Here are the results of a monthly index model of stock returns for FinCorp Stock:

$r($ Fincorp $)=\mathrm{.}001+\mathrm{.}8r(S$&$P500)+e$

The standard deviation of the monthly return on the S&P $500$ was $\mathrm{.}05.$

The standard deviation of the monthly value of the residual, $e,$ was $\mathrm{.}03.$

c$.$ What was the standard deviation of the return on FinCorp stock? Remember that e

and the return on the S&P $500$ are essentially uncorrelated.

d$.$ If you hold $$2$ million in FinCorp stock, how many $1-$month S&P futures contracts

must you sell to make your portfolio market neutral $($zero beta$)$ over the next

month? The S&P index is currently at $2000,$ and the contract multiplier is $$250.$

e$.$ What would be the standard deviation of your hedged position if you were to sell

this number of $S$&$P$ contracts? Assume the monthly risk$-$free rate is $0\mathrm{.}05\%$ and the

monthly dividend yield is $0\mathrm{.}01\%.$

f$.$ What percentage reduction in the variance of your rate of return is achieved by your

hedge? $[$Submit your answer as a percentage between $0$ and $100.]$