.23 14.88 19.83 100
Bottom Half 121 28.93 29.75 29.75 11.57 100
Small-Cap Funds
Top Half 170 44.71 40.59 11.76 2.94 100
Bottom Half 170 29.41 33.53 33.53 3.53 100
Multi-Cap Funds
Top Half 182 29.12 25.82 14.84 30.22 100
Bottom Half 182 20.33 23.08 30.77 25.82 100
Source: Standard & Poor’s. For Periods Ending September 30, 2009
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September/October 2009
AHEAD OF PRINT
1
Financial Analysts Journal
Volume 65 Number 5
©2009 CFA Institute
REIT Momentum and the Performance
of Real Estate Mutual Funds
Jeroen Derwall, Joop Huij, Dirk Brounen, and Wessel Marquering
REITs exhibit a strong and prevalent momentum effect that is not captured by conventional factor
models. This REIT momentum anomaly hampers proper judgments about the performance of
actively managed REIT portfolios. In contrast, a REIT momentum factor adds incremental
explanatory power to performance attribution models for REIT portfolios. Using this factor, this
study finds that REIT momentum explains a great deal of the abnormal returns that actively
managed REIT mutual funds earn in aggregate. Accounting for exposure to REIT momentum also
materially influences cross-sectional comparisons of the performances of REIT mutual funds. This
study has important implications for performance evaluation, alpha–beta separation, and manager
selection and compensation.
lthough real estate used to be an exclusive
investment alternative for a relatively
small group of investors, investing in real
estate through REITs, real estate mutual
funds, and private offerings is now easier than
ever. Managers of such real estate portfolios as real
estate mutual funds are compensated for the return
they produce on their portfolios relative to that of
a benchmark portfolio. The difference between the
return earned by the mutual fund manager and the
return on the benchmark—known as abnormal
return, or alpha—is attributed to managerial skill.
The benchmark return can be obtained from a fac-
tor model that is assumed to describe the cross-
section of expected returns. Using such a factor
model thereby ensures that the manager does not
receive compensation for exposures to common
factors. Fama and French (1992, 1993, 1996) and
Carhart (1997) advocated factor models composed
of proxies for market risk, size and book-to-market
premiums, and momentum to describe the cross-
section of returns on common stocks. Researchers
routinely use these factors when studying the per-
formance of broadly diversified and actively man-
aged equity mutual funds.1
Less consensus exists regarding whether these
factors suffice as an evaluation of such industry-
specific portfolios as REIT mutual funds or what
alternative factors might be needed. The choice of
factor model can substantially influence the per-
formance attributed to active portfolio manage-
ment.2 The essence of the problem is that alpha
estimated with incomplete factor specifications
may reflect exposure to omitted factors instead of
the portfolio manager’s security selection skill.
Some researchers have suggested that factor mod-
els originally introduced for a wide range of com-
mon stocks inadequately describe the expected
returns of portfolios that concentrate on various
capital market segments. For example, Fama and
French (1997) showed that conventional factor
models do not suffice to describe the returns on
certain industry portfolios.
We studied the REIT industry to see whether
momentum effects in U.S. REIT returns can influ-
ence both the validity of common factor models and
portfolio performance attribution. We were moti-
vated to focus on REIT portfolios by recent evidence
from Chui, Titman, and Wei (2003b). They demon-
strated that a basic REIT-specific momentum strat-
egy, which buys REITs with the highest past return
and sells short REITs with the lowest past return
,
produces a return that is economically larger than
that of the Jegadeesh and Titman (1993) common-
stock momentum strategy. Moreover, REITs have
generally been ignored in studies of the determi-
nants of stock returns (see, e.g., Fama and French
1993). A natural question that emerges is whether
REIT momentum is significantly underestimated
Jeroen Derwall is assistant professor of finance at
Maastricht University and at Tilburg University, the
Netherlands. Joop Huij is assistant professor of finance
at RSM Erasmus University and senior researcher at
Robeco, Rotterdam, the Netherlands. Dirk Brounen is
professor of finance and real estate at RSM Erasmus
University, Rotterdam, the Netherlands. Wessel Mar-
quering is quantitative researcher/risk manager at Taler
Asset Management Ltd., Gibraltar.
A
AHEAD OF PRINT
2 AHEAD OF PRINT ©2009 CFA Institute
Financial Analysts Journal
by conventional factor models that control for
common-stock momentum, such as the Carhart
(1997) model. This potential misspecification might
have important implications for existing views on
the benefits of active real estate portfolio manage-
ment, which stem from studies that rely on these
models (see, e.g., Kallberg, Liu, and Trzcinka 2000).
The Literature
Our research was inspired by a large number of
studies that explored patterns in REIT returns and
by studies that built on those patterns to develop
factor models that can be used to evaluate the per-
formance of REIT portfolios. What emerged from
those studies is a case for using multiple factors to
describe expected REIT returns. But researchers
have yet to reach a consensus on which set of factors
best describes REIT returns.
Consistent with the notion that REIT returns
are driven by factors not captured by aggregate
stock market dynamics, Titman and Warga (1986)
reported that risk-adjusted REIT returns are gener-
ally much higher under the capital asset pricing
model (CAPM) that includes a value-weighted
stock market proxy than under a multi-index
model extracted from factor analysis. Follow-up
studies (see, e.g., Chan, Hendershott, and Sanders
1990; Karolyi and Sanders 1998) recommended
multifactor models in the tradition of the intertem-
poral CAPM (ICAPM) of Merton (1973) and the
arbitrage pricing theory (APT) of Ross (1976).
More-recent research assigns considerable
importance to company-specific variables as candi-
date factors for explaining the cross-section of REIT
returns. Chen, Hsieh, Vines, and Chiou (1998)
found that the cross-section of REIT returns is bet-
ter explain ed by stock market beta and by
Fama–French (1992) company-specific variables
(i.e., company size and book-to-market) than by
macroeconomic variables similar to those in Chen,
Roll, and Ross (1986). Of the company-specific vari-
ables, size is the main robust cross-sectional deter-
minant of REIT returns over the 1978–94 sample
period. This evidence for the importance of
company-specific variables in explaining the cross-
section of expected REIT returns prompted the
creation of intertemporal asset pricing models.
Peterson and Hsieh (1997) suggested that time vari-
ation in (aggregate) equity REIT returns is best
explained by the three-factor model of Fama and
French (1993), which extends the equity CAPM
with factor returns concerning company size and
the book-to-market ratio. They concluded that
equity REITs earned positive abnormal returns
over the period 19761992 under the single-factor
CAPM and zero abnormal returns under a model
with the three Fama–French (1993) factors. Consis-
tent with the evidence of abnormal REIT returns,
Hartzell, Mühlhofer, and Titman (2007) reported
that including benchmarks that are sensitive to
company size, book-to-market ratios, and non-
REIT returns materially affects conclusions about
REIT portfolio performance.
Although the Fama–French (1993) model
appears to do a good job of explaining equity REIT
returns, recent studies have created an appetite
for a replacement model. Chui, Titman, and Wei
(2003a) showed that most of the previously
mentioned company-specific variables are not
robust cross-sectional determinants of REIT
returns over time; rather, REIT momentum is the
variable that consistently explains REIT returns.
According to Chui, Titman, and Wei (2003b),
past REIT return is a significant driver of future
REIT return both before and after 1990. Further-
more, they showed that the Fama–French (1993)
model cannot explain the returns of momentum-
sorted REIT portfolios—similar in spirit to the
momentum-sorted common-stock portfolios dis-
cussed in Jegadeesh and Titman (1993). These
findings suggest that using a factor model that
incorporates momentum, such as the Carhart
(1997) model, might be necessary in evaluating the
performance of REIT portfolios. None of the cited
studies, however, investigated whether REIT
mo me nt um is ex plain e d by co mmo n -st ock
momentum or presented a factor model that helps
capture this industry-specific anomaly.
The potential misspecification of factor models
can affect existing views on the value added by
REIT portfolio managers (see, e.g., Buttimer,
Hyland, and Sanders 2005). Damodaran and Liu
(1993) suggested that investment managers in the
real estate sector produce positive abnormal
returns because of their appraisal skills and their
information about real estate investment targets.
Supporting the active management argument of
Damodaran and Liu (1993), Kallberg, Liu, and
Trzcinka (2000) reported positive abnormal returns
for REIT mutual funds for the period 19861998
under both single-factor models that include either
the S&P 500 Index or a REIT index and multifactor
models that augment the single-factor model with
the Fama–French (1993) factors, a bond index, and
a real estate index. But none of the performance
attribution models incorporate REIT momentum.
Whether a REIT momentum effect underlies cur-
rent conclusions about REIT mutual fund perfor-
mance is a major focus of our study.
AHEAD OF PRINT
September/October 2009 AHEAD OF PRINT 3
REIT Momentum and the Performance of Real Estate Mutual Funds
Measuring the Performance of
REIT Portfolios
Actively managed portfolios are typically evalu-
ated by the return they generate in excess of the
expected return on a passive benchmark portfolio
of similar risk:
(1)
where p is Jensen’s (1969) alpha, Rp denotes the
average return on portfolio p over a specified
investment horizon, and E (Rp) indicates the aver-
age expected return on portfolio p with factor expo-
sures that match those of the evaluated portfolio. A
positive alpha indicates that the portfolio manager
has investment skills. In the context of REIT port-
folios, the expected return can be determined with
a linear REIT factor model:
(2)
where E (Rp, t) is the expected return on portfolio p
at time t, K, p is portfolio p’s exposure to factor K
(K = 1, 2, . . ., K), and XK, t is the return on factor K
at time t. Note that the estimates of the parameters
in Equation 2 are assumed to be time-invariant for
expositional convenience.
We can interpret REIT models that include a
mixture of factors along several lines. One interpre-
tation is that these models are similar to multifactor
models for common stocks. Theoretically, these
models can be justified by various alternatives to
the CAPM, such as the ICAPM of Merton (1973)
and the APT of Ross (1976). In this setup, the factors
are proxies for underlying risks in the economy that
are of concern to investors. Usually, factors are
measured as factor-mimicking return spreads (e.g.,
between a passive benchmark and the risk-free rate
of return), and the models’ betas measure the
funds’ risk-factor exposures. An alternative inter-
pretation is that the factors compose a performance
attribution model that essentially controls for pas-
sive investment return, as in Carhart (1997), where
the passive benchmarks multiplied by their esti-
mated weights (betas) most closely reproduce a
fund’s return variation. The excess return (Jensen’s
alpha in Equation 1) measures portfolio manage-
ment skill only if the performance attribution
model captures all factors that drive REIT returns
or accounts for all possible abnormal returns that
can be earned by pursuing certain investment
styles.3 Whether the misspecification problem
plagues REIT performance evaluation is addressed
throughout this article.
The models central to our study arose from a
large body of research on factors affecting common
stocks (see, e.g., Fama and French 1992, 1993, 1996,
1997; Jegadeesh and Titman 1993; Carhart 1997; and
Moskowitz and Grinblatt 1999) and from studies on
variables that explain returns on real estate securi-
ties (see, e.g., Smith and Shulman 1976; Peterson and
Hsieh 1997; Chui, Titman, and Wei 2003a, 2003b).
These models are also found in earlier research on
REIT mutual fund performance (see, e.g., Kallberg,
Liu, and Trzcinka 2000; Lin and Yung 2004).
The first model we consider is a single-factor
model in the tradition of the CAPM of Sharpe
(1964), Lintner (1965), and Mossin (1966), in which
the expected return on a portfolio is a function of
the portfolio’s systematic risk. The estimated ver-
sion of the CAPM that we use predicts the follow-
ing relationship between beta and expected return:
(3)
where Rf, t is the risk-free rate at time t and Rm, t is
the return on the stock market at time t.
The second model accounts for activities in the
real estate sector. The model predicts a similar rela-
tionship between beta and expected return as in
Equation 3, but the return on the REIT market is
used instead of the return on the stock market.
The third model is the three-factor model of
Fama and French (1993), who documented that 1, p
alone inadequately describes the cross-section of
returns on stock portfolios formed on market cap-
italization and book-to-market. Because evidence
suggests that company size and book-to-market
may be cross-sectional determinants of REIT
returns (see, e.g., Chui, Titman, and Wei 2003a), the
Fama–French factors could represent a legitimate
expected return model for REITs:
(4)
where SMBt is the return difference between a
small-cap stock portfolio and a large-cap stock
portfolio at time t and HMLt is the return difference
between a high-book-to-market stock portfolio and
a low-book-to-market stock portfolio at time t.
Our fourth model is the four-factor model orig-
inally introduced by Carhart (1997). In response to
evidence that the Fama–French (1993) model fails
to capture the returns of Jegadeesh and Titman’s
(1993) momentum strategy, Carhart proposed a
four-factor model that augments the three-factor
specification with a momentum factor. In addition,
Chui, Titman, and Wei (2003b) determined that
price momentum is a cross-sectional determinant
α p p pR E R= − ( ) ,
E R X X
X
p t p
p t p t
K p K t
, ,
,
, ,
, ,… ,
( ) =
+ +
+ +
γ β
β
β
1 1 2 2 E R R R Rp t f t p m t f t, , , , , ,( ) = + −( )β1
E R R R R
SMB HML
p t f t p m t f t
p t p t
, , , , ,
, , ,
( ) = + −
( )
+ +
β
β β
1
2 3
AHEAD OF PRINT
4 AHEAD OF PRINT ©2009 CFA Institute
Financial Analysts Journal
of REIT returns by controlling for other company-
specific factors, such as size and book-to-market.
This model takes the following form:4
(5)
where WMLt is the return difference between a
common-stock portfolio with high past returns
and a common-stock portfolio with low past
returns at time t.
