Assignment $6(5$ points$)$

Suppose that the price of Asset X at close of trading yesterday was $100$ and its volatility

was estimated as X$.$X$\%$ per day. The price of X at the close of trading today is $96.$

Suppose that daily gains $($losses$)$ are normally distributed with standard deviation of $$6$

million.

Estimate the minimum regulatory capital the bank is required to hold. Assume a

multiplicative factor of $4\mathrm{.}0.$

Assignment $7(5$ points$)$

A fund's risk appetite is such that it wants to be $97\mathrm{.}5\%$ certain it will not lose more than

$20\%$ in any one year.

The performance of the S&P $500$ between $1970$ and $2021$ shows a mean and standard

deviation of returns over the period of $12\mathrm{.}45\%$ and $16\mathrm{.}88\%.$

Assume an annual risk$-$free rate of $4\%.$

Using the performance of the S&P $500$ between $1970$ and $2021,$ determine the beta the fund

should have.