Find an effective hedge financial hedge if a U$.$S$.$ firm holds an asset in Great Britain and faces the following scenario:

State $1$ State $2$ State $3$

Probability $25\%50\%25\%$

Spot rate $ $2\mathrm{.}20/$ $ $2\mathrm{.}00/$ $ $1\mathrm{.}80/$

P$*3,0002,5002,000$

P $ $6,600$ $ $5,000$ $ $3,600$

P$*=$ Pound sterling price of the asset held by the U$.$S$.$ firm

P $=$ Dollar price of the same asset

The CFO runs a regression of the form P $=$ a $+$ b $\backslash$times S $+$ e

The regression coefficient beta is calculated as b $=$ COV$($P$,$S$)$VAR$($S$)$

Where

Cov$($P$,$S$)=0\mathrm{.}25\backslash$times $($$$6,600$ $$5,050)\backslash$times $($$$2\mathrm{.}20$ $$2\mathrm{.}00)$

$+0\mathrm{.}50\backslash$times $($$$5,000$ $$5,050)\backslash$times $($$$2\mathrm{.}00$ $$2\mathrm{.}00)$

$+0\mathrm{.}25\backslash$times $($$$3,600$ $$5,050)\backslash$times $($$$1\mathrm{.}80$ $$2\mathrm{.}00)$

Cov$($P$,$S$)=77\mathrm{.}50+0+72\mathrm{.}50$

Cov$($P$,$S$)=150$

b $=1500\mathrm{.}02$

$=7,500$

The variance of the exchange rate is calculated as

E$($S$)=0\mathrm{.}25\backslash$times $$2\mathrm{.}20+0\mathrm{.}50\backslash$times $$2\mathrm{.}00+0\mathrm{.}25\backslash$times $$1\mathrm{.}80$

$=$ $$\mathrm{.}55+$ $$1+$ $$\mathrm{.}45$

$=$ $$2\mathrm{.}00$

VAR$($S$)=0\mathrm{.}25($$$2\mathrm{.}20$ $$2\mathrm{.}00)2+0\mathrm{.}50($$$2\mathrm{.}00$ $$2\mathrm{.}00)2+0\mathrm{.}25($$$1\mathrm{.}80$ $$2\mathrm{.}00)2$

$=0\mathrm{.}01+0+0\mathrm{.}01$

$=0\mathrm{.}02$

The expected value of the investment in U$.$S$.$ dollars is:

E$[$P$]=0\mathrm{.}25\backslash$times $$6,600+0\mathrm{.}50\backslash$times $$5,000+0\mathrm{.}25\backslash$times $$3,600=$ $$5,050$

Suppose that you implement your hedge at F$1($$$/)=$ $$2/.$ Your cash flows in state $1,2,$ and $3$ respectively will be

Multiple Choice

none of the options

$$5,000,$ $$5,000,$ $$5,000.$

$$5,100,$ $$5,000,$ $$5,100.$

$$5,100,$ $$5,100,$ $$5,100.$