To develop these models, we used stock and
T-bill rate data from French (2008) and data on
REITs from the CRSP/Ziman Real Estate Data
Series. Arguably the most complete source of REIT
data, the CRSP/Ziman Real Estate Data Series
includes all REITs that have been traded on the
NYSE, Amex, and NASDAQ since 1980. Following
the majority of related studies, we defined Rm,t as
the monthly returns on a value-weighted portfolio
comprising all NYSE–Amex–NASDAQ stocks. We
used the one-month T-bill rate from Ibbotson Asso-
ciates as a proxy for the risk-free rate (Rf, t ). The
construction of the factor-mimicking portfolios
related to size and book-to-market effects (SMBt and
HMLt) and of the common-stock momentum factor
(WMLt) is described in Fama and French (1993) and
French (2008). Finally, we collected REIT data from
the CRSP/Ziman Real Estate Data Series to develop
our measure of aggregate REIT return (VWREITt),
which we defined as the value-weighted return on
all available REITs. We required each REIT to have
at least 12 consecutive return observations in order
to be included in our dataset.
Our inspection of the factors produced several
observations. Over the entire sample period, the
REIT market earned a relatively high premium. The
annual average excess REIT return (6.65 percent) is
similar to the annual average excess return on the
stock market (6.55 percent). Consistent with Ross
and Zisler (1991), we observed that the REIT market
correlates with common-stock portfolios. For
example, we found that the monthly return on a
value-weighted portfolio of all REITs traded on the
NYSE–Amex–NASDAQ correlates positively with
the value-weigh ted portfolio comprising all
NYSE–Amex–NASDAQ stocks (a correlation of
0.55). The correlations also indicate that REITs fall
on the high end of the company size (SMB) and
value (HML) spectrums, which is in line with
important REIT characteristics: REITs are typically
small or midsize companies that pay out relatively
high dividends (REITs are legally required to dis-
tribute at least 90 percent of their taxable income to
shareholders annually in the form of dividends).
Furthermore, REITs generally have high book-to-
market values because they hold mostly tangible
assets in the form of real estate, consistent with their
behaving like value stocks that correlate positively
with the HML factor (in contrast to, e.g., IT compa-
nies, which usually have low book-to-market ratios
and negative exposure to HML).
The REIT Momentum Effect
Starting with Jegadeesh and Titman (1993), a sub-
stantial body of research in the area of common
stocks has documented economically large returns
on a strategy that buys past-12-month-return win-
ners and sells short past losers. In the area of com-
mon stocks, momentum returns have posed a great
challenge to asset pricing models because evidence
shows that momentum returns cannot be explained
by market beta or by the size and book-to-market
effects on returns. Carhart (1997) captured mar-
ketwide momentum profits by using a four-factor
model that extends the Fama–French factors with a
stock-momentum factor.
Prior evidence suggests that momentum
effects are also prevalent in the REIT industry.
Chui, Titman, and Wei (2003a) demonstrated that
past REIT returns are a consistently accurate pre-
dictor of future REIT returns, and Chui, Titman,
and Wei (2003b) reported that REIT momentum
profits are stronger than momentum effects in
other U.S. industries. Therefore, we reexamined the
strength and prevalence of REIT momentum for
our sample period and tested whether the conven-
tional factors central to our study suffice to capture
REIT momentum profits.
We examined momentum in REIT portfolio
returns by studying all U.S. equity REITs in the
CRSP/Ziman Real Estate Data Series over the
period January 1980–September 2008. For every
month in our sample period, we ranked all available
REITs by their past-11-month returns (one-month
lagged) and grouped them into equally weighted
tercile portfolios. We then evaluated the REIT port-
folios’ postformation returns for the following
month by using the single-, three-, and four-factor
performance attribution models, and we performed
a GRS (Gibbons, Ross, and Shanken 1989) test to
determine whether the returns on momentum-
sorted REIT portfolios can be fully described by
exposures to the factors in the models.5 The GRS test
is underpinned by the simple condition that an accu-
rately specified factor model leave no cross-sectional
variation in returns unexplained; so, all alphas have
an expected value of zero. In other words, we for-
mally tested the hypothesis that the portfolios’
alphas are jointly indistinguishable from zero.
E R R R R SMB
HML WML
p t f t p m t f t p t
p t p t
( )
,
, , , , , ,
, ,
= + −( ) +
+ +
β β
β β
1 2
3 4
AHEAD OF PRINT
September/October 2009 AHEAD OF PRINT 5
REIT Momentum and the Performance of Real Estate Mutual Funds
Table 1 presents the returns of momentum-
sorted REIT portfolios on the basis of 11-month
returns (one-month lagged) for various postforma-
tion periods. The results indicate that REITs that
did well in the past continue to do so in the future,
consistent with a REIT momentum effect. The post-
formation return on the top-ranked REIT tercile
portfolio is more than twice as large as the return
on its bottom-ranked counterpart. The results also
indicate that REIT momentum is prevalent up to
15 months after formation. Jegadeesh and Titman
(1993) reported that momentum strategies for
common stocks are anomalously profitable for
holding periods of 3–12 months. Therefore, we
conclude that REITs exhibit a strong and prevalent
momentum effect.
With respect to the ability of conventional fac-
tor models to explain REIT momentum, Table 2
shows the returns on momentum-sorted REIT port-
folios after controlling for common-stock and REIT
market beta, size, book-to-market, and momentum.
None of the conventional factor models can fully
explain the cross-section of returns on REIT portfo-
lios that are formed on the basis of past returns.
Average risk-adjusted returns tend to decrease as
tercile rank decreases, independent of any factor
model specification. In addition, for all specifica-
tions, the GRS test rejects the null hypothesis that
the REIT terciles jointly earn zero abnormal returns
(at the conventional significance levels). Although
our finding that the momentum effect is prevalent
in the REIT industry confirms the results of Chui,
Titman, and Wei (2003b), the most striking finding
from our analysis is that the common-stock
momentum factor does not suffice to capture the
REIT momentum anomaly. The spread in alpha
between the top tercile and the bottom tercile of
REITs sorted on past returns is 6.6 percent a year
under the Carhart (1997) model.
The REIT momentum effect also withstands a
number of robustness tests (unreported in tabular
form here). First, REIT momentum is unrelated to
the REIT IPO effect. Buttimer, Hyland, and Sanders
(2005) reported that REIT returns were largely
driven by the returns of REIT IPOs in the 1990s. We
accounted for the IPO effect by removing all initial
12 monthly returns for every REIT in our sample
prior to forming the tercile portfolios. The spread in
alpha between the top and bottom terciles remains
economically large and statistically significant—5.7
percent a year under the Carhart (1997) model.
Second, we investigated whether the REIT
momentum effect is also observed over more-
recent subperiods. With respect to the performance
of the tercile portfolios of REITs over the most
recent 10 years in our sample, the alpha spread
between the top and bottom terciles is large and
statistically significant under all four conventional
factor models. Under the Carhart (1997) model, the
spread equals 6.39 percent a year. Over the most
recent five years in our sample, the spread equals
6.29 percent.
Third, adding the Pastor and Stambaugh
(2003) liquidity risk factor to the Carhart (1997)
four-factor model does not help explain cross-
sectional variation in abnormal tercile returns.
None of the portfolios are significantly exposed to
the liquidity factor, and the alpha spread between
the top- and bottom-tercile portfolios continues to
be significant at 6.7 percent a year.
Finally, the REIT momentum anomaly shows
up with a model that corrects for autocorrelation.
Because REITs invest in illiquid assets that are
typically not actively traded and for which mar-
ket prices are not always readily available, their
reported returns tend to be smoother than true
economic returns. This phenomenon understates
REIT volatility and increases risk-adjusted perfor-
mance measures, such as the Sharpe ratio. To incor-
porate this feature of REIT returns, we applied a
model in the spirit of Dimson (1979) and Getman-
sky, Lo, and Makarov (2004) that includes lagged
values of the variables in our factor models together
with the original factors. After this correction is
applied, the alpha spread between the top and
bottom terciles remains large and statistically sig-
nificant under all four conventional factor models.
Under the model that includes the four Carhart
(1997) factors and their lagged values, the alpha
spread is 6.6 percent a year.
Table 1. Strength and Prevalence of REIT Momentum, January 1980–
September 2008
Months after Formation
0 3 6 9 12 15 18
P1 (top) 9.51% 9.51% 9.80% 9.85% 10.45% 10.67% 8.49%
P2 8.94 8.23 6.97 8.92 6.83 7.02 9.21
P3 (bottom) 2.68 3.27 4.40 4.20 5.09 6.10 6.86
Top bottom 6.83% 6.24% 5.40% 5.66% 5.36% 4.57% 1.63%
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Financial Analysts Journal
Practical Implications: A New
Model to Measure Real Estate
Mutual Fund Performance
Thus far, our findings suggest that investors can
follow a basic REIT momentum strategy and pro-
duce returns that are not fully explained by
conventional factor models. Because the superior
return on REIT momentum portfolios—relative to
that on common-stock momentum portfolios—
could mask the true value added by active REIT
management under conventional factor models, we
investigated whether this misspecification problem
affects REIT mutual fund performance.
The obvious question is whether REIT mutual
fund performance is tied to REIT momentum. To
examine this issue, we constructed a REIT momen-
tum factor by taking the differential return between
the top- and bottom-ranked REIT tercile portfolios.
The new factor model takes the following form:
(6)
where REITWMLt is the return difference between
the portfolio of REITs with high past returns and the
portfolio of REITs with low past returns at time t.
To demonstrate the usefulness of our REIT
momentum factor in evaluating performance, we
first had to show its ability to explain the cross-
sectional variation in returns on momentum-
sorted REIT portfolios. Table 3 reveals that our
REIT momentum factor is indeed able to do so. We
found that many of the abnormal returns on the
momentum-sorted tercile portfolios disappear
under the Fama–French (1993) three-factor model
augmented with the REIT momentum factor. Not
surprisingly, the GRS test cannot reject the null
hypothesis that the alphas are jointly zero. More-
over, that an increased exposure to the REIT
momentum factor is associated with an increase in
tercile rank supports the notion that our REIT
momentum factor can explain the returns on the
momentum-sorted REIT portfolios.
To examine the role of REIT momentum in
explaining REIT mutual fund performance, we
analyzed the returns of professionally managed
investment vehicles in the form of mutual funds
that hold REIT securities (i.e., REIT mutual funds).
Table 2. Momentum-Sorted REIT Portfolios and Common-Stock Factor Models, January 1980–
September 2008
CAPM VWREIT FamaFrench 3FM
Carhart 4FM
Alpha Alpha-t Adj. R2 Alpha Alpha-t Adj. R2 Alpha Alpha-t Adj. R2 Alpha Alpha-t Adj. R2
P1 (top) 7.12% 3.67 0.25 4.64% 3.89 0.72 3.36% 1.88 0.41 3.18% 1.73 0.41
P2 6.72 3.01 0.18 3.40 2.89 0.77 1.32 0.67 0.41 2.02 1.00 0.41
P3 (bottom) 0.08 0.03 0.20 3.81 2.66 0.76 5.92 2.58 0.42 3.39 1.49 0.46
GRS 7.43 6.97 5.71 3.17
(p-Value) (0.00) (0.00) (0.00) (0.00)
Notes: This table reports the returns of momentum-sorted REIT portfolios on the basis of 11-month returns (one-month lagged). The
returns are evaluated by using the CAPM with a common-stock market factor and with a REIT market factor (VWREIT), the
Fama–French three-factor model (3FM), and the Carhart four-factor model (4FM). The table presents alphas with t-statistics (alpha-t),
adjusted R2 (adj. R2), and the GRS test statistic with p-values to determine whether the returns can be fully described by exposures
to the factors in the models.
E R R R R SMB
HML REITWML
p t f t p m t f t p t
p t p
, , , , , ,
, ,
( ) = + −( ) +
+ +
β β
β β
1 2
3 4 tt ,
Table 3. Momentum-Sorted REIT Portfolios and REIT Momentum, January 1980–September 2008
Fama–French 3FM + REITWML
Alpha Alpha-t RMRF SMB HML REITWML REITWML-t Adj. R2
P1 (top) 0.58% 0.34 0.53 0.46 0.52 0.30 7.41 0.49
P2 1.46 0.72 0.53 0.45 0.64 0.02 0.32 0.41
P3 (bottom) 0.58 0.34 0.53 0.46 0.52 0.70 17.32 0.70
GRS 0.20
(p-Value) (0.90)
Notes: See notes to Table 2. The returns are evaluated by using the Fama–French three-factor model augmented with our REIT
momentum factor (3FM + REITWML). The table presents alphas with t-statistics (alpha-t), factor exposures, adjusted R2 (adj. R2), and
the GRS test statistic with p-values to determine whether the returns can be fully described by exposures to the factors in the models.
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September/October 2009 AHEAD OF PRINT 7
REIT Momentum and the Performance of Real Estate Mutual Funds
We used data on all U.S. REIT mutual funds from
the 2008 CRSP Survivor-Bias-Free U.S. Mutual
Fund Database.6 The CRSP universe includes data
on all U.S. mutual funds that existed between Jan-
uary 1962 and July 2008. We thus overcame the
types of survivorship bias described in Brown,
Goetzmann, Ibbotson, and Ross (1992) and Carpen-
ter and Lynch (1999). We focused on mutual funds
that were classified as investments in real estate
securities. Using the Carhart (1997) model and the
Fama–French (1993) model augmented with our
REIT momentum factor, we estimated alphas for all
funds having at least 36 consecutive monthly
return observations in our sample. The resulting
sample covers returns of 282 REIT mutual funds
over January 1980–July 2008.
