SOCIETY OF ACTUARIES
EXAM FM FINANCIAL MATHEMATICS
EXAM FM SAMPLE QUESTIONS
Financial Economics
June 2014 changes
Questions 1-30 are from the prior version of this document. They have been edited to
conform more closely to current question writing style, but are unchanged in content.
Question 31 is the former Question 58 from the interest theory question set.
Questions 32-34 are new.
January 2015 changes
Questions 35-46 are new.
Some of the questions in this study note are taken from past examinations.
These questions are representative of the types of questions that might be asked of
candidates sitting for the Financial Mathematics (FM) Exam. These questions are intended
to represent the depth of understanding required of candidates. The distribution of
questions by topic is not intended to represent the distribution of questions on future exams.
Copyright 2015 by the Society of Actuaries.
FM-09-15 PRINTED IN U.S.A.
1
,1.
Determine which statement about zero-cost purchased collars is FALSE
(A) A zero-width, zero-cost collar can be created by setting both the put and call
strike prices at the forward price.
(B) There are an infinite number of zero-cost collars.
(C) The put option can be at-the-money.
(D) The call option can be at-the-money.
(E) The strike price on the put option must be at or below the forward price.
2.
You are given the following:
The current price to buy one share of XYZ stock is 500.
The stock does not pay dividends.
The annual risk-free interest rate, compounded continuously, is 6%.
A European call option on one share of XYZ stock with a strike price of K that
expires in one year costs 66.59.
A European put option on one share of XYZ stock with a strike price of K that
expires in one year costs 18.64.
Using put-call parity, calculate the strike price, K.
(A) 449
(B) 452
(C) 480
(D) 559
(E) 582
2
,3.
Happy Jalapenos, LLC has an exclusive contract to supply jalapeno peppers to the
organizers of the annual jalapeno eating contest. The contract states that the contest
organizers will take delivery of 10,000 jalapenos in one year at the market price. It will
cost Happy Jalapenos 1,000 to provide 10,000 jalapenos and today’s market price is 0.12
for one jalapeno. The continuously compounded annual risk-free interest rate is 6%.
Happy Jalapenos has decided to hedge as follows:
Buy 10,000 0.12-strike put options for 84.30 and sell 10,000 0.14-stike call options for
74.80. Both options are one-year European.
Happy Jalapenos believes the market price in one year will be somewhere between 0.10
and 0.15 per jalapeno.
Determine which of the following intervals represents the range of possible profit one year
from now for Happy Jalapenos.
(A) –200 to 100
(B) –110 to 190
(C) –100 to 200
(D) 190 to 390
(E) 200 to 400
3
, 4.
Zero-coupon risk-free bonds are available with the following maturities and annual
effective yield rates:
Maturity (years) Yield Rate
1 0.060
2 0.065
3 0.070
Susan needs to buy corn for producing ethanol. She wants to purchase 10,000 bushels one
year from now, 15,000 bushels two years from now, and 20,000 bushels three years from
now. The current forward prices, per bushel, are 3.89, 4.11, and 4.16 for one, two, and
three years respectively.
Susan wants to enter into a commodity swap to lock in these prices.
Determine which of the following sequences of payments at times one, two, and three will
NOT be acceptable to Susan and to the corn supplier.
(A) 38,900; 61,650; 83,200
(B) 39,083; 61,650; 82,039
(C) 40,777; 61,166; 81,554
(D) 41,892; 62,340; 78,997
(E) 60,184; 60,184; 60,184
4
