CHAPTER 21
PROBLEM 3: JUNE KLEIN, CFA, MANGES A $ 100 MILLION (MARKET VALUE) U.S. GOVERNMENT
BOND PORTFOLIO FOR AND INSTITUTION. She anticipates a small parallel shift in the yield curve
and wants to fully hedge the portfolio against any such change.
PORTFOLIO AND TREASURY BOND FUTURES CONTRACT CHARACTERISTICS
CONVERSION
FACTOR FOR
PORTFOLIO
VALUE/
MODIFIED
BASIC POINT
CHEAPEST TO
SECURITY
DURATION
VALUE
DELIVER BOND
PORTFOLIO
10 YEARS
FUTURE
CONTRACT
$ 100,000.00
NOT APPLICABLE
PRICE
$
1000,000.00
U.S. TREA BOND
94-05
8 YEARS
$ 75.32
1
(a) DISCUSS THE TWO REASONS FOR USING FUTURES RATHER THAN SELLING BONDS TO HEDGE
A BOND PORTFOLIO. NO CALCULATIONS REQURED.
(e) Described a zero-duration hedging strategy using only the government bond portfolio and
options on U.S. Treasury bond futures contracts. No calculations required.
PROBLEM 4: A BOND SPECULATOR CURRENTLY HAS POSITIONS IN TWO SEPARATE CORPORATE
BOND PORTFOLIOS: A LONG HOLDING NIN PORTFOLIO 1 AND A SHOR HOLDING IN PORTFOLIO
2. ALL THE BONDS HAVE THE SAME CREDT QUALITY. OTHER RELEVANT INFORMATION ON
THESE POSITIONS INCLUDES.
MARKET
COUPON
COMPOUNDING
RATE
FREQUENCY
YIELD TO
PORTFOLIO
MATUR
BOND
VALUE (MIL)
MATURITY
1
7.31%
A
$ 6.0
0.0%
Annual
3yrs
B
4-0
0-0
Annual
14yrs
C
11.5
4.6
Annual
9yrs
7-31
2
7.31
Treasury bond futures (based on $ 100,000 face value of 20-year T-bonds having an 8 percent
semi-annual coupon) with a maturity exactly six months from now are currently priced at 109-24
with a corresponding yield to maturity of 7.082 percent. The “yield betas” between the future
contract and Bond A, B, and C are 1.13, 1.03, and 1.01, respectively. Finally the modified
duration for the T-bond underlying the future contract is 10.355 years.
(a) Calculate the modified duration (expressed in years) for each of the two bond portfolios.
What will be the approximate percentage change in the value of each f all yields increase by 60
basis points on an annual basis.
(b) Assuming the bond speculator wants to hedge her net bond position, what is the optimal
number of futures contracts that must be bought or sold? Start by calculating the optimal hedge
ratio between the futures contract and the two bond portfolios separately and then combine
them.
PROBLEM 6: As a relationship officer for a money-center commercial bank, one of your
corporate accounts has just approached you about a one-year loan for $ 1,000,000. The
customer would pay a quarterly interest expense based on the prevailing level of LIBOR at the
beginning of each three-month period. As is the bank’s convention on all such loans, the
amount of the interest payment would then be paid at the end of the quarterly cycle when the
new rate for the next cycle is determined. You observe the following LIBOR yield curve in the
cash market.
90-days LIBOR
4.60%
180-day LIBOR
4.75
270-day LIBOR
5.00
360-day LIBOR
5.30
(a) If 90-day LIBOR rises to the levels “predicted” by the implied forward rates, what will the
dollar level of the bank’s interest receipt be at the end of each quarter during the one-year loan
period.
(b) Assuming the yield interred from the Eurodollar futures contract prices for the next three
settlement periods are equal to the implied forward rates, calculate the annuity value that would
leave the bank indifferent between making the floating-rate loan and hedging it in the futures
market and making a one-year fixed-rate loan. Express this annuity value in both dollar and
annual (360-day) percentage terms.
PROBLEM 9: Alex Andrew, who manages a $ 95 million large-capitalization U.S. equity portfolio,
currently forecasts that equity market will decline soon. Andrew prefers to avoid the transaction
coast of making sales but wants to hedge $ 15 million of the portfolio’s current value using S&P
500 futures.
Because Andrew realizes that his portfolio will not track the S&P 500 Index exactly, he performs a
regression analysis on his actual portfolio returns versus the S&P futures return over the past
year. The regression analysis indicates a risk-minimizing beta of 0.88 with an R2 of 0.92
FUTURES CONTRACT DATA
S&P 500 futures price
1,000
S&P 500 index
999
S&P 500 index multiplier
250
(a) Calculate the number of futures contracts required to hedge $ 15 million of Andrew’s
portfolio, using the date shown. State whether the hedge is long or short. Show all calculations.
(b) Identify two alternative methods (other than selling securities from the portfolio or using
futures) that replicate the strategy in part a. Contract each of these methods with the futures
strategy.
PROBLEM 10: The treasurer of a middle market, import-export company has approached you
for advice on how to best invest some of the firm’s short-term cash balances. The company,
which had been a client of the bank that employs you for a few years, has $ 250,000 that it is
able to commit for a one-year holding period. The treasurer is currently considering two
alternatives: (1) invest all the funds in a one-year U.S. Treasury bill offering a bond equivalent
yield of 4.25 percent, and (2) invest all the funds in a Swiss government security over the same
horizon, locking in the spot and forward currency exchanges in the FX market. A quick call to the
bank’s FX desk gives you the following two-way currency exchange quotes.
SWISS FRANCS PER
U.S. DOLLARS PER
U.S. DOLLAR
SWISS FRANC
Spot
1.5035
0.6651
1-year CHF futures
------
0.6586
(CHF)
(a) Calculate the one-year bond equivalent yield for the Swiss government security that would
support the interest rate parity condition.
(b) Describe the transactions that arbitrageur could use to take advantage of this apparent
mispricing, and calculate what the profit would be for a $ 250,000 transaction.
PROBLEM 11: Bonita Singer is a hedge fund manager specializing in futures arbitrage involving
stock index contracts. She is investigating potential trading opportunities in the S&P 500 stock
index futures to see if there are any inefficiencies that she can exploit. She knows that the S&P
500 stock index is currently trading at 1.100.
(a) Assume that the Treasury yield curve is flat at 3.2 percent and annualized dividend yield on
the S&P index is 1.8 percent. Using the cost of carry model, demonstrate what the theoretical
contract price should be for a futures position expiring six months from now.
(b) Assuming that total round-trip arbitrage transaction costs are #20 for the set trades
described in part B, calculate the upper and lower bounds for the theoretical contract price such
that arbitrage trading would not be profitable.
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