Table 4 shows that although REIT mutual
funds, on average, earn an alpha of 2.98 percent
under the Carhart (1997) model, the outperfor-
man ce evaporates once REIT momentum is
accounted for. This decline in alpha suggests that
the abnormal returns that REIT mutual funds earn
according to earlier studies are caused by exposure
to REIT momentum.
We next investigated whether REIT momen-
tum explains persistence in the performance of
REIT mutual funds. Lin and Yung (2004) reported
persistence in the performance of REIT mutual
funds after correcting for several factors, including
common-stock momentum. Given our findings
that a common-stock momentum factor does not
suffice to capture REIT momentum and that REIT
mutual funds with relatively high returns tend to
be more exposed to REIT momentum, we could a
priori expect that performance attribution that
accounts for REIT momentum deepens our under-
standing of the potential sources of persistence in
the performance of REIT mutual funds.
In our analysis of persistence in REIT mutual
fund returns, for every month, we ranked and allo-
cated all REIT mutual funds to one of three tercile
portfolios on the basis of past-12-month returns, in
the tradition of Hendricks, Patel, and Zeckhauser
(1993). We then evaluated the postformation
returns of the tercile portfolios by using the Carhart
(1997) model and the model that replaces common-
stock momentum with our REIT momentum factor.
Table 5 shows that the postformation return
spread between the top and bottom terciles is about
4.4 percent a year. Although persistence in REIT
fund returns is statistically insignificant, several
observations suggest that our REIT momentum fac-
tor incrementally helps explain returns of REIT
funds ranked on past return. First, the top-ranked
tercile of REIT funds (P1) appears to have a rela-
tively greater Carhart (1997) alpha than do other
terciles because of a stronger and statistically sig-
nificant exposure to the REIT momentum factor
(t-statistic of 3.17). Second, consistent with the
results of Table 4, Table 5 shows that the economi-
cally large abnormal returns that REIT funds gen-
erally earn under the Carhart (1997) model are
eliminated when the common-stock momentum
factor is replaced with REIT momentum. The three
REIT mutual fund terciles earn near zero or even
negative alphas under the three-factor model with
Table 4. REIT Momentum and REIT Mutual Fund Performance, January 1980–July 2008
Carhart 4FM Fama–French 3FM + REITWML
Alpha Alpha-t WML WML-t Adj. R2 Alpha Alpha-t REITWML REITWML-t Adj. R2
Mean 2.98% 0.53 0.12 1.09 0.41 0.07% 0.05 0.22 1.35 0.41
Std. dev. 3.99 0.73 0.14 0.90 0.10 3.46 0.72 0.18 1.05 0.09
Median 2.87 0.65 0.06 0.97 0.39 0.29 0.05 0.22 1.59 0.40
Percentile
10 0.81% 0.20 0.33 2.34 0.29 3.93% 0.76 0.01 0.09 0.32
20 0.66 0.16 0.26 1.80 0.33 2.02 0.49 0.10 0.73 0.36
30 1.56 0.36 0.14 1.50 0.35 1.27 0.31 0.17 1.06 0.37
40 2.39 0.55 0.08 1.26 0.37 0.33 0.08 0.20 1.30 0.38
50 2.93 0.66 0.06 0.98 0.39 0.30 0.06 0.22 1.59 0.40
60 3.82 0.73 0.05 0.79 0.41 0.72 0.17 0.25 1.66 0.41
70 4.89 0.90 0.04 0.64 0.43 1.33 0.27 0.30 1.88 0.43
80 5.76 1.01 0.03 0.34 0.46 2.58 0.44 0.36 2.19 0.45
90 7.67 1.18 0.01 0.07 0.53 3.62 0.64 0.43 2.50 0.50
Notes: This table compares alphas of REIT mutual funds under the Carhart four-factor model (4FM) augmented with a common-stock
momentum factor with alphas under the Fama–French three-factor model augmented with our REIT momentum factor (3FM +
REITWML). For both models, the table presents each alpha’s mean, standard deviation, and median, as well as the percentiles of each
alpha’s distribution.
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Financial Analysts Journal
REIT momentum. Third, including the REIT
momentum factor increases the R2 of the perfor-
mance attribution model for the top-ranked funds.
To further illustrate how the choice of factor
model has practical implications for the evaluation
of REIT mutual fund performance, Table 6 shows
the extent to which the two models agree about
ranking REIT mutual funds on the basis of their
alphas. The main finding is that REIT momentum
has a sizable influence on REIT mutual fund rank-
ing. The Carhart (1997) model produces a ranking
that is different from the one we obtain when we
replace the common-stock momentum factor with
our REIT momentum factor. For example, of the
REIT funds that appear in the top quintile under
Carhart’s (1997) model, more than 40 percent move
to a lower-ranked quintile when we control for REIT
momentum. For all other quintile ranks, the dis-
agreement between the two models is also strong.
Hence, our tests show that controlling for REIT
momentum alters our view of REIT mutual fund
performance along two lines. Exposure to REIT
momentum not only explains a great deal of the
abnormal performance of REIT mutual funds as a
whole; it also materially affects cross-sectional
rankings of those funds.
Table 5. REIT Momentum and Persistence in REIT Mutual Fund
Performance, January 1980–July 2008
Carhart 4FM
Return Alpha Alpha-t RMRF SMB HML WML WML-t Adj. R2
P1 (top) 8.86% 1.14% 0.46 0.65 0.36 0.61 0.04 0.93 0.41
P2 7.93 1.39 0.57 0.58 0.37 0.60 0.02 0.36 0.39
P3 (bottom) 4.51 2.30 1.02 0.66 0.41 0.62 0.05 1.27 0.49
GRS 3.58
(p-Value) (0.01)
Fama–French 3FM + REITWML
Return Alpha Alpha-t RMRF SMB HML REITWML REITWML-t Adj. R2
P1 (top) 8.86% 0.12% 0.05 0.68 0.40 0.67 0.18 3.17 0.44
P2 7.93 0.27 0.11 0.61 0.41 0.66 0.14 2.54 0.40
P3 (bottom) 4.51 3.62 1.61 0.68 0.42 0.66 0.06 1.18 0.49
GRS 3.46
(p-Value) (0.02)
Notes: This table presents the returns of momentum-sorted REIT mutual fund portfolios on the basis of
12-month returns. The returns are evaluated by using the Carhart four-factor model (4FM) and the
Fama–French three-factor model augmented with our REIT momentum factor (3FM + REITWML). The
table presents alphas with t-statistics (alpha-t), factor exposures, adjusted R2 (adj. R2), and the GRS test
statistic with p-values to determine whether the returns can be fully described by exposures to the factors
in the models.
Table 6. REIT Momentum and REIT Mutual Fund Rankings, January 1980–
July 2008
Fama–French 3FM + REITWML
Carhart 4FM P1 (Top) P2 P3 P4 P5 (Bottom)
P1 (top) 59% 21% 18% 2% 0%
P2 41 34 5 13 7
P3 0 39 47 11 4
P4 0 5 29 48 18
P5 (bottom) 0 0 2 26 72
Notes: This table compares alpha rankings of REIT mutual funds under the Carhart four-factor model
(4FM) augmented with a common-stock momentum factor with alpha rankings under the Fama–French
three-factor model augmented with our REIT momentum factor (3FM + REITWML). The table shows
the percentages of REIT mutual funds ranked by quintile on the basis of alphas from both models.
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September/October 2009 AHEAD OF PRINT 9
REIT Momentum and the Performance of Real Estate Mutual Funds
Conclusion
Conventional performance attribution approaches
focus on whether the returns of an actively
managed portfolio can be mimicked by exposure
to a set of benchmark factors. Any unexplained
return is then attributed to managerial skill. Our
study found that the cross-section of returns of
momentum-sorted REIT portfolios is not explained
by conventional factor models, which implies that
abnormal returns derived from those models may
mask the true value of active REIT portfolio man-
agement. Returns on momentum portfolios that are
long in high-return REITs and short in low-return
REITs are economically significant for up to 15
months after formation. Our study is the first to
emphasize that momentum profits in the REIT
industry are significantly underestimated by con-
ventional factor models that control for beta, size,
and book-to-market effects and by Carhart’s (1997)
common-stock momentum factor.
Because we found that the returns of REIT
momentum portfolios cannot be replicated by expo-
sure to common-stock factors, we hypothesized that
residual returns of actively managed REIT portfo-
lios might reflect exposure to an omitted REIT
momentum factor instead of managerial skill. Our
evaluation of U.S. REIT mutual funds suggests that
this hypothesis is true. The REIT momentum factor
that we incorporated into performance attribution
influences REIT mutual fund alphas in two ways.
First, REIT momentum plays a key role in explaining
the outperformance that REIT funds as a whole
display under the conventional four-factor model of
Carhart (1997). The positive alphas that REITs
deliver under conventional factor models dissipate
under a model that includes the three Fama–French
(1993) factors and a REIT momentum factor. Second,
we showed that a consideration of REIT momentum
affects our understanding of cross-sectional varia-
tion in the performance of REIT funds. Therefore,
factoring REIT momentum into performance attri-
bution has important consequences for the evalua-
tion of REIT fund managers.
In essence, at least three practical implications
emerge from our study. The choice of factor model
clearly has important ramifications for the selection
of a REIT manager, whether for a mutual fund or a
private offering. Furthermore, because REIT man-
agers appear to be providing less alpha than they
have been given credit for in previous studies, rel-
atively unsophisticated or inexperienced investors
might be wise to turn to indexation. Finally,
because common benchmarking models for judg-
ing REIT managers are inadequate, our findings
encourage a rethinking of the structure of incentive
fees that are paid to REIT managers.
Several avenues for further research remain.
One unanswered question concerns the nature of
the momentum effect in REITs. What drives REIT
momentum? No consensus on the source of the
momentum effect exists. Most research seems to
suggest that underreaction and overreaction of
investors to good and bad news concerning
company-specific information are at the root of the
momentum effect. For example, Hong and Stein
(1999) and Hong, Lim, and Stein (2000) found that
the momentum effect is consistent with the theory
of “gradual diffusion of information.” They showed
that especially bad news travels slowly over time.
Consistent with this theory, they further showed
that the profitability of a momentum strategy
declines sharply with an increase in company size
and that a momentum strategy is more profitable
for companies with little analyst coverage. Conrad
and Kaul (1998) argued that a momentum strategy’s
average profitability simply reflects cross-sectional
variation in unconditional mean returns.
Vayanos and Woolley (2008) recently showed
that money inflow in winning mutual funds and
money outflow in losing mutual funds create a
momentum effect because of the buying pressure
in winning stocks and the selling pressure in losing
stocks arising from the money flows. Often, win-
ning mutual funds concentrate on value stocks and
losing ones focus on growth stocks, and vice versa.
In this case, no skill is needed to produce the win-
ning or the losing mutual fund.
Another important issue is whether REIT-
specific factors other than momentum should be
used to construct a factor model for REITs. For
example, although several studies have indicated
that REIT returns are positively correlated with size
and book-to-market factors, whether the Fama and
French (1993) factors suffice to fully capture size
and value effects in REIT returns is unclear.
Whether performance evaluation is further affected
by REIT-specific size and book-to-market factors is
an interesting question that awaits further research.
For their valuable comments, we thank Mathijs
Cosemans, Piet Eichholtz, Martin Martens, Anthony
Sanders, Peter Schotman, seminar participants at
Maastricht University and the University of Grenoble,
and participants at the Professional Asset Management
conference at the Rotterdam School of Management.
This article qualifies for 1 CE credit.
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Financial Analysts Journal
Notes
1. See, for example, Grinblatt and Titman (1992); Hendricks,
Patel, and Zeckhauser (1993); Goetzmann and Ibbotson
(1994); Brown and Goetzmann (1995); and Carhart (1997)
for studies of the performance of actively managed equity
mutual funds.
2. See Elton, Gruber, Das, and Hlavka (1993).
3. For example, such a model could explain the return dynamics
associated with such widely researched investment styles as
trading based on the size effect (Banz 1981), the book-to-
market (value) effect (Lakonishok, Schleifer, and Vishny
1994), and the momentum effect (Jegadeesh and Titman 1993).
4. For expositional convenience, we used the same notation
for the beta parameters in Equations 3, 4, and 5. Note,
however, that they take different values.
5. We circumvented the problem of overlapping samples by
not measuring REIT momentum in terms of cumulative
average returns, unlike Jegadeesh and Titman (1993).
6. Our study benefited from using a cross-section of REIT
mutual funds that was larger than the cross-section exam-
ined in earlier research.
References
Banz, Rolf W. 1981. “The Relationship between Return and
Market Value of Common Stocks.” Journal of Financial Economics,
vol. 9, no. 1 (March):3–18.
Brown, S.J., and W.N. Goetzmann. 1995. “Performance Persis-
tence.” Journal of Finance, vol. 50, no. 2 (June):679–698.
Brown, S.J., W.N. Goetzmann, R.G. Ibbotson, and S.A. Ross.
1992. “Survivorship Bias in Performance Studies.” Review of
Financial Studies, vol. 5, no. 4 (Winter):553–580.
Buttimer, Richard J., David C. Hyland, and Anthony B. Sanders.
2005. “REITs, IPO Waves, and Long-Run Performance.” Real
Estate Economics, vol. 33, no. 1 (March):51–87.
Carhart, Mark M. 1997. “On Persistence in Mutual Fund Perfor-
mance.” Journal of Finance, vol. 52, no. 1 (March):57–82.
Carpenter, Jennifer N., and Anthony W. Lynch. 1999. “Survi-
vorship Bias and Attrition Effects in Measures of Performance
Persistence.” Journal of Financial Economics, vol. 54, no. 3
(December):337–374.
Chan, K.C., Patric H. Hendershott, and Anthony B. Sanders.
1990. “Risk and Return on Real Estate: Evidence from Equity
REITs.” AREUEA Journal, vol. 18, no. 4:431–452.
