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 $6\%$ per year, with a SD of $20\%.$ The hedge fund risk premium is

estimated at $4\%$ with a SD of $23\%.$ 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 $0\mathrm{.}2,$

what is the covariance between the returns? $($Round your answer to $3$

decimal places.$)$

Annual covariance