16.36 5 y .01 A 2 .01 5 21.132 .5089   This means that the optimal risky portfolio, with the given data, is attractive enough for an investor with A 5 to invest 50.89% of his or her wealth in it. Since stock A makes up 68.18% of the risky portfolio and stock B makes up 31.82%, the investment proportions for this investor are   Stock A: .5089 68.18 34.70% Stock B: .5089 31.82 16.19% Total 50.89%   4. Efficient frontiers derived by portfolio managers depend on forecasts of the rates of return on various securities and estimates of risk, that is, the covariance matrix. The forecasts themselves do not control outcomes. Thus preferring managers with rosier forecasts (northwesterly frontiers) is tantamount to rewarding the bearers of good news and punishing the bearers of bad news. What we should do is reward bearers of accurate news. Thus if you get a glimpse of the frontiers (forecasts) of portfolio managers on a regular basis, what you want to do is develop the track record of their forecasting accuracy and steer your advisees toward the more accurate forecaster. Their portfolio choices will, in the long run, outperform the field. 5. a. Portfolios that lie on the CAL are combinations of the tangency (optimal risky) portfolio and the risk-free asset. Hence they are just as dependent on the accuracy of the efficient frontier as portfolios that are on the frontier itself. If we judge fore- casting accuracy by the accuracy of the reward-to-variability ratio, then all port- folios on the CAL will be exactly as accurate as the tangency portfolio. b. All portfolios on CAL1 are combinations of portfolio P1 with lending (buying T-bills). This combination of one risky asset with a risk-free asset leads to a linear relationship between the portfolio expected return and its standard deviation:   E(rP ) rf E(rP) rf P P (5.b)   The same applies to all portfolios on CAL2; just replace E(rP ), P in equation 5.b 1 1 with E(rP ), P . 2 2 An investor who wishes to have an expected return between E(r ) and 1 E(r ) must find the appropriate portfolio on the efficient frontier of risky assets 2 between P1 and P2 in the correct proportions.