Understanding Treasury Futures

Understanding

Treasury Futures

NOVEMBER 2017

Nicholas Johnson

Economist

Research & Product Development

John Kerpel

Manager

Research & Product Development

Jonathan Kronstein

Senior Director

Research & Product Development

Understanding Treasury Futures

Table of Contents

Treasury Cash Market Basics

Coupon-Bearing Treasury Securities ...............................................................1

Price/Yield Relationship .........................................................................1

Quotation Practices ............................................................................2

Accrued Interest and Settlement Practices ..........................................................2

Treasury Auction Cycle .........................................................................3

The “Run” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

The Roll and Liquidity ...........................................................................4

Repo Financing ...............................................................................4

Treasury Cash & Futures Relationships

Treasury Futures Delivery Practices ...............................................................5

Conversion Factor Invoicing System ................................................................5

Cheapest-to-Deliver ............................................................................6

The Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Why Is One Issue CTD? .........................................................................8

Conversion Factor Eects ........................................................................8

Implied Repo Rate .............................................................................9

Basis Optionality ..............................................................................10

Hedging with Treasury Futures

Measuring Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Basis Point Value (BPV) ........................................................................11

Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

CF Weighted Hedge ...........................................................................12

BPV Weighted Hedge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Crossover Risks ..............................................................................14

Portfolio Hedging .............................................................................15

Bullets and Barbells ...........................................................................16

Comparing Returns of Cash to Futures & Repo

The Delivery Timetable for Treasury Futures ........................................................18

Treasury Futures Contracts Summary .............................................................19

December 2017 Ten-Year T-Note Futures Basis .....................................................20

Understanding Treasury Futures

Treasury Bond futures were introduced on the Chicago

Board of Trade in 1977. The Treasury futures product line

has been augmented over the years by the introduction of

Ultra 10-year, 10-year, 5-year, 2-year Treasury note and

Ultra Treasury bond futures.

This product line has experienced tremendous success

as the scale and global signicance of U.S. Treasury

investment has grown over the years. Today, these

products are utilized on an international basis by

institutional and individual investors for purposes of both

abating and assuming risk exposures.

This document is intended to provide an overview of the

fundamentals of trading U.S. Treasury bond and note

futures. We assume only a cursory knowledge of coupon-

bearing Treasury securities. Thus, we begin with a primer

on the operation of cash Treasury markets before moving

on to provide some detail regarding the features of the

U.S. Treasury futures contracts as well as a discussion of

risk management applications with U.S. Treasury futures.

Coupon-Bearing Treasury Securities

U.S. Treasury bonds and notes represent a loan to the

U.S. government. Bondholders are creditors rather than

equity- or share-holders. The U.S. government agrees to

repay the face or principal or par amount of the security

at maturity, plus coupon interest at semi-annual intervals.

Treasury securities are often considered “riskless”

investments given that the “full faith and credit” of the U.S.

government backs these securities.

The security buyer can either hold the bond or note until

maturity, at which time the face value becomes due; or,

the bond or note may be sold in the secondary markets

prior to maturity. In the latter case, the investor recovers

the market value of the bond or note, which may be more

or less than its face value, depending upon prevailing

yields. In the meantime, the investor receives semi-annual

coupon payments every six months.

1 U.S. Treasury Note and Bond Futures are listed for trading on and subject to the rules and

regulations of the Board of Trade of the City of Chicago, Inc. (CBOT). CBOT lists futures

on Treasury securities covering a broad set of maturities, including the benchmark 10-Year

Treasury Note futures. CME Group is the parent of four U.S. based futures exchanges that are

registered under the Commodity Exchange Act (“CEA”) with the CFTC as designated contract

markets (“DCMs”): Chicago Mercantile Exchange (“CME”), the Board of Trade of the City of

Chicago, Inc. (“CBOT”), New York Mercantile Exchange, Inc. and Commodity Exchange, Inc.

(collectively, the “CME Group Exchanges” or “Exchanges”).

Treasury Futures Avg Daily Volume

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

2-Year (TU) 5-Year (FV) 10-Year (TY)

T-Bond (US) Ultra T-Bond (UB) Ultra-10 (TN)

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

E.g., you purchase $1 million face value of the 2-1/4% note

maturing in August 2027. This security pays half its stated

coupon or 1-1/8% of par on each six-month anniversary of

its issue. Thus, you receive $22,500 (= 2-1/4% of $1 million)

annually, paid out in semi-annual installments of $11,250 in

February and August. Upon maturity in August 2027, the $1

million face value is re-paid and the note expires.

Price/Yield Relationship

A key factor governing the performance of bonds in the

market is the relationship of yield and price movement. In

general, as yields increase, bond prices will decline; as

yields decline, prices rise. In a rising rate environment,

bondholders will witness their principal value erode; in a

decline rate environment, the market value of their bonds

will increase.

IF Yields Rise  THEN Prices Fall 

IF Yields Fall  THEN Prices Rise 

This inverse relationship may be understood when one

looks at the marketplace as a true auction. Assume an

investor purchases a 10-year note with a 2% coupon when

yields are at 2%. Thus, the investor pays 100% of the face

or par value of the security. Subsequently, rates rise to

3%. The investor decides to sell the original note with the

2% yield, but no one will pay par as notes are now quoted

at 3%. Now he must sell the note at a discount to par in

order to move the note. I.e., rising rates are accompanied

by declining prices.

Falling rates produce the reverse situation. If rates fall to

1%, our investment yields more than market rates. Now

the seller can oer it at a premium to par. Thus, declining

rates are accompanied by rising prices. Should you hold

the note until maturity, you would receive the par or face

value. In the meantime, of course, one receives semi-

annual coupon payments.

Quotation Practices

Unlike money market instruments (including bills and

Eurodollars) that are quoted on a yield basis in the cash

market; coupon-bearing securities are frequently quoted in

percent of par to the nearest 1/32nd of 1% of par.

E.g., one may quote a bond or note at 97-18. This equates

to a value of 97% of par plus 18/32nds. The decimal

equivalent of this value is 97.5625. Thus, a one million-

dollar face value security might be priced at $975,625. If the

price moves by 1/32nd from 97-18 to 97-19, this equates to

a movement of $312.50 (per million-dollar face value).

But often, these securities, particularly those of shorter

maturities, are quoted in ner increments than 1/32nd. For

example, one may quote the security to the nearest 1/64th.

If the value of our bond or note in the example above were

to increase from 97-18/32nds by 1/64th, it may be quoted

at 97-18+. The trailing “+” may be interpreted as +1/64th.

Or, you may quote to the nearest 1/128th. If our note

were to increase from 97-18/32nds by 1/128th, it might be

quoted on a cash screen as 97-182. The trailing “2” may

be read as +2/8ths of 1/32nd; or, 1/128th. If the security

rallies from 97-18/32nds by 3/128ths, it may be quoted

as 97-186. The trailing “6” may be read as +6/8ths of

1/32nd or 3/128ths. Sometimes, quotation systems use

an alternate fractional reference. E.g., the value of 97-

182 might be displayed as 97-18¼. Or a value of 97-18+

might be displayed as 97-18½. A value of 97-186 might be

displayed as 97-18¾.

Futures quotation practices are similar but not entirely

identical. A quote of 97-182 is the same no matter whether

you are looking at a cash or a futures quote. It means 97%

of par plus 18/32nds plus 1/128th.

Quotation Practices

Cash Price Means

Decimal Equivalent

(% of Par)

Futures

Quote

97-18 97-18/32nds 97.5625000 97-18

97-182 or 97-18¼ 97-18/32nds +

1/128th

97. 5703125 97-182

97-18+ or 97-18½

97-18/32nds +

1/64th

97. 578125 0 97-185

97-186 or 97-18¾ 97-18/32nds +

3/128ths

97. 5 859375 97-187

But in the case of the cash markets, that trailing “2” means

2/8ths of 1/32nd = 1/128th. In the case of the futures

markets that trailing “2” represents the truncated value of

0.25 x 1/32nd or 1/128th. A quote of 97-18+ in the cash

markets is equivalent to 97-185 in the futures market. That

trailing “5” represents 0.5 x 1/32nd or 1/64th. A quote of

97-186 in the cash markets is equivalent to 97-187 in the

futures market. The trailing “7” represents the truncated

value of 0.75 x 1/32nd = 3/128ths.

The normal commercial “round-lot” in the cash markets is

$1 million face value. Anything less might be considered

an “odd-lot.” However, you can purchase Treasuries in

units as small as $1,000 face value. Of course, a dealer’s

inclination to quote competitive prices may dissipate as

size diminishes. Ultra Treasury bond, Treasury bond,

Ultra 10-year, 10-year and 5-year Treasury note futures,

however, are traded in units of $100,000 face value.

