Capital Markets
Case Study: Arbitrage in the Government Bond Market?
Directions:
The case write-up should be no more than five pages, double-spaced and answer the following four
questions. This will be a two-draft assignment with peer review. Each student will complete an initial
draft of their assignment, review another students initial draft, and then complete a final draft based on
your peer’s comments.
Case Questions:
1) Create the two synthetic bonds described in the case. How should the price of these synthetics
relate to the callable bonds? Why? On January 7, 1991, how much would it cost to create the
synthetic using the ‘05s? The ‘00s?
2) On January 7, 1991, how could Thompson exploit this apparent anomaly for investors who own
the 8.25 May ’00-05? What can investors not owning the callable bond do to profit?
3) What might underlie the odd relative prices of the bonds Thompson is considering?
4) Why should the treasury issue callable debt? When should they exercise their right to call or
redeem the bonds? Why would corporations issue callable debt? Why should investors want to
buy callable debt?

Arbitrage in the Government Bond Market?

1

On January 7, 1991, Samantha Thompson, who analyzed and traded government bonds for
the firm of Mercer and Associates, noticed what she thought were major discrepancies in the prices of
a number of long-maturity U.S. Treasury bonds. These apparent discrepancies might permit Mercer
and its clients to substitute superior bonds for existing holdings, and pocket a positive pricing
difference as well. Her firm could also capture arbitrage profits by taking offsetting positions to the
extent that they were able to establish short positions in the overpriced securities.
What made this alleged arbitrage opportunity so unusual was that it existed in the U.S.
government bond market, the largest, most liquid, and closely watched fixed-income market. As of
December 1990, the U.S. Treasury had almost $2.2 trillion of Treasury bills, notes, and bonds
outstanding.2 To put this market’s magnitude in perspective, Treasury obligations outstanding at the
end of 1990 were 1.8 times as large as total U.S. corporate bonds outstanding, 3.2 times as large as
total bank loans outstanding, and 3.0 times as large as total municipal bonds outstanding.3
Throughout the 1980s and early 1990s, raising Treasury debt through the capital markets served as
the mechanism for funding the large budget deficits incurred by the federal government.
The Treasury market was significant not only for its size, but also for its liquidity. On an
average day, approximately 5% of all government securities changed hands.4 In comparison,
turnover in the New York Stock Exchange in 1990 was 46% for the year, or approximately .2% per
day.5 The closely-watched Treasury market was an unlikely place to find arbitrage opportunities.

1This case study describes the situation analyzed in the working paper, “Negative Put and Call Prices Implicit in

Callable Treasury Bonds,” by Michael E. Edleson, David Fehr and Scott P. Mason. This topic is also treated by
Francis A. Longstaff in “Are Negative Option Prices Possible? The Callable U.S. Treasury Bond Puzzle” Journal
of Business 65 (October 1992), pp. 571-592.
2A Treasury bill has an original maturity (maturity at issue) of less than or equal to 1 year, Treasury notes have
maturities of 2-10 years, and Treasury bonds have maturities of greater than 10 years. As of December 1990
there were $527 billion, $1,265 billion, and $388 billion of bills, notes, and bonds outstanding, respectively
(Economic Report of the President, February 1992, p. 394).
3Federal Reserve Bulletin, September 1991, p. A-43. Only the $3.85 trillion outstanding balance of mortgages (all
classes) account for more funds than Treasury securities.
4Joint Report on the Government Securities Markets, January 1992, p. B-28.
5New York Stock Exchange Fact Book, 1991, p. 77.
Professors Michael E. Edleson and Peter Tufano wrote this case from public sources as the basis for class discussion rather
than to illustrate either effective or ineffective handling of an administrative situation. The case, while set in a hypothetical
organization, uses actual trade data and is patterned after a real situation.
Copyright © 1993 by the President and Fellows of Harvard College. To order copies or request permission to
reproduce materials, call 1-800-545-7685 FREE or write Harvard Business School Publishing, Boston, MA 02163. No
part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in
any form or by any means—electronic, mechanical, photocopying, recording, or otherwise—without the
permission of Harvard Business School.

