Finance Derivative homework 1 question

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FIN 412 Group Assignment

3

G. Smith Due: December 4 by 5:00 PM

Preliminary commentary: Investing abroad

Consider what happens when an investor makes an investment outside his or her country of

domicile. As an example, consider a Canadian making an investment in a US equity index ETF

that trades in the United States. Because the asset trades in the US, the investor must first buy

US dollars (USD). The investor then takes those US dollars and purchases the ETF.

Consequently, our investor is exposed to two things that have uncertain returns, the USD ETF

and the US dollar itself.

Suppose our investor does this, purchasing an ETF at time 0 at USD price P0. The exchange rate

at the time of purchase was C0, which represents the number of Canadian dollars (CAD) per US$

at the time of purchase. Thus, the value of the purchase in Canadian dollar terms is P0C0.

Suppose, one period later, we wish to know the holding period return (HPR) from this

investment. At the end of period 1 the US dollar price of the ETF is P1 and the exchange rate is

C1, meaning the CAD value of the investment is now P1C1. Consequently, the HPR over the

period is given by: 1 1
1

0 0

1
PC

HPR
P C

  .

You can see clearly from the above that the Canadian investor’s return is a function of the USD

return on the investment (P1/P0, which is (1+HPR) for the ETF in US) and percentage change in

the exchange rate (C1/C0, which is (1+HPR) to a Canadian from holding one USD).

A quick numerical example follows. Suppose our investor buys a share of the ETF at time 0 and

is computing his HPR at the end of period 1. For simplicity, assume no dividend is paid. Prices

and exchange rates are as follows:

Time USD Price
per share

CAD/USD

0 $10 1.03

1 $11 1.01

Two relevant things happened over the period. The price of the ETF went up by 10% and the

CAD appreciated relative to USD (equivalently, the USD depreciated relative to CAD). The HPR

experienced by a US investor is 10%, but our Canadian investor is less fortunate. The Canadian’s

HPR on this investment is     1 0 1 0 1 11 10 1.01 1.03 1 7.86%P P C C     . The Canadian’s

return is lower than that received by a US investor as the USD became less valuable over the

holding period. One can easily see that if the currency had moved in the opposite direction to

that of the example, our Canadian investor would have received a higher return than a US

investor holding the same ETF.

FIN 412 Group Assignment 3 Due: Dec 4 by 5:00 PM

2

Currency returns can be quite volatile. As the numbers above show, currency movements

impact returns experienced on foreign investments. Few investors make foreign equity

investments because they want the currency exposure. There are much simpler and more

direct ways to get the currency exposure, should that exposure be sought. Typically, foreign

investments are sought because they are thought to be able to improve a portfolio by offering

better returns or enhanced diversification. Thus, the potential currency impact can be troubling

to investors

Fortunately, the advent of derivative markets has made it possible for investors to hedge the

currency risk inherent in an international investment. The example above demonstrates a

straightforward, unhedged investment by a Canadian in a US equity. Our investor could have

proceeded differently. To hedge the currency risk in this investment, the investor could have

done the following at initiation of the investment:

 Buy USD

 Buy the ETF

 Sell USD forward contract. This would lock in the exchange rate at which you would sell

the USD at a future date.

This has eliminated the currency risk related to this investment. Note that there would still be

some currency impact, as the forward price at which one contract to sell the USD will, in

general, be different from the spot rate.
1
However, this impact would be certain as we would

have contracted a price at which to sell the USD at the end of the period.

The point of all this is to say that currency effects can be significant, but that we are able to

hedge these effects by using derivative positions. We can hedge the currency risk. The

important question is if we should do so.

The Question

You work as an analyst at a Canadian institutional investment manager. Your firm is about to

begin a passive investment program in the US equity market, wherein the firm will replicate the

MSCI USA index, a broad market capitalization-weighted US equity index. This passive portfolio

will be make up 50% of your firm’s equity portfolio, with the other 50% being a S&P/TSX

Composite Canadian Index passive replication fund.

Your firm’s investment committee is grappling with the question of whether or not the currency

exposure inherent in the US investment should be hedged. The committee chairperson makes

the following statement:

1
Pricing and general structure of currency forward contracts is beyond the scope of this course, but is touched on in the

textbook and is covered extensively in other courses (e.g. FIN 413).

