For Example 9.3, represent the uncertainty in the expected returns of the two stocks in the form of u +e, where E[e] = 0 with covariance matrix of e equal to Q.

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Example 9.3 (Various angles) Consider the case of two correlated risky assets and a risk-free asset. Without loss of generality, as before, we take ry = 0. The other parameters are u = 0.11, u = 0.06, 0 = 0 = 0.20, p = 0.7. From the general solution for two risky assets, equation (6.11), we find the optimal weights to be W = - (u1u2) (1 - p) 0.11 -0.06 x .7 (0.11 +0.06).3 .068 = 1.333 (9.10) .051 W21-w = -.333. (9.11) These weights lead to an overall portfolio return of 7 = wu+w2u2 = 0.1267. The corresponding total variance is o = 0.04 (w+2pw, w+w2) = 0.0507. Finally, the tangent of the critical angle is tan(0)=7/ = 0.5627, which corresponds to an angle 8 of 29.37. See the column labeled "Theory" in Table 9.2. Next, we introduce an estimation error e = 0.02, which (in two separate cases) is either added to or subtracted from u (and hence has expected value 0). The corre- sponding results for "think" are in the "Think" columns of the table, and the results for "actual" are shown in the "Actual" columns. As predicted, the inequality relations between the three views is confirmed. Also, both the value of "actual" and the average value of "think" deviate from "theory" only by second order.