Exam Study Guide
MATH 5034 – Investments
Review Questions
1. Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 18%. T-bills offer a risk-free 7% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to bills? You may use the following utility function: U Er 0.005 A 2 .
2. The optimal proportion of the risky asset in the complete portfolio is given by the
2
equation y* = (E[rP] rf) / (.01A P ). For each of the variables on the right side of the equation, discuss the impact the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume that the investor is risk averse.
3. You are evaluating two investment alternatives. One is a passive market portfolio with an expected return of 10% and a standard deviation of 16%. The other is a fund that is actively managed by your broker. This fund has an expected return of 15% and a standard deviation of 20%. The risk-free rate is currently 7%. Answer the questions below based on this information.
What is the slope of the Capital Market Line?
What is the slope of the Capital Allocation Line offered by your broker's fund?
Draw the CML and the CAL on one graph.
What is the maximum fee your broker could charge and still leave you as well off as if you had invested in the passive market fund? (Assume that the fee would be a percentage of the investment in the broker's fund, and would be deducted at the end of the year.)
How would it affect the graph if the broker were to charge the full amount of the fee?
4. Derive the optimum portfolio weights for a portfolio with two uncorrelated assets.
5. Suppose there n mutually uncorrelated assets. The return on asset i has variance i2 , i 1,2,..., n but the expected rates of return are unspecified at this point. The weight of asset i in the market portfolio is xi , i 1,2,..., n . Assume there is a risk-free asset with rate of return
Review Questions
1. Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 18%. T-bills offer a risk-free 7% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to bills? You may use the following utility function: U Er 0.005 A 2 .
2. The optimal proportion of the risky asset in the complete portfolio is given by the
2
equation y* = (E[rP] rf) / (.01A P ). For each of the variables on the right side of the equation, discuss the impact the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume that the investor is risk averse.
3. You are evaluating two investment alternatives. One is a passive market portfolio with an expected return of 10% and a standard deviation of 16%. The other is a fund that is actively managed by your broker. This fund has an expected return of 15% and a standard deviation of 20%. The risk-free rate is currently 7%. Answer the questions below based on this information.
What is the slope of the Capital Market Line?
What is the slope of the Capital Allocation Line offered by your broker's fund?
Draw the CML and the CAL on one graph.
What is the maximum fee your broker could charge and still leave you as well off as if you had invested in the passive market fund? (Assume that the fee would be a percentage of the investment in the broker's fund, and would be deducted at the end of the year.)
How would it affect the graph if the broker were to charge the full amount of the fee?
4. Derive the optimum portfolio weights for a portfolio with two uncorrelated assets.
5. Suppose there n mutually uncorrelated assets. The return on asset i has variance i2 , i 1,2,..., n but the expected rates of return are unspecified at this point. The weight of asset i in the market portfolio is xi , i 1,2,..., n . Assume there is a risk-free asset with rate of return