FIN 412 Group Assignment 3 Due: Dec 4 by 5:00 PM
3

“The whole purpose of our investment in US equities in the first place is to improve the risk

characteristics of our overall portfolio. It is a market that is not perfectly correlated to our

Canadian equity assets, so our portfolio will be improved in terms of expected return to risk by

making this change. But I have no opinion about the direction of the US dollar relative to the

Canadian dollar and I never will. It is just too unpredictable. Over time, returns to holding

currency are effectively zero. But it’s the volatility that comes from the currency that concerns

me. I want equity exposure from the US market. The currency component is an unsought risk

factor, so I think we should hedge the currency component. Why take a risk that we are not

seeking when we can easily eliminate it? It seems pretty obvious that we should hedge the

currency exposure.”

Given the committee chair’s stated purpose of the US investment and his expectation that

currency returns average zero over time, do you agree with his conclusion that the currency

exposure inherent in the US Equity investment should be hedged? Explain your answer.

To assist you in your analysis, the companion spreadsheet contains 10 years of monthly returns

data on the S&P/TSX Composite Index (in CAD terms), MSCI USA (in USD terms), unhedged

returns to a Canadian from holding USD, and returns to a Canadian from holding one-month

forward hedged USD positions. We know that historical data can give us a good idea of

variances and correlations, but is less helpful in giving us an idea of future expected return.

Thus, in your analysis, assume that the expected return on currency is zero and that the

expected return on both equity indexes are equal, but that the volatility and correlation

structure inherent in the provided data is representative of what will hold in the future.

Response

		Group Members
Family Name	Given Name	Student ID #

Enter your response here. Alter the size of the box, if required. Please clearly reference any quantitative work doen elsewhere in the workbook.

