(a) Consider the following linear relationship between the return to an asset j, r, and the...

  

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(a) Consider the following linear relationship between the return to an asset j, r, and the return to the market portfolio m, rm O jm rj - rf = (rm -rf) 0 m2 where r denotes the return to the risk free asset, jm denotes the covariance between the returns to asset j and the market portfolio m, and o2 denotes the variance of the market portfolio return. Provide an interpretation of the above linear relation- ship. In particular, what is the risk premium of asset j? Why? What is the Beta of asset j? What is its relationship to non- diversifiable market risk? Support your answers with the help of a graph, where you clearly identify the Capital Market Line and the Efficiency Frontier. [10] (b) Make all necessary assumptions to derive the CAPM principal estimating equation: r; -rf = a; + B (rm -rf) + ; OTHE where ; is i.i.d. N(0,02). In particular, show that 3; = [10] (c) Suppose that you estimated the above relationship by OLS, and that you find that your coefficient estimate of a, is significant and statistically different from zero. Would this invalidate the CAPM predictions? Under which assumption(s) would you ex- pect the constant coefficient estimate to be positive? Why? [10] (d) Finally, describe a statistical procedure that would allow you to test the validity of the CAPM. (Hint: consider the Arbitrage Pricing Model. Does it nest the CAPM? Under which null hy- pothesis?) [10] (a) Consider the following linear relationship between the return to an asset j, r, and the return to the market portfolio m, rm O jm rj - rf = (rm -rf) 0 m2 where r denotes the return to the risk free asset, jm denotes the covariance between the returns to asset j and the market portfolio m, and o2 denotes the variance of the market portfolio return. Provide an interpretation of the above linear relation- ship. In particular, what is the risk premium of asset j? Why? What is the Beta of asset j? What is its relationship to non- diversifiable market risk? Support your answers with the help of a graph, where you clearly identify the Capital Market Line and the Efficiency Frontier. [10] (b) Make all necessary assumptions to derive the CAPM principal estimating equation: r; -rf = a; + B (rm -rf) + ; OTHE where ; is i.i.d. N(0,02). In particular, show that 3; = [10] (c) Suppose that you estimated the above relationship by OLS, and that you find that your coefficient estimate of a, is significant and statistically different from zero. Would this invalidate the CAPM predictions? Under which assumption(s) would you ex- pect the constant coefficient estimate to be positive? Why? [10] (d) Finally, describe a statistical procedure that would allow you to test the validity of the CAPM. (Hint: consider the Arbitrage Pricing Model. Does it nest the CAPM? Under which null hy- pothesis?) [10]

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The provided question is a multipart question related to modern portfolio theory and the Capital Asset Pricing Model CAPM I will address each part of the question a Interpretation of the Linear Relati... View the full answer