Chen, Nai-Fu, Richard Roll, and Stephen A. Ross. 1986. “Eco-
nomic Forces and the Stock Market.” Journal of Business, vol. 59,
no. 3 (July):383–403.
Chen, Su-Jane, Chengho Hsieh, Timothy W. Vines, and Shur-
Nuaan Chiou. 1998. “Macroeconomic Variables, Firm-Specific
Variables and Returns to REITs.” Journal of Real Estate Research,
vol. 16, no. 3:269–278.
Chui, Andy C.W., Sheridan Titman, and K.C. John Wei. 2003a.
“The Cross-Section of Expected REIT Returns.” Real Estate
Economics, vol. 31, no. 3 (September):451–479.
———. 2003b. “Intra-Industry Momentum: The Case of REITs.”
Journal of Financial Markets, vol. 6, no. 3 (May):363–387.
Conrad, J., and G. Kaul. 1998. “An Anatomy of Trading Strate-
gies.” Review of Financial Studies, vol. 11, no. 3 (Fall):489–519.
Damodaran, A., and C.H. Liu. 1993. “Insider Trading as a Signal
of Private Information.” Review of Financial Studies, vol. 6, no. 1
(Spring):79–119.
Dimson, E. 1979. “Risk Measurement When Shares Are Subject
to Infrequent Trading.” Journal of Financial Economics, vol. 7,
no. 2 (June):197–226.
Elton, E.J., M.J. Gruber, S. Das, and M. Hlavka. 1993. “Efficiency
with Costly Information: A Reinterpretation of Evidence from
Managed Portfolios.” Review of Financial Studies, vol. 6, no. 1
(Spring):1–22.
Fama, Eugene F., and Kenneth R. French. 1992. “The Cross-
Section of Expected Stock Returns.” Journal of Finance, vol. 47,
no. 2 (June):427–465.
———. 1993. “Common Risk Factors in the Returns on Stocks
and Bonds.” Journal of Financial Economics, vol. 33, no. 1
(February):3–56.
———. 1996. “Multifactor Explanations of Asset Pricing Anom-
alies.” Journal of Finance, vol. 51, no. 1 (March):55–84.
———. 1997. “Industry Costs of Equity.” Journal of Financial
Economics, vol. 43, no. 2 (February):153–193.
French, Kenneth R. 2008. “Fama–French Factors” (http://mba.
tu c k . d a r t m ou t h. e d u /p a g e s/ f a c ult y / k en . f r en c h /d a ta _
library.html).
Getmansky, Mila, Andrew W. Lo, and Igor Makarov. 2004. “An
Econometric Model of Serial Correlation and Illiquidity in
Hedge Fund Returns.” Journal of Financial Economics, vol. 74,
no. 3 (December):529–609.
Gibbons, Michael R., Stephen A. Ross, and Jay Shanken. 1989.
“A Test of the Efficiency of a Given Portfolio.” Econometrica,
vol. 57, no. 5 (September):1121–1152.
Goetzmann, William N., and Roger G. Ibbotson. 1994. “Do
Winners Repeat? Patterns in Mutual Fund Performance.” Jour-
nal of Portfolio Management, vol. 20, no. 2 (Winter):9–18.
Grinblatt, Mark, and Sheridan Titman. 1992. “The Persistence of
Mutual Fund Performance.” Journal of Finance, vol. 47, no. 5
(December):1977–1984.
Hartzell, Jay, Tobias Mühlhofer, and Sheridan Titman. 2007.
“Alternative Benchmarks for Evaluating REIT Mutual Fund
Performance.” Working paper, University of Texas at Austin
(29 October).
Hendricks, D., J. Patel, and R. Zeckhauser. 1993. “Hot Hands in
Mutual Funds: Short-Run Persistence of Relative Performance,
19741988.” Journal of Finance, vol. 48, no. 1 (March):93–130.
Hong, Harrison, and Jeremy C. Stein. 1999. “A Unified Theory of
Underreaction, Momentum Trading, and Overreaction in Asset
Markets.” Journal of Finance, vol. 54, no. 6 (December):2143–2184.
Hong, Harrison, Terence Lim, and Jeremy C. Stein. 2000. “Bad
News Travels Slowly: Size, Analyst Coverage, and the Profitabil-
ity of Momentum Strategies.” Journal of Finance, vol. 55, no. 1
(February):265–295.
Jegadeesh, Narasimhan, and Sheridan Titman. 1993. “Returns to
Buying Winners and Selling Losers: Implications for Stock Mar-
ket Efficiency.” Journal of Finance, vol. 48, no. 1 (March):65–91.
AHEAD OF PRINT
September/October 2009 AHEAD OF PRINT 11
REIT Momentum and the Performance of Real Estate Mutual Funds
Jensen, Michael C. 1969. “Risk, the Pricing of Capital Assets,
and the Evaluation of Investment Portfolios.” Journal of Busi-
ness, vol. 42, no. 2 (April):167–247.
Kallberg, Jarl G., Crocker L. Liu, and Charles Trzcinka. 2000.
“The Value Added from Investment Managers: An Examination
of Funds of REITs.” Journal of Financial and Quantitative Analysis,
vol. 35, no. 3 (September):387–408.
Karolyi, G. Andrew, and Anthony B. Sanders. 1998. “The Vari-
ation of Economic Risk Premiums in Real Estate Returns.”
Journal of Real Estate Finance and Economics, vol. 17, no. 3
(November):245–262.
Lakonishok, Josef, Andrei Schleifer, and Robert W. Vishny.
1994. “Contrarian Investment, Extrapolation, and Risk.” Journal
of Finance, vol. 49, no. 5 (December):1541–1578.
Lin, Crystal Yan, and Kenneth Yung. 2004. “Real Estate Mutual
Funds: Performance and Persistence.” Journal of Real Estate
Research, vol. 26, no. 1 (January):69–93.
Lintner, John. 1965. “The Valuation of Risk Assets and the
Selection of Risky Investments in Stock Portfolios and Capital
Budgets.” Review of Economics and Statistics, vol. 47, no. 1
(February):13–37.
Merton, R.C. 1973. “An Intertemporal Capital Asset Pricing
Model.” Econometrica, vol. 41, no. 5 (September):867–887.
Moskowitz, Tobias J., and Mark Grinblatt. 1999. “Do Industries
Explain Momentum?” Journal of Finance, vol. 54, no. 4
(August):1249–1290.
Mossin, J. 1966. “Equilibrium in a Capital Asset Market.” Econo-
metrica, vol. 34, no. 4 (October):768–783.
Pastor, Lubos, and Robert F. Stambaugh. 2003. “Liquidity Risk
and Expected Stock Returns.” Journal of Political Economy, vol. 111,
no. 3 (June):642–685.
Peterson, James D., and Cheng-Ho Hsieh. 1997. “Do Common
Risk Factors in the Returns on Stocks and Bonds Explain Returns
on REITs?” Real Estate Economics, vol. 25, no. 2 (June):321–345.
Ross, Stephen A. 1976. “The Arbitrage Theory of Capital Asset
Pricing.” Journal of Economic Theory, vol. 13, no. 3 (Decem-
ber):341–360.
Ross, Stephen A., and Randall C. Zisler. 1991. “Risk and Return
in Real Estate.” Journal of Real Estate Finance and Economics, vol. 4,
no. 2 (June):175–190.
Sharpe, William F. 1964. “Capital Asset Prices: A Theory of
Market Equilibrium under Conditions of Risk.” Journal of
Finance, vol. 19, no. 3 (September):425–442.
Smith, Keith V., and David Shulman. 1976. “Institutions Beware:
The Performance of Equity Real Estate Investment Trusts.” Finan-
cial Analysts Journal, vol. 32, no. 5 (September/October):61–66.
Titman, Sheridan, and Arthur Warga. 1986. “Risk and the
Performance of Real Estate Investment Trusts: A Multiple Index
Approach.” AREUEA Journal, vol. 14, no. 3:414–431.
Vayanos, Dimitri, and Paul Woolley. 2008. “An Institutional
Theory of Momentum and Reversal.” Working paper (22
November): http://ssrn.com/abstract=1305671.
AHEAD OF PRINT
Deal or No Deal, That is the
Question: The Impact of Increasing
Stakes and Framing Effects on
Decision-Making under Risk
ROBERT BROOKS, ROBERT FAFF, DANIEL MULINO AND
RICHARD SCHEELINGS
Department of Accounting and Finance Faculty of Business and Economics,
Monash University, Melbourne, Australia
ABSTRACT
In this paper, we utilize data from the Australian version of the TV game
show, ‘Deal or No Deal’, to explore risk aversion in a high real stakes setting.
An attractive feature of this version of the game is that supplementary
rounds may occur which switch the decision frame of players. There are four
main findings. First, we observe that the degree of risk aversion generally
increases with stakes. Second, we observe considerable heterogeneity in
people’s willingness to bear risk – even at very high stakes. Third, we find that
age and gender are statistically significant determinants of risk aversion,
while wealth is not. Fourth, we find that the reversal of framing does have a
significant impact on people’s willingness to bear risk.
I. INTRODUCTION
The analysis of decisions under uncertainty is fundamental to modern
economics and finance. This paper contributes to a recently developing
empirical literature that adopts the central research question: How risk averse
are individuals? Subsidiary questions regarding risk aversion that we address
include its heterogeneity and how it varies with individual demographic
characteristics (especially age, wealth and gender). While the theoretical
literature on risk aversion and expected utility theory is large and long-
standing, the literature explicitly testing for risk aversion is comparatively
small. Such empirical tests as exist, either in laboratory or field experiments
involving real stakes, have mostly been confined to small cash values. There has
been a recent debate doubting the applicability of such estimates when
extrapolated to high real stakes (see Rabin 2000). Our paper exploits an
Australian game show dataset to explore the nature of risk aversion of
contestants who face an environment of very high stakes.
r 2009 The Authors. Journal compilation r International Review of Finance Ltd. 2009. Published by Blackwell
Publishing Ltd., 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.
International Review of Finance, 9:1–2, 2009: pp. 27–50
DOI: 10.1111/j.1468-2443.2009.01084.x
‘Deal or No Deal’ is a half-hour TV game show in which contestants make a
series of choices between a sure thing and a lottery.1 It is ideal for studying a
range of issues relating to economic decision making. The show consists of a
chosen contestant faced with 26 suitcases, randomly containing amounts
ranging from 50 cents to US$200,000 dollars. There are up to nine ‘normal’
rounds in the main stage of the game. Unlike other versions of the show, the
Australian version of ‘Deal or No Deal’ also involves the potential for one of two
extra rounds – the Chance round and the SuperCase round.
First, when only two suitcases are left, the contestant may be offered a
‘Chance’ round, allowing them to exchange the certain amount that they’ve
already won for a 55 lottery between the two remaining prizes. Second, when all
suitcases have been revealed, the contestant may be given the option of
swapping the certain amount that they have won for the ‘SuperCase’, which is a
lottery in which one of eight prizes may be won. Both these possibilities are
entirely at the discretion of the producers. These special rounds involve a
reversal of the contestants’ frame of reference and, hence, are ideal for testing
framing effects. Accordingly, we exploit this feature of our dataset.
Our paper investigates two fundamental issues. First, we explore the
willingness of contestants to take risks with large monetary gambles. Second,
we assess whether contestant decision-making reflects framing effects. Regard-
ing the first issue, we find that, while on average most contestants on ‘Deal or
No Deal’ are probably risk averse, their willingness to bear risk is greater than
had previously been found in studies of US game shows. Moreover, many
contestants are willing to take very risky gambles, even when the stakes are
high. There is a high degree of heterogeneity among contestants. Our results
also re-affirm the prior literature that people become more risk averse as stakes
rise (Holt and Laury 2002).
The theoretical and scientific attraction of expected utility theory is that it
posits a consistent preference relation regardless of changes in the ‘frame’ of the
decision, especially with respect to changes in a decision-maker’s wealth.
Prospect theory (which implies loss aversion2) is a well-known example of a
theory of decision-making under uncertainty where that is not the case. The
Australian version of the ‘Deal or No Deal’ game show is well-suited to test
framing effects because some contestants face a reversal of the framing of their
choice when they participate in either the Chance round or the SuperCase
1 We use data from the Australian version of Deal or No Deal, although the show has now been
syndicated in over 30 countries. It should be emphasized that the show, although franchised
from the same Dutch source (the Endemol TV entertainment company) is not identical across
all its franchises. Variations in the game show introduced by different countries leads to
different datasets. Confining our attention to a single version of Deal or No Deal has the
advantage of giving us a uniform experimental setting.
2 ‘Loss aversion’ describes how a person’s welfare will fall more as a result of losing a specified
amount of money than it rises when they win the same amount of money. People who are loss
averse will be willing to take large risks to avoid losses but will tend to be risk averse with
potential gains. See, for example, Kahneman and Tversky (1979).
International Review of Finance
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round described above. In the ‘normal’ rounds, contestants face the prospect of
swapping their rights to the lottery for a sure amount of money. In contrast, in
the Chance and SuperCase rounds, contestants face the prospect of exchanging
a certain amount of money already won (via the ‘Deal’ agreed to earlier) for a
gamble.
Approximately 40% of the contestants in our dataset participate in one of
these ‘special’ rounds. We find that contestants exhibit a considerably higher
level of risk aversion in both the Chance and SuperCase rounds than in the
normal rounds. Assuming the validity of an underlying assumption that
contestants are characterizable by some type of non-expected utility model, this
appears to provide some support for a kind of preference reversal or framing
effect. Notably, other game show studies in the literature, as well as versions of
the ‘Deal or No Deal’ game show exhibited in other countries, do not involve
such a reversal of the choice framework, and so were not able to test this
behavioral effect.