Returns

US$ US$

2

0

HPRs
TSX	MSCI USA	Unhedged	Hedged
Date	in C$	In		US$
1/31/	0	-0.004362107	-0.0141019086	-0.0038213368	0.0002255215
2/28/02	-0.0003742241	-0.019525914	0.0089925795	0.000182367
3/29/02	0.0301509003	0.0372887259	-0.0056715488	0.0001869741
4/30/02	-0.0233730308	-0.0648573452	-0.0161088128	0.0002507208
5/31/02	0.0004419109	-0.007438094	-0.0265655858	0.0004332038
6/28/02	-0.064554355	-0.0762089972	-0.0046465969	0.0006413613
7/31/02	-0.0746793699	-0.0718881919	0.0416858439	0.0007166809
8/30/02	0.0022174812	0.0047604594	-0.0153380042	0.0008584233
9/30/02	-0.0629425065	-0.1128414972	0.0167948718	0.0009487179
10/31/02	0.0121231254	0.0908375112	-0.0130500567	0.000857395
11/29/02	0.0527665061	0.0601941755	0.0007026509	0.0009453849
12/31/02	0.0091397332	-0.0603897036	0.0084258905	0.0011872846
1/31/03	-0.0054126604	-0.0241492126	-0.0305101912	0.0012153437
2/28/03	-0.0002108557	-0.0152201879	-0.0272917211	0.001142596
3/31/03	-0.0297464436	0.0093123821	-0.0126527051	0.0013827359
4/30/03	0.0390634751	0.0835486759	-0.0247119209	0.0015228254
5/30/03	0.0432039906	0.0536558396	-0.0427296807	0.0017984107
6/30/03	0.0205498415	0.0123944538	-0.0105949174	0.0016529527
7/31/03	0.0400908176	0.0185699019	0.0364305428	0.0020091996
8/29/03	0.0362565345	0.0187639068	-0.0149831351	0.0017539499
9/30/03	-0.010009927	-0.0115437399	-0.0271780269	0.0014562232
10/31/03	0.0484189354	0.0570827433	-0.0232687391	0.0014746749
11/28/03	0.0124681356	0.0096816398	-0.0137703426	0.0014263495
12/31/03	0.048320447	0.0519631817	-0.0058850681	0.0014847296
1/30/04	0.0375358735	0.0181170429	0.0295221513	0.0014006578
2/27/04	0.0324306608	0.0121334693	0.0085312688	0.0012101624
3/31/04	-0.021079013	-0.0158823437	-0.0204956214	0.0010657723
4/30/04	-0.0389019781	-0.0153536096	0.0464143047	0.0009815484
5/31/04	0.0225485611	0.0133019576	-0.0077440465	0.0008652972
6/30/04	0.0172819809	0.0188912968	-0.0174776491	0.0008280815
7/30/04	-0.0092407012	-0.0340486171	-0.0087637516	0.000611598
8/31/04	-0.0080985164	0.00512022	-0.0085778781	0.0004815651
9/30/04	0.0367017495	0.0109803691	-0.039503643	0.0004022465
10/29/04	0.0243694955	0.0152926089	-0.0361897989	0.0004503971
11/30/04	0.01940965	0.0411218627	-0.025169092	0.0005083009
12/31/04	0.0264268579	0.0350537406	0.0076531685	0.000336403
1/31/05	-0.0039804354	-0.0247566353	0.0355548137	0.0002003088
2/28/05	0.0517281981	0.0208553143	-0.0093088858
3/31/05	-0.0037806451	-0.0159713656	-0.015741946	-0.0000569476
4/29/05	-0.0238039383	-0.0180676611	0.0372773484	-0.0002149027
5/31/05	0.02689734	0.0326910471	-0.0006374756	-0.0004462329
6/30/05	0.0332752529	0.0025060683	-0.0234023043	-0.0005262528
7/29/05	0.053116143	0.0375739594	0.0009389288	-0.0006694971
8/31/05	0.0250403692	-0.0092856318	-0.0308740161	-0.0008320078
9/30/05	0.0341335554	0.0085687404	-0.0231461998	-0.0008669304
10/31/05	-0.0565044453	-0.0164050058	0.0163277615	-0.0008443908
11/30/05	0.0441778369	0.0404071494	-0.0093255903	-0.0008562587
12/30/05	0.0441189565	0.0005614527	-0.0003423046	-0.0009413376
1/31/06	0.0606128	0.0272947893	-0.021272953	-0.0009159783
2/28/06	-0.0201631185	0.001014709	-0.0046794367	-0.000787195
3/31/06	0.0390066294	0.0128255969	0.0251768531	-0.0007293818
4/28/06	0.0088918563	0.0131822858	-0.0394736842	-0.0008486199
5/31/06	-0.03564226	-0.0295902745	-0.0174914105	-0.0008210254
6/30/06	-0.0082026716	0.0011216877	0.0101276171	-0.0007902266
7/31/06	0.0203113935	0.0033390691	0.0163204748	-0.0009621437
8/31/06	0.0226394011	0.0241568052	-0.0181375802	-0.0009643884
9/29/06	-0.023204599	0.0254574262	0.0053165127	-0.0008920928
10/31/06	0.050939695	0.034173984	0.0043024246	-0.0008784117
11/30/06	0.035206434	0.0198441059	0.0192333437	-0.0008657236
12/29/06	0.0149754739	0.012145004	0.0190017513	-0.0009457093
