1. The Capital Asset Pricing Model (throughout this question, assume a riskless rate Rf is available for borrowing and lending).
(a) The CAPM predicts that the market portfolio is mean-variance efficient. Explain why this is the case.
(b) What does the previous statement imply for the cross-section of expected security returns? What is the intuition behind that result?
(c) Taken literally, what are the implications of CAPM for portfolio management?
(d) What are value and growth stocks? Are average returns on value and growth stocks consistent with the CAPM?
(e) Suppose you observe that some portfolio of securities consistently earns positive CAPM alpha. More precisely, suppose the expected excess return on the market is μεM, market volatility is σM, and let αp, βp and σ2(εp) denote respectively the alpha of the portfolio, its market beta and residual variance. You are a mean-variance investor and you can hold, besides a risk free as-set, any combination of an index fund and that portfolio. What combination would you choose?
2. Linear factor models.
(a) What is the advantage of factor models over the use of sample moments for estimating the variance-covariance matrix of a large set of N asset returns?
(b) Describe four approaches to the choice of factors and the corresponding estimation issues.
(c) Explain one way of assessing the quality of a linear factor model as a risk model.
3. Time-varying expected returns.
(a) What is the sign of the slope coefficient in a predictive regression of market returns on the price-to-dividend ratio P/D? What if instead one uses cay, the proxy for consumption-to-wealth ratio constructed by Lettau and Ludvigson (2001)? Give a brief rationale for these findings.
(b) Give two other variables that are known to have some ability to predict market returns.
(c) Explain why the investment horizon is irrelevant for the allocation problem between a risk free asset and the stock market in an i.i.d. world, assuming the distribution of stock market return is known.
(d) Asset management professionals often advise young investors to invest more aggressively in stocks than older investors. Can you make sense of that advice? Are there conditions under which the optimal percentage of wealth allocated to stocks vs. a risk free asset by buy-and-hold investors could be non-monotonic or even decreasing in the investment horizon?
(e) Consider two stocks A and B and two periods of time 1 and 2. Assume CAPM holds period per period. The betas of stock A in periods 1 and 2 are respectively 0.5 and 1.25, while the betas of stock B are respectively 1.5 and 0.75. Suppose the market risk premium is 10% in period 1 and 20% in period 2. What would you conclude if you tested the CAPM over the two periods using stocks A and B as test assets? Can you tell a story along these lines to explain the value effect?
4. The Black-Litterman model of portfolio management.
(a) In the Black-Litterman model, what is the mean of the prior distribution for expected excess returns?
(b) What types of views can an analyst feed into the esti-mation of expected excess returns? How are these views specified formally?
(c) How are the views optimally blended with the prior?
(d) In what sense is the Black-Litterman procedure better than standard Markowitz optimization using historical mean excess returns? Intuitively, how does the optimal portfolio resulting from the Black-Litterman procedure relate to the views?
(e) The Black-Litterman model does not take explicitly into account historical data in the estimation of expected excess returns. How would you use (or extend) the Black-Litterman pro-cedure to incorporate data on past returns in the estimation of expected excess asset returns?
5. Strategies generating superior returns.
(a) Explain carefully how you would implement a momentum strategy on a given universe of US stocks.
(b) What empirical regularity do we refer to as the "post-earnings announcement drift"? How would you design a portfolio strategy that exploits this empirical regularity?
(c) Using monthly return data over the sample period January 1995-December 2008, you find that a zero-cost long-short US equity strategy yields positive average returns. What are the alternative interpretations of your finding, how could you try to tell them apart, and what are their implications for portfolio choice?
6. Currency returns, international portfolio choice and currency hedging.
(a) Explain the well-known currency carry trade strategy. Is there evidence that engaging in carry trade is risky?
(b) Analytically, how does currency risk affect the mean and volatility of returns (measured in your domestic currency) on your foreign stock holdings?
(c) You are based in the United States. On top of a riskfree asset, you can take positions in the S&P500 (asset D) and in the MSCI Emerging Market Index (asset F). Based on historical data, the standard deviations of the domestic and foreign asset dollar returns are respectively σD = 10% and σF = 15%, and their correlation is p = 0.5. The average dollar rates of return on the two assets in excess of the US riskfree rate are respectively μeD = 7% and μeF = 12%. In that situation, Markowitz's theory prescribes that the risky part of your portfolio should be equally invested in assets D and F.
What numerical computation underpins the previous statement (you do not need to actually perform this computation)? Does the validity of that statement rely on an implicit assumption on your risk appetite?
(d) Why should one be cautious about using measures of return correlations across national stock markets based on historical data? In what sense could those measures lead one to over¬estimate the benefits from international portfolio diversification?
(e) Explain the three approaches to currency management analyzed in Philippe Jorion's paper "Mean-Variance Analysis of Currency Overlays". Compare the efficiency of these three ap¬proaches in theory and in practice.