3-year and 2-year Treasury note futures are traded in units

of $200,000 face value.

Accrued Interest and Settlement Practices

In addition to paying the (negotiated) price of the coupon-

bearing security, the buyer also typically compensates

the seller for any interest accrued between the last semi-

annual coupon payment date and the settlement date of

the security.

E.g., it is October 10, 2017. You purchase $1 million face

value of the 2-1/4% Treasury security maturing in August 2027

(a ten-year note) for a price of 99-01 ($990,312.50) to yield

2.36%, for settlement on the next day, October 11, 2017.

In addition to the price of the security, you must further

compensate the seller for interest of $3,485.05 accrued

during the 57 days between the original issue date of August

15, 2017 and the settlement date of October 11, 2017.

Understanding Treasury Futures

This interest is calculated relative to the 57 days between

issue date of August 15, 2017 and the next coupon

payment date of February 15, 2018 or $3,485.05

[= (57/184) x ($22,500/2)]. The total purchase price

is $993,797.55.

Price of Note $990,312.50

Accrued Interest $3,485.05

Total $9 9 3 ,797.5 5

Typically, securities are transferred through the Fed wire

system from the bank account of the seller to that of the

buyer vs. cash payment. That transaction is concluded

on the settlement date which may be dierent from the

transaction date.

Unlike the futures market where trades are settled on the

same day they are transacted, it is customary to settle a

cash transaction on the business day subsequent to the

actual transaction. Thus, if you purchase the security on a

Thursday, you typically settle it on Friday. If purchased on

a Friday, settlement will generally be concluded on the

following Monday.

Sometimes, however, a “skip date” settlement is specied.

E.g., one may purchase a security on Monday for skip

date settlement on Wednesday. Or, “skip-skip date”

settlement on Thursday; “skip-skip-skip date” settlement

on the Friday, etc. Skip or forward date settlements may

be useful in order to match Treasury transaction payments

with one’s anticipated future cash ows at current market

prices. Theoretically, there is no eective limitation on the

number of days over which one may defer settlement.

Thus, these cash securities may eectively be traded as

forward contracts.

Treasury Auction Cycle

Treasury securities are auctioned on a regular basis by

the U.S. Treasury which accepts bids on a yield basis

from security dealers. A certain amount of each auction is

set aside, to be placed on a non-competitive basis at the

average yield lled.

Prior to the actual issuance of specic Treasuries,

they may be bought or sold on a “WI” or “When Issued”

basis. When traded on a WI basis, bids and oers are

quoted as a yield rather than as a price in anticipation of

the establishment of the coupon subsequent to the

original auction.

U.S. Treasury Auction Schedule

Fixed-Principal, Fixed-Coupon Notes and Bonds

Maturity Auctioned

Treasury

Notes

2-, 3-, 5- and 7-Year Monthly

10 -Year February, May, August &

November with re-openings in

other 8 months

Treasury

Bonds

30 -Year February, May, August &

November with re-openings in

other 8 months

Security dealers purchase these recently auctioned

securities and subsequently market them to their

customers including pension funds, insurance companies,

banks, corporations and retail investors. The most recently

issued securities of a particular maturity are referred to

as “on-the-run” securities. On-the-runs are typically the

most liquid and actively traded of Treasury securities and,

therefore, are often referenced as pricing benchmarks.

Less recently issued securities are known as “o-the-run”

securities and tend to be less liquid.

The Treasury currently issues 4-week, 13-week, 26-week

and 52-week bills; 2-year, 3-year, 5-year, 7-year and

10-year notes; 2-year Floating Rate Notes (FRNs); and,

30-year bonds on a regular schedule. In the past, the

Treasury had also issued securities with a 4-year and 20-

year maturity. Further, the Treasury may issue very short

term cash management bills along with Treasury Ination

Protected Securities or “TIPS.”

The “Run”

If you were to ask a cash dealer for a quotation of “the

run,” he would quote yields associated with the on-the-

run securities from the current on-the-run Treasury bills,

through notes, all the way to the 30-year bond, sometimes

referred to as the “long-bond” because it is the longest

maturity Treasury available.

Quoting ‘the Run’ (As of October 10, 2017)

Coupon Maturity Price Yield

2-Yr Note 1-3/8% 09/30/19 99-237 1.506%

3-Yr Note 1-3/8% 09/15/20 99-08+ 1.630%

5-Yr Note 1-7/8% 09/30/22 99-21+ 1.943%

7-Yr Note 2-1/8% 09/30/24 99-19+ 2.190%

10-Yr Note 2-1/4% 08/15/27 99-01 2.360%

30-Yr Bond 2-3/4% 08/15/47 97-122 2.881%

The most recently issued security of any tenor may be

referred to as the “new” security. Thus, the second most

recently issued security of a particular original tenor may

be referred to as the “old” security, the third most recently

issued security is the “old-old” security, the fourth most

recently issued security is the “triple old” security.

As of October 10, 2017, the most recently issued 10-year

note was identied as the 2-1/4% note maturing in August

2027; the old note was the 2-3/8% note of May 2027; the

old-old note was the 2-1/4% of February 2027; the triple

old note was the 2% of November 2026.

Beyond that, one is expected to identify the security of

interest by coupon and maturity. For example, the “2s of

‘26” refers to the note with a coupon of 2% maturing on

November 15, 2026. As of October 10, 2017, there were

not any “WI” or “when issued” 10-year notes.

10-Year Treasury Notes (As of October 10, 2017)

Coupon Maturity Price Yield

On-the-Run 2-1/4% 8/15/2027 99-01 2.36%

Old Note 2-3/8% 5/15/2027 100-05+ 2.35%

Old-Old 2-1/4% 2/15/2027 99-05+ 2.35%

Triple Old 2% 11/15/2026 97- 07+ 2.34%

1-1/2% 8/15/2026 93-14 2.32%

1-5/8% 5/15/2026 94-21+ 2.31%

1-5/8% 2/15/2026 94-29 2.30%

2-1/4% 11/15/2025 99-25 2.28%

2% 8/15/2025 98-03 2.26%

2-1/8% 5/15/2025 99-05+ 2.24%

2% 2/15/2025 98-14+ 2.23%

2-1/4% 11/15/2024 100-09+ 2.20%

2-3/8% 08/15/2024 101-07+ 2.18%

The Roll and Liquidity

Clearly, traders who frequently buy and sell are interested

in maintaining positions in the most liquid securities

possible. As such, they tend to prefer on-the-run (OTR) as

opposed to o-the-run securities.

It is intuitive that on-the-runs will oer superior liquidity

when one considers the “life-cycle” of Treasury securities.

Treasuries are auctioned, largely to broker-dealers, who

subsequently attempt to place the securities with their

customers. Often these securities are purchased by

investors who may hold the security until maturity. At some

point, securities are “put-away” in an investment portfolio

until their maturity. Or, they may become the subjects of

a strip transaction per the STRIPS (Separate Trading of

Registered Interest and Principal on Securities) program.

As these securities nd a home, supplies may become

scarce. As a result, bid/oer spreads may inate and the

security becomes somewhat illiquid. Liquidity is a valuable

commodity to many. Thus, you may notice that the price

of on-the-runs may be bid up, resulting in reduced yields,

relative to other similar maturity securities. This tends to be

most noticeable with respect to the 30-year bond.

Traders may be interested in conducting a “roll” transaction

where one sells the old security in favor of the new

security, in order to maintain a position in the on-the-run

and most liquid security. Thus, dealers will quote a bid/

oer spread in the roll, oering the opportunity to sell the

old note/buy the new note; or, buy the old note/sell the

new note, in a single transaction.

The “old note” in our table above was quoted at a yield

of 2.35% while the “new note” was seen at 2.36%. In this

case, the roll is quoted at approximately negative 1 basis

point (-0.01% = 2.35% - 2.36%).

Repo Financing

Leverage is a familiar concept to futures traders. Just as

one may margin a futures position and thereby eectively

extend one’s capital, the Treasury markets likewise permit

traders to utilize “repo” nancing agreements to leverage

Treasury holdings.

A repurchase agreement, repo or simply RP represents

a method by which one may borrow funds, typically on a

very short-term basis, collateralized by Treasury securities.

In a repo agreement, the lender will wire transfer same-

day funds to the borrower; the borrower wire transfers the

Treasury security to the lender with the provision that the

transactions are reversed at term with the borrower wiring

back the original principal plus interest.

