Note: This problem set can be completed in groups of 1--4 people. If a group contains more than two people, then each group member must turn in sealed envelopes with a group evaluation form. This form should assign proportions (totaling 100%) to the other group members. I encourage you do as many of the assignment questions as possible on your own. If you can do the questions in this assignment, then you are in good shape for the final exam.

- What is the covariance of FDX's return with DUK's?
- Compute the means and standard deviations of portfolios of FDX and DUK with the following percentages in FDX, and the complement in DUK: (i) 100%, (ii) 60%, (iii) 30%, and (iv) 0%.
- Plot the points in (b) and smooth a curve of potential means and standard deviations that could be achieved with portfolios of FDX and DUK.

Asset P_0 D_1 P_1

1 $60 $4.00 $71.00 2 $10 $0.30 $13.00 3 $30 $2.00 $52.00 4 $50 $6.00 $50.00

- If you had a portfolio with weights of 0.2, 0.1, 0.6 and 0.3 in the 4 risky assets of problem 6, what borrowing or lending did you do?
- With a riskless rate of 8%, what was your portfolio's return for the period?
- If the
*expected*returns on the risky securities were 12%, 20%, 15%, and 9%, respectively, what was the expected return on your portfolio?

Portfolio A has weights (0.5 0.5 0), and portfolio B has weights (0 0.5 0.5).V= .04 -.03 .005 -.03 .09 .01 .005 .01 .01E= .20 .18 .12

- What is the standard deviation of each individual asset? What are the variances?
- What are the correlations of each asset with each other asset? Covariances?
- What are the standard deviations of portfolios A and B? What is their covariance? What is their correlation? What are the portfolios' means?

- Briefly, what is an efficient portfolio? What is an inefficient portfolio?
- Portfolio A, B, and C have means and standard deviations given by {.12, .20}; {.15, .30}; and {.14, .19}; respectively. Can you say for sure that any of these portfolios are inefficient? Explain.

E= IBM .12 Polaroid .15 Gold .08 Riskless .06V= .0625 .05 .0037 .05 .16 .006 .0037 .006 .0225V^-1= 21.3 -6.6 -1.7 -6.6 8.34 -1.14 -1.7 -1.14 44.9

- What are the proportions in the optimal portfolio of risky assets
(for IBM, Polaroid, and Gold)? Show
*some*of your calculations. - If you decided that you wish to have a portfolio standard deviation of 30%, what is the maximum expected return that you can achieve? (Hint: compute the capital market line first.)
- What portfolio would you hold to achieve your goal in (b)?
- If someone else looked at these same assets and agreed with you on the covariance, but thought that the mean returns could be (.20 .15 .06 .06), respectively, what optimal mix of risky assets should she hold? Compare this portfolio to that in (a). Is it different in sensible ways?

- Briefly, what is the CAPM?
- What does the CAPM say about risk measurement for assets? Explain what the relevant risk of an asset's return is for investors who behave optimally.
- Why is it that an asset's
*covariance*shows up in risk measurement?

- What is "alpha" for a security. Why is it used in performance evaluation?
- What is the "characteristic line" for a security?
- If security A has a return of 6% when the market has a return of -5% and the riskless rate is 7%, what is the security A's abnormal return?

- Using the CAPM and
*Value Line*(which is available in the library), explain how you a novice investment advisor, can make rational estimates for the expected returns on 1700 stocks. Use 7% for the risk free return and 13% as the expected market return. - After scanning
*Value Line*, what range will cover most stocks' expected returns?

- The riskless rate is 7% and the expected return on the market is
13%. Given the stocks and their betas listed below, find the equilibrium
expected returns on all of these assets.
*Beta*American Express 1.45 AT\&T 0.80 CBS 1.05 Chase Manhattan 1.10 Cal Fed (S\&L) 1.80 Duke Power 0.65 Delta Airlines 1.02 Eastern Airlines(!!!) 1.50 Exxon 0.80 Financial Corp. of America 1.95 General Motors 1.15 IBM 1.00 Merrill Lynch 1.90 Marriott Corp. 1.11 First Boston 1.40 Sony 1.15 Nationsbank 0.95 Fuqua Industries 1.10 First Wachovia 0.80

- What is the beta for a portfolio with the following weights: American Express 20%, Merrill Lynch 30%, First Boston 30%, and Eastern Airlines 20%?