I. Suppose that there are many stocks in the security market and that the characteristics of stocks A and B are given as follows: Stock Expected Return Standard Deviation A 12% 6% B 15% 8%

I. Suppose that there are many stocks in the security market and that the characteristics of stocks A and B are given as follows:

Stock      Expected Return     Standard Deviation

A             12%                          6%

B             15%                        8%

Correlation : -1

Suppose that it is possible to borrow at the risk-free rate Rf. What must be the value of the risk-free rate ? (Hint: Think about constructing a risk-free portfolio from stocks A and B) Please include your calculations for each question.

II. Suppose you have a project that has a 70% chance of doubling your investment in a year and a 30% change of halving your investment in a year.  What is the standard deviation of the rate of return on this investment? Please include your calculations for each question.

III. Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either 70000 USD or 190000 USD with equal probabilities of 50%. The alternative risk-free investment in T bills pays 5% per year.

Please include your calculations for each question.

III.a

If you require a risk premium of 8%, how much will you be willing to pay for the portfolio?

III.b

Suppose that the portfolio can be purchased for the amount you found in III.a. What will be the expected rate of return on the portfolio?

III.c

Now suppose that you require a risk premium of 12%. What is the price that you will be willing to pay?

III.d

Comparing your answers to III.a and III.c, what do you conclude about the relationship between the required risk premium on a portfolio and the price at which the portfolio will sell?

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