The borrower is said to have executed a repurchase

agreement; the lender is said to have executed a reverse

repurchase agreement. Many banks and security dealers

will oer this service, once the customer applies and

passes a requisite credit check.

Understanding Treasury Futures

The key to the transaction, however, is the safety

provided the lender by virtue of the receipt of the (highly-

marketable) Treasury security. These repo transactions

are typically done on an overnight basis but may be

negotiated for terms such as one-week, two-weeks, or one

month. A third party custodian is frequently used to add an

additional layer of safety between the lender and borrower,

i.e., a tri-party repo agreement. Overnight repo rates are

typically quite low, in the vicinity of the eective federal

funds rate.

Any Treasury security may be considered “good” or

“general” collateral. Sometimes when particular Treasuries

are in short supply, dealers will announce that the security

is “on special” and oer below-market nancing rates in an

eort to attract borrowers.

Treasury Futures Delivery Practices

While some traders refer to original or “classic” Treasury

bond futures as “30-year bond futures,” that reference is

actually quite misleading. Treasury bond futures permit

the delivery in satisfaction of a maturing contract of any

U.S. Treasury security provided it matures within a range

of 15 to less than 25 years from the date of delivery. That

delivery window once reduced from 15 to 30 years and,

thus, the characterization of the Treasury bond contract as

a “30-year bond futures” was apt.

Note that the Ultra T-bond futures contract calls for the

delivery of any bond that does not mature for a period of

at least 25 years from the date of delivery. Subsequent

to the development of the Ultra bond contract, the

delivery window of the original T-bond futures contract

was amended from 15-30 years to 15-25 years. As such,

the Ultra T-bond futures contract currently is most aptly

referred to as the 30-year bond contract while the original

bond futures contract, as amended, is referred to as the

“classic” bond futures contract.

Because of the rather broadly dened delivery

specications, a signicant number of securities, ranging

widely in terms of coupon and maturity, may be eligible

for delivery. This applies with equal eect to 2-, 3-, 5-, 10-,

and Ultra 10-year Treasury note futures; as well as the

classic and Ultra T-bond futures contracts. Table 2 included

below provides a complete description of the contract

specications of CME Group Treasury futures products.

Conversion Factor Invoicing System

Securities with varying characteristics, such as coupon

and maturity, will of course be more or less valued by

the investment community. High-coupon securities, for

example, will naturally command a greater price than

comparable low-coupon securities.

These dierences must be reected in the futures contract.

In particular, when a short makes delivery of securities in

satisfaction of a maturing futures contract, the long will pay

a specied invoice price to the short.

As discussed above, the futures contract permits the delivery

of a wide range of securities at the discretion of the short.

That invoice value must be adjusted to reect the specic

pricing characteristics of the security that is tendered.

Accordingly, Treasury futures utilize a “conversion factor”

invoicing system to reect the value of the security that is

tendered by reference to the 6% futures contract standard.

The “Principal Invoice Amount” paid from long to short

upon delivery may be identied as the Futures Settlement

Price multiplied by the Conversion Factor (CF) multiplied

by $1,000.

That $1,000 constant reects the $100,000 face value

futures contract size associated with most T-note and T-bond

futures. Note that the 2-year T-note contract is based on a

$200,000 face value amount. Thus, this constant must be

reset at $2,000 for 2-year Treasury futures.

Principal Invoice Price

= Futures Settlement x Conversion Factor (CF)

x $1,000

Any interest accrued since the last semi-annual interest

payment date is added to the principal invoice amount to

equal the “total invoice amount.”

Total Invoice Amount

= Principal Invoice Amount

+ Accrued Interest

A conversion factor may be thought of as the clean price of

$1 face value of the delivered security at a yield to maturity

of 6%. Clearly, high-coupon securities will tend to have

high CFs while low-coupon securities will tend to have low

CFs. In particular, bonds or notes with coupons less than

the 6% contract standard will have CFs that are less than

1.0; bonds or notes with coupons greater than 6% have

CFs greater than 1.0.

E.g., the conversion factor for delivery of the 2-3/8%

T-note of Aug-24 vs. December 2017 10-year T-note

futures is 0.8072. This suggests that a 2-3/8% security

is approximately valued at 81% as much as a 6%

security. Assuming a futures price of 125-08+/32nds (or

125.265625 expressed in decimal format), the principal

invoice amount may be calculated as follows.

Principal Invoice Price

= 125.265625 x 0.8072 x $1,000

= $101,114.41

E.g., the conversion factor for delivery of the 1-7/8%

T-note of Aug-24 vs. December 10-year T-note

futures is 0.7807. This suggests that a 1-7/8% security

is approximately valued at 78% as much as a 6%

security. Assuming a futures price of 125-08+/32nds

(or 125.265625), the principal invoice amount may be

calculated as follows.

Principal Invoice Price

= 125.265625 x 0.7807 x $1,000

= $97,794.87

In order to arrive at the total invoice amount, one must of

course further add any accrued interest since the last semi

annual interest payment date to the principal

invoice amount.

Cheapest-to-Deliver

The intent of the conversion factor invoicing system is

to render equally economic the delivery of any eligible-

for-delivery securities. Theoretically, the short who has

the option of delivering any eligible security should be

indierent as to his selection.

However, the CF system is imperfect in practice as we nd

that a particular security will tend to emerge as “cheapest-

to-deliver” (CTD) after studying the relationship between

cash security prices and principal invoice amounts.

E.g., on October 10, 2017, one might have been able to

purchase the 2-3/8% of 8/24 at 101-07+ ($101,234.38

per $100,000 face value unit). The 1-7/8% of 8/24 was

valued at 98-01+ ($98,031.25 per $100,000 face value

unit). Compare these cash values to the principal invoice

amounts as follows.

2-3/8%-8/24 1-7/8%-8/24

Futures Price 125-085 125-085

x CF 0.8072 0.7807

x $1,000 $1,000 $1,000

Principal Invoice $101,114.41 $97,79 4.87

Cash Price ($101,234.38) ($98,031.25)

Delivery Gain/Loss ($119.97) ($236.38)

Our analysis suggests that a loss of $119.97 may be

associated with the delivery of the 2-3/8% of 8/24 while an

even larger loss of $236.38 might be associated with the

delivery of the 1-7/8% of 8/24. Thus, we might conclude

that the 2-3/8% of 8/24 note is cheaper or more economic

to deliver than the 1-7/8% of 8/24.

The Basis

Typically, we expect to nd a single security, or perhaps

a handful of similar securities, will emerge as CTD. This

identication has important implications for basis traders

who arbitrage cash and futures markets. A basis trader

will seek out arbitrage opportunities or situations where

they might be able to capitalize on relatively small pricing

discrepancies between cash securities and Treasury

futures by buying “cheap” and selling “rich” items.

Understanding Treasury Futures

Arbitrageurs will track these relationships by studying the

“basis.” The basis describes the relationship between

cash and futures prices and may be dened as the cash

price less the “adjusted futures price” or the futures price

multiplied by the conversion factor.

Thus, the basis is analogous to the gain or loss that

might be realized upon delivery. Unlike that gain or loss,

however, the basis is typically expressed in terms of

32nds. E.g., 1-1/4 points might be shown as 40/32nds. It

is also “inverted” in the sense that we are comparing cash

less adjusted futures prices - rather than futures invoice

price less cash prices.

Basis = Cash Price-Adjusted Futures Price

Adjusted

Futures Price

= Futures Price x Conversion Factor

E.g., a comparison of cash and adjusted futures prices

provides us with a quote for the basis associated with the

2-3/8%-8/24 and 1-7/8%-8/24 Treasury securities.

2-3/8%-24 1-7/8%-24

Cash Price 101-07+ 98-01+

Futures Price 125-085 125-085

x CF 0.8072 0.7807

Adjusted Futures (101-04) (97-255)

Basis (32nds) 3.339 8.064

The basis of 3.339/32nds associated with the 2-3/8%-8/24

corresponds to a loss on delivery of $119.97 as shown

above. Similarly, the basis of 8.064/32nds associated with the

1-7/8%-8/24 corresponds to a loss on delivery of $236.38.

As suggested above, and as a general rule, the security

with the lowest basis (and highest implied repo rate),

i.e., the largest gain or smallest loss on delivery, may be

considered CTD. Clearly, the 2-3/8%-8/24 is cheaper-to-

deliver than the 1-7/8%-8/24.

