Question

Greta, an elderly investor, has a degree of risk aversion of a = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the s&p 500 and a hedge fund, as well as a number of one-year strategies. (all rates are annual and continuously compounded.) the s&p 500 risk premium is estimated at 5% per year, with a sd of 20%. The hedge fund risk premium is estimated at 10% with a sd of 35%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the s&p 500 and the hedge fund in the same year is zero, but greta is not fully convinced by this claim. Compute the estimated annual risk premiums, sds, and sharpe ratios for the two portfolios

Answer 1

Answer:

Risk premiums = Alpha A x Risk Premium

S&P Portfolio Risk premiums = 3 x 5% = 15%

Hedge Fund Portfolio Risk premiums = 3 x 10% = 30%

SDs = Sd x √(A)

S&P Portfolio = 20% x √(3) = 34.64%

Hedge Fund Portfolio = 35% x √(3) = 60.62%

Sharpe ratios = Risk premium / SDs

S&P Portfolio = 15% / 34.64% = 0.43

Hedge Fund = 30% / 60.62% = 0.49