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trage-free capital market.
b. Once again using the appropriate payoff diagrams, provide an explanation for the put-
call-forward parity relationship of the following equation:
F0, I
S0 5
(1 1 RFR) r
5. You are a market maker in derivative instruments linked to KemCo stock. In addition to acting as a
dealer in KemCo call options, put options, and forward contracts, you also spend part of your time
surveying other dealers in the industry looking for arbitrage profit opportunities. Currently, the
market-clearing (i.e., zero-value) contract price for a KemCo forward contract with nine months to
maturity is $45. Also, an average of the last few trades involving nine-month KemCo puts with a
$45 exercise price revealed a contract price of $3.22.
a. If the nine-month T-bill is priced to yield an annual return of 6.5 percent, what bid-ask spread
would you quote for a nine-month KemCo call option struck at a price of $45? In establishing
this spread, first calculate the theoretical no-arbitrage price for the contract and then round this
price up (or down) to the nearest one-eighth of a dollar for your ask (or bid) quote.
b. Given the prevailing market prices for the forward and put option contracts, what should be the
fair market value of KemCo stock at the present time?


1. CFA Examination Level III (2004)
The Glover Scholastic Aid Foundation has received a ‚¬20 million global government bond portfolio
from a Greek donor. This bond portfolio will be held in euros and managed separately from Glover™s
existing U.S. dollar-denominated assets. Although the bond portfolio is currently unhedged, the
portfolio manager, Raine Sofia, is investigating various alternatives to hedge the currency risk of the
The bond portfolio™s current allocation and the relevant country performance data are given in
Exhibits 21.1 and 21.2. Historical correlations for the currencies being considered by Sofia are given
in Exhibit 21.3. Sofia expects that future returns and correlations will be approximately equal to
those given in Exhibits 21.2 and 21.3.
A. Calculate the expected total annual return (euro-based) of the current bond portfolio if Sofia de-
cides to leave the currency risk unhedged. Show your calculations.
B. Explain, with respect to currency exposure and forward rates, the circumstance in which Sofia
should use a currency forward contract to hedge the current bond portfolio™s exposure to a given
C. Determine which one of the currencies being considered by Sofia would be the best proxy hedge
for Country B bonds. Justify your response with two reasons.
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40 Web Problems

Exhibit 21.1 Glover Scholastic Aid Foundation Current Allocation Global Government
Bond Portfolio

Country Allocation (%) Maturity (years)

Greece 25 5
A 40 5
B 10 10
C 10 5
D 15 10

Exhibit 21.2 Country Performance Data (in local currency)

5-year 10-year Liquidity
Excess Excess Unhedged of 90-day
Cash Bond Bond Currency Currency
Return Return Return Return Forward
Country (%) (%) (%) (%) Contracts

Greece 2.0 1.5 2.0 “ Good
A 1.0 2.0 3.0 Good
B 4.0 0.5 1.0 2.0 Fair
C 3.0 1.0 2.0 Fair
D 2.6 1.4 2.4 Good

Exhibit 21.3 Historical Currency Correlation Table (1998“2003, Weekly Observations)

‚¬ (Greece)
Currency A B C D

‚¬ (Greece) 20.77 20.57
1.00 0.45 0.77
20.61 20.70
A “ 1.00 0.56
B “ “ 1.00 0.88
C “ “ “ 1.00
D “ “ “ “ 1.00

2. CFA Examination Level II (2002)
Pamela Itsuji, a currency trader for a Japanese bank, is evaluating the price of a six-month Japanese
yen/U.S. dollar currency futures contract. She gathers the currency and interest rate data shown in
Exhibit 21.4.
A. Calculate the theoretical price for a six-month Japanese yen/U.S. dollar currency futures
contract, using the data in Exhibit 21.4 and Japanese yen as the local currency. Show your
Itsuji is also reviewing the price of a three-month Japanese yen/U.S. dollar currency futures
contract, using the currency and interest rate data shown in Exhibit 21.5. Because the three-
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Chapter 21

month Japanese interest rate has just increased to 0.50 percent, Itsuji recognizes that an
arbitrage opportunity exists and decides to borrow $1 million U.S. dollars to purchase Japan-
ese yen.
B. Calculate the yen arbitrage profit from Itsuji™s strategy, using the data in Exhibit 21.5. Show
your calculations.

Exhibit 21.4 Currency Exchange Rate and Six-Month Interest Rate Data Japan and U.S.

Japanese Yen/U.S. Dollar Spot Currency Exchange Rate ¥ 124.30000/$1.00000
Six-month Japanese Interest Rate 0.10%
Six-month U.S. Interest Rate 3.80%

Exhibit 21.5 Currency Exchange Rate and Three-Month Interest Rate Data Japan and U.S.