Table 3 included at the end of this document depicts the

basis and implied repo rates for all eligible-for-delivery

securities vs. the December 2017 10-year T-note futures

contract as of October 10, 2017. Referring to Table 3, one

may conrm that the 2-3/8%-8/24 exhibited the lowest

basis and, therefore, may be considered the CTD security.

Note, however, that there are quite a few securities, with

similar coupons and maturities, which are near CTD. In

fact, the entire universe of eligible-for-delivery securities

features reasonably similar coupons and maturities.

It is important to identify the CTD security to the extent that

Treasury futures will tend to price or track or correlate most

closely with the CTD. This has interesting implications from

the standpoint of a “basis trader” or a hedger as discussed

in more detail below.

Suce it to say at this point that basis trading is a

frequent practice in the Treasury futures markets. Certain

terminology has been developed to identify basis positions.

One may “buy the basis” by buying cash securities and

selling futures. One may “sell the basis” by selling cash

securities and buying futures.

Basis transactions are typically transacted in a ratio that

reects the conversion factor of the security involved

in the trade.

“Buy the Basis” =

Buy cash securities

& sell futures

“Sell the Basis” =

Sell cash securities

& buy futures

E.g., if one were to buy the basis by buying $10 million

face value of the 2-3/8%-8/24 note, one might sell 81

December 2017 futures by reference to the conversion

factor of 0.8072.

E.g., if one were to sell the basis by selling $10 million

face value of the 1-7/8%-8/24 note, one might buy 78

December futures by reference to the conversion factor

of 0.7807.

By transacting the basis in a ratio identied by reference

to the CF, one may roughly balance the movement or

volatility on both legs of the spread. This is intuitive to the

extent that the conversion factor generally reects the

value of the cash position relative to that of the futures

contract. If the CF reects relative value then presumably

it will reect relative volatility or price movement as well.

Why Is One Issue CTD?

If the conversion factor invoicing system performed

awlessly, all eligible-for-delivery securities would have

a similar basis and be equally economic to deliver. As

suggested above, however, a single security or several

similar securities tend to emerge as CTD.

The CF invoicing system is imperfect because it is

implicitly based on the assumption that - (1) all eligible-for-

delivery securities have the same yield; and (2) that yield

is 6%. But there are any number of “cash market biases”

that impact upon the yield of a Treasury security.

Further mathematical biases in the conversion factor

calculation will tilt the eld towards securities of particular

coupons and maturities when yields are greater than or

less than the 6% contract standard. Hence, we may further

speak of “conversion factor biases.”

Conversion Factor Effects

Perhaps more important that these cash market factors,

there are observable biases associated with the

mathematics of the conversion factor system or conversion

factor biases.

Long duration, i.e., low-coupon, long-maturity securities,

will become CTD when yields are signicantly greater

than the 6% contract standard. When yields fall below the

6% contract standard, these factors will bias towards the

delivery of short-duration, i.e., high-coupon,

short-maturity securities.

If yields > 6% 

Bias to long duration

(

i.e.,

low-coupon,

long-maturity) securities

If yields < 6% 

Bias to short duration

(

i.e.,

high-coupon,

short-maturity) securities

CTD Driven by Yields

100

Short

Duration

Security

Long

Duration

Security

Consider the period between March and September 2017

as depicted in our graphic. During this period, the price of

the December 2017 Ten-year T-note futures experienced a

price decline in late June 2017 from approximately 126.5%

to 124.5% of par. Subsequently, the market has trended

higher to a new high of nearly 127.5% of par.

Dec-17 10-Yr Note Futures

123.0

123.5

124.0

124.5

125.0

125.5

126.0

126.5

127.0

127.5

128.0

Yields Falling

Yields Rising

3/22/17

3/29/17

4/5/17

4/12/17

4/19/17

4/26/17

5/3/17

5/10/17

5/17/17

5/24/17

5/31/17

6/7/17

6/14/17

6/21/17

6/28/17

7/5/17

7/12/17

7/19/17

7/26/17

8/2/17

8/9/17

8/16/17

8/23/17

8/30/17

9/6/17

In other words, prices dropped briey as yields spiked,

only to be followed by an extended period of prices rising

as yields fell. During the entirety of this period, prices were

well above par while yields were well below the 6% futures

contract standard. Still, conversion factor biases were

diminished or weakened as prices strengthened only to

decline once again as the market broke.

Understanding Treasury Futures

The impact of these strengthening and subsequently

weakening conversion factor biases may be observed

by examining the basis for several eligible-for-delivery

securities. Actually, the simple and graudual convergence

of cash and futures prices may be the feature that is most

apparent from an examintion of this graphic.

Dec-17 10-Yr Basis

2-3/8%-Aug-24 1-7/8% Aug-24

2%-Nov-26 2-3/8%-May-27

2-1/8%-Jul-24

100

150

200

250

300

3/22/17

3/29/17

4/5/17

4/12/17

4/19/17

4/26/17

5/3/17

5/10/17

5/17/17

5/24/17

5/31/17

6/7/17

6/14/17

6/21/17

6/28/17

7/5/17

7/12/17

7/19/17

7/26/17

8/2/17

8/9/17

8/16/17

8/23/17

8/30/17

Long Duration Basis Rising

Long Duration Basis Falling

As prices advanced and yields fell since late June, notice

that the basis was buoyed upwards to the extent that its

price rose faster than futures price which traced a shorter

duration CTD. Again, as yields fall below or further below

the 6% futures contract standard, long duration securities

tend to become less economic to deliver.

Yields Rising above 6% Yields Falling Under 6%

Sell long duration basis, i.e., sell

long duration securities & buy

futures

Buy long duration basis, i.e., buy

long duration securities & sell

futures

Buy short duration basis, i.e., buy

short duration securities & sell

futures

Sell short duration basis, i.e., sell

short duration securities & buy

futures

As prices declined and yields rose in late June, the basis

for long duration securities such as the 2%-26 or the

2-3/8%-27 tended to decline more sharply than the basis

for short duration securities such as the CTD 2-3/8%-8/24.

This is consistent with our observation above that, as

yields rise, long duration securities tend to become more

economic to deliver.

It is clear that the performance of the basis is strongly

driven by directional price movement in the Treasury

markets. Thus, “buying the basis” or “selling the basis”

may be motivated by expectations regarding rising or

falling yields. The key is to get a sense of market direction

and then identify the long or short duration securities

whose basis values will be impacted by any sizable price

(or yield) movement.

Implied Repo Rate

We often suggest that the security with the lowest basis is

cheapest-to-deliver. But to be more precise, we may point

out that the structure of coupon receipts and reinvestment

of such coupon income plays some (generally small) part

in establishing a particular security as cheapest-to-deliver

as well. Hence, traders often calculate the “implied repo

rate” (IRR) associated with eligible for delivery securities to

account for such factors.

The IRR is calculated as the annualized rate of return

associated with the purchase of a security, sale of futures

and delivery of the same in satisfaction of the maturing

futures contract. This calculation takes into account all the

cash ows associated with the security. The assumption

that the basis for any particular security may completely

converge to zero is implicit in the IRR calculation.

E.g., if one were to buy the 2-3/8%-8/24 basis by buying

the cash securities, selling futures in a ratio dictated by

the conversion factor and making delivery, or at least

witnessing full cash-futures convergence, one would lock-

in a return of 1.42%.

E.g., if one were to buy the 1-7/8%-8/24 basis by buying

cash securities and selling futures in a ratio indicated by

reference to the conversion factor and making delivery,

or at least witnessing full cash-futures convergence, one

would lock-in a rate of return of 0.32%.

Clearly, it would be preferable to lock-in a return of 1.42%

rather than a return of 0.32%. Thus, the 2-3/8%-8/24 is

cheaper to deliver relative to the 1-7/8%-8/24. In fact, if

we scan the IRRs associated with all securities eligible to

be delivered into the December 2017 contract in Table 3

below, we nd that the IRR of 1.42% associated with the

2-3/8%-8/24 is superior to all other IRRs.

Thus, the 2-3/8%-8/24 Treasury security is associated

with the lowest basis and the highest IRR as of October

10, 2017. As a general rule, the security with the lowest

basis will likewise exhibit the highest implied repo rate. It is

possible that a security with the lowest basis may not quite

have the highest IRR because of cash ow considerations.

But this statement is generally true. In any event, this

observation conrms the CTD status of the 2-3/8%-8/24 as

of October 10, 2017.

By buying the basis of a Treasury security, or buying

cash and selling futures, one becomes obligated to make

delivery of the Treasury in satisfaction of the maturing

futures contract.

Thus, buying the basis of the cheapest-

to-deliver 2-3/8%- 8/24 vs. a futures contract that matures

two or three months hence, may be considered analogous

to other short-term investment alternatives.

