Question

3. Stocks A, B, C and D have the same standard deviation of 10% and the same expected return of 5%. The following table shows the correlation coefficient between the returns on these stocks. (note that correlation with itself is always 1). Stock B Stock C Stock D Stock A Stock B Stock C Stock D Stock A 1.0 -0.4 0.9 -0.1 1.0 0.1 1.0 -0.5 -0.2 1.0 (a) Consider a portfolio P = 0 A+ B+ C, calculate the portfolio's expected return E(rp) and its volatility op. (3 points) (b) If your current portfolio is entirely invested in Stock A and you have another $100 that you can spend on ONLY one of these four stocks. Assume you are risk averse, which stock would you choose? Explain your answer. [3 points)

Answer 1

Asset x) A Weight (W) 33.33% 33.33% 33.33% 0.00% Mean Answer a. Return (x] 0.05 0.05 0.05 0.05 Product (Wºx) 0.017 0.017 0.017 0.000 0 050 с D Assetix) Variance=w*(x-Mean Weight (W] Return (x] 33.33% 0,05 33.33% 0.05 33.33% 0.05 0.00% 0.05 Variance Standard Deviation Answerb Now, for two-asset portfolio, portfolio variance is as under: O? = W0* + W202 + 2w1w2 Covariance (12) Where, wi is weight of first asset, w is weight of second asset, is variance of first asset and and is variance of second asset and Covariance (12) shows covariance of the two assets. Since covariance equals the product of correlation coefficient and standard deviation of each asset, we can rewrite the above equation as under: wo+ W202 +2w W.00.0 Ris the correlation coefficient of returns of first and second asset. O Hence variance and standard deviation will be minimum for maximum negatively correlated assets. Hence, Stock B should be considered with stock A. Answer If I am risk loving then maximum risk is for maximum positive correlated assets. Hence, Stock C should be considered with stock A. Answerd My answer will still be same as expected return of risk free asset and all stocks is same. But, if we consider Stock B with A variance (risk) will be reduced as compared to risk free asset.