Chapter Eleven
Fundamentals of Interest Rate Futures
Answers to Problems and Questions
1. Unlike shares in a particular common stock or bushels of inspected
soybeans, not all Treasury bonds are identical. Differences in coupon rate
and in maturity are material, because they influence the level of interest rate
risk associated with the bond. Bonds with high coupons are more desirable
than bonds with low coupons if everything else is held constant. High
coupons that last for a long time are particularly attractive. Conversions are
necessary to provide greater flexibility during the bond delivery process,
because there is only a limited quantity of bonds with the precise
characteristics described in the futures contract.
2. The bond equivalent yield allows more direct comparison among
investment alternatives. The two key adjustments made by this calculation
are the fact that there are 365 days in a year rather than 360, and the fact
that the actual investment required is the discounted price, not the face
value.
3. Money market funds are short term in nature. It would not be desirable to
hedge short term rates using a long term instrument.
4. A bond that is callable is not fungible with a non-callable bond. To
standardize the contract and ensure users know what they are dealing in, the
provision about call protection is needed.
5. An especially good example is a fund manager who will soon receive
money to invest in short-term money market securities and wants to lock in
the current rate.
6. Interest rate risk increases with the duration of the fixed income securities,
everything else being equal. If risk is greater, the hedgeable interest is
greater, too.
7. This ratio determines “how many bonds” must be delivered against a
futures contract. You want to deliver as few as possible, everything else
being equal.
8. Individual response.
39
Chapter Eleven. Fundamentals of Interest Rate Futures
9. No. If you hedge completely, you remove risk, and riskless positions will
only earn the riskless rate of interest. For this reason, a policy of
completely hedging 100% is not normally a good one.
10. Hedging, by definition, involves risk transfer. If you have already
transferred all the existing risk, additional hedging really becomes
speculation.
11. In your mind one bond may be preferable to another (as in the case of
determining the bond cheapest to deliver). If this is the case, from your
perspective the bonds differ in quality.
12. The timing option reflects the fact that the holder of a short position in Tbond futures can initiate the delivery process anytime during the delivery
month. The wild card option reflects the fact that the holder of a short
position may choose to initiate delivery up to six hours after the underlying
T-bonds stop trading.
13. The T-bill is quoted at 92.33. This reflects a discount of 100% - 92.33% =
7.67%. The price of the bill is then
$1,000,000 - x 360
x
 .0767
$1,000,000
91
Solving for x, the price of $1 million in T-bills is $980,612.
14. Buy @ 93.34. This indicates a yield of 6.66%.
90/360 x 0.0666 = .01665
$1 million/1.01665 = $983,622.68
Sell @ 93.40. This indicates rates have fallen to 6.60%.
90/360 x .0660 = .01650
$1 million/1.0165 = $983,767.83
There is a gain of $983,767.83 - $983,622.68 = $145.15 on each of four
contracts, for a total gain of $580.60.
40
Chapter Eleven. Fundamentals of Interest Rate Futures
15. a) discount amount = $10,000 - $9,800 = $200
discount amount = face value x (days/360) x ask discount
$200 = $10,000 x (88/360) x ask discount
ask discount = 8.18%
b) bond equivalent yield:
discount amount 365
$200 365
x

x
 8.46%
discount price
days $9,800 88
16. Because there is only one cash flow with a zero coupon bond, its duration
equals its maturity.
17. Using the CONVFACT excel file, we find the conversion factor for a 16
year, 7% bond is 1.1019.
Invoice price = (settlement price x conversion factor) + accrued interest
= (0.92 x $100,000 x 1.1019) + 0 = $104,680.50
18. 1.1926
19. 1.3555
20. The annual interest earned on $100,000 par of a 6.5% coupon bond is .065
x $100,000 = $6,500. Every six months the bond will pay half this
amount, or $3,250. Midway through an interest payment cycle the bond
will have accrued half this amount, or $1,625. The conversion factor on
this bond (found using the CONVFACT file) is 1.0632. The invoice price
is therefore
(0.92 x $100,000 x 1.0632) + $1,625 = $99,439.40
21. The bond price is irrelevant. The conversion factor is 1.4078.
22. Individual response. The appropriate action is to buy 4 or 5 T-bill futures
contracts now.
41
Chapter Eleven. Fundamentals of Interest Rate Futures
23. The annual interest earned on $100,000 par of a 9%% coupon bond is .09
x $100,000 = $9,000. Every six months the bond will pay half this
amount, or $4,500. Midway through an interest payment cycle the bond
will have accrued half this amount, or $2,250. The conversion factor on
this bond (found using the CONVFACT file) is 1.3467. The invoice price
is therefore
(0.92 x $100,000 x 1.3467) + $2,250 = $126,146.40
24. The TED spread is a trade involving T-bill futures and Eurodollar futures,
where one contract is long and the other short. Traders use this as a way to
take advantage of anticipated changes in the global risk premium between
short-term interest rates in the United States and in Europe.
25. One possibility would be increased tension in Europe, causing traders to
believe that interest rates in Europe are likely to rise relative to those in the
United States. Rising ED rates would cause Eurodollar futures to fall. To
take advantage of this, someone might sell ED futures and buy T-bill
futures.
26. The NOB spread, “notes over bonds,” is a way to take advantage of an
anticipated change in the slope of the yield curve. For instance, a trader
can sell the long end of the yield curve (selling T-bond futures) and buy
the middle portion (buying T-note futures) if he or she believes that long
term rates are going to fall more than intermediate term rates.
27. Individual response. The appropriate action is to buy 4 or 5 T-bill futures
contracts.
28. Like the NOB spread, the LED spread is appealing to someone who
anticipates a change in the slope of the Eurodollar yield curve or who
believes there is a discrepancy in the existing Eurodollar rates and those
implied in the forward rates.
29. The MOB spread, “municipals over bonds,” is a method for speculating on
changes in the spread of taxable securities over non-taxable municipal
securities. This spread periodically widens or narrows based on public
sentiment, changes in tax laws, and the general economy.
42