E.g., we might compare the IRR = 1.42% associated with

the CTD security to the prevailing 13-week T-bill yield of

1.04%; or to the eective Fed Funds rate of 1.15%; or, to a

3-month ICE LIBOR rate at 1.34%.

In this example, the IRR associated with the CTD security

was essentially equivalent to other short-term investment

opportunities. As a general rule, however, the IRR even for

the CTD security tends to run at a level that is a bit inferior

to the returns associated with comparable short-term

investment alternatives. The IRRs associated with all other

non CTD securities are even lower.

This begs the question – why would anyone ever want to

buy the basis if the returns do not appear to be competitive?

The answer lies in the fact that the basis conveys other

opportunities apart simply from the opportunity to use the

futures contract as a delivery conveyance.

Consider any discrepancy with respect to the CTD to

represent a risk premium of sorts. If one buys the CTD

security and sells futures with the intention of making

delivery, the worst case scenario has the basis converging

fully to zero and the hedger essentially locking in a return

equal to the IRR, in this case 1.42%.

But if market conditions should change such that another

security becomes CTD, this implies that the basis may

advance, or at least fail to completely converge to zero.

As a result, the trader may realize a rate of return that is in

fact greater than the currently calculated IRR.

2 One may, of course, opt to offset the short futures contract prior to the delivery

period and effectively abrogate such obligation.

Basis Optionality

In other words, there is a certain degree of “optionality”

associated with the purchase or sale of the basis. Buying

the basis is analogous to buying an option which, of

course, implies limited risk. Buying the basis implies

limited risk to the extent that, even under the worst of

circumstances, you make delivery of the security which is

eectively equivalent to the possibility that the basis fully

converges to zero.

But “crossovers” or “switch” may occur such that the basis

converges at a slower rate than otherwise anticipated or

actually advances. As a result, this short-term investment

may generate a return which is (at least theoretically)

unbounded on the upside. Limited risk accompanied by

unbounded upside potential is reminiscent of the risk/

reward prole of a long option position, thus the analogy

between a long basis position and a long option.

The best one may hope by selling the basis, or selling

securities and buying futures with the possibility of

eectively replacing the sold security by standing long in

the delivery process, is that the basis fully converges to

zero. This implies limited prot potential.

But in the event of signicant changes in market

conditions, the basis may advance sharply, exposing

the seller of the basis to (theoretically) unbounded risks.

Limited prot potential accompanied by unbounded risk

is reminiscent of the risk/reward prole of a short option

position, thus the analogy between a short basis position

and a short option.

As discussed above, the basis even for the CTD security

tends to be in excess of cost of carry considerations. This is

manifest in the fact that the IRR even for the CTD is typically

a bit below prevailing short-term rates. This premium in the

basis essentially reects the uncertainties associated with

which security may become CTD in the future.

Thus, the basis performs much akin to an option. Like any

other option, the basis will be aected by considerations

including term, volatility and strike price. The relevant

term in this case is the term remaining until the presumed

delivery date vs. the futures contract. Market volatility

aects the probability that a crossover may occur.

Rather than speak of a strike or exercise price, it is

more appropriate to assess the market’s proximity to a

“crossover point” or a price/yield at which one might expect

an alternate security to become CTD.

Understanding Treasury Futures

Consider the purchase or sale of the CTD basis. The

degree to which this basis performs like a call or a put

option is contingent upon the relationship between market

prices and the 6% futures contract standard.

If yields are below the 6% futures contract standard, the

CTD basis may be expected to advance if prices decline

(rates rise) towards 6%; or, decline if prices advance (rates

fall). Thus, buying the CTD basis when rates are below

6% is akin to the purchase of a put option. Conversely, the

sale of the CTD basis when rates are less than 6% is akin

to the sale of a put option where the value of transaction

is capped if prices should advance while losses may be

unbounded if prices should decline.

If yields are above the 6% futures contract standard, the

CTD basis may be expected to advance if prices rise

(rates fall) towards 6%; or, decline if prices fall (rates rise).

Thus, buying the CTD basis when rates are above 6%

is akin to the purchase of a call option. Conversely, the

sale of the CTD basis when rates are above 6% is akin

to the sale of a call option where the value of transaction

is capped if prices should decline while losses may be

unbounded if prices should advance.

Finally, if rates are close to the 6% futures contract standard,

the basis for what is currently CTD may be dictated by

considerations apart from conversion factor biases.

Thus, there may be signicant crossovers regardless of

whether rates rise or fall. Buying the CTD basis under

these considerations may be considered akin to the

purchase of an option straddle (i.e., the simultaneous

purchase of call and put options).

Under these circumstances the basis buyer may be

indierent between advancing or declining prices but has

an interest in seeing prices move signicantly in either

direction. Selling the CTD basis when rates are near the

6% contract standard is akin to selling a straddle (i.e., the

simultaneous sale of both call and put options). The basis

is sold under these circumstances because the trader

anticipates an essentially neutral market.

Buy CTD Basis Sell CTD Basis

Yields < 6% Buy Put Option Sell Put Option

Yields = 6% Buy Straddle Sell Straddle

Yields > 6% Buy Call Option Sell Call Option

Of course, the basis premium over carry should accrue to

the short basis trader under circumstances of continued

price stability. But the short basis trader is exposed to the

risk of dramatic price movements in either direction.

As of October 10, 2017, the IRR of the CTD 2-3/8%-

8/24 security at 1.42% fell squarely within the range of

other short-term investment alternatives. This suggests

negligible optionality, i.e., the probability of a crossover or

switch is negligible. This is driven by the fact that yields

are well below the 6% futures contract standard. Further,

the duration of the 2-3/8%-8/24, with its high coupon and

short maturity, was the shortest relative to other eligible for

delivery securities. Thus, the market assessed a negligible

probability that this security would not remain CTD by the

time we enter the December 2017 delivery period.

Measuring Risk

There are a couple of popular ways to measure the risks

associated with coupon-bearing (and money-market)

instruments including basis point value (BPV) and duration.

Basis Point Value (BPV)

BPV represents the absolute price change of a security

given a one basis point (0.01%) change in yield.

These gures may be referenced using any number of

commercially available quotation services or software

packages. BPV is normally quoted in dollars based on a

$1 million (round-lot) unit of cash securities. The following

table depicts the BPVs of various on-the-run Treasuries as

of October 30, 2017.

Measuring Volatility (As of October 30, 2017)

Coupon Maturity

Duration

(Yrs)

BPV

(per mil)

2-Yr Note 1-1/2% 10/31/19 1.978 $196

3-Yr Note 1-5/8% 10/15/20 2.896 $287

5-Yr Note 2% 10/31/22 4.783 $473

7-Yr Note 2-1/4% 10/31/24 6.516 $645

10-Yr Note 2-1/4% 08/15/27 8.794 $863

30-Yr Bond 2-3/4% 08/15/47 20.241 $1,946

E.g., this suggests that if the yield on the 30-year bond were to rise by a

single basis point (0.01%), the price should decline by some $1,946 per

$1 million face value unit.

Duration

If BPV measures the absolute change in the value of a

security given a yield uctuation; duration may be thought

of as a measure of relative or percentage change. The

duration (typically quoted in years) measures the expected

percentage change in the value of a security given a one-

hundred basis point (1%) change in yield.

Duration is calculated as the average weighted maturity of

all the cash ows associated with the bond, i.e., repayment

of “corpus” or face value at maturity plus coupon

payments, all discounted to their present value.

E.g., the 30-year bond is associated with duration of 20.2

years. This implies that if its yield advances by 100 basis

points (1.00%), we expect a 20.2% decline in the value of

the bond.

In years past, it was commonplace to evaluate the

volatility of coupon-bearing securities simply by reference

to maturity. But this is quite misleading. If one simply

examines the maturities of the current 2-year note and 10-

year note, one might conclude that the 10-year is 5 times

as volatile as the 2-year.

But by examining durations, we reach a far dierent

conclusion. The 10-year note (duration of 8.794 years) is

only about 4-½ times as volatile as the 2-year note (duration

of 1.978 years). The availability of cheap computing power

has made duration analysis as easy as it is illuminating.

Risk Management

Treasury futures are intended to provide risk averse xed

income investors with the opportunity to hedge or manage

the risks inherent in their investment activities. Eective

use of these contracts, however, requires a certain

grounding in hedge techniques.