On the important issue of the variation in risk aversion with agent
characteristics, we find, consistent with much of the pre-existing literature,
that attributes like age and gender have a statistically significant effect. While
the evidence to date on this issue is mixed, where studies have found an impact,
it is almost always that women are more risk averse than men. Our findings are
consistent with Hartog et al. (2000) using survey data from the Netherlands,
with Holt and Laury (2002), using experimental data, and with Cohen and
Einav (2007), who utilize a large car insurance dataset to structurally estimate
risk aversion and attributes long thought to influence risk aversion. A similar
gender effect has also been found in several studies in the finance literature (see,
e.g., Cohn et al. 1975; Lewellen et al. 1978).
The remainder of this paper is organized as follows. The next section briefly
outlines the relevant literature. Section III outlines the ‘Deal or No Deal’ game
show and describes the data it generates. Section IV presents and discusses our
empirical results, and Section V concludes.
II. RELEVANT LITERATURE
Researchers have, to date, largely relied upon three methods to study the
magnitude and variability (with stakes) of risk aversion. First, they have run
experiments in which people face actual monetary gambles.3 Given the funding
limits of such studies, many (though not all) were perforce small-stakes. The
second method is to rely upon responses to surveys (see the discussion at the
beginning of Camerer 1995). This permits the consideration of people’s
attitudes to gambles involving much larger sums – but such studies are limited
to hypothetical choices and there is no reason for thinking that what people say
3 See for example the survey of the laboratory auction literature by Bajari and Hortascu (2005),
and also Holt and Laury (2002), Harrison et al. (2003) and Goeree et al. (2000).
Deal or No Deal, That is the Question
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they will do when faced with high stakes, is what they in fact will do (see Holt
and Laury 2002, and the discussion in Hartog et al. 2000). Finally, there is the
use of ‘field experiments,’ or situations of data-generation outside the direct
control of the researcher in which people are faced with large gambles. This
includes a game show literature as well as a small literature utilizing
experiments conducted in developing countries. Collectively, these studies
have found that people are generally (though only moderately) risk averse in
high stakes environments, and that they become more risk averse as the stakes
of the gamble increase (though, again, only mildly).
Most of the game show papers are limited in their direct comparability to our
paper because they involve strategic interaction rather than, as is the case with
‘Deal or No Deal’, pure decision theoretic considerations. Papers concerning
strategic game shows focus on the disjunction and possible means of
reconciliation between actual play and the theoretically prescribed optimal
play, an issue since resolved in laboratory experiments via the use of quantal
response equilibrium models (see McKelvey and Palfrey 1995).4 A game show
paper that focuses explicitly on measuring risk aversion is Gertner (1993). He
utilizes data from the show ‘Card Sharks’. Gertner finds a very high coefficient
of risk aversion. Further, Gertner finds that individual player-behavior is
inconsistent with expected utility theory. Fullenkamp et al. (2003) consider
lottery games and find risk aversion displayed and also that it varies with the
size of the stakes. Hersch and McDougall (1997) consider the same type of data
for lottery games and find that income is not a significant determinant, a
finding replicated in the current paper. Beetsma and Schotman (2001) consider
the show ‘Lingo’ and find evidence of risk aversion.
An advantage of the current paper compared with other game show papers is
that ‘Deal or No Deal’ requires no special skills in order to succeed. This has
been recognized as an important characteristic by researchers – so much so, that
a rapidly expanding literature using ‘Deal of No Deal’ data has emerged
contemporaneous with our work. Such studies are well represented by
Bombardini and Trebbi (2005), Blavatskyy and Pogrebna (2006, 2008), Post
et al. (2008), de Roos and Sarafidis (2006) and Andersen et al. (2006a, b and 2008).
Bombardini and Trebbi (2005), analyze the Italian version of the ‘Deal or No
Deal’ global franchise and structurally estimate a sample average constant risk
aversion parameter of about unity. Contrary to our work, they find no evidence
for the dependence of risk aversion on agent characteristics like age and gender.
In a finding relevant to our paper, they are unable to rule out that their dataset
was generated via contestants possessing non-expected utility preferences. Two
further papers utilizing the Italian version of the show are Blavatskyy and
Pogrebna (2006, 2008). The main focus of the first of these is in confirming that
contestant risk aversion is invariant under differing likelihoods of identical
4 Three papers consider the show ‘The Price is Right’: Bennett and Hickman (1993), Berk,
Hughson and Vandezande (1996) and Healy and Noussair (2004). A paper by Metrick (1995)
examines data from the game show ‘Jeopardy.’ None of them explicitly test for risk aversion.
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gains. In the second paper, the authors exploit a special suitcase-swapping
feature of the Italian version of the game show to directly test for (and refute)
contestant loss aversion. Andersen et al. (2006a, b) find evidence for probability
weighting, but not for loss aversion. The paper by Post et al. (2008) uses
combined data from the German, Dutch and Belgium franchises and they find
that, independent of nationality, player behavior is both path-dependent and
frame-dependent. Like us, de Roos and Sarafidis (2006) employ Australian data.
They obtain (in a model which ignores the supplementary rounds) a structural
estimate of risk aversion of one half (assuming zero initial wealth). They too are
unable to rule out the hypothesis that their dataset was generated via
contestants possessing non-expected utility preferences.
III. THE GAME SHOW
A. Description of the show
The TV game ‘Deal or No Deal’ is comprised of three stages. The first two
involve the selection of a player (‘the contestant’) chosen to play the game
(they reduce the contestant pool from 150 to one), and the third stage deals
with the playing of the game proper.
In Stage 1, the 150 members of the studio audience are sorted into six groups
of 25. One of these groups is chosen at random. An additional, 26th person is
chosen at random from the remaining pool of 125. These 26 people progress to
Stage 2. Stage 2 is a trivia contest based on three simple questions. Of the Stage 2
participants that answer the most questions correctly, the chosen contestant is
the person with the fastest reaction time. The contestant then moves on to
Stage 3, which is the segment of the game that is of interest for this paper.
Stage 3 constitutes the game proper, and is the part which generates the
dataset used in this paper. It starts with 26 numbered suitcases, each of which
contains a concealed, pre-determined monetary prize. The 26 unique money
prizes range from 50 cents to a maximum of US$200,000, with most of the
values falling below US$10,000. The schedule of prizes is contained in Appendix
A. The schedule of prizes remains the same in each show, although the amount
allocated to each numbered suitcase is determined randomly before the start of
each show.
At the start of Stage 3, the contestant chooses one suitcase, which is set aside.
If the contestant plays Stage 3 to its ultimate conclusion, the contestant will
win the prize contained in that suitcase. The remaining 25 suitcases are given to
the 25 unsuccessful participants in Stage 2 (‘the suitcase contestants’).
Next, in Round 1 of the game, the contestant chooses six suitcases, from the
remaining 25, for removal. As the contestant nominates each suitcase for
removal, the monetary prize contained in that suitcase is revealed by the
suitcase contestant holding it. Once a money prize has been revealed, it is
removed from the game and can no longer be won.
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After the first six suitcases have been removed, the ‘Bank’ (i.e. the producers
of the game show) makes an offer to the contestant via the host of the game
show: the ‘Bank Offer’. The Bank Offer is a cash prize – determined, in part, by
which money prizes remain available to be won in the 20 remaining unopened
suitcases. The contestant can either accept this offer by choosing ‘Deal’, or
continue to the next round of Stage 3 by choosing ‘No Deal’. When making this
and all future decisions, the contestant is fully aware of which prizes remain
available to be won.5
If ‘Deal’ is chosen, the contestant wins the money offered by the Bank but
forfeits the right to continue playing Stage 3. If ‘No Deal’ is chosen, then the
contestant moves to Round 2 of the game and must nominate a further five
suitcases for removal from the 19 unopened cases still held by suitcase
contestants. The contestant may not nominate the suitcase originally set aside.
After the money prizes contained in these five suitcases are revealed, the
contestant receives a second, revised Bank Offer. If, after the second Bank Offer,
the contestant chooses ‘No Deal’, a further four suitcases must be
removed
(Round 3). The Bank then makes a third Bank Offer based on the remaining 11
suitcases.6
The contestant again chooses either ‘Deal’ or ‘No Deal’. If ‘No Deal’ is chosen,
the contestant moves to a fourth Round and must nominate a further three
suitcases for removal. After their removal, the Bank makes a fourth offer, based
on the remaining eight unopened suitcases. The contestant again chooses ‘Deal’
or ‘No Deal’. If ‘No Deal’ is chosen, two more suitcases must be removed in
Round 5, after which a fifth Bank Offer is made. If ‘No Deal’ is chosen after the
fifth offer, the game enters a phase (Rounds 6–9) in which suitcases held by the
suitcase contestants are removed one by one. After the removal of each suitcase,
a new Bank Offer is made.
When only one unopened suitcase held by a suitcase contestant remains, the
contestant must either accept the 9th Bank Offer or choose their own suitcase
over the suitcase held by the single remaining suitcase contestant.
If at any time during the game the contestant has accepted a Bank Offer, s/he
will continue to nominate suitcases for removal ‘as if’ s/he were still playing
Stage 3. This heightens tension allowing TV viewers to imagine ‘what might
have been.’ Finally, this counter-factual exercise allows for the possibility (since
5 One possible issue that could be raised concerning the mechanics of the bank’s offer is whether
it involves some strategic or informative element, transforming the environment of the field
experiment from a pure decision-theoretic to a game theoretic one. We found that the
correlation between, on the one hand, the ratio of the bank offer to the expected value of the
remaining suitcases, and, on the other, the ratio of the contestant’s initially chosen suitcase to
the expected value of the remaining suitcases, was 0.08 – a value sufficiently low to suggest
that strategic behavior is a non-issue. Moreover, this correlation falls in the final two rounds
and even turns slightly negative in round nine. Thus, our operating assumption in this paper –
that the contestants find themselves in a pure decision-theoretic environment – is justified.
6 That is, the suitcase originally chosen by the contestant and the 10 unopened cases still held
by suitcase contestants.
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this occurs at the discretion of the producers) of one of the two supplementary
rounds (the Chance and SuperCase rounds) to be played. These rounds, unique
to the Australian game show, are important for our test of framing effects.
Appendix B contains a characterization of the rounds of play in the Australian
version of ‘Deal or No Deal’. Appendix C summarizes the play in nine normal
rounds and a Chance round from an illustrative actual game from our dataset in
which the contestant wins US$100,000.
B. Description of the data
We have data for 102 episodes from the second and third series of the Australian
version of the ‘Deal or No Deal’ game show. Table 1 displays descriptive statistics.
The mean value of prizes won in these episodes is US$15,810 with a standard
deviation of US$18,541.7 The minimum prize won was US$1 and the maximum
US$105,000. Not surprisingly, the Bank Offers in the initial rounds were generally
low relative to the expected value of the remaining suitcases. Given that there is
only one contestant per show, the producers have a strong incentive to ensure
that each contestant plays at least a few rounds. In our sample, no contestants
accepted an offer in Rounds 1, 2 or 3, and only one contestant accepted in the
fourth round. A total of 91 contestants played until at least Round 6.
However, these averages obscure interesting behavioral heterogeneity at the
agent level. Perhaps most notably, 49 Bank Offers that were greater than the
Table 1 Basic descriptive statistics
Obs Mean SD Minimum Maximum
Prize Won 102 US$15, 810 US$18, 541 US$1 US$105, 000
OFFER 741 US$8, 717 US$9, 783 US$1 US$105, 000
MALE 728 0.48 0.49 0 1
AGE 728 32 years 9.7 years 18 years 66 years
INCOME 720 US$421 US$86 US$250 US$650
HINCOME 720 US$920 US$200 US$450 US$1, 750
FINCOME 720 US$1, 089 US$256 US$550 US$1, 750
This table reports basic descriptive statistics for the full sample of rounds for the Australian
version of the TV game show ‘Deal or No Deal’. The statistics shown are number of observations;
mean; standard deviation; minimum value and maximum value. The variables are: Prize won;
OFFER: the value of the bank offer; MALE: a dummy variable that takes the value of unity if the
contestant is a male; AGE: the contestant’s age measured in years; INCOME: is individual income
proxied by the average weekly income associated with the postcode (analogous to zip code) of the
contestant based on data from the 2001 Australian Census; HINCOME: is household income
proxied by the average weekly household income associated with the postcode of the contestant
based on data from the 2001 Australian Census; FINCOME: is family income proxied by the
average weekly family income associated with the postcode of the contestant based on data from
the 2001 Australian Census.
7 For comparative purposes it should be noted that the 26 suitcases that are available to be won
at the beginning of each game have a mean of US$19,112 and standard deviation of
US$44,576.
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expected value of the remaining suitcases were rejected. Of these 49 rejected
offers, 14 were 4US$8000, 10 were for 4US$10,000 and three exceeded
US$20,000. The mean Bank Offer greater than expected value that is rejected is
US$6000. Out of a sample of 102, eight different contestants rejected at least
one offer greater than an expected value of more than US$10,000. As such, this
represents a sizeable minority of the sample who exhibit risk-loving behavior
with very large stakes.
We have data on three personal characteristics of each contestant: gender;
age; and the postcode in which they reside.8 Forty-eight percent of contestants
in the sample were male. The age of contestants varied from 18 to 66 years, with
a mean of 32 and standard deviation of 10. For each postcode, we obtained
average income data from the 2001 Australian Census, and used this as a proxy
for individual wealth.
