Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/, Exercise 95, 3/10/7
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May 2006 Casualty Actuarial Society Course 8 Examination, Problem No. 30
(multiple choice answers added)
Consider the following information from one year ago:
• Futures exchange rate was 0.80 pounds per dollar.
• Initial exchange rate was 0.75 pounds per dollar.
• British risk-free rate was 9.0% per annum, continuously compounded.
One year ago, a U.S. investor invested in a one-year risk-free British government bill.
Also at that time, the investor hedged the exchange rate risk in the investment by using a
futures contract. Calculate the dollar-denominated risk-free continuously compounded
interest rate that the investor locked into one year ago.
A. 2.55%
B. 2.75%
C. 2.90%
D. 3.25%
E. 3.50%
Solution.
Consider the entire transaction as performed in U.S. dollars, and view the British pound
as an interest-bearing instrument on which a futures contract is purchased. The spot price
1
1
4
5
of a British pound is
= dollars. The futures price of a British pound is
=
0.75 3
0.80 4
dollars. Let r be the unknown risk-free rate on the U.S. dollar. Using the futures-spot
parity we obtain
5 4 ( r " 0.09 )
= !e
.
4 3
This gives
" 15
%
r = ln $ ! e0.09 ' ( 2.546148%.
# 16
&
Answer A.
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