Most pointedly, one may attempt to assess the relative

volatility of the cash item to be hedged relative to the

futures contract price. This relationship is often identied

as the futures “Hedge Ratio” (HR). Hedge ratios reect

the expected relative movement of cash and futures and

provide risk managers with an indication as to how many

futures to use to oset a cash exposure.

CF Weighted Hedge

Treasury futures contract specications conveniently

provide a facile means by which to assess the relative

risks associated with cash and futures. As discussed

above, the conversion factor (CF) represents the price

of a particular bond as if it were to yield 6%. Thus, the

CF reects the relative value and, by implication, the

relative volatility between cash and futures prices. Most

basis trades are in fact concluded in a ratio identied by

reference to the CF.

E.g., if one held $10 million face value of the 2-3/8%-

8/24 note, one might sell 81 December 2017 futures by

reference to the conversion factor of 0.8072 to execute a

hedge.

E.g., if one held $10 million face value of the 1-7/8%-

8/24 note, one might sell 78 December 2017 futures by

reference to the conversion factor of 0.7807 to execute a

hedge.

A conversion factor weighted hedge is likely to be quite

eective if you are hedging the cheapest-to-deliver

security. Treasury futures will tend to price or track or

correlate most closely with the CTD security.

But other securities with dierent coupons and maturities

may react to changing market conditions dierently. Thus,

one might question if you can or should do better than a

CF weighted hedge?

Understanding Treasury Futures

BPV Weighted Hedge

In order to understand the most eective techniques

with which to apply a hedge, consider the fundamental

objective associated with a hedge. An “ideal” hedge is

intended to balance any loss (prot) in the cash markets

with an equal and opposite prot (loss) in futures.

Our goal, therefore, is to nd a hedge ratio (HR) that

allows one to balance the change in the value of the cash

instrument to be hedged (∆hedge) with any change in the

value of the futures contract (∆futures). Note that we use

the Greek letter delta or ∆ to denote the abstract concept

of change in value.

We solve for the hedge ratio (HR) as follows.

Because we have not dened what we mean by “change

in value,” the equation above is of an abstract nature and

cannot be directly applied. Thus, let’s backtrack to discuss

the relationship between Treasury futures and cash prices.

Per our discussion above, principal invoice amount paid

from long to short upon deliver will be equal to the futures

price multiplied by the conversion factor of the cash

security being delivered. Rational shorts will, of course,

elect to tender the cheapest-to-deliver security. Thus,

we might designate the futures price and the conversion

factor of the cheapest-to-deliver as Pfutures and CFctd,

respectively.

Because the basis of the CTD is generally closest to

zero, relative to all other eligible securities, we might

assume that the futures price level and, by implication,

any changes in the futures price level (∆futures) will be a

reection of any changes in the value of the CTD (∆ctd)

adjusted by its conversion factor (CFctd) as follows.

Substituting this quantity into our equation specied above,

we arrive at the following formula.

We might further rearrange the equation as follows.

Unfortunately, this concept of “change in value” remains

abstract. Let us “operationalize” the concept by substituting

the basis point value of the hedged security (BPVhedge)

and the basis point value of the cheapest-to-deliver

(BPVctd) for that abstract concept.

Recall from our discussion above that a basis point value

represents the expected change in the value of a security,

expressed in dollars per $1 million face value, given a one

basis point (0.01%) change in yield. Thus, we identify the

basis point value hedge ratio (or “BPV HR”) as follows.

Our analysis implicitly assumes that any changes in the

yield of the hedged security and that of the cheapest-

to-deliver security will be identical. I.e., that we will

experience “parallel” shifts in the yield curve. This

analysis further presumes that you are able to identify

the cheapest-to-deliver security and that it will remain

cheapest-to-deliver. The latter assumption is, of course,

questionable in a dynamic market.

E.g., let us nd the basis point value hedge ratio (HR)

required to hedge $10 million face value of the 2-3/8%-

5/27 note security. This security carried a BPV = $8,558

per $10 million. The CTD security was the 2-3/8%-8/24

with a BPV = $63.78 per $100,000 face value and a

conversion factor of 0.8072 vs. December 2017 Ten-year

T-note futures. The hedge ratio may be identied as 108

contracts per $10 million face value of the 2-3/8%-5/27.

Note that the HR = 108 is signicantly greater than the 75

contracts suggested by reference to the conversion factor

(0.7455) of the 2-3/8%-5/27 security.This is due to the fact

that the CTD security carries a relatively short duration of

6.437 years compared to the duration associated with the

hedged security of 8.662 years.

It is no coincidence that the ratio of durations is roughly

equal to the ratio between the BPV and CF hedge ratios

or (6.437 ÷ 8.662) ~ (75 ÷ 108). I.e., the futures contract is

pricing or tracking or correlating most closely with a shorter

duration security. Consequently, futures prices will react

rather mildly to uctuating yields. Therefore, one requires

more futures to enact an eective hedge.

E.g., what would our hedge ratio be if the CTD security

was the on-the-run 2-1/4%-8/27 with a rather longer

duration of 8.958 years? This security has a BPV of

$86.99 per $100,000 face value and a conversion factor

for delivery vs. December 2017 Ten-year T-note futures of

0.7314. Our analysis suggests that one might hedge with

73 contracts per $10 million face value of 2-1/4%-8/27.

Note that this hedge ratio of 73 contracts is signicantly

less than the 108 contracts suggested by our analysis

above and reasonably similar to the 75 contracts

suggested by the CF hedge ratio. This can be explained

by the fact that the 2-1/4%-8/27 has pricing characteristics

that are quite similar to 2-3/8%-5/27 security which is the

subject of the hedge. In particular, the 2-1/4%-8/27 had a

duration of 8.958 years which is reasonably close to the

8.662 duration of the 2-3/8%-5/27. Because of the similar

risk characteristics of the CTD and hedged security, the

CF may do a reasonable job of identifying an appropriate

hedge ratio.

Crossover Risks

This further suggests that, if there is a crossover in the

CTD from a short duration security to a longer duration

security, the number of futures needed to hedge against

the risk of declining prices is decreased. This may be a

favorable circumstance for the hedger who is long cash

Treasuries and short futures in a ratio prescribed by the

BPV technique.

Consider that as prices decline and longer duration

securities become CTD, one is essentially over-hedged in

a declining market. If on the other hand, prices advance

and even shorter duration securities become CTD, the

appropriate hedge ratio will tend to increase. Thus, the

long hedger becomes under-hedged in a rising market.

Another way of saying this is that there is a certain degree

of “convexity” inherent in the relationship that favors the

long hedger or long basis trader (long cash and short

futures). Conversely, this convexity tends to work to the

disadvantage of the short hedger or short basis trader

(short cash and long futures).

Once again, we may liken the basis to an option to the

extent that option premiums are also aected by convexity.

Further, because the long basis trader eectively owns

the option, he pays an implicit premium in the dierence

between prevailing short-term yields and the return on the

basis trade as might be simulated in the absence of any

CTD crossovers.

The short basis trader is eectively short an option and

receives this implicit premium. This implicit premium is

reected in a comparison of the Implied Rate of Return

(IRR) relative to prevailing short-term rates.

Note that the BPV of a debt security is dynamic and

subject to change given uctuating yields. As a general

rule, BPV declines as a function of maturity; and, as yields

increase (decrease), BPVs decline (advance). This implies

that the hedge ratio is likewise dynamic. Over a limited

period of time, however, HRs may be reasonably stable,

provided there is no crossover in the cheapest-to-deliver.

As a general rule in practice, it would be commonplace for

hedgers to re-valuate and readjust the hedge if rates were

to move by perhaps

20-25 basis points.

Portfolio Hedging

Thus far, our discussion has centered about comparisons

between a single security and a Treasury futures contract,

a “micro” hedge if you will. But it is far more commonplace

for an investor to become concerned about the value of

a portfolio of securities rather than focus on a single item

within a presumably diversied set of holdings.

Understanding Treasury Futures

How might one address the risks associated with a

portfolio of securities, i.e., how to execute a “macro”

hedge? The same principles apply whether hedging a

single security or a portfolio of securities. Thus, we need

to evaluate the risk characteristics of the portfolio in terms

of its BPV and duration just as we would examine an

individual security. Then we may simply apply the BPV

hedge ratio for these purposes.

E.g., assume that you held a $100 million xed income

portfolio with a BPV = $80,000 and a duration of 8 years.

This duration is similar to the duration associated with

securities deliverable against the 10-year T-note futures

contract, suggesting use of the 10-year as a hedge

vehicle. As of October 10, 2017, the CTD security was the

2-3/8%-8/24 with a BPV = $63.78 per $100,000 face value

unit and a CF = 0.8072. Our analysis suggests that one

might sell 1012 futures to hedge the portfolio.

