Question

Greta, an elderly investor, has a degree of risk aversion of A = 5 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 12% with a SD of 40%. 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.

If the correlation coefficient between annual portfolio returns is actually 0.3, what is the covariance between the returns?

Greta, an elderly investor, has a degree of risk aversion of A 5 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 12% with a SD of 40%. 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. If the correlation coefficient between annual portfolio returns is actually 0.3, what is the covariance between the returns? (Round your answer to 3 decimal places.) Annual covariance

Answer 1

Covariance between the returns = Correlation coefficient * standard deviation of returns of 1st portfolio * standard deviation of returns of second portfolio

= 0.3 * 20% *40%

= 0.3*0.2*0.4

= 0.024