19. Our firm receives foreign exchange remittances in several different currencies. We are...

19. Our firm receives foreign exchange remittances in several different currencies. We are interested in hedging two remittances in six months time from Europe (200 in EUR) and from Japan (400,000 in JPY). If the sales were made today, we would receive the USD equivalent of these remittances at today's spot exchange rates. However, there may be a big change in spot FX rates by the end of the six-month period. In order to ensure that there are no surprises, we want to hedge the risk of changes in FX rates from now to six months ahead. The following tables give the correlations and covariances of changes in spot FX and forward FX rates. The notation below is such that S(usd,eur) stands for dollars per euro.

Note that the matrices of changes above reflect the change in USD amounts per unit of the foreign currency. This follows from the fact that the exchange rates are expressed as dollars per unit of foreign currency. If we want to hedge an inflow of EUR 200 and JPY 400,000, how many units of foreign currency must we hold in forward FX contracts to get the best hedge? Note that the best hedge is one that minimizes the variance of changes in the total remitted amount. Carry out your analysis in the following three steps:

(a) Compute what the variance of changes in remitted USD amount is if we do no hedging.
(b) Compute what the variance of changes in remitted USD amount is if we do one-for-one hedging.
(c) Compute what the variance of changes in remitted USD amount is if we do minimum-variance hedging.