C. Strengths and limitations of the data
i. Strengths
Two important advantages of our data are that they describe decisions with
both high stakes and real financial consequences. Notably, Holt and Laury
(2002) find evidence that people’s risk aversion is different when there are real
stakes as opposed to hypothetical choices. Further, several studies (Binswanger
1980; Holt and Laury 2002) find that risk aversion increases along with the
stakes of a gamble. It is important to stress that the stakes in ‘Deal or No Deal’
are higher than any feasible experiment and almost any other game shows. The
mean prize won by contestants is almost US$16,000 with the highest prize
being US$105,000.9
‘Deal or No Deal’ also offers contestants very simple, stark choices. Almost all
other game shows that have been studied by economists involve some element
of skill, whether it be knowledge of trivia, skill in word games or an ability to
compute the odds in a game of chance involving cards. The only skill needed in
‘Deal or No Deal’ is the comparison of a gamble with a certain offer: precisely
the computational capacity in which economists are interested when studying
decision making under uncertainty.
Finally, the format of the Australian version of ‘Deal or No Deal’ (or, more
precisely, the existence of the Chance and SuperCase rounds), is ideal for testing
framing effects as many contestants face a change of framing in the final round
of the game. This feature is not present in other game shows based on lottery
choices, and is also not present in other franchises of the ‘Deal or No Deal’
paradigm shown in other countries.
8 Postcodes in Australia are analogous to Zip Codes in the United States.
9 Put another way, to perform this experiment from scratch would have required a total prize
pool of approximately US$1.6 million.
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ii. Limitations
The possibility of selection bias in the contestant pool is an issue for this paper,
as it is for all studies based upon game show data. The process of selecting the
contestant in Stages 1 and 2 is likely to mitigate this problem.
As just explained above, there are two stages in the selection of the
contestant. First, 26 people are randomly chosen from the audience. It is not
clear that the people who volunteer for quiz show audiences are systematically
more risk averse or more risk seeking than the broader population. Arguments
might plausibly be made that, for example, they may be more extroverted, on
average, than the general population, or that they may have more free time on
average. But even if these conjectures are true, there can be no a priori
supposition that these qualities are correlated with risk aversion, and certainly
there is nothing in the existing literature to suggest that they are.
In the second stage, the 26 people randomly chosen from the audience
compete to become the contestant by participating in a very simple trivia quiz
in which the emphasis is on speed. There is no reason to think that there is any
correlation between reaction time in a simple quiz and risk aversion.
The fact that the contestant is, in effect, randomly chosen from the audience
via a two-stage process means that it is simply not possible for the producers of
the show to engage in as much vetting of contestants as they would if
contestants were chosen directly via an application process.
The artificial environment of the game show could potentially increase or
decrease people’s risk aversion. On the one hand, the excitement of being on
television, surrounded by lights and a screaming audience could make people
more prone to risk taking or to errors of judgement. On the other hand, some
people may become more risk averse when in front of a national audience and
carefully avoid doing anything embarrassingly foolish. The possibility that
these factors are roughly in balance, on average, is consistent with earlier
studies of game shows which have found that contestants display levels of risk
aversion broadly in line with participants in experimental studies.
IV. EMPIRICAL FINDINGS
A. Baseline analysis ignoring supplementary rounds
To explore our main research questions, we conduct probit regression
modelling of the likelihood of accepting a bank offer against a number of
factors related to the game and observable agent heterogeneity. Factors which
raise the likelihood of accepting bank offers can be said to be covariates of risk
aversion. Panel A of Table 2 shows both the chosen regressors and the results for
the full dataset comprising Rounds 1–9 of such a probit regression (where the
dependent variable is whether or not a Bank Offer is accepted). It is reported as
model (1).
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Previous studies have found that risk aversion increases with rising stakes (see
Binswanger 1980; Kachelmeier and Shehata 1992; and Holt and Laury 2002).
Our results lend support to this. The higher is the Bank Offer relative to the
expected value of the remaining suitcases, the more likely a person is to accept.
The marginal effect of this ratio is 0.35. We also found a mild scale effect. The
higher is the offer, the more likely is a person to accept. The marginal effect of a
change in the offer of US$10,000 is 0.04. With respect to observable personal
characteristics, only age was statistically significant.10 The model was better at
approximating the effects of age when a quadratic, rather than linear, form was
used. In unreported results, we also tested a model that included the standard
deviation of the remaining prizes and various measures of regret.11 Neither of
these variables was statistically significant.12
To check the robustness of our initial finding with respect to gender, we also
included it as an interaction dummy. The results are contained in panel A of
Table 2 as model (2). We interact gender with the offer and with the ratio of the
offer to the expected value of the remaining suitcases. Males are more likely to
have increasing risk aversion as the stakes of the gamble rise. They are also less
likely than females to accept an offer for a given ratio between the offer and the
expected value (i.e. to be less risk averse). The current consensus, in what is a
still-developing literature, appears to be that when gender has been found to
have a significant effect on the measurement of risk aversion (not all studies
show an effect), the effect has been that women are more risk averse than men.
Our results fit comfortably into this consensus.13
Panel B of Table 2 shows the hit-miss table for model (2) i.e. the likelihood of
model (2) correctly predicting the decision for each observation when
considering Rounds 1–9. Of the 728 offers made, 609 were rejected and 119
accepted. Our model correctly predicts 586 of the rejections (96%) and 49 of the
acceptances (41%). This represents a 22% improvement over a baseline model
that predicts rejection in all rounds. Notably, an alternative benchmark that
separately predicts each round individually does no better than the benchmark
10 In supplementary analysis, we experimented with all three proxies for income for which we had
data: household income, family income and personal income. The results for household
income are shown. None of these measures of income was
statistically significant.
11 To test regret, we included the ratio of the current Bank Offer to the immediately preceding
Bank Offer and, alternatively, the ratio of the current Bank Offer to the highest previous Bank
Offer made to the contestant. We also tested the difference between the current Bank Offer and
the immediately preceding/highest previous Bank Offer. None of these was statistically
significant. Results are not reported to conserve space.
12 For each of the models tested in the paper, we also estimated results for a panel specification
(fixed effects), grouping each agent’s sequence of decisions. Depending upon which variables
we included and the subset of our sample that we used (i.e. whether we included all rounds or
just Rounds 6–9), we found that the results either reverted to the non-panel specification or that
our estimates of the ratio of the variance of the individual effects to the total variance were not
statistically significant.
13 For a recent survey see Crossen and Gneezy (2004).
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used as there is a 450% chance of accepting in only Rounds 8 and 9 and it is
only slightly higher than 50% in those rounds (51% and 52%, respectively).
Rounds 1–5 are relatively uninformative since the Bank Offers are typically
set low enough to ensure rejection. Given that there is only one contestant per
show, it is necessary for there to be at least five rounds to create a meaningful
half an hour TV program. As a consequence, almost all of the interesting
choices occur in Rounds 6–9. Accordingly, Table 3 shows the probit results and
hit-miss table when the data for estimation is confined to Rounds 6–9. Note
that focusing solely on later rounds reduces concern about the assumption of
myopic decision-making made in this paper.
Focusing on Rounds 6–9 reduces the sample size to 233. Both the ratio of the
Bank Offer to the expected value of the remaining suitcases and the size of the
Bank Offer remain statistically significant in model (1) and the ratio is
significant in model (2). Age is only statistically significant at the 10% level,
which probably reflects the smaller sample size. Gender and income remain
statistically insignificant.
The results for model (2) in panel A of Table 3 include interaction dummies
with gender for Rounds 6–9. The interaction dummies remain statistically
Table 2 Probit model of accepting the bank offer in the TV game show ‘Deal or No
Deal’ – all nine rounds
Panel A: Regression estimates
Model 1 Model 2
Coefficient
(z-stat)
Marginal
effect
Coefficient
(z-stat)
Marginal
effect
Constant �1.24 – �1.74n –
(�1.66) (�2.56)
OFFER 0.294nn 0.04 0.223nn 0.03
(4.74) (3.31)
RATIO 2.40nn 0.35 2.57nn 0.37
(11.76) (10.94)
MALE �0.01 �0.001 – –
(�0.04)
AGE �0.08n �0.01 �0.07 �0.01
(�2.23) (�1.79)
AGE2 0.83 0.12 0.63 0.09
(1.65) (1.23)
HINCOME �0.15 �0.02 – –
(�0.43)
MALE�OFFER – – 0.37nn 0.05
(2.79)
MALE�RATIO – – �0.29 �0.04
(�1.46)
Number of Obs 720 728
Pseudo R2 0.371 0.381
Deal or No Deal, That is the Question
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Journal compilation r International Review of Finance Ltd. 2009 37
significant (although only at the 10% level for the interaction with the ratio)
and once again indicate that males are more likely to become risk averse as the
stakes increase but that males are also less likely than females to be swayed by a
positive bank offer-expected value ratio.
As shown in panel B of Table 3, model (2) now correctly predicts 55% of
acceptances, although the prediction rate for rejections falls to 83%.
Overall, the model represents a 33% improvement over the baseline case in
Rounds 6–9.
Panel B: Hit-miss tables for model 2
Estimated equation Constant probability
DV50 DV51 Total DV50 DV51 Total
P(DV51)�0.5 586 70 656 609 119 728
P(DV51)40.5 23 49 72 0 0 0
Total 609 119 728 609 119 728
Correct 586 49 635 609 0 609
%Correct 96.22 41.18 87.22 100.00 0.00 83.61
%Incorrect 3.78 58.82 12.78 0.00 100.00 16.39
Total Gain �3.78 41.18 3.61 – – –
%Gain – 41.18 22.03 – – –
This table reports the results of two probit regression models of the probability of accepting the
bank offer in a given round of the Australian version of the TV game show ‘Deal or No Deal’. The
data used in this analysis are for the complete set of nine normal rounds of the game. Panel A
shows the probit regressions results for model 1 – no interaction terms and model 2 – including
interaction terms. The dependent variable (DV) takes a value of unity if the bank offer is accepted
by the contestant and zero otherwise. The independent variables are defined as follows: OFFER is
the value of the bank offer measured in US$10,000 units; RATIO is the ratio of the bank offer to
the expected value of the gamble; MALE is a dummy variable that takes the value of unity if the
contestant is a male; AGE is the contestant’s age measured in years; AGE2 is the square of the
contestant’s age measured in years2; HINCOME is proxied by the average household income
associated with the postcode (analogous to zip code) of the contestant based on data from the
2001 Australian Census. Immediately below each estimated coefficient in parentheses are the
associated z-statistics. The reported coefficient on and marginal effect of AGE2 are both scaled by
103 to enhance readability.
nn and n Statistical significance at the 1% and 5% levels is indicated, respectively.
Panel B shows hit-miss tables associated with Model 2 estimates reported in panel A. These
contingency tables show a 2�2 scheme of correct and incorrect classifications. In the left hand
side of the panel (‘estimated equation’) the predicted probability of each observation is
determined relative to a 0.5 probability cut-off value. In this case a correct classification occurs
when the predicted probability �0.5 (40.5) coincides with an actual value for the dependent
variable equal to 0 (1). In the right hand side of the panel (‘constant probability’) a naı̈ve
prediction is made that all observations are equal to the most common case i.e. the offer is not
accepted (DV50). In this case all DV50 (DV51) observations are correctly (incorrectly) classified.
The ‘predictive ability’ of the model is gauged by a measure of the gain achieved from applying
the probit specification relative to the naı̈ve case, and is recorded as the Total Gain: in percentage
points and Percent Gain: as a percentage of the incorrect classifications in the constant
probability model.
Table 2 (Continued)
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Journal compilation r International Review of Finance Ltd. 200938
B. Extended analysis incorporating supplementary rounds
One of the most serious challenges to expected utility theory is the potential for
preference reversals when the framing of a choice changes. Prospect theory is
one example of a framing effect in which individuals will behave differently,
depending upon their ‘reference point’. Prospect theory asserts that people will
display an asymmetry in their attitude to risk delineated by gains versus losses.
Specifically, prospect theory posits that people will generally be risk averse in
lottery choices involving gains and risk seeking in lottery choices involving
losses. In particular, prospect theory suggests a utility function that is (i) defined
on deviations from the reference point (not on overall wealth); (ii) is concave
for gains and convex for losses and (iii) is steeper for losses than gains. This
results in the well known S-shaped utility function of Kahneman and Tversky
(1979) and Tversky and Kahneman (1992).
It was mentioned in the section describing the rules of the game that, even
once a contestant has accepted a Bank Offer, the game does not technically end.
Rather, the contestant is required to engage in the counter-factual exercise of
Table 3 Probit model of accepting the bank offer in the TV game show ‘Deal or No
Deal’ – rounds 6–9
Panel A: Regression estimates
Model 1 Model 2
Coefficient
(z-stat)
Marginal
effect
Coefficient
(z-stat)
Marginal
effect
Constant 0.70 – �0.17 –
(0.65) (�0.17)
OFFER 0.16n 0.06 0.11 0.04
(2.40) (1.55)
RATIO 1.41nn 0.10 1.61nn 0.63
(5.49) (5.57)
MALE �0.12 �0.05 – –
(�0.66)
AGE �0.10 �0.04 �0.09 �0.03
(�1.98) (�1.64)
AGE2 1.16 0.45 0.94 0.37
(1.65) (1.34)
HINCOME �0.42 �0.17 – –
(�0.92)
MALE�OFFER – – 0.52nn 0.21
(2.73)
MALE�RATIO – – �0.39 �0.15
(�1.84)
Number of Obs 230 233
Pseudo R2 0.137 0.156
Deal or No Deal, That is the Question
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Journal compilation r International Review of Finance Ltd. 2009 39
continuing to remove suitcases from the remaining suitcases until only two
remain, at which time the possibility (since this is entirely at the
discretion of the producers) of playing a supplementary Chance or SuperCase
round arises.
