Problem 1. A three-asset portfolio has the following characteristics:
Asset Expected Return Standard Deviation Weight
X 15% 22% 0.50
Y 10 8 0.40
Z 6 3 0.10
What is the expected return on this three-asset portfolio?
Problem 2: The following figure shows plots of monthly rates of return and the stock market for two stocks.
a. Which stock is riskier to an investor currently holding her portfolio in a diversified portfolio of common stock?
b. Which stock is riskier to an undiversified investor who puts all of his funds in only one of these stocks?
rA - rf
rM - rf
rB - rf
rM -
The following data apply to Problems 22-24:
problem 3: Portfolio Theory
Month Market Return Generic Return
1 0% -2%
2 0 0
3 -1 0
4 -1 -2
5 -1 -4
6 -1 -2
Hennessy & Associates manages a $30 million equity portfolio for the multimanager Wilstead Pension Fund. Jason Jones, financial vice president of Wilstead, noted that Hennessy had rather consistently achieved the best record among the Wilstead's six equity managers. Performance of the Hennessy portfolio had been clearly superior to that of the S&P 500 in four of the past five years. In the one less favorable year, the shortfall was trivial.
Hennessy is a "bottom-up" manager. The firm largely avoids any attempt to "time the market." It also focuses on selection of individual stocks, rather than the weighting of favored industries.
There is no apparent conformity of style among the six equity managers. The five managers, other than Hennessy, manage portfolios aggregating $250 million, made up of more than 150 individual issues.
Jones is convinced that Hennessy is able to apply superior skill to stock selection, but the favorable results are limited by the high degree of diversification in the portfolio. Over the years, the portfolio generally held 40-50 stocks, with about 2% to 3% of total funds committed to each issue. The reason Hennessy seemed to do well most years was that the firm was able to identify each year 10 or 12 issues that registered particularly large gains. Based on this overview, Jones outlined the following plan to the Wilstead pension committee:
Let's tell Hennessy to limit the portfolio to no more than 20 stocks. Hennessy will double the commitments to the stocks that it really favors and eliminate the remainder. Except for this one new restriction, Hennessy should be free to manage the portfolio exactly as before.
All the members of the pension committee generally supported Jones's proposal, because all agreed that Hennessy had seemed to demonstrate superior skill in selecting stocks. Yet, the proposal was a considerable departure from previous practice, and several committee members raised questions.
Answer the following:
a. Will the limitation of 20 stocks likely increase or decrease the risk of the portfolio? Explain.
b. Is there any way Hennessy could reduce the number of issues from 40 to 20 without significantly affecting risk? Explain.