Chapter Twelve
Futures Contracts and Portfolio Management
Answers to Problems and Questions
1. Immunization refers to the situation in which the effects of interest
rate risk and reinvestment rate risk largely cancel.
2. Bullet immunization seeks to ensure that a predetermined sum of
money is available at a specific time in the future. Bank
immunization seeks to ensure that net worth does not decline due to
changing interest rates. This latter type requires consideration of
both the interest sensitive assets and the interest sensitive liabilities
on the balance sheet.
3. If interest rates rise, bond prices will fall, but coupons received can
be reinvested at a higher rate than before the interest rate change.
The converse is true if rates fall. Interest rate risk and reinvestment
rate risk generally affect a portfolio in opposite directions. Under
bullet immunization, the effects of the two types of risk cancel.
4. The funds gap is the difference between a firm’s rate sensitive
assets and its rate sensitive liabilities. The wider the funds gap, the
greater the potential that changing interest rates might hurt an
institution.
5. Banks normally are much more able to make changes to the left
side of their balance sheet.
6. Bonds, mortgages, and marketable certificates of deposit are rate
sensitive; savings bonds, passbook accounts, and checking accounts
are not.
7. Sell rate sensitive assets and hold cash. Use cash to buy rate
sensitive assets. Sell long term bonds and buy short term bonds.
Sell low coupon securities and buy higher coupon securities.
8. For technical reasons, the published conversion factors only make
bonds exactly equivalent when the long-term bond rate is exactly
6%. If the rate deviates from this value, the conversion factors
introduce modest error.
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Chapter Twelve. Futures Contracts and Portfolio Management
9. The basis point value is the change in the price of a bond for a one
basis point change in the yield to maturity of the bond. The basis
point value concept facilitates comparing the dollar impact of
portfolio adjustments.
10. Immunization often reduces the interest rate risk of the portfolio
and usually reduces the portfolio yield. It may be costly in terms of
trading fees. Also, it may require additional managerial time to
maintain the immunization.
11. Immunization is instantaneous only because bond durations change
as time passes and as interest rates change. Duration is a first
derivative statistic, and its predications may deviate from reality as
underlying conditions change.
12. Treasury bonds have varying characteristics, and, as a consequence,
are not fungible. The conversion factors seek to make the delivery
process easier by making numerous T-bonds economically feasible
to use for delivery.
Year
1
2
3
4
5
6
Total
Interest
13.
10%
1
8,800
8%
8%
8%
8%
2
3
4
5
9,504 10,264.30 11,085.47 11,972.30
8,800
9,504 10,264.30 11,085.47
8,800
9,504 10,264.30
8,800
9,504
8,800
8,800 18,304.00 28,568.30 39,653.77 51,260.07
8%
6
12,930.09
11,972.30
11,085.47
10,264.30
9,504
8,800
64,556.16
Bond Value
101,451.96
Total $166,008.12
14.
Security
XYZ
DEF
ALQ
LLG
FFQ
T-bills
44
Value
Duration
0
$63,728
40,376
48,810
69,972
50,860
5.20
7.55
5.79
8.38
1.88
0.25
Weighted
Duration
0
1.76
0.85
1.49
0.48
0.05
 4.63
Chapter Twelve. Futures Contracts and Portfolio Management
15. Individual response
16. Funds gap = rate sensitive assets minus rate sensitive liabilities
= $45 million - $22 million = $23 million
17. Hedge ratio = 0.9150 x
# contracts =
$10 million
x 1 .82  182 contracts
$100,000
18. Hedge ratio = 0.8450 x
# contracts =
100 x 14.6
 1.82
98 x 7.5
100 x 8.6
 0.77
99 x 9.5
$130 million
x 0.77  1,001 contracts
$100,000
19. Using the CONVFACT file, 1.1929
20. Using the CONVFACT file, 1.3085
21. BPV 
6.44 x $56 million x 0.0001
 $34,560.01
1  .087
2
22. The “portfolio value” for a futures contract is $100,000:
BPV 
5.5 x $100,000 x 0.0001
 $65.54
(1  .066 ) x 0.8124
2
45