Problems for Finance - "Investment Analysis & Portfolio Management"

Problem #1. You are evaluating various investment opportunities currently available and you have calculated expected returns and standard deviations for five different well-diversified portfolios of risky assets:

Portfolio                     Expected Return                               Standard Deviation

    Q                                  7.8%                                          10.5%

    R                                  10.0                                           14.0

    S                                  4.6                                            5.0

    T                                  11.7                                          18.5

    U                                  6.2                                            7.5

a. For each portfolio, calculate the risk premium per unit of risk that you expect to receive ([E(R) - RFR] / σ). Assume that the risk-free rate is 3.0 percent.

b. Using your computations in Part a, explain which of these five portfolios is most likely to be the market portfolio. Use your calculations to draw the capital market line (CML).

c. If you are only willing to make an investment with σ = 7.0%, is it possible for you to earn a return of 7.0 percent?

d. What is the minimum level of risk that would be necessary for an investment to earn 7.0 percent? What is the composition of the portfolio along the CML that will generate that expected return?

e. Suppose you are now willing to make an investment with σ = 18.2%. What would be the investment proportions in the riskless asset and the market portfolio for this portfolio? What is the expected return for this portfolio?

Problem #2. You are an analyst for a large public pension fund and you have been assigned the task of evaluating two different external portfolio managers (Y and Z). You consider the following historical average return, standard deviation, and CAPM beta estimates for these two managers over the past five years:

Additionally, your estimate for the risk premium for the market portfolio is 5.00 percent and the risk-free rate is currently 4.50 percent.

a. For both Manager Y and Manager Z, calculate the expected return using the CAPM. Express your answers to the nearest basis point (i.e., xx.xx%).

b. Calculate each fund manager's average "alpha" (i.e., actual return minus expected return) over the five-year holding period. Show graphically where these alpha statistics would plot on the security market line (SML).

c. Explain whether you can conclude from the information in Part b if: (1) either manager outperformed the other on a risk-adjusted basis, and (2) either manager out-performed market expectations in general.

Question #3.

If the mutual fund cash position were to increase close to 12 percent, would a technician consider this cash position bullish or bearish? Give two reasons for this opinion.

Question #4.

Assume a significant decline in credit balances at brokerage firms. Discuss why a technician would consider this bullish or bearish.