In the chance situation, the Bank Offers the contestant a chance to
retract the ‘Deal’ they had accepted in an earlier round. If the contestant
accepts the retraction, they swap all winnings from that previously made deal
for a lottery. Since the Chance round only ever occurs in Round 9 when just two
prize outcomes remain, the Chance round represents a choice between a 55
Panel B: Hit-Miss table for model 2
Estimated equation Constant probability
DV50 DV51 Total DV50 DV51 Total
P(DV51)�0.5 109 45 154 132 101 233
P(DV51)40.5 23 56 79 0 0 0
Total 132 101 233 132 101 233
Correct 109 56 165 132 0 132
%Correct 82.58 55.45 70.82 100.00 0.00 56.67
%Incorrect 17.42 44.55 29.18 0.00 100.00 43.33
Total Gain �17.42 55.45 14.15 – – –
%Gain – 55.45 32.66 – – –
This table reports the results of two probit regression models of the probability of accepting the
bank offer in a given round of the Australian version of the TV game show ‘Deal or No Deal’. The
data used in this analysis are for rounds six to nine only. Panel A shows the probit regressions
results for model 1 – no interaction terms and model 2 – including interaction terms. The
dependent variable (DV) takes a value of unity if the bank offer is accepted by the contestant and
zero otherwise. The independent variables are defined as follows: OFFER is the value of the bank
offer measured in US$10,000 units; RATIO is the ratio of the bank offer to the expected value of
the gamble; MALE is a dummy variable that takes the value of unity if the contestant is a male;
AGE is the contestant’s age measured in years; AGE2 is the square of the contestant’s age measured
in years2; HINCOME is proxied by the average household income associated with the postcode
(analogous to zip code) of the contestant based on data from the 2001 Australian Census.
Immediately below each estimated coefficient in parentheses are the associated z-statistics. The
reported coefficient on and marginal effect of AGE2 are both scaled by 103 to enhance readability.
nn and n Statistical significance at the 1% and 5% levels is indicated, respectively.
Panel B shows hit-miss tables associated with Model 2 estimates reported in panel A. These
contingency tables show a 2�2 scheme of correct and incorrect classifications. In the left hand
side of the panel (‘estimated equation’) the predicted probability of each observation is
determined relative to a 0.5 probability cut-off value. In this case a correct classification occurs
when the predicted probability �0.5 (40.5) coincides with an actual value for the dependent
variable equal to 0 (1). In the right hand side of the panel (‘constant probability’) a naı̈ve
prediction is made that all observations are equal to the most common case i.e. the offer is not
accepted (DV50). In this case all DV50 (DV51) observations are correctly (incorrectly) classified.
The ‘predictive ability’ of the model is gauged by a measure of the gain achieved from applying
the probit specification relative to the naı̈ve case, and is recorded as the Total Gain: in percentage
points and Percent Gain: as a percentage of the incorrect classifications in the constant
probability model.
Table 3 (Continued)
International Review of Finance
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Journal compilation r International Review of Finance Ltd. 200940
gamble between two prizes versus the amount already won in a previous round
when the bank offer had been accepted. It is important to note that the Chance
round is only ever offered when the two remaining prizes differ by a large
magnitude, highlighting the contrast between the risky and the safe options.
For example, in one actual game, the contestant faced a choice between a
certain offer of US$15,100 and a gamble between US$10 and US$75,000. The
person chose the sure amount of money. Accepting the ‘Chance’ offer is not
compulsory. In our sample, the Chance option was offered 20 times, with the
mean value of the two cases being US$18,229 compared with the considerably
lower mean value of already accepted deals of US$9824. Notwithstanding this,
in only seven Chance rounds was the suitcase gamble accepted, suggestive of
loss aversion at work.
The SuperCase round is played after all suitcases have been opened. If the
contestant elects to take the SuperCase option, they will win whatever cash
amount is revealed to be inside the SuperCase, and forfeit their previously
struck deal. In each game where it is offered, one of the following cash values
will be selected at random, and placed inside the SuperCase: US$0.50; US$100;
US$1000; US$2000; US$5000; US$10,000; US$20,000 or US$30,000. The mean
and standard deviation of the SuperCase option are US$8510 and US$11,000,
respectively. In our sample, the SuperCase was offered 24 times, with the
contestants having previously accepted deals ranging from US$2100 to
US$17,800. The mean of previously accepted deals was US$8750. For example,
in one game, the contestant had previously accepted a Deal of US$6350. After
all suitcases had been revealed, the contestant was offered the SuperCase
option. The contestant accepted, and won US$20,000. In only eight SuperCase
rounds was the SuperCase chosen.
It can be seen from this description of the two supplementary rounds that
they involve a change in the framing of the choice faced by the contestant. On
the one hand, in Rounds 1–9, the contestant chooses whether or not to swap
his/her right to a lottery for a sure amount of money. The choices involve only
possible gains, not possible losses. The contestant ‘owns’ the right to keep
removing suitcases until only the suitcase initially nominated remains and to
receive Bank Offers after each round of this process. Each time a Bank Offer is
made, the contestant is being asked to sell this lottery. On the other hand, in
the Chance and SuperCase rounds, the choice is reversed, and the possibility of
making a loss is introduced. Specifically, the contestant has already accepted a
Deal and is being asked to swap his/her sure winnings for a gamble. In other
words, the contestant is now being asked to buy a new lottery. If the
contestant’s current winnings become the new reference point (as suggested
by prospect theory), then accepting either the Chance or SuperCase deals will
mean accepting a positive probability of suffering a loss relative to the reference
point and a positive probability of enjoying a gain relative to the reference
point. Specifically, consider the Chance round in which a person will face a
choice between the two remaining suitcases or a sure amount of money. Thus,
in the Chance round, the contestant chooses between a 50–50 chance of losing
Deal or No Deal, That is the Question
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Journal compilation r International Review of Finance Ltd. 2009 41
or gaining relative to the reference position or status quo. A person with an
S-shaped utility function which is steeper for losses than gains will be less likely
to accept a Chance (or SuperCase) round gamble.
To explore the issue of loss aversion, we again re-estimate the probit
regression but this time include the impact of the Chance and SuperCase
rounds on the willingness of a contestant to accept an offer. While the offer is
usually the Bank Offer, in the Chance and SuperCase rounds, the offer
represents the status quo. The results of this new probit regression are shown in
Table 4.
Panel A of Table 4 contains the results of a Probit for Rounds 1–9 that
includes dummies for whether the decision is made during a Chance or
SuperCase round. A further variable, ‘high cases remaining’ is also included.
The highcase variable is the proportion of remaining suitcases that are higher
than that round’s Bank Offer. We include it to capture the possible heuristic
Table 4 Probit model of accepting the bank offer in the TV game show ‘Deal or No
Deal’ incorporating the chance and SuperCase rounds – all nine rounds
Panel A: Regression estimates
Coefficient (z-stat) Marginal effect
Constant �1.69n –
(�2.16)
OFFER 0.375nn 0.04
(4.42)
RATIO 3.13nn 0.31
(9.91)
CHANCE 2.77nn 0.81
(5.37)
SUPERCASE 4.07nn 0.95
(4.19)
HIGHCASE �2.56nn �0.25
(�2.86)
AGE �0.08 �0.01
(�1.78)
AGE2 0.70 0.07
(1.20)
MALE�OFFER 0.274 0.03
(1.81)
MALE�RATIO �0.65n �0.06
(�2.04)
MALE�CHANCE �1.63n �0.05
(�2.41)
MALE�SUPERCASE �1.97 �0.05
(�1.65)
MALE�HIGHCASE 1.77 0.18
(1.76)
Number of Obs 728
Pseudo R2 0.485
International Review of Finance
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Journal compilation r International Review of Finance Ltd. 200942
behavior by contestants – that the contestant takes account of how many
remaining suitcases are above the Bank Offer for that round.
The Chance and SuperCase dummy variables and the highcase variable are
all statistically significant at the 1% level. Further, the Chance and SuperCase
dummies have a high marginal effect. Males are less likely to accept the Bank
Offer in the Chance and SuperCase rounds (i.e. they are more likely to take the
Panel B: Hit-miss table
Estimated Equation Constant probability
DV50 DV51 Total DV50 DV51 Total
P(DV51)�0.5 586 59 645 609 119 728
P(DV51)40.5 23 60 83 0 0 0
Total 609 119 728 609 118 728
Correct 586 60 646 609 0 609
%Correct 96.22 50.42 88.74 100.00 0.00 83.61
%Incorrect 3.78 49.58 11.26 0.00 100.00 16.39
Total Gain �3.78 50.42 5.13 – – –
%Gain – 50.42 31.30 – – –
This table reports the results of a probit regression model of the probability of accepting the bank
offer in a given round of the Australian version of the TV game show ‘Deal or No Deal’. The data
used in this analysis incorporates all nine normal rounds of the game, as well as the
supplementary ‘Chance’ and ‘SuperCase’ rounds. Panel A shows the probit regressions results.
The dependent variable (DV) takes a value of unity if the bank offer is accepted by the contestant
(or, in the case of the Chance and SuperCase rounds, the contestant opts for the previously
accepted Bank Offer) and zero otherwise. The independent variables are defined as follows: OFFER
is the value of the bank offer measured in US$10,000 units; RATIO is the ratio of the bank offer to
the expected value of the gamble; CHANCE is a dummy variable that takes the value of unity if
the round is a chance round; SUPERCASE is a dummy variable that takes the value of unity if the
round is a SuperCase round; HIGHCASE is the proportion of remaining suitcases that are higher
than that of the bank’s current offer; AGE is the contestant’s age measured in years; AGE2 is the
square of the contestant’s age measured in years2; MALE is a dummy variable that takes the value
of unity if the contestant is a male. Immediately below each estimated coefficient in parentheses
are the associated z-statistics. The reported coefficient on and marginal effect of AGE2 are both
scaled by 103 to enhance readability.
nn and n Statistical significance at the 1% and 5% levels is indicated, respectively.
Panel B shows hit-miss tables associated with the model estimates reported in panel A. These
contingency tables show a 2�2 scheme of correct and incorrect classifications. In the left hand
side of the panel (‘estimated equation’) the predicted probability of each observation is
determined relative to a 0.5 probability cut-off value. In this case a correct classification occurs
when the predicted probability �0.5 (40.5) coincides with an actual value for the dependent
variable equal to 0 (1). In the right hand side of the panel (‘constant probability’) a naı̈ve
prediction is made that all observations are equal to the most common case i.e. the offer is not
accepted (DV50). In this case all DV50 (DV51) observations are correctly (incorrectly) classified.
The ‘predictive ability’ of the model is gauged by a measure of the gain achieved from applying
the probit specification relative to the naı̈ve case, and is recorded as the Total Gain: in percentage
points and Percent Gain: as a percentage of the incorrect classifications in the constant
probability model.
Table 4 (Continued)
Deal or No Deal, That is the Question
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Journal compilation r International Review of Finance Ltd. 2009 43
gamble by giving up their already won prize) and are also less likely to be
affected by the high case rule of thumb. The statistical significance and high
marginal effect of the dummies for the Chance and SuperCase rounds in these
probit regressions is suggestive of a reference point switching explanation for
any greater reluctance to accept risk in the Chance or SuperCase rounds
compared with the scenario faced in earlier rounds.
Panel B of Table 4 repeats the earlier exercise of comparing the predictive
power of the model against the benchmark. The model performs considerably
better than the model in the previous section, correctly predicting 50% of
acceptances and representing an overall 31% improvement on the benchmark
model.
Table 5 tests the same model as outlined in Table 4, but using data only from
Rounds 6 to 9. As discussed, almost all of the difficult choices faced by
Table 5 Probit model of accepting the bank offer in the TV game show ‘Deal or No
Deal’ incorporating the chance and SuperCase rounds – Rounds 6–9
Panel A: Regression estimates
Coefficient (z-stat) Marginal effect
Constant �0.80 –
(�0.76)
OFFER 0.247nn 0.01
(2.85)
RATIO 2.32nn 0.92
(6.08)
CHANCE 2.17nn 0.60
(4.17)
SUPERCASE 3.01nn 0.66
(3.02)
HIGHCASE �2.06n �0.81
(�2.12)
AGE �0.08 �0.03
(�1.34)
AGE2 0.78 0.31
(1.02)
MALE�OFFER 0.419n 0.17
(2.04)
MALE�RATIO �0.69n �0.27
(�2.01)
MALE�CHANCE �1.59n �0.42
(�2.36)
MALE�SUPERCASE �1.78 �0.44
(�1.44)
MALE�HIGHCASE 1.64 0.64
(1.50)
Number of Obs 233
Pseudo R2 0.256
International Review of Finance
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Journal compilation r International Review of Finance Ltd. 200944
contestants are in Rounds 6–9. Once again, most variables are statistically
significant at the 1% level and the Chance and SuperCase dummies have a high
marginal effect. Once more, the highcase variable is statistically significant and,
as expected, its marginal effect is much higher for these later rounds than it was
for the entire sample. Despite a small loss of accuracy on the rejections, we see a
44% overall improvement on the benchmark.
