Question

In addition to risk-free securities, you are currently invested in the Tanglewood Fund, a broad-based fund of stocks and other securities with an expected return of 12% and a volatility of 26%. Currently, the risk-free rate of interest is 5%. Your broker suggests that you add a venture capital fund to your current portfolio. The venture capital fund has an expected return of 21%, a volatility of 79%, and a correlation of 0.2 with the Tanglewood Fund. Assume you follow your broker's advice and put 50% of your money in the venture fund: a. What is the Sharpe ratio of the Tanglewood Fund? b. What is the Sharpe ratio of your new portfolio? c. What is the optimal Sharpe ratio you can obtain by investing in the venture fund? (Hint: Use Excel and round your answer to two decimal places.)

Answer 1

1 Tanglewood fund Expected return = 12% Standard deviation = 26% Sharpe ratio = (Return on portfolio - risk free rate)/ standard deviation of portfolio Sharpe ratio = (12% - 5%)/26% Sharpe ratio = 0.27 For a minimum variance portfolio, w1 will be = (6242-p12*61*62)/(61^2+2^2-2*p*c1*62) w1 = (0.7942-0.2*0.26*0.79)/(0.26^2+0.79^2-2*0.2*0.26*0.79) w1= 95.65% w2 = 1-w1 w2 = 4.35% New portfolio Expected return = W1*R1+W2*R2 Expected return = 50%*12%+50%*21% Expected return = 16.50% Expected return = W1*R1+W2*R2 Expected return = 95.65%*12%+4.35%*21% Expected return 12.39% Standard deviation=(W1^2*01^2+W2^2*o2^2+2*W1*W2*1*2*p) Standard deviation=(0.52*0.26^2+0.542*0.7912+2*0.5*0.5*0.26*0.79*0.2) Standard deviation= 19.35% Standard deviation=(W1^2*61^2+W2^2*62^2+2*W1*W2*1*62*p) Standard deviation=(0.9565^2*0.26^2+0.0435^2*0.79^2+2*0.9565*0.0435*0.26*0.79*0.2) Standard deviati 6.64% Sharpe ratio = (Return on new portfolio - risk free rate)/ standard deviation of new portfolio Sharpe ratio = (16.5% - 5%)/ 19.35% Sharpe ratio = 0.594 Sharpe ratio = (Return on optimal portfolio - risk free rate)/ standard deviation of optimal portfolio Sharpe ratio = (12.39% - 5%)/ 6.64% Sharpe ratio = 1.11