The 10-Year Treasury Note Market

Christopher G. Lamoureux & George Theocharides

December 2nd, 2010Cyprus University of Technology

Motivation

• 10-year T-Note market provides a unique laboratory to explore effects of various nonconvexities on financial asset prices. Why?– Securities have no default risk so that future cash flows are

certain.– There exist stripped securities (redundant) in the market that

can replicate the cash flows of each note, and allow us to benchmark these notes to their fundamental value.

– Derivatives are actively traded on the notes.– There have been important technological enhancements in the

trading process during our period that allow us to isolate an exogenous change in liquidity.

Evolution of Open Interest & Volume in the Futures Market

OPEN INTEREST & VOLUME IN THE 10-YEAR U.S. TREASURY FUTURES CONTRACT

-500000

0

500000

1000000

1500000

2000000

2500000

3000000

3500000

19

91

.06

19

91

.11

19

92

.05

19

92

.11

19

93

.05

19

93

.11

19

94

.05

19

94

.10

19

95

.04

19

95

.10

19

96

.04

19

96

.10

19

97

.04

19

97

.09

19

98

.03

19

98

.09

19

99

.03

19

99

.09

20

00

.03

20

00

.08

20

01

.02

20

01

.08

20

02

.02

20

02

.08

20

03

.02

20

03

.08

20

04

.01

20

04

.07

20

05

.01

20

05

.07

20

06

.01

20

06

.07

20

07

.01

20

07

.07

20

07

.12

PERIOD

AM

OU

NT

Open_Interest Volume

Pricing Deviations5/

15/1

997

9/15

/199

7

1/15

/199

8

5/15

/199

8

9/15

/199

8

1/15

/199

9

5/15

/199

9

9/15

/199

9

1/15

/200

0

5/15

/200

0

9/15

/200

0

1/15

/200

1

5/15

/200

1

9/15

/200

1

1/15

/200

2

5/15

/200

2

9/15

/200

2

1/15

/200

3

5/15

/200

3

9/15

/200

3

1/15

/200

4

5/15

/200

4

9/15

/200

4

1/15

/200

5

5/15

/200

5

9/15

/200

5

1/15

/200

6

5/15

/200

6

9/15

/200

6

1/15

/200

7

5/15

/200

7

9/15

/200

7

1/15

/200

8

5/15

/200

8

-200

-100

0

100

200

300

400

Pricing Deviation (On-the-run, first-off-the-run, non-deliverable)

OTR FIRST-OFFNON-DELIVERABLE

DATE

PR

C. D

EV

IAT

ION

(cen

ts/$

100

par)

OTR FIRST-OFF

NON-DELIVERABLE

Aim of Project

• Examine apparent violations of the law of one price in the market for 10-year Treasury notes.

• Examine the relationship between price premia, repo specialness, and liquidity.

• Examine the impact of the futures market on the underlying spot market.

Preview of Results• Markets are becoming more closely integrated (less segmented)

over time.• The OTR premium is not idiosyncratic, but is related to a factor

that affects most notes and is diminishing with the age of the note:

– Since 2005, 80% of the variation in the price deviations in all outstanding notes is explained by a single factor.

• Despite the fact that the distinction in liquidity between the OTR note and older notes has increased with the proliferation of electronic trading in the former, the relative pricing deviations between the on-the-run note and its predecessors has shrunk. This casts doubt on the notion that the on-the-run price premium is solely the result of this note being more liquid than older notes.

Preview of Results…Cont’d.

• As in previous studies, we show though that the pricing deviations we document may not imply that an arbitrage opportunity exists:- Consistent with previous findings, we show that the deviations between the note and the replicating portfolio of coupon STRIPS cannot be exploited by stripping and reconstituting, as the principal strip-necessary to reconstitute the note-inherits the price premium of the note itself.

- Consistent with previous findings, we find a strong correlation between the pricing deviation and specialness, i.e. an arbitrageur seeking to short the overpriced security will earn a lower rate on the cash collateral than she would on general collateral.

