The chart at the bottom corresponds with the questions
Ald can be seen Fund U.S. Stock - Percent Arula frard Devotion Proin , , where is the mean 1 2. Based on the article provided to you in class, compute the optimal portfolio weights of two national security markets (2) compute the SHP ratio for each individual national market as well as your optimal international portfolio Your international portfolio includes two national security markets: U.S. Stock Market and European Stock Market (1) Compute optimal portfolio weights for each national market (30 points) (2) Compute SHP ratio for each national market (20 points) (3) Compute SHP ratio for the optimal international portfolio (10 points) U.S. Bond Table 2 Correlations Among the Five Funds' Returns Monthly Returns. 1980 to 1198 Fund US Stock European Stock U.S. Stock 1.00 59 European Stock Pacific Stock U.S. Band U S. Money Market Pacie Stock 33 53 1.00 U.S. Money Market -05 - 13 -10 E 22 14 1.00 1.00 If : 5% 32 November December Coulus, Sk) Pus, EU = . cov (US,EU) Ous X OES New England Economic Review rates generally corresponded to periods of low stock prices. On the other hand, the stock markets exhibited similar movements during this period, as reflected in their positive correlations. Figure 2 plots monthly returns of the three stock indexes from 1980 to 1998. The positive correlation among their returns is easily seen in the plots. One can also see that the Pacific index has been considerably more volatile than the U.S. and European indexes. Given this information on returns, risks, and correlations of individual assets, we can calculate both the risk and the return on any portfolio consisting of these assets. The return on the portfolio is a weighted average of the returns on the assets in it, with the weight given to each asset equal to its share in the portfolio, as can be seen in Equation 1: 1,- Ew, (1) where r, is the return on the portfolio, r, is the return on asset i, and w, is the proportion of asset i in the portfolio (its portfolio weight). Consequently, the where o, is the variance of the portfolio, and o, are standard deviations of assets i andj, w, and w, are their respective weights in the portfolio, and hy is the correlation coefficient between the two assets. The standard deviation of the portfolio's return, which is the square root of variance, is the measure of risk that is used in all subsequent statistical analysis. Note that the risk of the portfolio depends not just on the standard deviations of the returns on assets that constitute it, but also on their correlations. The lower the correlation coefficient among the assets, the lower the risk of the overall portfolio. This is the reason why diversification reduces risk. The goal of optimization is to find the blend of assets that would minimize the standard deviation of the portfolio's return for any given level of expected return. The optimization problem is usually subject to constraints. In particular, the weights must sum to one (the budget constraint) and cannot be negative (no short-selling). Some institutional investors can, in fact, sell assets short. However, to keep this example real- istic from the point of view of an individual investor allocating the portfolio among easily available mutual U.S. Money Market -05 Table 2 Correlations Among the Five Funds' Returns Monthly Returns, 1980 to 1998 Fund U.S. Stock European Stock U.S. Stock 1.00 59 European Stock Pacific Stock U.S. Bond U.S. Money Market Pacific Stock 33 53 1.00 U.S. Bond 29 22 14 1.00 -.13 - 10 .14 1.00 If = 5% New England Economic Reviews 32 November December Coulus, N) Pus, eu = cov(USEU) , EU Ous X OES Ald can be seen Fund U.S. Stock - Percent Arula frard Devotion Proin , , where is the mean 1 2. Based on the article provided to you in class, compute the optimal portfolio weights of two national security markets (2) compute the SHP ratio for each individual national market as well as your optimal international portfolio Your international portfolio includes two national security markets: U.S. Stock Market and European Stock Market (1) Compute optimal portfolio weights for each national market (30 points) (2) Compute SHP ratio for each national market (20 points) (3) Compute SHP ratio for the optimal international portfolio (10 points) U.S. Bond Table 2 Correlations Among the Five Funds' Returns Monthly Returns. 1980 to 1198 Fund US Stock European Stock U.S. Stock 1.00 59 European Stock Pacific Stock U.S. Band U S. Money Market Pacie Stock 33 53 1.00 U.S. Money Market -05 - 13 -10 E 22 14 1.00 1.00 If : 5% 32 November December Coulus, Sk) Pus, EU = . cov (US,EU) Ous X OES New England Economic Review rates generally corresponded to periods of low stock prices. On the other hand, the stock markets exhibited similar movements during this period, as reflected in their positive correlations. Figure 2 plots monthly returns of the three stock indexes from 1980 to 1998. The positive correlation among their returns is easily seen in the plots. One can also see that the Pacific index has been considerably more volatile than the U.S. and European indexes. Given this information on returns, risks, and correlations of individual assets, we can calculate both the risk and the return on any portfolio consisting of these assets. The return on the portfolio is a weighted average of the returns on the assets in it, with the weight given to each asset equal to its share in the portfolio, as can be seen in Equation 1: 1,- Ew, (1) where r, is the return on the portfolio, r, is the return on asset i, and w, is the proportion of asset i in the portfolio (its portfolio weight). Consequently, the where o, is the variance of the portfolio, and o, are standard deviations of assets i andj, w, and w, are their respective weights in the portfolio, and hy is the correlation coefficient between the two assets. The standard deviation of the portfolio's return, which is the square root of variance, is the measure of risk that is used in all subsequent statistical analysis. Note that the risk of the portfolio depends not just on the standard deviations of the returns on assets that constitute it, but also on their correlations. The lower the correlation coefficient among the assets, the lower the risk of the overall portfolio. This is the reason why diversification reduces risk. The goal of optimization is to find the blend of assets that would minimize the standard deviation of the portfolio's return for any given level of expected return. The optimization problem is usually subject to constraints. In particular, the weights must sum to one (the budget constraint) and cannot be negative (no short-selling). Some institutional investors can, in fact, sell assets short. However, to keep this example real- istic from the point of view of an individual investor allocating the portfolio among easily available mutual U.S. Money Market -05 Table 2 Correlations Among the Five Funds' Returns Monthly Returns, 1980 to 1998 Fund U.S. Stock European Stock U.S. Stock 1.00 59 European Stock Pacific Stock U.S. Bond U.S. Money Market Pacific Stock 33 53 1.00 U.S. Bond 29 22 14 1.00 -.13 - 10 .14 1.00 If = 5% New England Economic Reviews 32 November December Coulus, N) Pus, eu = cov(USEU) , EU Ous X OES
