# The real interest rate approximately equals the nominal rate

Chapter 5:

1. The real interest rate approximately equals the nominal rate minus

the inflation rate. Suppose the inflation rate increases from 3% to

5%. Does the Fisher equation imply that this increase will result in a

fall in the real rate of interest? Explain.

2. When estimating a Sharpe ratio, would it make sense to use the

average excess real return that accounts for inflation?

3. You’ve just decided upon your capital allocation for the next year,

when you realize that you’ve underestimated both the expected

return and the standard deviation of your risky portfolio by a

multiple of 1.05. Will you increase, decrease, or leave unchanged

your allocation to risk-free T-bills?

4. Suppose your expectations regarding the stock market are as

follows:

State of the Economy | Probability | HPR |

Boom | 0.3 | 44% |

Normal economy | 0.4 | 14% |

Recession | 0.3 | -16% |

Compute the mean and standard deviation of the HPR on stocks.

5. Using the historical risk premiums as your guide, what is your

estimate of the expected annual HPR on the market index stock

portfolio if the current risk-free interest rate is 3%?

6. Consider a risky portfolio. The end-of-year cash flow derived from

the portfolio will be either $50,000 or $150,000, with equal

probabilities of 0.5. The alternative riskless investment in T-bills

pays 5%. If you require a risk premium of 10%, how much will you

be willing to pay for this portfolio?

7. You manage an equity fund with an expected risk premium of 10%

and a standard deviation of 14%. The rate on Treasury bills is 6%.

Your client chooses to invest $60,000 of her portfolio in your equity

fund and $40,000 in a T-bill money market fund. What is the

expected return and standard deviation of your client’s portfolio?

8. A portfolio of non-dividend-paying stocks earned a geometric mean return of 5% between January 1, 2010, and December 31, 2016. The arithmetic mean return for the same period was 6%. If the market value of the portfolio at the beginning of 2010 was $100,000,

what was the market value of the portfolio at the end of 2016?

Chapter 6:

1. In forming a portfolio of two risky assets, what must be true of the

correlation coefficient between their returns if there are to be gains

from diversification? Explain.

2. An investor ponders various allocations to the optimal risky portfolio and risk-free T-bills to construct his complete portfolio. How would the Sharpe ratio of the complete portfolio be affected by his choice?

3. Suppose that many stocks are traded in the market and that it is

possible to borrow at the risk-free rate, *rf. *The characteristics of two

of the stocks are as follows:

Stock | Expected Return | Standard Deviation |

8% | 40% | |

13 | 60 |

Correlation = -1

Could the equilibrium *rf *be greater than 10%? (*Hint: *Can a particular stock portfolio be substituted for the risk-free asset?)

4. Assume expected returns and standard deviations for all securities,

as well as the risk-free rate for lending and borrowing, are known.

Will investors arrive at the same optimal risky portfolio? Explain.

5. What is the relationship of the portfolio standard deviation to the

weighted average of the standard deviations of the component assets?

6. A project has a 0.7 chance of doubling your investment in a year

and a 0.3 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment?

7. Investors expect the market rate of return this year to be 10%. The

expected rate of return on a stock with a beta of 1.2 is currently

12%. If the market return this year turns out to be 8%, how would

you revise your expectation of the rate of return on the stock?

[Hint: Use the CAPM equation you learnt in basic finance (FI3300):

E(R) = Rf + β [E(Rm) – Rf], E(R) is expected return, Rf is riskfree rate,

Rm is the market-return]

8. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and

corporate bond fund, and the third is a T-bill money market fund

that yields a sure rate of 5.5%. The probability distributions of the

risky funds are:

Expected Return | Standard Deviation | |

Stock fund (S) | 15% | 32% |

Bond fund (B) | 23 |

The correlation between the fund returns is 0.15.

What is the Sharpe ratio of the best feasible CAL?

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