Thus far, our examples illustrated situations where we

had eectively hedged individual securities or portfolios in

their entirety. In the process, we might eectively push the

risk exposure down to near $0 as measured by BPV or 0

years as measured by duration. But it would actually be

uncommon to see an asset manager adjust an actual xed

income risk exposure all the way down to zero.

Asset managers generally measure their performance by

reference to a designated “benchmark” or “bogey.” The

benchmark is often identied as an index of xed income

securities such as the Barclays U.S. Aggregate Bond

Index or some other commonly available measure.

The returns on this benchmark may be identied as the

“core” or “beta” returns associated with the portfolio.

In addition, the asset manager may exercise some

limited degree of latitude in an attempt to outperform the

benchmark, or to capture some excess return known as

“alpha” in current investment parlance.

Asset managers may be authorized to adjust the duration

of the portfolio upwards by a limited amount in anticipation

of rate declines and price advances. Or, to adjust duration

downwards by a limited amount in anticipation of rate

advances and price declines. The following formula

provides the appropriate hedge ratio for these operations.

Where Dtarget is the target duration; Dcurrent is the

current duration.

E.g., let’s return to our example of a $100 million xed

income portfolio. Assume that the portfolio duration of 8

years was designed to coordinate with the duration of the

designated benchmark. Thus, the portfolio manager may

be authorized to adjust portfolio duration between 6 and

10 years in pursuit of “alpha.” The asset manager is now

concerned about the prospects for rate advances and

wishes downwardly to adjust duration from 8 to 6 years.

Our analysis suggests that this may be accomplished by

selling 253 futures.

The application of this formula provides asset managers

with a great deal of exibility to adjust the portfolio

duration – either upward or downward – to meet the

demands of the moment.

Bullets and Barbells

Typically, one looks to hedge a Treasury portfolio with the

use of Treasury futures which correspond most closely in

terms of duration to the average weighted portfolio duration.

E.g., if one held a portfolio with an average weighted

duration of 4 years, it would be natural to look to 5-year

Treasury note futures as a suitable risk layo vehicle. If

the portfolio had an average weighted duration of 8 years,

it would be natural to look to either 10-year Treasury note

futures or the recently launched Ultra 10-year Treasury

note futures, which tracks one of the three most recently

auctioned 10-year notes.

This analysis would tend to work well when the portfolio

is constructed predominantly of securities which were

close in terms of their durations to the average portfolio

duration. Certainly, if the entire portfolio were populated

with a variety of recently issued 5-year T-notes, it would

behoove the hedger to utilize 5-year Treasury note futures

as a hedge, minimizing basis risk and the need for any

subsequent hedge management.

Hedged with Short Futures

Return

Market Prices

Prices Decline &

Yields Advance

Prices Advance &

Yields Decline

Fixed Income Portfolio

Fully Hedged

Partially Hedged

A portfolio constructed in such a manner might be

labeled a “bullet” portfolio to the extent that it contains

reasonably homogeneous securities in terms of maturity

and presumably coupon. Under these circumstances, one

might simply “stack” the entire hedge in a single Treasury

futures contract which most closely conforms to the

duration of the portfolio constituents.

Of course, one may attempt to introduce a certain

speculative element into the hedge by using longer- or

shorter-term futures contracts as the focus of the hedge.

If the yield curve were expected to steepen, a hedge using longer-

term futures, e.g., 10- or 30-year Treasury futures rather than

5-year futures, would allow one to capitalize on movement in the

curve beyond simply immunizing the portfolio from risk. If the yield

curve is expected to atten or invert, a hedge using shorter-term

futures, e.g., 2-year or 3-year Treasury futures rather than 5-year

futures, could likewise provide yield enhancement.

But a portfolio need not necessarily be constructed per the

“bullet” approach. Consider a portfolio with a duration of

4 years that is constructed using a combination of 2- and

10-year notes and no 5-year notes whatsoever.

A portfolio constructed in such a manner may be labeled a

“barbell” portfolio to the extent that it is “weighted” with two

extreme duration securities with no intermediate duration

securities at all. If one were to simply stack the hedge

into 5-year Treasury note futures, the investor becomes

exposed to the risk that the shape of the yield curve

becomes distorted such that 5-year yields sag below yields

in the 2- and 10-year sectors of the curve.

The holder of a barbell portfolio might instead attempt to

utilize a combination of various tenured Treasury futures

which is weighted with an eye to the proportion of the

portfolio devoted to each sector of the yield curve. As

such, the hedger may insulate from the risks that the

shape of the yield curve will shift.

Thus, an asset manager might categorize his holdings into

various sectors of the curve corresponding to available

Treasury futures “buckets,” i.e., 2-, 5-, 10- and 30-year

securities. Then, the asset manager may calculate the

BPV HRs applicable to each of those bucketed portfolios

and essentially hedge each element separately.

If, however, the investor wished to introduce a speculative

element into the hedge, the use of longer- or shorter-

maturity Treasuries driven by an expectation of a

steepening or attening yield curve, respectively, may be in

order.

Comparing Returns of Cash to

Futures & Repo

Investors are frequently faced with the choice of allocating

funds to Treasury futures or notes. Based upon a similar

analysis for an earlier period, we compared returns

of investing in CTD Treasury notes to earning income

by investing proceeds from the sale of the CTD notes

at overnight repo rates and establishing long 10-year

Treasury futures (Globex: ZN, Bloomberg: TY) positions.

In our analysis, we assumed that investors either:

• Maintained long positions in Treasury notes that were

CTD for the 10-year Treasury note futures or

• Sold those CTD notes and invested proceeds from

the sale at overnight rates, which were compounded

for each applicable holding period, and purchased the

equivalent long position via Treasury note futures.

Understanding Treasury Futures

We examined quarterly returns of the long CTD Treasury

notes position and the long Treasury futures and repo

positions from the September 2005 contract month through

the June 2017 contract month, 48 quarters. We determined

that the combined 10-year Treasury futures and repo

positions produced average annual returns of 4.85%,

compared to 4.71% for CTD Treasury notes. As a result, the

futures and repo positions produced average annual returns

14 basis points higher than the CTD note positions.

The chart below depicts returns for the CTD notes

(dark blue line) and futures + repo positions (light blue line)

compounded quarterly for the 12-year period.

Comparing Returns of CTD Treasury Notes (CTD)

to 10-Year Futures and Repo (TYF)

Compounded Quarterly-September 2005 through

June 2017 Contracts

100

102

104

106

108

110

112

114

116

118

TYU2005

TYH2006

TYU2006

TYH2007

TYU2007

TYH2008

TYU2008

TYH2009

TYU2009

TYH2010

TYU2010

TYH2011

TYU2011

TYH2012

TYU2012

TYH2013

TYU2013

TYH2014

TYU2014

TYH2015

TYU2015

TYH2016

TYU2016

TYH2017

CTD TYF

Base Value=100

(Compounded Quarterly Sep 05-Jun 17)

The similar but superior returns of the long Treasury

futures and repo positions compared to CTD Treasury

note positions demonstrate that Treasury futures produced

nearly identical investment income over an extended

period of 12-years as the CTD notes, which the futures

are tracking. Despite not being a direct source of coupon

income, Treasury futures price movements are passed to

position holder daily via variation settlement and reect the

accrued coupon and price changes of the CTD Treasury

notes over time.

Treasury futures provide a means to similar returns

with access to broad and deep pools of liquidity that are

comparable, if not superior, to the OTR cash notes and

bonds, which are generally considered the most liquid in

the cash markets (by extension, more liquid than CTD

notes). For a recent comparison of Treasury futures and

OTR notes and bonds, please refer to The New Treasury

Market Paradigm, published by CME Group in June 2016.

Additionally, Treasury futures oer many operational

eciencies such as o-balance sheet exposure,

concentration of positions in a single line item, netting,

transparency, and initial margins that reect one-day

period of risk.

Table 1: The Delivery Timetable for Treasury Futures*

(All times refer to Chicago time.)

Short Clearing Firm CME Clearing Long Clearing Firm

First Position

Day

By 8:00 pm, two business days prior to

the rst day allowed for deliveries into

an expiring futures contract (ie, rst day

of delivery month), clearing rms report

to CME Clearing all open long positions,

grouped by account origin (customer or

house) and position vintage date.

Day 1:

Intention Day

By 6:00 pm, the short clearing rm

noties CME Clearing that it intends to

make delivery on an expiring contract.