Panel B: Hit-miss table
Estimated equation Constant probability
DV50 DV51 Total DV50 DV51 Total
P(DV51)�0.5 111 21 132 132 101 233
P(DV51)40.5 36 65 101 0 0 0
Total 147 86 233 132 101 233
Correct 111 65 176 132 0 132
%Correct 75.51 75.58 75.54 100.00 0.00 56.67
%Incorrect 24.49 24.42 24.46 0.00 100.00 43.33
Total Gain �24.49 75.58 18.87 – – –
%Gain – 75.58 43.55 – – –
This table reports the results of a probit regression model of the probability of accepting the bank
offer in a given round of the Australian version of the TV game show ‘Deal or No Deal’. The data
used in this analysis incorporates data for rounds six to nine, as well as the supplementary
‘Chance’ and ‘SuperCase’ rounds. Panel A shows the probit regressions results. The dependent
variable (DV) takes a value of unity if the bank offer is accepted by the contestant (or, in the case
of the Chance and SuperCase rounds, the contestant opts for the previously accepted Bank Offer)
and zero otherwise. The independent variables are defined as follows: OFFER is the value of the
bank offer measured in US$10,000 units; RATIO is the ratio of the bank offer to the expected value
of the gamble; CHANCE is a dummy variable that takes the value of unity if the round is a chance
round; SUPERCASE is a dummy variable that takes the value of unity if the round is a SuperCase
round; HIGHCASE is the proportion of remaining suitcases that are higher than that of the bank’s
current offer; AGE is the contestant’s age measured in years; AGE2 is the square of the contestant’s
age measured in years2; MALE is a dummy variable that takes the value of unity if the contestant
is a male. Immediately below each estimated coefficient in parentheses are the associated
z-statistics. The reported coefficient on and marginal effect of AGE2 are both scaled by 103 to
enhance readability.
nn and n Statistical significance at the 1% and 5% levels is indicated, respectively.
Panel B shows hit-miss tables associated with the model estimates reported in panel A. These
contingency tables show a 2�2 scheme of correct and incorrect classifications. In the left hand
side of the panel (‘estimated equation’) the predicted probability of each observation is
determined relative to a 0.5 probability cut-off value. In this case a correct classification occurs
when the predicted probability �0.5 (40.5) coincides with an actual value for the dependent
variable equal to 0 (1). In the right hand side of the panel (‘constant probability’) a naı̈ve
prediction is made that all observations are equal to the most common case i.e. the offer is not
accepted (DV50). In this case all DV50 (DV51) observations are correctly (incorrectly) classified.
The ‘predictive ability’ of the model is gauged by a measure of the gain achieved from applying
the probit specification relative to the naı̈ve case, and is recorded as the Total Gain: in percentage
points and Percent Gain: as a percentage of the incorrect classifications in the constant
probability model.
Table 5 (Continued)
Deal or No Deal, That is the Question
r 2009 The Authors
Journal compilation r International Review of Finance Ltd. 2009 45
V. CONCLUSION
In this paper, we analyze a simple lottery-choice setting within the Australian
version of the TV game show, ‘Deal or No Deal’, that allows us to explore a range
of issues related to risk aversion in the context of both very high and wide-
ranging (possible) payoffs. Notably, a feature of the game is especially
convenient for testing non-expected utility theories relating to the effects of
changes in reference points.
The main findings of our analysis are easily summarized. First, we generally
observe that as the stakes of this lottery game increase, so to does the degree of
risk aversion (similar to Holt and Laury 2002). Having said that however, we
observe considerable heterogeneity in people’s willingness to bear risk – indeed,
a sizeable proportion of contestants in our sample appear to be risk-loving.
Moreover, such risk loving behavior is sometimes evident with decisions
involving very high stakes. We also find heterogeneity with respect to
observable agent characteristics, with age and gender being statistically
significant determinants of risk aversion, while wealth is not.
Second, we are able to exploit a special feature of the game show that
sometimes appears at the final decision-stage and which reverses the choice
faced by contestants up till that time. Specifically, instead of being offered a
sure-thing in exchange for a lottery, contestants who are entitled to end the
show with money already secured, are offered a lottery in exchange for that
sure-thing. In this context, we find that the reversal of framing has a significant
impact on people’s willingness to bear risk, and that their high level of risk
aversion during the Chance and SuperCase rounds is consistent with the
existence of framing effects.
Robert Faff
Department of Accounting and Finance
Faculty of Business and Economics
Monash University
Victoria
3800
Australia
Robert.Faff@Buseco.Monash.edu.au
REFERENCES
Andersen, S., G. Harrison, M. Lau, and E. Rutstrom (2006a), Dynamic choice
behaviour in a natural experiment, Working Paper 06-10, Department of
Economics, College of Business Administration, University of Central Florida.
International Review of Finance
r 2009 The Authors
Journal compilation r International Review of Finance Ltd. 200946
mailto:Robert.Faff@Buseco.Monash.edu.au
Andersen, S., G. Harrison, M. Lau, and E. Rutstrom (2006b), Dual criteria decisions,
Working Paper 06-11, Department of Economics, College of Business Administra-
tion, University of Central Florida.
Andersen, S., G. Harrison, M. Lau, and E. Rutstrom (2008), ‘Risk Aversion in Game
Shows’, in J. Cox and G. Harrison (eds), Risk Aversion in Experiments. Research in
Experimental Economics, Volume 12, Bingley, UK: Emerald.
Bajari, P., and A. Hortascu (2005), Are structural estimates of auction models
reasonable? Evidence from experimental data, Mimeo.
Beetsma, R., and P. Schotman (2001), ‘Measuring Risk Attitudes in a Natural
Experiment: Data from the Television Game Show LINGO’, CEPR Economic Journal,
111, 821–48.
Bennett, R., and K. Hickman (1993), ‘Rationality and the ‘‘price is right’’ ’, Journal of
Economic Behavior and Organization, 21, 99–105.
Berk, J., E. Hughson, and K. Vandezande (1996), ‘The Price is Right, But are the
Bids? An Investigation of Rational Decision Theory’, American Economic Review, 86,
954–70.
Binswanger, H. (1980), ‘Attitudes Toward Risk: Experimental Measurement in Rural
India’, American Journal of Agricultural Economics, 62, 395–407.
Blavatskyy, P., and G. Pogrebna (2006), Loss Aversion? Not with Half a Million on the
Table! Mimeo, University of Zurich.
Blavatskyy, P., and G. Pogrebna (2008), ‘Risk Aversion When Gains are Likely and
Unlikely: Evidence from a Natural Experiment with Large Stakes’, Theory and
Decision, 64, 395–420.
Bombardini, M., and F. Trebbi (2005), Risk Aversion and Expected Utility
Theory: A Field Experiment with Large and Small Stakes. Mimeo, Harvard
University.
Camerer, C. (1995), ‘Individual Decision Making’, in John H. Kagel and Alvin E. Roth
(eds), The Handbook of Experimental Economics. Princeton, NJ: Princeton University
Press, pp. 587–703.
Cohen, A., and L. Einav (2007), ‘Estimating Risk Preferences from Deductible Choice’,
American Economic Review, 97, 745–88.
Cohn, R., W. Lewellen, R. Lease, and G. Schlarbaum (1975), ‘Individual Investor Risk
Aversion and Investment Portfolio Composition’, Journal of Finance, 30, 605–20.
Crossen, R., and U. Gneezy (2004), Gender differences in preferences, in Handbook of
Experimental Results.
De Roos, N., and Y. Sarafidis (2006), Decision Making Under risk in Deal or No Deal.
Mimeo, University of Sydney.
Fullenkamp, C., R. Tonerio, and R. Battalio (2003), ‘Assessing Individual Risk Attitudes
Using Field Data from Lottery Games’, Review of Economics and Statistics, 85, 218–25.
Gertner, R. (1993), ‘Game Shows and Economic Behavior: Risk-Taking on ‘‘Card
Sharks’’’, Quarterly Journal of Economics, 108, 507–21.
Goeree, J., C. Holt, and T. Palfrey (2000), Risk Averse Behavior in Asymmetric
Matching Pennies Games, Mimeo.
Harrison, G., E. Johnson, M. McInnes, and E. Rutstrom (2003), Individual Choice
and Risk Aversion in the Laboratory: A Reconsideration. Mimeo, University of Central
Florida.
Hartog, J., A. Ferrer-i-Carbonell, and N. Jonker (2000), On a Simple Measure of
Individual Risk Aversion, Tinbergen Institute Discussion Paper, TI 2000-074/3.
Healy, P., and C. Noussair (2004), ‘Bidding Behaviour in the Price is Right
Game: An Experimental Study’, Journal of Economic Behavior & Organization, 54,
231–47.
Hersch, P., and G. McDougall (1997), ‘Decision Making Under Uncertainty when Stakes are
High: Evidence from a Lottery Game Show’, Southern Economic Journal, 64, 75–84.
Deal or No Deal, That is the Question
r 2009 The Authors
Journal compilation r International Review of Finance Ltd. 2009 47
Holt, C., and S. Laury (2002), ‘Risk Aversion and Incentive Effects’, American Economic
Review, 92, 1644–55.
Kachelmeier, S., and M. Shehata (1992), ‘Examining Risk Preferences Under High
Monetary Incentives: Experimental Evidence from the People’s Republic of China’,
American Economic Review, 82, 1120–41.
Kahneman, D., and A. Tversky (1979), ‘Prospect Theory: An Analysis of Decision
Under Risk’, Econometrica, 47, 263–91.
Lewellen, W., K. Stanley, R. Lease, and G. Schlarbaum (1978), ‘Some Direct Evidence
on the Dividend Clientele Phenomenon’, Journal of Finance, 33, 1385–99.
McKelvey, R., and T. Palfrey (1995), ‘Quantal Response Equilibrium for Normal form
Games’, Games and Economic Behavior, 10, 6–38.
Metrick, A. (1995), ‘A Natural Experiment in ‘‘Jeopardy!’’’, American Economic Review,
85, 240–53.
Post, T., M. van den Assem, G. Baltussen, and R. Thaler (2008), ‘Deal or No Deal?
Decision Making Under Risk in a Large-Payoff Game Show’, American Economic
Review, 98, 38–71.
Rabin, M. (2000), ‘Risk Aversion and Expected Utility Theory: A Calibration Theorem’,
Econometrica, 68, 1281–92.
Tversky, A., and D. Kahneman (1992), ‘Advances in Prospect Theory: Cumulative
Representation of Uncertainty’, Journal of Risk and Uncertainty, 5, 297–323.
APPENDIX A
Table A1 Schedule of prizes in ‘Deal or No Deal’ TV game
show
US$0.50 US$1000
US$1 US$1500
US$2 US$2000
US$5 US$3000
US$10 US$5000
US$25 US$7500
US$50 US$10,000
US$75 US$15,000
US$100 US$25,000n
US$150 US$50,000
US$250 US$75,000
US$500 US$100,000
US$750 US$200,000
nIn 41 of the 102 episodes of the game show for which we have data, a new
car was substituted as the prize in place of the US$25,000 amount. The car
was worth approximately US$25,000 and, therefore, for convenience, we
used the monetary value of US$25,000 for that suitcase in all instances.
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Journal compilation r International Review of Finance Ltd. 200948
APPENDIX B
Table B1 Characterization of the rounds of play in the ‘Deal or No Deal’ TV game
show
Round
#
# of
beginning
cases
# of
cases
removed
# of
ending
cases
Bank
offer
Decision Outcome
1 26 6 20 US$BO1 Reject Play next round
Accept Take US$BO1 (denote as
US$WIN)1
2 20 5 15 US$BO2 Reject Play next round
Accept Take US$BO2 (US$WIN)1
3 15 4 11 US$BO3 Reject Play next round
Accept Take US$BO3 (US$WIN)1
4 11 3 8 US$BO4 Reject Play next round
Accept Take US$BO4 (US$WIN)1
5 8 2 6 US$BO5 Reject Play next round
Accept Take US$BO5 (US$WIN)1
6 6 1 5 US$BO6 Reject Play next round
Accept Take US$BO6 (US$WIN)1
7 5 1 4 US$BO7 Reject Play next round
Accept Take US$BO7 (US$WIN)1
8 4 1 3 US$BO8 Reject Play next round
Accept Take US$BO8 (US$WIN)1
9 3 1 2 US$BO9 Reject Win US$prize in own case
(US$WIN)1
Accept Take US$BO9 (US$WIN)1
Chance2 – – – Lottery:
Case A or
Reject Retain US$WIN
Case B Accept Win US$A or US$B
Super-
Case3
– – – Lottery:
SC1 or SC2
or SC3 or
SC4 or . . .
SC8
Reject Retain US$WIN
Accept Win US$0.50 or US$100 or
US$1000 or . . . .
US$30,000
1This may not be the final outcome of the game – the contestant may be invited to partake in the
Chance or SuperCase round, after Round #9.
2In the Chance round the bank offers the (uncertain) lottery choice involving the two cases
remaining in Round #9: Case A or Case B.
3In the SuperCase round the bank offers the (uncertain) lottery choice involving eight different
super case values – denoted SC1, SC2, . . ., SC8. The possible values contained in the super case
are: US$0.50; US$100; US$1000; US$2000; US$5000; US$10,000; US$20,000 and US$30,000.
Deal or No Deal, That is the Question
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Journal compilation r International Review of Finance Ltd. 2009 49
APPENDIX C
Table C1 Illustration of the rounds of play in an actual episode of the ‘Deal or No
Deal’ TV game show
Round
#
# of beg
cases
Cases removed # of end
cases
Bank
offer
Decision Outcome
1 26 6 cases:
US$75,000;
US$750; US$50;
US$25;
US$25,000;
US$50,000
20 US$9100 Reject Play next
round
2 20 5 cases:
US$200,000;
US$0.50; US$2;
US$3,000;
US$100
15 US$3800 Reject Play next
round
3 15 4 cases: US$500;
US$5; US$1000;
US$10
11 US$6910 Reject Play next
round
4 11 3 cases: US$2000;
US$1; US$250
8 US$8450 Reject Play next
round
5 8 2 cases: US$7500;
US$15,000
6 US$7400 Reject Play next
round
6 6 US$10,000 5 US$9900 Reject Play next
round
7 5 US$75 4 US$12,250 Reject Play next
round
8 4 US$150 3 US$17,700 Accept Take
US$11,400
9 3 US$1500 2 NA NA NA
Chance – – – Lottery:
US$5000 or
US$100,000
Accept Win
US$100,000
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Journal compilation r International Review of Finance Ltd. 200950
