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 25 % Currently, the risk-free rate of interest is 4 %Your broker suggests that you add a venture capital fund to your current portfolio. The venture capital fund has an expected return of 20%, volatility of 80 %, and a correlation of 0.2 with the Tanglewood Fund. Assume you follow your broker's advice and put50 % 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?

Answer 1

a.

Sharpe ratio for Tanglewood fund = (Expected rate of return – Risk-free rate)/Standard deviation of Tanglewood

Sharpe ratio for Tanglewood fund = (12% - 4%)/25% = 32.00%

b.

Expected return on portfolio = 12% x 50% + 20 x 50% = 16%

Now, calculate standard deviation of portfolio:

w(1) = the portfolio weight of the first asset = 50%

w(2) = the portfolio weight of the second asset = 50%

o(1) = the standard deviation of the first asset = 25%

o(2) = the standard deviation of the second asset = 80%

Correlation(1,2) = c, where q(1,2) is the correlation between the two assets = 0.20

The formula for standard deviation in a two-asset portfolio is:

Standard deviation portfolio = ((w(1)^2 x o(1)^2) + (w(2)^2 x o(2)^2) + (2 x c x (w(1) x o(1) x w(2) x o(2)))^0.5

Standard deviation of new portfolio = ((25%^2 x 50%^2) + (80%^2 x 50%^2) + (2 x 0.2 x 25% x 50% x 80% x 50%))^0.5                

Standard deviation of new portfolio = 44.230%

.

Now, we can calculate Sharpe ratio:

.

Sharpe ratio of new portfolio = (Expected return - Risk-free return) / Standard deviation of new portfolio

Sharpe ratio of new portfolio = (16% - 4%) / 44.230%

Sharpe ratio of new portfolio = 27.13%