I need to construct a one factor model, but im not given the portfolio error term e, in the end i should have a correlation matrix of the residuals and the variance of both the stocks and the error. I was told to use this formula:
Example 8.2 (Four stocks and the market) Let us rework Example 8 1 by using the excess market return as a factor We assume that the market consists of just the four stocks, with equal weights Therefore the market return in any year is just the average of the returns of the four stocks. These are shown in the upper portion of Table 8.2. We also adjoin the historical value of the risk-free rate of return for each of the 10 years The relevant statistical quantities are computed by the same estimating formulas as in the earlier example, except that the factor is taken to be the excess return on the market, which will change the formula for a, to a, As seen from the table, a large portion of the variability of the stock returns is explained by the factor In other words, there is relatively low nonsystematic risk Furthermore, a side calculation shows that the errors are close to being uncorrelated with each other and with the market return. For example, the data provide the estimates cov (e1, e2) = -14 and cov (e2, e3) = 2, which are much smaller than for the earlier model We conclude that this single-factor model is an excellent representation of the stock returns of the four stocks. In other words, for this example, the market return serves as a much better factor than the industrial index factor used earlier. However, this may not be true for other examples
ri-rf = di + Bi (rm -rf) + ei. = Example 8.2 (Four stocks and the market) Let us rework Example 8.1 by using Factor Model with Market the excess market return as a factor. We assume that the market consists of just the Year Stock 1 Stock 2 Stock 3 Stock 4 Market Riskless four stocks, with equal weights. Therefore the market return in any year is just the average of the returns of the four stocks. These are shown in the upper portion of Table 8.2. We also adjoin the historical value of the risk-free rate of return for each of the 10 years. The relevant statistical quantities are computed by the same estimating formulas as in the earlier example, except that the factor is taken to be the excess return on the market, which will change the formula for a; to QiAs seen from the table, a large portion of the variability of the stock returns is explained by the factor. In other words, there is relatively low nonsystematic risk Furthermore, a side calculation shows that the errors are close to being uncorrelated with each other and with the market return. For example, the data provide the estimates cov (ej, eo) = 14 and cov (ez, ez) = 2, which are much smaller than for the earlier model. We conclude that this single-factor model is an excellent representation of the stock returns of the four stocks. In other words, for this example, the market return serves as a much better Nos the factor is taken to be the excess rerum on the market portfolio The variation in stock returns is largely explained by this return, and the errors factor than the industrial index factor used earlier. However, this may not be true foi are uncorrelated with each other and with the market This model provides other examples 1 2 3 4 5 6 7 8 9 10 11.91 18 37 3.64 24.37 30 42 -145 2011 9.28 17.63 15.71 29 59 15.25 3.53 17.67 12 74 -2.56 25.46 6.92 973 25 09 23.27 1947 -6.58 15 08 16.24 -15.05 17 80 18.82 3.05 16.94 27.24 1705 10.20 20 26 1984 1.51 12.24 16.12 22 93 3.49 23.00 17.54 2 70 19.34 19.81 -4.39 18.90 12.78 13.34 15.31 6.20 6.70 6.40 5.70 5.90 5.20 4.90 5.50 610 5.80 aver 5.84 var COV B 15 00 90.28 65 08 90 1 95 31.54 14 34 107.24 73 62 1 02 34 32.09 10.90 162 19 100.78 140 -6.11 21 37 15 09 68 27 48 99 68 3.82 34.99 13.83 72 12 72 12 1 00 0.00 e-var in excellent fit to the data ri-rf = di + Bi (rm -rf) + ei. = Example 8.2 (Four stocks and the market) Let us rework Example 8.1 by using Factor Model with Market the excess market return as a factor. We assume that the market consists of just the Year Stock 1 Stock 2 Stock 3 Stock 4 Market Riskless four stocks, with equal weights. Therefore the market return in any year is just the average of the returns of the four stocks. These are shown in the upper portion of Table 8.2. We also adjoin the historical value of the risk-free rate of return for each of the 10 years. The relevant statistical quantities are computed by the same estimating formulas as in the earlier example, except that the factor is taken to be the excess return on the market, which will change the formula for a; to QiAs seen from the table, a large portion of the variability of the stock returns is explained by the factor. In other words, there is relatively low nonsystematic risk Furthermore, a side calculation shows that the errors are close to being uncorrelated with each other and with the market return. For example, the data provide the estimates cov (ej, eo) = 14 and cov (ez, ez) = 2, which are much smaller than for the earlier model. We conclude that this single-factor model is an excellent representation of the stock returns of the four stocks. In other words, for this example, the market return serves as a much better Nos the factor is taken to be the excess rerum on the market portfolio The variation in stock returns is largely explained by this return, and the errors factor than the industrial index factor used earlier. However, this may not be true foi are uncorrelated with each other and with the market This model provides other examples 1 2 3 4 5 6 7 8 9 10 11.91 18 37 3.64 24.37 30 42 -145 2011 9.28 17.63 15.71 29 59 15.25 3.53 17.67 12 74 -2.56 25.46 6.92 973 25 09 23.27 1947 -6.58 15 08 16.24 -15.05 17 80 18.82 3.05 16.94 27.24 1705 10.20 20 26 1984 1.51 12.24 16.12 22 93 3.49 23.00 17.54 2 70 19.34 19.81 -4.39 18.90 12.78 13.34 15.31 6.20 6.70 6.40 5.70 5.90 5.20 4.90 5.50 610 5.80 aver 5.84 var COV B 15 00 90.28 65 08 90 1 95 31.54 14 34 107.24 73 62 1 02 34 32.09 10.90 162 19 100.78 140 -6.11 21 37 15 09 68 27 48 99 68 3.82 34.99 13.83 72 12 72 12 1 00 0.00 e-var in excellent fit to the data