1
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For the exclusive use of C. Johanes, 2015.
293-093

Arbitrage in the Government Bond Market?

New Treasury securities were brought to market regularly, a wide group of dealers actively traded
them, and prices were widely disseminated.
Of the $388 billion of Treasury bonds outstanding at the beginning of 1991, 26 issues with
aggregate face value of $98 billion were callable. Callable Treasury bonds, issued during the 19731984 period, typically had original maturities of 30 years and coupon rates ranging from 7% to 14%.6
What differentiated callable Treasuries from noncallable Treasury bonds was the call feature that the
government retained. The Treasury retained the right, but not the obligation, to redeem the callable
Treasuries at par (100) on any semiannual interest payment date within five years of maturity,
provided that it gave investors four months’ notice. For example, the government could redeem the
7% callable Treasury bond maturing on May 15, 1998, at face value on any of the ten semiannual
interest payment dates beginning in May 15, 1993.7 If the Treasury chose to redeem the bonds on May
15, 1993 (the first possible call date), it would need to give notice to investors no later than January 15,
1993. Exhibit 1 shows the Treasury’s call policy over the past half century.

3

On January 7, 1991, Samantha Thompson’s attention was caught by the pricing of the 8 May
00-05, or the 8.25% coupon Treasury bond8 maturing May 15, 2005, first callable on May 15, 2000,
whose price appeared out of line relative to other bonds in the market. By combining noncallable
bonds maturing in 2005 with zero coupon Treasuries (or STRIPS)9 maturing in 2005, Ms. Thompson
could create a synthetic bond with semiannual interest payments of $4.125 per $100 face value and
whose final payment of $100 at maturity exactly matched those of the callable bond—if the callable
bond was not called. Because this synthetic bond did not surrender a redemption right to the
government, it should be worth more to investors (i.e., have a higher price or a lower yield) than the
callable bond of the same maturity.
Alternatively, Ms. Thompson could construct another synthetic noncallable Treasury bond by
combining noncallable bonds maturing in 2000 with STRIPS maturing in 2000; this synthetic should
also be worth more than the callable 00-05. This synthetic matched the callable bond—if it was called at
the first possible date. It too should be worth more than the callable bond. Based on the prices on
January 7, 1991, these simple pricing relations seemed to be violated. Current prices for that day are
given in Exhibit 2; a time series of price data for the callable bond is shown in Exhibit 3.
If Ms. Thompson’s analysis was correct, it suggested a way for clients who owned the callable
00-05s to profit. Clients who paid taxes had to concern themselves with the tax ramifications of these
trades (see Exhibit 4), but clients who did not pay taxes, such as pension funds, could immediately
capitalize on the price discrepancy.
Investors who did not own the callable 00-05s could also profit, to the extent that they could
establish short positions in the relatively overpriced security and long positions in the relatively
underpriced security. “Selling short” entails borrowing a security from another party, selling it today,
and promising to redeliver the security to the lender at some future time. Exhibit 5 gives additional
details on short selling in the bond market and the practice of reverse repurchase agreements.
The apparent relative mispricing of the bonds had been rather persistent over the past few
weeks. Ms. Thompson wondered how she could best take advantage of this pricing situation for the
benefit of her various investment clients. Also, she knew that Mercer was active in the repo markets

6Longstaff, p. 573.
7In the price listing, this callable Treasury would show up as 7 May 93-98. The first year is the call year, and the

second is the final maturity if the bond is not called.
8There is $4.2 billion (in face value) worth of this particular Treasury bond issue outstanding.
9STRIPS (Separate Trading of Registered Interest and Principal of Securities) are effectively zero coupon bonds

that are direct obligations of the federal government.
2
This document is authorized for use only by Chefanya Johanes in Capital Markets – fall 2015 taught by Joshua D Spizman, Loyola Marymount University from October 2015 to March 2016.

For the exclusive use of C. Johanes, 2015.
Arbitrage in the Government Bond Market?

293-093

and occasionally participated in bond arbitrage on its own account. As she analyzed the numbers, she
weighed the risks and rewards presented by this opportunity.

3
This document is authorized for use only by Chefanya Johanes in Capital Markets – fall 2015 taught by Joshua D Spizman, Loyola Marymount University from October 2015 to March 2016.

