Example 8.2 (Four stocks and the market) Let us rework Example 81 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 retum 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 (1.c) = -14 and cov (es, ex) = 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 84 ARBITRAGE PRICING THEORY 207 TABLE 8.2 Factor Model with Market Year Stock 1 Stock 2 Stock 3 Stock 4 Market Riskless 1 2 3 4 5 6 7 119) 18 37 3 64 24 37 3042 - 45 2011 9.28 1763 15 71 29 59 15 25 353 1767 12 74 -256 25 46 692 973 25 09 23 27 19 47 -658 15 08 16 24 -15 OS 1780 18 82 305 16 94 27 24 1705 10 20 20 26 19.84 151 12 24 16 12 2293 3.49 23 00 17 54 270 1934 19.81 -439 18.90 12 78 13 34 15 31 6 20 6.70 6.40 570 590 5.20 490 5 50 610 580 9 10 584 aver var cov 15 00 90 28 65 08 90 195 31 54 107 24 73 62 1 02 34 32.09 10 90 162 19 100 78 140 -611 2137 15 09 68 27 48 99 68 382 34 99 1383 72 12 72 12 1 00 000 a Now the factor in to Be the actor de materie The are stocks largely plained by and her are merreted with each od with the market model pode cellente e de Example 8.2 (Four stocks and the market) Let us rework Example 81 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 retum 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 (1.c) = -14 and cov (es, ex) = 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 84 ARBITRAGE PRICING THEORY 207 TABLE 8.2 Factor Model with Market Year Stock 1 Stock 2 Stock 3 Stock 4 Market Riskless 1 2 3 4 5 6 7 119) 18 37 3 64 24 37 3042 - 45 2011 9.28 1763 15 71 29 59 15 25 353 1767 12 74 -256 25 46 692 973 25 09 23 27 19 47 -658 15 08 16 24 -15 OS 1780 18 82 305 16 94 27 24 1705 10 20 20 26 19.84 151 12 24 16 12 2293 3.49 23 00 17 54 270 1934 19.81 -439 18.90 12 78 13 34 15 31 6 20 6.70 6.40 570 590 5.20 490 5 50 610 580 9 10 584 aver var cov 15 00 90 28 65 08 90 195 31 54 107 24 73 62 1 02 34 32.09 10 90 162 19 100 78 140 -611 2137 15 09 68 27 48 99 68 382 34 99 1383 72 12 72 12 1 00 000 a Now the factor in to Be the actor de materie The are stocks largely plained by and her are merreted with each od with the market model pode cellente e de