• Nevertheless, our analysis suggests that, similar to liquidity, expected future specialness is not the only non-convexity affecting prices, i.e. price premia, repo specialness, and liquidity are at least partially distinct phenomena.

• We show that being deliverable against the 10-year note futures contract is valuable as well:- All the deliverable securities exhibit a “deliverability” premium that is increasing in

recent years.- Notes that are no longer available for delivery against the futures contracts have a price

deviation from the underlying STRIPS that bounces around zero.

Related Literature

• Related Literature:– Limits of Arbitrage: Shleifer and Vishny (JF, 1997), Gromb and Vayanos

(JFE, 2002), Brunnermeier and Pedersen (RFS, 2009), Xu, Pan, and Wang (WP, 2010), Gromb and Vayanos (Annual Review of Financial Economics, 2010).

– Deliverability Premium: Simpson and Ireland (JFQA, 1985), Garbade (1985), Kuipers (JFM, 2008).

– On-the-Run Premium: Babbel et al. (WP, 2001), Cherian et al. (Review of Derivatives Research, 2004), Graveline and McBrady (WP, 2005). Pasquariello and Vega (JFE, 2008), Vayanos and Weill (JF, 2008).

- Securities Shorting/Repo Specialness: Duffie (JF, 1996), Jordan and Jordan (JF, 1997), Duffie, Garleanu, and Pedersen (JFE, 2002), Krishnamurthy (JFE, 2002), Nashikkar (WP, 2007), Nashikkar and Pedersen (WP, 2007).

- Idiosyncratic/Systematic Variation of the Markets: Duffee (JF, 1996).

Institutional Background

• Treasury Market: – Auction of 10-year note every 3 months. (February, May, August,

December).– In certain periods, re-issuance every 1 or 3 months.– Announcement/Auction/Issue Date – This 2-week period is considered

the “When-Issued” market.– On-the-Run premium: Believed to be due to note’s higher liquidity.– Trading volume is concentrated in the OTR issues. (Barclay,

Hendershott, Kotz (JF, 2006)].– Transition to electronic communications networks has enhanced liquidity.

[Mizrach and Neely (Fed Reserve Bank of St. Louis Review, 2006)].

Institutional Background

• Treasury Futures Market:– Trade on the old CBOT, now part of CME Group.– Expire on a quarterly cycle (March, June, September, December).– Several options for the short side (delivery, timing, end-of-month, and wild-card

options).– Deliverable basket includes any note (excluding TIPS) with a remaining time to

maturity of 6.5 to 10 years, on the first day of the delivery month.– Each contract is for $100,000 face value of the Treasury note.– Usually one note from this basket is considered the CTD.– CME Group uses a standardization procedure through a conversion factor for each

note [price the note would have on the first day of the delivery month, were its yield to maturity equal to the specified notional yield (6% since 2000), on a $1 par].

– If market yields are lower than 6%, then the shortest-term note is considered the CTD, otherwise it’s the one with the longest time to maturity.

Repo Market

• Private Market:– Cash vs. bond lending.– Regular securities are traded at the general collateral rate.– Securities in high demand are traded at a special rate

(lower than the general collateral rate, ex. OTR, CTD).– Majority are overnight transactions.

• Federal Reserve’s Securities Lending Program:– Lender of last resort.– Securities traded here are considered to be on special.– Bond vs. bond lending.– Minimum loan fee (only at 5 basis point since April 7,

2009).

Private Repo MarketDealer Lender

Money lent

Securities(collateral)

Money lent + Repo interest

Securities

Beginning

of term

End

of term

Fed’s Securities Lending Program

Fed Investor

Security(collateral)

Security in

demand

Security (collateral)

Security in demand + interest rate

Beginning

of term

End

of term

Data

• Treasury Note Market:– Provided through Bloomberg.– Daily pricing on the 10-year and 7-year notes.– Sample starts on June 3, 1991, until June 30, 2008.– Pricing on STRIPS to create an intrinsic value for each note (due to lack of

availability through Bloomberg, sample starts between May 15, 1997, until June 30, 2008).

– In cases of missing STRIPS information, we searched for the data through Wall Street Journal archives.

