Problem $5.($Opposite hedge variance$)$ Assume that cash flow is given by $y=$

$S_{T}W+(F_T-F_0)h.$

Let ${}_S^2=$var$(S_T),{}_F^2=$var$(F_T),$ and ${}_{ST}=$cov$(S_T,F_T).$

a$)$ In an equal and opposite hedge, $h$ is taken to be an opposite equivalent

dollar value of the hedging instrument. Therefore $h=-kW,$ where $k$ is

the price ratio between the asset and the hedging instrument. Express the

standard deviation of $y$ with the equal and opposite hedge in the form

${}_y=W{}_{S}B$

$($That is$,$ find B$.)$

b$)$ Apply this to the last example in Chapter $8$ PPT $($i$.$e$.$ the example about

German Marks and Danish Kroner$)$ and compare with the minimum$-$

variance hedge.