For the exclusive use of C. Johanes, 2015.
293-093

Arbitrage in the Government Bond Market?

Exhibit 1

Summary of Postwar U.S. Treasury Call Policy, 1946-1991

Callable Bond
3.000 June 1946-48
3.125 June 1946-49
2.000 Mar. 1948-50
2.000 Dec. 1948-50
2.750 Mar. 1948-51
2.000 June 1949-51
2.000 Sep. 1949-51
2.000 Dec. 1949-51
2.000 Mar. 1950-52
2.000 Sep. 1950-52
2.500 Sep. 1950-52
4.250 Oct. 1947-52
3.125 Dec. 1949-52
2.000 Sep. 1951-53
2.000 Sep. 1951-53
2.000 Sep. 1951-53
2.000 Sep. 1951-53
2.500 Dec. 1949-53
2.250 Dec. 1951-53
2.750 June 1951-54
2.000 Dec. 1952-54
2.250 June 1952-55
2.250 June 1952-53
2.250 June 1952-53
3.000 Sep. 1951-55
2.000 June 1953-55
2.000 Dec. 1951-55
2.000 Dec. 1951-55
2.000 Dec. 1951-55
3.750 Mar. 1946-56
2.250 June 1954-56
2.375 Mar. 1957-59
2.250 Sep. 1956-59
2.750 Sep. 1956-59
2.875 Mar. 1955-60
2.750 June 1958-63
2.750 Dec. 1960-65
2.750 Dec. 1960-65
2.750 Dec. 1960-65
2.750 Dec. 1960-65
2.750 Dec. 1960-65
7.500 Aug. 1988-93

Summary of Postwar U.S. Treasury Call Policy
Optimal Call Date
Called
Price
June 1946
June 1946
Mar. 1948
Dec. 1948
Mar. 1948
June 1949
Sep. 1949
Dec. 1949
Mar. 1950
Sep. 1950
Sep. 1950
Oct. 1947
Dec. 1949
Sep. 1951
Mar. 1952
Sep. 1952
Mar. 1953
Dec. 1949
Dec. 1951
June 1951
June 1954
June 1952
Dec. 1952
June 1954
Sep. 1951
June 1953
Dec. 1951
June 1954
Dec. 1954
Mar. 1946
June 1954
Sep. 1958
Sep. 1958
Sep. 1956
Mar. 1955
June 1958
Dec. 1960
June 1961
Dec. 1961
June 1962
Dec. 1962
Apr. 1991

Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
Yes
Yes
Yes
No
No
No
Yes
Yes
Yes
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
Yes
No

101.000
101.031
100.343
100.434
100.688
100.313
100.297
100.434
100.359
100.359
100.625
100.281
100.922
100.016
100.094
100.188
100.031
100.688
100.719
100.594
100.281
100.156
100.188
100.531
100.063
100.188
100.031
100.188
100.656
101.125
100.594
100.406
100.375
100.406
100.844
100.375
100.156
100.438
100.531
100.625
100.313
100.625

Source:

Francis A. Longstaff, “Are Negative Option Prices Possible? The Callable U.S.
Treasury-Bond Puzzle,” Journal of Business 65 (October 1992), p. 583.

Note:

This exhibit lists each of the Treasury bonds that should have been called during the
1946-91 period. The first part of “Callable Bond” (e.g., 3.000) indicates the coupon
rate (e.g., 3%). The first year is the call year, and the second is the final maturity if the
bond is not called. “Optimal Call Date” indicates the month in which the Treasury had
the opportunity to make a call for a bond that was trading at or above par at the
beginning of the call notice month (four months prior to the actual date on which the
bond could be called). “Called” indicates whether the Treasury made the call. “Price”
is the bid price of the security as reported in the U.S. Treasury Bulletin at the
beginning of the call notice month.

4
This document is authorized for use only by Chefanya Johanes in Capital Markets – fall 2015 taught by Joshua D Spizman, Loyola Marymount University from October 2015 to March 2016.

For the exclusive use of C. Johanes, 2015.
Arbitrage in the Government Bond Market?

