Risk and Return: Theory

Questions and Short Problems: Chapter 3

1. Assume that the assumptions underlying the CAPM hold. Evaluate whether the following statements are true or false.

A. A firm with high variance will have a higher beta than one with lower variance.

True False

B. A portfolio is efficient if it has no unsystematic risk.

True False

C. A firm which is highly correlated with the market will have a higher beta than one which is less correlated.

True False

D. If the variance of the overall market goes up, the betas of all firms will go down

True False

E. A well managed firm will have a lower beta than a badly managed firm

True False

F. The market portfolio is efficient and therefore contains only the best stocks in the market.

True False

G. A risk lover will hold the riskiest stocks in the market, where a risk averse investor will hold the safest stocks.

True False

2. You are in a world where there are only two assets, gold and stocks. You are interested in investing your money in one, the other or both assets. Consequently you collect the following data on the returns on the two assets over the last six years.
 Gold Stock Market Average Return 8% 20% Standard Deviaton 25% 22% Correlation -0.4

A. If you were constrained to pick just one, which one would you choose?

B. A friend argues that this is wrong. He says that you are ignoring the big payoffs that you can get on gold. How would you go about alleviating his concern?

C. How would a portfolio composed of equal proportions in gold and stocks do in terms of mean and variance?

D. You now learn that GPEC (a cartel of Gold producing countries) is going to vary the amount of gold it produces with stock prices in the US. (They will produce less gold when stock markets are up and more when it is down.) What effect will this have on your portfolios? Explain.

3. You have just learnt about the Markowitz frontier and are eager to put it into practice.

A. What steps would you have to go through?

- Defining universe

- Data requirements

- Calculations and Statistics

B. Assume you have succeeded in deriving the frontier. How would you go about providing investment advice to naive investors who come to you for recommendations? If you use this as a basis for your investment recommendations, what assumptions are you making?

C. How would the frontier that you have calculated change if

- A massive disaster wiped out a hundred firms that used to be part of your universe

- You ignored foreign stocks initially, but now added them on

- A breakthrough in technology occurs, which cuts in half the cost of making computer chips

4. Assume that the average variance of return for an individual security is 50 and that the average covariance is 10. What is the expected variance of a portfolio of 5, 10, 20, 50 and 100 securities. How many securities need to be held before the risk of a portfolio is only 10% more than the minimum?

5. The CAPM has been attacked on several different dimensions. Summarize the criticism of the CAPM and evaluate whether it is justified.

6. You are comparing the arbitrage pricing model to the capital asset pricing model.

A. What are the similarities between the two models? What are the differences?

B. You are estimating the expected returns for a stock using both the CAPM and the arbitrage pricing model. Under what conditions would you get the same expected return? If the expected returns are different, how would you explain the difference?