You are a hedge fund manager and need to create a portfolio that will hopefully outperform the stock market. The expected return and risk of your potential choices are: Asset S&P 500 Real Estate Fund (REITS) International Stock Fund S&P 500 REITS International Stock Fund Expected Return (%) 8% 12% 14% S&P 500 0.0256 0.0128 0.0128 0.0400 REITS Standard Deviation (%) 16% Variance-Covariance Matrix 0.0176 0.0088 20% 22% International Stock Fund 0.0176 0.0088 0.0484 The risk-free rate over this period is 3%. All given rates are annual rates. a) If you choose to hold 25% of your wealth in the S&P 500, 50% in REITS, and the rest in the international stock fund, what is the expected return of your portfolio? [2 marks] 850.25% 0.08 +0.54 0.12 +0++x0.14 = 11.5% b) What is the standard deviation of your portfolio? [4 marks] Varop = wisi+ W + W5 53 +2 WW2 Cov12 +2 Wing Cov13 +24214, 2 = 0. 0.10 + 0.5 0.2 +2.25 0.22 +20.25-0.5*0.0128 +2-Qur.225.0.0176 +2.0.250.5x0.0088 = 0.022225 c) Suppose the S&P 500 is a good proxy for the market portfolio. What are the individual betas for each asset in your portfolio? What is your 0.0176 0.162 -=0.6875 Bp=0.25.1 +0.5 0.256 +0.15-0.6875 = 0.549875 d) If the actual annual returns of your portfolio over the last 10 years was 15%. Compared to your expected portfolio return calculation from part (a), what is the alpha of your portfolio? [1 mark] portfolio's beta? [4 marks] PM = 1 BRAUT = 0.01723 = 0.256 Pint'l. aEralphaEr?CAPM? ?CAPMEraEr? e) Now you are having doubts as to whether the CAPM is the right asset pricing model for your portfolio and now thinking about using an alternative model, such as the APT, because your portfolio is exposed to more risk factors than you thought. The betas to the risk factors and expected risk premium are: Factor Beta Expected Risk Premium (%) ? (c) () 2 ( CAPM (Market) Size Book-to- Market ? 1.5 0.5 4.0% 6.5% ER (CAPM) -1423? What is your portfolio's expected returns using APT? What is the portfolio's alpha with respect to APT? [4 marks]