7. Four different investors request the portfolio manager to construct own stock portfolio. Coincidently, the expected return for each case is identical. There are differences on the volatility of the return of the portfolio. Here are each investor's request. Investor A: Construct equally weight portfolio with 10 individual stocks. The manager figures out that the average variance of individual stock is 10% and the average covariance between stocks is 2%. Investor B: Construct equally weighted portfolio with 50 individual stocks. The manager figures out that the volatility of each stock commonly has 10% and the correlation between each pair of stocks is 75%. Investors C: Construct 2-stock portfolio with the following weights: (stock AA, stock BB) = (65%, 35%). The volatilities of stock AA and BB are 10% and 20%, respectively and there is no correlation between these two indi- vidual stocks. Investor D: Construct equally weight portfolio with infinite number of individ- ual stocks. The volatility of each individual stock is 25% and the associated correlation between each pair of the stock is 30%. (a) [5 points] Calculate the volatility of the return of the portfolio for each investor. Which investor has the lowest volatility of the return of the portfolio? (b) (2.5 points] Consider the case of investor C. Out of possible asset mixes, which weight of two individual stocks can generate the minimum variance portfolio? 7. Four different investors request the portfolio manager to construct own stock portfolio. Coincidently, the expected return for each case is identical. There are differences on the volatility of the return of the portfolio. Here are each investor's request. Investor A: Construct equally weight portfolio with 10 individual stocks. The manager figures out that the average variance of individual stock is 10% and the average covariance between stocks is 2%. Investor B: Construct equally weighted portfolio with 50 individual stocks. The manager figures out that the volatility of each stock commonly has 10% and the correlation between each pair of stocks is 75%. Investors C: Construct 2-stock portfolio with the following weights: (stock AA, stock BB) = (65%, 35%). The volatilities of stock AA and BB are 10% and 20%, respectively and there is no correlation between these two indi- vidual stocks. Investor D: Construct equally weight portfolio with infinite number of individ- ual stocks. The volatility of each individual stock is 25% and the associated correlation between each pair of the stock is 30%. (a) [5 points] Calculate the volatility of the return of the portfolio for each investor. Which investor has the lowest volatility of the return of the portfolio? (b) (2.5 points] Consider the case of investor C. Out of possible asset mixes, which weight of two individual stocks can generate the minimum variance portfolio