Suppose that an actively managed equity fund$$s average monthly return is $1\mathrm{.}4\%$ and its volatility is $6\mathrm{.}8\%.$ A regression of the fund$$s returns on an S&P $500$ index fund $($assumed to represent the market portfolio$)$ yields a beta of $0\mathrm{.}5.$ The riskless rate has been $0\mathrm{.}3\%$ and the average return on the S&P $500$ fund has been $1\%$ over the sample period of the analysis. The volatility of the market return is $3\mathrm{.}9\%.$

What fraction of the fund$$s return variance is idiosyncratic based on the market model?

A$.$

$8\mathrm{.}22\%$

B$.$

$91\mathrm{.}78\%$

C$.$

$57\mathrm{.}35\%$

D$.$

$42\mathrm{.}65\%$