1/31/07	0.0115350767	0.0181223338	0.0143507777	-0.0009108877
2/28/07	0.002538518	-0.0182894682	-0.006650288	-0.0008048119
3/30/07	0.0117487092	0.01081526	-0.0161187156	-0.0009381263
4/30/07	0.0206678536	0.0428660604	-0.0420404802	-0.0008754822
5/31/07	0.049913912	0.0350197922	-0.0326200063	-0.0009229516
6/29/07	-0.0081785504	-0.0167205052	-0.0050042091	-0.0009540735
7/31/07	-0.0012656309	-0.0309531878	0.003760282	-0.000733255
8/31/07	-0.0129420908	0.0151847678	-0.0092718333	-0.000786701
9/28/07	0.0345581668	0.0379580774	-0.0606418679	-0.000623907
10/31/07	0.0390961581	0.0168522856	-0.0441783234	-0.000301902
11/30/07	-0.0621557246	-0.0422109765	0.052432091	-0.0000736997
12/31/07	0.0133697704	-0.0057099236	-0.012655062	-0.0004001601
1/31/08	-0.0471755874	-0.0606901181	0.0215309793	-0.0003951568
2/29/08	0.0344649604	-0.0310894745	-0.0285657608	0.0007934934
3/31/08	-0.0143029802	-0.0036834963	0.0476312028	0.0005411476
4/30/08	0.0459751618	0.0494975115	-0.0184688855	0.0006140052
5/30/08	0.0579367241	0.0159566464	-0.0133055307	0.000278026
6/30/08	-0.0141486142	-0.0815062181	0.0209821878	0.0004629164
7/31/08	-0.0586024707	-0.0114366253	0.0108422453	0.0004336898
8/29/08	0.0154412309	0.0136967908	0.0334454683	0.0004290381
9/30/08	-0.1444585898	-0.0917258515	0.0031608246	0.0004340237
10/31/08	-0.166688091	-0.1710158728	0.143575997	-0.0017118134
11/28/08	-0.0473641023	-0.0737851779	0.0208496114	0.0003947855
12/31/08	-0.0263918903	0.0129661973	-0.0053980019	0.000056397
1/30/09	-0.0296107886	-0.0814663144	0.0043337384	0.0005184285
2/27/09	-0.0631082902	-0.102490145	0.0233899262	0.0003871436
3/31/09	0.0778863224	0.0856889499	-0.0084328329	0.0000315246
4/30/09	0.0726089294	0.0960180217	-0.0556769861	-0.0000715336
5/29/09	0.1146323662	0.0550189698	-0.0776870634	-0.0001346688
6/30/09	0.0034419186	0.0022632108	0.0598193101	-0.0002007666
7/31/09	0.0421771993	0.0753768183	-0.0691006157	-0.000180824
8/31/09	0.0094698464	0.0347797814	0.0158634724	-0.0001109981
9/30/09	0.0514130302	0.0387893774	-0.0227179604	-0.0000273162
10/30/09	-0.0404337098	-0.0193700061	0.0036336532	-0.0000465853
11/30/09	0.051548086	0.0594935024	-0.0213052358	-0.0000092833
12/31/09	0.0292587899	0.0205995728	-0.0055963955	0.0000094854
1/29/10	-0.0534787907	-0.0350799989	0.0163590404	-0.0000286164
2/26/10	0.0497297051	0.030861947	-0.0080244017	0.0000469263
3/31/10	0.0380793891	0.0598854842	-0.0401154265	0.0000473059
4/30/10	0.0166564357	0.0160232002	-0.0016756197	0.0000098566
5/31/10	-0.0347820206	-0.0806271717	0.0360369255	-0.0000888582
6/30/10	-0.0371355523	-0.0531759998	0.0126745128	0.0000762377
7/30/10	0.0395892939	0.0698896774	-0.0307721263	0.0001882087
8/31/10	0.0189689203	-0.0444192839	0.0353415214	0.0003592407
9/30/10	0.0408814969	0.0909166349	-0.0379800253	0.0004688892
10/29/10	0.027104933	0.0393794876	-0.0080421114	0.000682361
11/30/10	0.0237035349	0.0011152362	0.0093356918	0.000668239
12/31/10	0.040908611	0.0668766681	-0.0325674228	0.0006328498
1/31/11	0.0098614004	0.0239762851	0.0066421778	0.0006340261
2/28/11	0.0443684469	0.0335271648	-0.0256935766	0.0005698575
3/31/11	0.0012460065	0.0011900944	-0.0018470063	0.0006361911
4/29/11	-0.0102170503	0.0305998839	-0.0245695194	0.0006579286
5/31/11	-0.0086739138	-0.0108402931	0.0210781472	0.0006955789
6/30/11	-0.0333023445	-0.0169553795	-0.0038705682	0.0008257212
7/29/11	-0.0249834701	-0.0194775737	-0.0113459745	0.0007771215
8/31/11	-0.0120880672	-0.0553118916	0.0248388618	0.0006602735
9/30/11	-0.0866141553	-0.0719236527	0.0656542414	0.0007465358
10/31/11	0.0560705394	0.1098657618	-0.0468307663	0.000758121
11/30/11	-0.0021122077	-0.002741676	0.023659703	0.0006946892
12/30/11	-0.0169901014	0.0094670676	0.0014752889	0.0007868208