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Unformatted text preview: M: mi = mz + betai x (mM ‐ mz), where mi is the expected return of asset i, and mz is the expected return of an asset (zero‐beta portfolio) uncorrelated with the market return mM. Used in the absence of a risk‐free asset. Compared to the traditional CAPM, Black’s zero‐beta CAPM replaces the risk free asset with the zero‐beta portfolio on the inefficient part of the frontier. Part b. (5 points) Assume that the CAPM holds. The risk‐free rate rf is 2% and the market return rM is 7%. Consider the following three stocks: Stocks ROE 1‐b β
A 1.2 0.1 0.9 B 1 0.1 0.8 C 0.8 0.1 0.6 β ‐ market beta of each stock ROE – return on equity b – retention ratio Compute the P/E ratio of the three stocks, assuming a constant growth model with endogenous earnings growth. The P/E ratio is computed using the formula: P/E = (1‐b)/(k – b x ROE). The required rate of return k for the three stocks: kA = 0.02 + 1.2 x (0.07 – 0.02) = 0.08; kB = 0.02 + 1 x (0.07 – 0.02) = 0.07; kC = 0.02 + 0.8 x (0.07 – 0.02) = 0.06. P/EA = 0.9/(0.08 – (1‐0.9) x 0.1) = 12.86; P/EB = 0.8/(0.07 – (1‐0.8) x 0.1) = 16; P/EC = 0.6/(0.06 – (1‐0.6) x 0.1) = 30; Part c. (3 points) Given your results in Part b, explain the differences in the P/E ratio between the three stocks, having in mind the relationship between the required return, ROE and the plow‐back ratio (b). ROE>k for each of the stocks; in this case the higher the plow‐back rate, the higher the P/E ratio. Also, holding other things equal, riskier stocks have higher required rates of return (i.e. higher k) and lower P/E. 8 Part d. (5 points) Liquidity is a known priced factor in the cross‐section of asset returns. Thus, consider the following model instead of the CAPM: ri = α i + β i rM + γ i Liq + ei where ri is the return on asset i (i=A, B, C), Liq is the return on a liquidity factor (i.e. the return of a portfolio that mimics the evolution of market liquidity), γi is the loading on the liquidity factor for asset i, and ei is the idiosyncratic source of risk for asset i. Consider the same three stocks from Part b and the following additional information: The variance of the market factor: σ2(rM) = 0.04 The variance of the liquidity factor: σ2(Liq) = 0.02 The variance of the idiosyncrat...
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- Spring '14