Exhibit 2

293-093

Capital Markets Data at January 7, 1991
Ask

Bid

101:08
129:29
104:16

101:04
129:23
104:12

46:21
30:10

46:08
29:29

Treasury Bonds

3

8 May 00-05
12 May 05
8 May 00

f

Treasury STRIPS
May 00
May 05
Note:

By the conventions of the bond market, colons in bid and ask
quotes represent 32nds; 101:08 means 101-8/32 or 101.25.
For both the bonds and STRIPS, these prices reflect a
purchase of $100 principal or par value of these securities.

5
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For the exclusive use of C. Johanes, 2015.
293-093

Exhibit 3

Arbitrage in the Government Bond Market?

Price of the 83 May 00-05 Treasury Bond

6
This document is authorized for use only by Chefanya Johanes in Capital Markets – fall 2015 taught by Joshua D Spizman, Loyola Marymount University from October 2015 to March 2016.

For the exclusive use of C. Johanes, 2015.
Arbitrage in the Government Bond Market?

Exhibit 4

293-093

Tax Considerations in Buying and Selling U.S. Treasury Bonds and Notes

The taxation of Treasury bonds and notes reflects the fact that holders of these securities earn
taxable income (and possibly losses) through three mechanisms: explicit payments of interest, implicit
payments of interest, and capital gains and losses. Bond investors subject to federal taxation need to
consider all of these tax ramifications. The following general principles characterize the tax treatment
of Treasury bonds and notes:
•

Explicit interest payments are treated as ordinary income in the year in which
they are made. Interest on Treasury securities is exempt from state and local
taxes.

•

If you pay a premium (a price over par) to buy a bond, this premium can be
deducted (amortized) over time to offset a portion of taxable interest. In effect,
investors are able to accelerate their recognition of these particular taxable losses
and offset them against interest income.

•

Changes in the price of the bond from purchase to sale are generally treated as
capital gains or losses, and recognized when the bond is sold, with the exception
of the following point.

•

Changes in the price of a security because of implicit payments of interest (which
primarily affect zero-coupon bonds or STRIPS) are taxable income each year,
even though no cash interest is paid and even if the investor does not sell the
bond.

The specific rules on the tax treatment of Treasury securities can be quite complex and change
over time. The following examples illustrate typical applications of current tax codes:
1. Investor A buys a 7% coupon bond for $90. The semi-annual interest payments of
$3.50 are taxable interest in the year received. Later, the bond is worth $95. If A
a
sells the bond at that time, she realizes a $5 capital gain, taxable in the year of
sale. If A holds the bond to maturity, in that tax year she will recognize a $10
taxable capital gain ($100 par value received less $90 paid).
2. Investor B pays $46.32 for a 10-year STRIP (zero-coupon bond) when it is first
offered. Over the coming 10 years, B receives no interest payments, and he holds
the STRIP to maturity to receive $100, a gain of $53.68 over the price paid. The
increase in value from $46.32 to $100 is not treated as a capital gain at maturity.
Rather, this bond, selling at an original issue discount (OID), is treated as having
made taxable implicit interest payments each year. Because $46.32 grows to $100
in 10 years at an 8% effective annual rate (constant yield), the bond is treated as if
it pays 8% interest per year. In investor B’s case, he will report OID interest in the
first year of $3.71, or $46.32 H 8%. If instead of holding the STRIP to maturity, B
sells it after one year for $51.32 (a $5 profit), $3.71 would be reported as interest,
and the remainder, $1.29, would be taxable as a capital gain.

7
This document is authorized for use only by Chefanya Johanes in Capital Markets – fall 2015 taught by Joshua D Spizman, Loyola Marymount University from October 2015 to March 2016.

For the exclusive use of C. Johanes, 2015.
293-093

Exhibit 4

Arbitrage in the Government Bond Market?