Japanese Yen/U.S. Dollar Spot Currency Exchange Rate ¥ 124.30000/$1.00000
New Three-month Japanese Interest Rate 0.50%
Three-month U.S. Interest Rate 3.50%
Three-month Currency Futures Contract Value ¥123.26050/$1.00000

3. CFA Examination Level II (2004)
Maria VanHusen suggests to Sandra Kapple that using forward contracts on fixed income securities
can be used to protect the value of the Star Hospital Pension Plan™s bond portfolio against the rising
interest rates that Kapple expects. VanHusen prepares the following example to illustrate for Kapple
how such protection would work:
• A 10-year bond with a face value of $1,000 is issued today at par value. The bond pays an annual
• An investor intends to buy this bond today and sell it in six months.
• The six-month risk-free interest rate today is 5.00% (annualized).
• A six-month forward contract on this bond is available, with a forward price of $1,024,70. The
contract is not an off-market forward contract.
• In six months, the price of the bond, including accrued interest, will be $798.40 as a result of a
rise in interest rates.
A. Based on VanHusen™s example:
i. State whether the investor should buy or sell the forward contract to protect the value of the
bond against rising interest rates during the holding period.
ii. Calculate the value of the forward contract for the investor at the maturity of the forward
contract. Show your calculations.
iii. Calculate the change in value of the combined portfolio (the underlying bond and the appro-
priate forward contract position) six months after contract initiation. Show your calculations.
Kapple tells VanHusen, “Your example does not address the credit risk that will exist at the expira-
tion date of the forward contract.”
B. Determine if credit risk exists for each of the following parties in VanHusen™s example:
i. Buyer of the forward contract
ii. Seller of the forward contract
Justify each of your responses with one reason.
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42 Web Problems

4. CFA Examination Level II (2004)
Sandra Kapple asks Maria VanHusen about using futures contracts to protect the value of the Star
Hospital Pension Plan™s bond portfolio if interest rates rises as Kapple expects.
VanHusen states:
• “Selling a bond futures contract will generate positive cash flow in a rising interest rate environ-
ment prior to the maturity of the futures contract.”
• “The cost of carry causes bond futures contracts to trade for a higher price than the spot price of
the underlying bond prior to the maturity of the futures contract.”
Indicate whether each of VanHusen™s two statement is accurate or inaccurate. Support each of your
responses with one reason.
5. There are currency futures contracts that allow for the exchange of Mexican pesos and U.S. dollars,
while other contracts allow for the exchange of Swiss francs and U.S. dollars. If I am an investor
based in Zurich, explain how I could use these contracts to convert the payoff to a peso-denominated
asset back into francs in two months.
6. It is March 1, and you are a new derivatives trader making a market in forward contracts in Com-
modity W. One month ago (February 1), you began your operations with the following transactions,
which are described from your perspective:
• With Client A: (1) Short a June 1 forward for 10,000 units at a contract price of $25.50/unit.
(2) Long a September 1 forward for 15,000 units at a contract price of $26.20/unit.
• With Client B: (3) Short a September 1 forward for 25,000 units at a contract price of $26.40/unit.
Your current (i.e., March 1) contract price quotes are as follows:

Contract Bid Ask

June $24.95 $25.15
September 25.65 25.85

The appropriate discount is 9 percent per annum.
a. If Client A just called you wanting to unwind both of its contracts, calculate a fair cash amount
that can be used in settlement today. Would you pay or receive this amount?
b. If these contracts had been exchange-traded futures contracts instead of OTC forward contracts,
how would this settlement amount need to be adjusted (assuming the same March 1 contract
c. Calculate the dollar amount you would lose if Client B called you to default its contractual obliga-
tion. (Hint: Compute this amount in the same manner you calculated the net settlement in Part a.)
d. At the time you negotiated the three original agreements (i.e., February 1) did you have any price
exposure on the September contracts? If so, what type of future price movements would be harm-
ful to your net profit on the expiration date?
7. The corporate treasurer of XYZ Corp. manages the firm™s pension fund. On February 15, 1993, the
treasurer is informed that the pension fund will be required to sell its $100 million (face value) Trea-
sury bond portfolio on August 15, 1993, because of a pending change in the structure of the plan.
The portfolio consists entirely of a single bond issue with a maturity date of August 2019. The
bond pays coupons of 71„4 percent and is currently priced at 97“12. This corresponds to a yield of
7.479 percent. These T-bonds were originally purchased at par, so the current price reflects a modest
capital loss. The treasurer is concerned that further weakness in the dollar could raise market rates
and exacerbate this loss before the August sale date.
Your task is to construct a hedge using T-bond futures to offset, or at least reduce, the risk expo-
sure. Assume an August 1993 futures contract exists with the quoted price of 101“04 and a refer-
ence yield to maturity of 7.887 percent (based on an 8 percent coupon and 20 years to maturity). To
complete the task, construct a numerical example to show the optimal number of contracts neces-
sary to provide the desired price protection.
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Chapter 21

a. Assuming that interest rates do not change between February and August 1993, what will be the
value of the T-bond portfolio? Briefly explain why this differs from the current value of $97.375
b. As of August 1993, calculate the respective durations of the bond issue in the portfolio and the
bond underlying the futures contract. Using the current yields to maturity, translate these into
modified duration form. (Note: In your computation, recall that T-bonds pay semiannual interest.)
c. Assuming that the yield beta ( bt ) between the instruments is equal to one, calculate the number
of futures contracts required to form the optimal hedge. In this calculation, keep in mind that the
face value of the bond underlying the futures contract is $100,000
8. CFA Examination Level III


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