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 returns are limited by the high degree of diversification in the portfolio. Over the years, the portfolio generally held 40-50 stocks, with about 2%-3% of total funds committed to each issue. The reason Hennessy seemed to do well most years was be- cause the firm was able to identify each year 10 or 12 issues which registered particularly large gains. Based on this overview, Jones outlined the following plan to the Wilstead pension com- mittee: Lets 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 Joness proposal be- cause 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 commit- tee members raised questions. Respond to each of the following questions. 15. a. Will the limitations 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. 16. One committee member was particularly enthusiastic concerning Joness proposal. He suggested that Hennessys performance might benefit further from reduction in the number of issues to 10. If the reduction to 20 could be expected to be advantageous, ex- plain why reduction to 10 might be less likely to be advantageous. (Assume that Wilstead will evaluate the Hennessy portfolio independently of the other portfolios in the fund.) 17. Another committee member suggested that, rather than evaluate each managed portfo- lio independently of other portfolios, it might be better to consider the effects of a change in the Hennessy portfolio on the total fund. Explain how this broader point of view could affect the committee decision to limit the holdings in the Hennessy port- folio to either 10 or 20 issues. The following data are for problems 18 through 20.   The correlation coefficients between pairs of stocks are as follows: Corr(A,B) .85; Corr(A,C) .60; Corr(A,D) .45. Each stock has an expected return of 8% and a standard deviation of 20%. 18. If your entire portfolio is now composed of Stock A and you can add some of only one stock to your portfolio, would you choose (explain your choice): a. B. b. C. c. D. d. Need more data. 19. Would the answer to problem 18 change for more risk-averse or risk-tolerant investors? Explain. 20. Suppose that in addition to investing in one more stock you can invest in T-bills as well. Would you change your answers to problems 18 and 19 if the T-bill rate is 8%?