Back in 1990, East Germany was in the process of merging into West Germany. Its national currency was to be replaced by the Deutsche mark (DM). A U.S. dollar-based investor has a portfolio worth DM 100 million in German bonds. The current spot exchange rate is 2 DM/$. The current one-year market interest rates are 6% in DM and 10% in dollars. One-year currency options are quoted in Chicago with a strike price of 50 U.S. cents per DM; a call DM is quoted at 1 U.S. cent and a put
DM is quoted at 1.2 U.S. cents; these option prices are for one DM.
You are worried that the integration of East and West Germany will cause inflation in Germany and a drop in the DM. So, you consider using forward contracts or options to hedge the currency risk.
a. What is the one-year forward exchange rate DM/$?
b. Simulate the dollar value of your portfolio assuming that its DM value stays at DM 100 million; use DM/$ spot exchange rates equal in one year to: 1.6, 1.8, 2, 2.2, and 2.4. First consider a currency forward hedge, then a currency-option insurance.
c. What could make your forward hedge imperfect?

Question

Quizplus · Accepted Answer

The Answer is a. The one-year forward exchange rate is:

F = 2 \frac { 1 + 6 \% } { 1 + 10 \% } = 1.9273

DM/$.
b. I need to buy DM puts. As the premium is paid in dollars, there is no exchange risk on the option premium. Assuming that I can finance the premium at a dollar interest rate of 0%, I would buy 100 million DM puts at a cost of:
Premium = ($0.012 per DM put) * (100 million DM puts) = $1.2 million.

\begin{array}{l}\hline ext { Simulation of the Portfalia Value (in s million) }\\hline \begin{array} { c c c c } \begin{array} { c } ext { Exchange } \ ext { Rate }\end{array} & ext { Unhededed } & ext { Hedged } & ext { Insured } \\hline 1.6 & 62.50 & 51.89 & 01.30 \1.8 & 55.56 & 51.89 & 54.36 \2.0 & 50.00 & 51.89 & 48.80 \2.2 & 45.45 & 51.89 & 48.80 \2.4 & 41.67 & 51.89 & 48.80 \\hline\end{array}\end{array}

c. Basis risk and cross-hedge risk.

Back in 1990, East Germany Was in the Process of Merging