Krzyś Ostaszewski, http://www.math.ilstu.edu/krzysio/
Author of a study manual for exam FM available at:
http://smartURL.it/krzysioFM (paper) or http://smartURL.it/krzysioFMe (electronic)
Instructor for online seminar for exam FM: http://smartURL.it/onlineactuary
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SOA Sample Questions for Derivatives Markets, Problem No. 18, and Dr.
Ostaszewski’s online exercise No. 232 posted October 24, 2009
You are a jeweler who buys gold, which is the primary input needed for your products.
One ounce of gold can be used to produce one unit of jewelry. Assume that the cost of all
other inputs is negligible. You are able to sell each unit of jewelry for 700 plus 20% of
the market price of gold in one year. In one year, the actual price of gold will be in 1 of 3
possible states, corresponding to the following probability table:
Market Price of Gold in 1-year
Probability
750 per ounce
0.2
850 per ounce
0.5
950 per ounce
0.3
You are considering utilizing forward contracts to lock in 1-year gold prices, in which
case you would charge the customer (one year from now) 700 plus 20% of the forward
price. The 1-year forward price for gold is 850 per ounce. How much does your expected
1-year profit, per unit of jewelry sold, increase if you buy forward the 1-year price of
gold?
A. 0
B. 8
C. 12
D. 20
E. 32
Solution.
First, we calculate the expected one-year profit without using the forward. This equals
0.2 ⋅ ( 700 + 150 − 750 ) + 0.5 ⋅ ( 700 + 170 − 850 ) + 0.3⋅ ( 700 + 190 − 950 ) = 12.
Next, we calculate the expected one-year profit when buying the 1-year forward for 850.
This simply equals 700 + 170 – 850 = 20. Thus, the expected profit increases by 8 as a
result of using the forward.
© Copyright 2009 by Krzysztof Ostaszewski. All rights reserved. Reproduction in
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