Tax Considerations in Buying and Selling U.S. Treasury Bonds and Notes (Continued)
3. Investor C pays $116 for a seasoned 12% coupon bond which delivers eight
semiannual payments of $6 and a final principal payment of $100. The $16
purchase price premium over par can be amortized over the 4 years to reduce net
interest that is taxable. If the bond was issued before September 27, 1985, C
would take a straight-line $4/year deduction, effectively reporting only 8%
interest.b By taking this deduction, C would reduce the tax basis of the bond
from $116 to $100 over the four years; thus there would be no capital gain or loss
at maturity.

a. Complex rules affect the capital status on such “market discount” bonds if they were issued after
July 18, 1984; in such cases, some of the gain will be reported as interest income instead of capital
gain.
b. For bonds issued on or after that date, the constant yield method (IRS Publication 1212) is used.

8
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For the exclusive use of C. Johanes, 2015.
Arbitrage in the Government Bond Market?

Exhibit 5

293-093

Establishing a Short Position through Short Selling and Reverse Repurchase Agreements
in the Bond Market

An investor with a “long position” in a security owns the security, and this position can be set
up by purchasing the security. Investors with long positions profit if the security’s price rises. An
investor with a “short position” in a security owes the security, and this position can be set up by
selling the security. Investors with short positions profit if the security’s price falls. It is quite
common for investors to sell bonds they do not own, either through short sales or reverse repurchase
agreements, thus creating a net short position.
SHORT SALES

3

Suppose the 8 of May 00-05 are “trading rich” (overpriced). A trader desires to sell the
bond, but does not own it. To set up a short position, the trader locates an owner of the bond who is
willing to lend it out. The trader borrows the bond and then sells it (a short sale). The borrowed
bond will be collateralized by either cash or securities; also, a fee is paid to the lender for the
borrowing privilege. The borrower must pay the lender any interest payments made while the
security was borrowed. Finally, the borrower must return the borrowed bond to the lender at some
time in the future, or upon the demand of the lender. At that time, having already sold that bond, the
borrower must either enter into another borrowing arrangement or purchase the bond in the open
market to replace the borrowed bond.
REVERSE REPURCHASE AGREEMENTS
In the Treasuries market, bond borrowing is less common than entering into reverse
repurchase agreements (“reverse repo”) for establishing a short position. If you own a security, you
could enter into a sale-and-repurchase-agreement (“repo”) by simultaneously selling the security and
agreeing to repurchase it at a later date, effectively obtaining a collateralized short-term loan. Viewed
from the other side of the transaction, this contract, known as a reverse repurchase agreement,
commits you to buy a security now and agree to resell it at a pre-set price in the future. The reverse
repo is similar to borrowing a security and providing cash collateral for a fixed term. You receive
interest on the cash collateral and pay an interest fee for the privilege of borrowing the security; the
resulting net interest rate is called the “repo rate.” Typical time frames for repos are one day
(overnight repos), term repos of a few days to a few months, or open repos that roll over daily
automatically unless terminated by either party. For example, investor D enters into a one-week, $10
million, 5.27% reverse repo with a dealer for the 8 bond of May 00-05. He has made a $10 million
short-term loan10 to the dealer; and in turn he gets possession of the bond as collateral. In a week,
investor D will get his money back (with $10,247 interest) but must return the bond.

3

Combining a reverse repo with a sale of the security effectively results in a short sale. In the
example above, suppose investor D enters into the reverse repo described and receives the 8 May
00-05 bond as collateral. At the same time, D sells the bond in the market (receiving $10 million). In
substance, D has established a short position in the bond, in that D profits if the price of the bond
falls. To see this, recognize that at the outset, D paid $10 million, but simultaneously received the
same amount for selling the bond. However, D is obligated to resell the bond to its counterparty in a
week for $10,010,247 (the repo amount plus interest). If the bond price decreases, D purchases the
bond in the market for less than $10,010,247, and delivers it at maturity of the reverse repo for a
profit.a

3

aPerhaps you could have received 5.87% (“market repo rate”) on your money; why take 60 basis points less? If

the 83 May 00-05s are in generally high demand (e.g., to deliver against short sales), traders will pay a fee, or
accept below-market rates, to gain possession of the “special” security. In rare cases, repo rates can drop to
almost 0% for particular special securities.
9
This document is authorized for use only by Chefanya Johanes in Capital Markets – fall 2015 taught by Joshua D Spizman, Loyola Marymount University from October 2015 to March 2016.