Suppose that daily gains $($losses$)$ are normally distributed with a standard deviation of $5$ million.

a$.$ Estimate the minimum regulatory capital the bank is required to hold. $($Assume a multiplicative factor of $4\mathrm{.}0.)$

b$.$ Estimate the economic capital using a one$-$year time horizon and a $99\mathrm{.}9\%$ confidence level assuming that there is a correlation of $0\mathrm{.}05$ between gains $($losses$)$ on successive days.

$28\mathrm{.}11$ Suppose that the economic capital estimates for two business units are

Business Units

$12$

Market Risk $1050$

Credit Risk $3030$

Operational Risk $5010$

The correlation between market risk and credit risk in the same business unit is $0\mathrm{.}3.$ The correlation between credit risk in one business unit and credit risk in another is $0\mathrm{.}7.$ The correlation between market risk in one business unit and market risk in the other is $0\mathrm{.}2.$ All other correlations are zero. Calculate the total economic capital. How much should be allocated to each business unit?