QUESTION 1 a. You have two estimates of the beta of a share listed on the London stock exchange. Both estimates are calculated by regressing returns on the share against returns on the FTSE -100 index over the last five years. One is computed using daily returns, while the other is computed using weekly returns. The first estimate is 0.72, and the second is 0.95. What explanations might there be for the difference? [6 marks] b. Consider two stocks A and B. Both have an expected return of 10%, and their standard deviations are 18% and 16% respectively. Also, their correlation is 0.35. If the risk-free rate of return is 3%, identify the tangency portfolio, and calculate its expected return and standard deviation. [12 marks] c. A portfolio is equally split between 10 different stocks, each of which has a beta of 1.5 and the same correlation with the market portfolio. The idiosyncratic component of returns is uncorrelated across stocks. The annualized volatility of the market is 15%, and of the portfolio's volatility is 24%. Required: i. What is the volatility of each stock? [10 marks] ii. What is the correlation between each stock and the market? [3 marks] iii. What is the correlation between one stock and another? [2 marks] TOTAL: 33 MARKS QUESTION 1 a. You have two estimates of the beta of a share listed on the London stock exchange. Both estimates are calculated by regressing returns on the share against returns on the FTSE -100 index over the last five years. One is computed using daily returns, while the other is computed using weekly returns. The first estimate is 0.72, and the second is 0.95. What explanations might there be for the difference? [6 marks] b. Consider two stocks A and B. Both have an expected return of 10%, and their standard deviations are 18% and 16% respectively. Also, their correlation is 0.35. If the risk-free rate of return is 3%, identify the tangency portfolio, and calculate its expected return and standard deviation. [12 marks] c. A portfolio is equally split between 10 different stocks, each of which has a beta of 1.5 and the same correlation with the market portfolio. The idiosyncratic component of returns is uncorrelated across stocks. The annualized volatility of the market is 15%, and of the portfolio's volatility is 24%. Required: i. What is the volatility of each stock? [10 marks] ii. What is the correlation between each stock and the market? [3 marks] iii. What is the correlation between one stock and another? [2 marks] TOTAL: 33 MARKS