Once CME Clearing has matched the

short clearing rm to the long clearing

rm(s) for delivery, this declaration

cannot be reversed.

At 8:00 pm, CME Clearing matches

the delivering short clearing rm to the

clearing rm(s) with long positions having

the oldest vintage date(s), and then

informs the short (long) party that the

opposite party will take (make) delivery.

By 8:00 pm, clearing rms report to CME

Clearing all open long positions in the

expiring futures contract, grouped by

account origin (customer or house) and

position vintage date.

Day 2:

Notice Day

By 2:00 pm (3:00 pm on Last Notice Day),

using calculations based on the expiring

contract’s Intention Day settlement price,

the short clearing rm must conrm

invoice details with CME Clearing.

At 4:00 pm, CME Clearing runs invoices

and provides them to long clearing rm(s)

matched to take delivery from the short

clearing rm making delivery.

By 4:00 pm, the long clearing rm

assigned to take delivery provides the

name and location of its bank to the short

clearing rm making delivery.

Day 3:

Delivery Day

Short and long clearing rms have until

9:30 am to resolve invoice differences. By

10:00 am, the short clearing rm deposits

Treasury securities for delivery into its

bank account, and it instructs its bank to

transfer the securities, via Fed wire, to the

long clearing rm’s account no later than

1:00 pm.

By 7:30 am, the long clearing rm makes

funds available, and noties its bank to

remit the funds upon accepting Treasury

securities. By 1:00 pm, the long clearing

rm’s bank has accepted the Treasury

securities and has remitted the invoice

amount via Fed wire to the short clearing

rm’s bank account.

* Operational details are subject to change, insofar as CME Clearing periodically reviews the physical delivery process and, when necessary, modies it to enhance its

efciency. For current information, please consult CBOT Rules.

Understanding Treasury Futures

Table 2: Treasury Futures Contracts Summary

2-Year T-Note 3-Year T-Note 5-Year T-Note 10-Year T-Note

Ultra 10-Year

T-Note Classic T-Bond Ultra T-Bond

Contract Size

($ Face Value)

200,000 200,000 100,000 100,000 100,000 100,000 100,000

Deliverable

Grade

Treasury notes.

Original term

to maturity: not

more than 5

years 3 months.

Remaining term

to maturity: at

least 1 year 9

months and not

more than 2

years.

Treasury notes.

Original term

to maturity:

not more

than 7 years.

Remaining term

to maturity: at

least 2 years

9 months and

not more than 3

years.

Treasury notes.

Original term

to maturity: not

more than 5

years 3 months.

Remaining term

to maturity: at

least 4 years 2

months.

Remaining term

to maturity of

at least 6 years

6 months, but

less than eight

years.

Treasury notes.

Remaining term

to maturity: at

least 9 years 5

months and not

more than 10

years.

Treasury bonds.

Remaining term

to maturity: at

least 15 years

and less than 25

years.

Treasury bonds.

Remaining term

to maturity: at

least 25 years.

Delivery Months The rst three consecutive contracts in the March, June, September, and December quarterly cycle.

Delivery Method Physical delivery of contract grade US Treasury securities via the Federal Reserve book-entry wire-transfer system. Delivery

invoice price equals the futures contract settlement price, times the size of the futures contract price point, times a conversion

factor, plus accrued interest from the delivered security’s last coupon payment date to the futures contract delivery date. The

conversion factor, computed and published by the Exchange, represents the price of $1 face value of the delivered security to

yield 6 percent per annum as of the rst day of the futures contract delivery month.

Trading Hours CME Globex: 5:00 pm - 4:00 pm, Chicago time, Sunday – Friday

Trading in an expiring contract ceases at 12:01 pm, Chicago time, on the contract’s last trading day.

Last Trading

Day

Last business day of the delivery month Seventh business day preceding the last business day of the delivery

month

Last Delivery

Day

Third business day following the Last Trading Day Last business day of the delivery month

Price Quote Points ($2,000) and eighths of 1/32

of a point.

Points ($1,000)

and quarters of

1/32 of a point.

Points ($1,000) and halves of 1/32

of a point.

Points ($1,000) and 1/32 of a point.

CME Globex

Ticker Symbol

ZT Z3N ZF ZN TN ZB UB

Clearing Code 26 3YR 25 21 TN 17 UBE

Table 3: December 2017 Ten-Year T-Note Futures Basis (As of October 10, 2017)

Securities Cheapest to Deliver Analysis

Coupon Maturity Mid CUSIP Issue

Delivery

Years

Clean

Cash

Price

Basis

Net of

Carry

Treasury

Conver-

sion Factor

(TCF) Yield

Futures

DV01

(Cash

DV01/

TCF)

Implied

Repo

Rate

2.375 8/15/2024 101.2266 912828D56 8/15/2014 6.67 101.2266 - 0.1185 0.8072 2.18% $76.51 1.42%

2.125 7/31/2024 99.6758 9128282N9 7/31/2017 6.58 99.6758 0.1633 0.7939 2.17% $76.56 0.68%

1.875 8/31/2024 98.0508 9128282U3 8/31/2017 6.67 98.0508 0.2718 0.7807 2.18% $78.02 0.32%

2 6/30/2024 98.9336 912828XX3 6/30/2017 6.5 98.9336 0.358 0.7873 2.17% $75.87 0.18%

2.25 11/15/2024 100.3008 912828G38 11/17/2014 6.92 100.3008 1.2816 0.7943 2.20% $79.37 -1.76%

2.125 9/30/2024 99.6016 9128282Y5 10/2/2017 6.75 99.6016 1.6159 0.7875 2.19% $78.28 -2.60%

2 2/15/2025 98.4531 912828J27 2/17/2015 7.17 98.4531 2.6975 0.7741 2.23% $82.58 - 5.15%

2.125 5/15/2025 99.1719 912828XB1 5/15/2015 7. 42 99.1719 3.9209 0.7748 2.24% $84.79 -7. 81%

2 8/15/2025 98.0938 912828K74 8/17/2015 7.67 98.0938 5.2038 0.7612 2.26% $ 87.70 -10.91%

2.25 11/15/2025 99.7813 912828M56 11/16/2015 7.92 99.7813 6.2525 0.7702 2.28% $89.57 -12.93%

1.625 2/15/2026 94.9063 912828P46 2/16/2016 8.17 94.9063 7. 9198 0.7252 2.30% $94.07 -17.91%

1.625 5/15/2026 94.6641 912828R36 5/16/2016 8.42 94.6641 9.0921 0.7185 2.31% $96.60 -20.69%

1.5 8/15/2026 93.4414 9128282A7 8/15/2016 8.67 93.4414 10.3718 0.7038 2.32% $99.69 -24.15%

2 11/15/2026 97. 2 3 05 912828U24 11/15/2016 8.92 97. 23 0 5 11.0751 0.7307 2.34% $100.38 -24.51%

2.25 2/15/2027 99.1641 912828V98 2/15/2017 9.17 99.1641 12.058 0.7421 2.35% $101.93 -26.19%

2.375 5/15/2027 100.168 912828X88 5/15/2017 9.42 100.168 13.147 0.7455 2.35% $103.77 -28.23%

2.25 8/15/2027 99.0391 9128282R0 8/15/2017 9.67 99.0391 14.4821 0.7314 2.36% $106.67 -31.73%

NOTES:

December 2017 futures were priced at 125-085 (125-8.5/32nds)

Securities highlighted in red represent least economic-to-deliver; highlighted in green represent most economic-to-deliver.

cmegroup.com

Data sources: Bloomberg, CME Group unless otherwise noted.

Neither futures trading nor swaps trading are suitable for all investors, and each involves the risk of loss. Swaps trading should only be undertaken by investors who are Eligible Contract

Participants (ECPs) within the meaning of Section 1a(18) of the Commodity Exchange Act. Futures and swaps each are leveraged investments and, because only a percentage of a contract’s value

is required to trade, it is possible to lose more than the amount of money deposited for either a futures or swaps position. Therefore, traders should only use funds that they can afford to lose

without affecting their lifestyles and only a portion of those funds should be devoted to any one trade because traders cannot expect to profit on every trade. All references to options refer to

options on futures.

Any research views expressed those of the individual author and do not necessarily represent the views of the CME Group or its affiliates. The information within this presentation has been

compiled by CME Group for general purposes only. CME Group assumes no responsibility for any errors or omissions. All examples are hypothetical situations, used for explanation purposes only,

and should not be considered investment advice or the results of actual market experience.

All matters pertaining to rules and specifications herein are made subject to and are superseded by official rulebook of the organizations. Current rules should be consulted in all cases concerning

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