Question 2 [30 marks] (a) An investor has R100 000 that she wants to use to buy two assets: asset A and asset B. The investor must use the following information to come up with the two-asset portfolio: Asset E(R) Standard deviation A 0.10 0.20 B 0.20 0.40 PAB = 0.5 If the investor wants to establish an optimal portfolio, how much of the total wealth (i.e., R100 000) must be invested in asset A and how much must be invested in asset B given that the portfolio expected return is: E(r, ) =0.15 [10] (b) Portfolio diversification can be crucially beneficial. Show that as the number of assets in a portfolio increases total portfolio risk decreases. [5][c] Show that the beta of a portfolio (tip) is a linear combination of individual asset betas. Also explain why the beta of a portfolio [y] is a better measure of risk than the standard deviation of a portfolio. [IS] (d) Investors have the opportunity to invest in varying combinations of riskless treasury bills and the market portfolio. Investors' investment portfolios will have expected returns equal to (RP) and standard deviations of returns equal to ct"p . Let wm be the proportion of a particular investor's wealth invested in the market portfolio. Thus the proportions invested in the riskless assets is w; = I - Wm Prove (or derive] the following: (I). o'p = wmom [2] 0' (to. snap] = rf + ctrFEW\" ] r; [4] (fit). I hope you have noted that equation (it) is a Capital Market Line {CML}. What happens to the slope of the CML as each investor's level of risk aversity increases? [3] Question 3 [20 marks] The APT can be summed up in two equations: K K r}! = a]. +253 + a\" and 01,): A\" +Zb..}t ,I'=l {=1 u If u I (1') How do you interpret 39- and lj? [2] (it) What is the difference between by and lj? [2] (iii) Explain, in detail, how the APT can be implemented. [8] (iv) What is the difference between APT and CAPM? Which one would you prefer to use and why? [8]