Greta has 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 1-year
strategies. (All rates are annual and continuously compounded.) The
S&P 500 risk premium is estimated at 10% per year, with a
standard deviation of 16%. The hedge fund risk premium is estimated
at 12% with a standard deviation of 31%. 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 return on the
S&P 500 and the hedge fund return in the same year is zero, but
Greta is not fully convinced by this claim.
a-1. Assuming the correlation between the annual
returns on the two portfolios is indeed zero, what would be the
optimal asset allocation? (Do not round intermediate
calculations. Enter your answers as decimals rounded to 4
places.)
S&P=
Hedge=
a-2. What is the expected risk premium on the
portfolio? (Do not round intermediate calculations. Enter
your answer as decimals rounded to 4 places.)
Expected risk premium=
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