Part V. Factor Models and Markowitz (Lecture 5) 1. Suppose you are a fund manager restricted to investing in 3 stocks, A, B and C. The risk free earns rf=3%. Your analyst tells you that a 2-factor model with uncorrelated factors accurately describes returns. Note that fl and f2 are factor surprises and the intercepts hence are the respective expected returns (e.g. E(r.)=0.36) : ra = 0.36 + 2 fl + 4 f2 + EA 1B = 0.225 + 3 f1 + 2 f2 + EB rc = 0.12 + 1 f1 + 1 f2+ &c Standard deviations are given by of1=0.1, 02=0.1, gA=0.15, o&B=0.28, gec=0.05. a. What is the covariance matrix between the three asset returns? [Hint: we are assuming that the factors are uncorrelated] b. What is the three Rs that your analyst got when he regressed the returns of A, B and C respectively on the factor realizations? c. What is the optimal risky portfolio of A, B and C? Its Sharpe ratio? Its factor loadings on fl and f2? [Hint: Markowitz portfolio optimization again!] d. Suppose that your clients do not want any exposure to Factor 2 risk. How does your optimal portfolio look now? 2. Two common factors, F1 and F2, drive stock returns. We have the following factor equations for stocks A, B and C: ra = 0.07 + 1 fl - 1 f2 + EA rb = 0.11 + 1 f1 + 1 f2 + EB rc = 0.16 + 2 fl + 1 f2 + EC Assume that these stocks are priced correctly. Note that fl and f2 are the factor surprises. a. What are the weights of the first pure factor portfolio, that is, a portfolio that has loadings of 1 and 0 on the two factors? b. What is the riskless rate? c. What are the risk premiums of the two factors? d. We have another stock with loadings of . = 1 and 2 = 2. This stock's expected return is 10%. Is this stock mispriced relative to the other stocks? Explain. Part V. Factor Models and Markowitz (Lecture 5) 1. Suppose you are a fund manager restricted to investing in 3 stocks, A, B and C. The risk free earns rf=3%. Your analyst tells you that a 2-factor model with uncorrelated factors accurately describes returns. Note that fl and f2 are factor surprises and the intercepts hence are the respective expected returns (e.g. E(r.)=0.36) : ra = 0.36 + 2 fl + 4 f2 + EA 1B = 0.225 + 3 f1 + 2 f2 + EB rc = 0.12 + 1 f1 + 1 f2+ &c Standard deviations are given by of1=0.1, 02=0.1, gA=0.15, o&B=0.28, gec=0.05. a. What is the covariance matrix between the three asset returns? [Hint: we are assuming that the factors are uncorrelated] b. What is the three Rs that your analyst got when he regressed the returns of A, B and C respectively on the factor realizations? c. What is the optimal risky portfolio of A, B and C? Its Sharpe ratio? Its factor loadings on fl and f2? [Hint: Markowitz portfolio optimization again!] d. Suppose that your clients do not want any exposure to Factor 2 risk. How does your optimal portfolio look now? 2. Two common factors, F1 and F2, drive stock returns. We have the following factor equations for stocks A, B and C: ra = 0.07 + 1 fl - 1 f2 + EA rb = 0.11 + 1 f1 + 1 f2 + EB rc = 0.16 + 2 fl + 1 f2 + EC Assume that these stocks are priced correctly. Note that fl and f2 are the factor surprises. a. What are the weights of the first pure factor portfolio, that is, a portfolio that has loadings of 1 and 0 on the two factors? b. What is the riskless rate? c. What are the risk premiums of the two factors? d. We have another stock with loadings of . = 1 and 2 = 2. This stock's expected return is 10%. Is this stock mispriced relative to the other stocks? Explain
