pair of stocks is .5. a. The portfolio expected return is invariant to the size of the portfolio because all stocks have identical expected returns. The standard deviation of a portfolio with n 25 stocks is   P [ 2/n 2(n 1)/n]1/2 [602/25 .5 602 24/25]1/2 43.27   b. Because the stocks are identical, efficient portfolios are equally weighted. To obtain a standard deviation of 43%, we need to solve for n:   432 60 .5 60 (n 1) n n 1,849n 3,600 1,800n 1,800 1,800 49 36.73   Thus we need 37 stocks and will come in with volatility slightly under the target. c. As n gets very large, the variance of an efficient (equally weighted) portfolio diminishes, leaving only the variance that comes from the covariances among stocks, that is   P 2 .5 602 42.43   Note that with 25 stocks we came within .84% of the systematic risk, that is, the nonsystematic risk of a portfolio of 25 stocks is .84%. With 37 stocks the standard deviation is 43%, of which nonsystematic risk is .57%. d. If the risk-free is 10%, then the risk premium on any size portfolio is 15 10 5%. The standard deviation of a well-diversified portfolio is (practically) 42.43%; hence the slope of the CAL is   S 5/42.43 .1178 II. Portfolio Theory 8. Optimal Risky Portfolio The McGraw−Hill Companies, 2001           252 PART II Portfolio Theory     APPENDIX B: THE INSURANCE PRINCIPLE: RISK-SHARING VERSUS RISK-POOLING   Mean-variance analysis has taken a strong hold among investment professionals, and in- sight into the mechanics of efficient diversification has become quite widespread. Common misconceptions or fallacies about diversification still persist, however. Here we will try to put some to rest.