2. A financial analyst has recently argued that portfolio managers who rely on asset allocation techniques spend too much time trying to estimate expected returns on different classes of securities and not enough time on estimating the correlations between their returns. The correlations are important, he argues, because a change in correlation, even with no change in expected returns, can lead to changes in the optimal portfolio. In particular, he argues that as the correlation between stock and bond returns ranges from 0.2 to 0.6, "the allocation to stocks remains fairly constant..but there are major asset shifts between cash and bonds. See if you can illustrate this point with the following example: A portfolio manager is considering three categories assets: stocks, bonds and cash. The expected returns, E(1), and standard deviations of returns for these assets are as follows: E(1) Std. Dev. Stock 0.14 0.17 Bonds 0.10 0.09 Cash 0.08 The average degree of risk aversion of the portfolio's clients is A=4. (a) What is the optimal complete portfolio composition if the correlation between stock and bond returns is 0.2? (10 points) (b) What is the optimal complete portfolio composition if the correlation between stock and bond returns is 0.6? (10 points) Are your answers to (a) and (b) consistent with the analyst's point? How would you explain what is happening as we move from the conditions in part (a) to those of part (b)? (10 points)