Answers Midterm Risk Management

Question 3

a. The investor expects the euro to depreciate with respect to the US$, since a depreciation will result in a lower euro return for the investor

b. The investor should take a short position in the $/€ forward contract. He expects the euro the depreciate, so taking a short position will - in case of a depreciation - result in a profit. This way he hedges his investment in the US equities and is protected if a depreciation occurs.

c. To find out what the arbitrage-free forward price is, we perform a replicating strategy: * Buy $ today  €1M x $1.35/€ x exp(-1%) = $1,337M * Borrow present value of F  F x €1M x exp (-2,5%) * F needs to be as such that this portfolio has a zero cost  F x €1M x exp (-2,5%) = $1,337M. F = 1.37

Or by plugging in the values in the formula:

F = S x e (r$ - re)
F = $1.35/€ x e (2.5% - 1%) = 1.37

d. Determine the optimal hedge ratio using the euro-denominated prices on a broad US equity market index, and the euro to the $US exchange rate (use linest function in excel). Explain why or why not it is higher/lower/equal than 1. Evaluate the quality of the hedge.

The optimal hedge ratio is nothing more than the beta of the regression of the Returns US Equity Market in euro on the Futures Returns euro to US$. By using the linest function in excel we find the optimal hedge ratio, namely 0,227. In other words, to hedge 10 million of the US equity market index unit, he should short 2.27M of the euro to the $US exchange