Question 1 The dataset assignment capm.csv contains daily returns, it includes the following variables: Mkt RF: excess return on a market portfolio (return on market portfolio minus the risk-free rate); SMB: measures the size factor; HML: measures the value factor; RF: risk-free rate as the U.S. Treasury Bill rate; IBM: Continuously compounded returns on IBM stock (tech company); Coca cola: Continuously compounded returns on Coca-Cola (retail company); NRG: Continuously compounded returns on NRG (energy company); (a) If we wish to invest in one stock, which one of these three stocks will you suggest? Give your reasoning (model estimation and R codes are not required in this question). (b) Estimate the basic CAPM model (only consider the market portfolio in the model) for each stock and write down the estimated models. (c) Interpret the and in the CAPM for IBM. (d) Is IBM an aggressive or conservative stock? Why? (e) Compare from three models. What does it tell you? (f) If the IBM stock is an independent portfolio (ie. = 0), do you agree that the percentage of idiosyncratic risk for this stock is 100%? Explain. (g) Compare and provide an economic interpretation of these three R2 values from the three regression models estimated in (b)? (h) Fit the Fama-French three-factor model to each stock and write down the estimated models. (i) Test whether Fama French three-Factor model outperforms the CAPM model. (j) Write a summary of the market risks based on the results of the CAPM models and three-factor models for three stocks.

2 Question 2 This question uses the same data given in Question 1. Suppose stock A=IBM, stock B=Coca Cola and stock C=NRG. Let rA denotes the return of IBM stock, rB denotes the return of Coca Cola stock and rC denotes the return of NRG stock, respectively;

2 A denotes the variance of return of IBM, 2 B denotes the variance of return of Coca Cola stock and 2 C denotes the variance of return of NRG, respectively. We consider the following FOUR possible portfolios: Portfolio 1: 30% stock A and 70% stock B; Portfolio 2: 50% stock B and 50% stock C; Portfolio 3: 60% stock A and 40% stock C; Portfolio 4: 40% stock A and 50% stock B and 10% Treasury Bill (Let assume Treasury Bill is independent of other three stocks); (a) Compute the expected value of returns and variances of returns for all four portfolios. You need to show the workings, for example: E(portfolio 9) = E(axA + bxB + cxC ) = aE(xA) + bE(xB) + cE(xC ), = 0.5 10% + 0.4 12% + 0.1 1.5% = 11.3% (b) If you were a conservative investor, which portfolio would you invest? Explain. (c) If you were aggressive investor, which portfolio would you invest? Explain.