Financial Portfolio Management

Questions: You have the 2 stocks A and B, and their returns along with SP/TSX return for the last 3 years Year Returns of A Returns of B Returns of SP/TSX 1 3% -2% 6% 2 11% -6% -1% 3 -1 7% 7% 1. Calculate the covariance and correlation between A and B. For this, use average (mean) return for the stocks. 2. If you are willing to invest 70% of your market money on A and 30% on B, calculate your expected return and risk of the portfolio. 3. Calculate the beta of stock A and B. Answer: (1). Average Return A = Average Return A = = 4.3333 Average Return B= Average Return B= = -0.3333 Covariance AB = = -74.66666667 Periods (n) = 3 Covariance = -74.66666667/3 = -24.8889 Since the covariance between stocks A nd B is negative, it is an indicator that the two moves in opposite directions. I.e. one of the stocks (A) is making a very high return, whereas the other (B) is making a too low return. Correlation coefficient = covariance AB/ standard deviation A*Standard deviation B Covariance AB = -24.8889 Standard deviation A = 6.11 Standard deviation B = 6.66 Correlation coefficient = -24.8889/ (6.11*6.66) = -24.8889/40.69 = -0.61 (2). Expected Return of a Portfolio E (Rp) = (Average return A * Proportion invested in A) + (Average return B * Proportion invested in B) E (Rp) = (4.3333 * 0.70) + (-0.3333 * 0.30) = 3.03 0.09999 = 2.93 The expected return of the portfolio lies between the lowest and the highest average return of each single stock. I.e. between -0.0333 and 4.3333 Risk of the portfolio is measured in terms of the variance of the portfolio Var RP = Where; a is the proportion of money invested in A, b is the proportion of money invested in B, is the variance of A, is the variance of B, and is the covariance of return A and B. Var RP = = 18.29 + 3.99 -10.45 = 11.83 The variance of the portfolio is way lower as compared to that of individual stocks The standard deviation of the portfolio = 3.44 The std of the portfolio is lower than that of individual stocks. (3). Beta = covariance (Ri, Rm) / Market Variance Covariance A, SP/TSX = -52/3 = -17.33 Beta A = -17.33/19 = -0.91 Covariance B, SP/TSX = 47/3 = 15.67 Beta B = 15.67/19 = 0.82. Bibliography Cherewyk, P. (2011). Calculating Covariance for Stocks | Investopedia. Khan, M. and Jain, P. (2007). Financial management. New Delhi: Tata McGraw-Hill. McNulty, D. (2008). Calculating Beta: Portfolio Math For The Average Investor | Investopedia. Nickolas, S. (2015). What is the formula for calculating beta? | Investopedia. Whittington, R. and Delaney, P. (2008). Wiley CPA exam review 2008. New York: John Wiley Sons.