• Treasury Futures Market:– Obtained from CBOT until Sept. 2005 contract, and remainder through

Bloomberg.– Sample spans 68 contracts.– Since 2003, we have data from both the auction and electronic platform.

Data

• Repurchase and Lending Rates:– Daily general collateral rates through Bloomberg from May 15, 1997, to

June 30, 2008.– Federal Reserve’s Securities Lending program – through the New York

Fed’s website.• Sample spans from April 29, 1999 to June 30, 2008.

– OTR special rates through Wells-Fargo, Inc. (comparison sample to the Fed data)• Daily sample spans from 1/2/2004 – 8/28/2007.

Empirical Methodology

• Examine the pattern of pricing deviations through time for different sub-samples (deviations constructed using an ALL fungible coupon STRIPS portfolio as well as a principal/coupon STRIPS portfolio).

• Examine the specialness/lending rates for identical sub-samples.• Conduct regressions to isolate causes of the pricing deviations for

different sub-samples (all observations, deliverable/non-deliverable notes, cheapest-to-deliver (CTD) note, OTR note).

• Examine the determinants of the specialness of the OTR security.• Explore the principal components structure of the pricing deviations,

and conduct formal inference on this structure using a posterior simulator.

• Examine 2 cases studies – The June 2005 “squeeze” episode, and the Summer & Fall 2003 “Delivery Fails” episode.

Table 2 Deviations from STRIPS-Implied-Value (ALL coupon STRIP

portfolio)       

No. of Unique No. of Obs. Mean

  Notes    

Panel A: All Notes

1997-2008 69 85,441 24

Pre-Jan. 1, 2003 47 43,339 20

Post-Jan. 1, 2003 49 42,102 28

[21.99]***

Panel B: On-the-Run Notes

1997-2008 37 2,886 151

Pre-Jan. 1, 2003 15 1,455 182

Post-Jan. 1, 2003 23 1,431 120

[30.41]***

Panel C: 1st-Off-the-Run Notes

1997-2008 36 2,877 109

Pre-Jan. 1, 2003 14 1,454 120

Post-Jan. 1, 2003 23 1,423 98

[10.75]***

Panel D: 2nd-Off-the-Run Notes

1997-2008 35 2,820 90

Pre-Jan. 1, 2003 13 1,389 91

Post-Jan. 1, 2003 23 1,431 88

      [1.60]

Table 2…Cont’d.

       No. of Unique No. of Obs. Mean

  Notes    Panel E: 3rd-Off-the-Run Notes

1997-2008 35 2,684 72Pre-Jan. 1, 2003 13 1,261 67Post-Jan. 1, 2003 23 1,423 77

[6.43]***Panel G: All Deliverables, excluding

On-the-Run, 1st, 2nd, and 3rd

Off-the-Run Notes

1997-2008 43 17,849 44Pre-Jan. 1, 2003 21 6,958 36Post-Jan. 1, 2003 25 10,891 49

[23.83]***Panel I: All Non-Deliverables

1997-2008 69 56,803 2Pre-Jan. 1, 2003 47 31,045 0Post-Jan. 1, 2003 49 25,758 4

      [19.67]***

Table 2…Cont’d.

Panel J: Pricing Deviation from SIV (coupon/principal STRIP portfolio)

No. of Obs. Mean

     

All Notes

1997-2008 63,101 3Pre-Jan. 1, 2003 26,347 2Post-Jan. 1, 2003 36,754 4

[7.68]***On-the-Run Notes

1997-2008 643 24Pre-Jan. 1, 2003 25 17Post-Jan. 1, 2003 618 24

[0.77]1st-Off-the-Run Notes

1997-2008 904 19Pre-Jan. 1, 2003 82 10Post-Jan. 1, 2003 822 20

[1.27]     

Table 3 Lending Rates

           

No. of Obs. No. of Obs. No. of Unique No. of Unique Mean

    with Specialness Notes Notes with Specialness (incl. zeros)

Panel A: All Notes

1999-2008 73,023 4,480 64 57 7

Pre-Jan. 1, 2003 28,857 1,007 42 34 6

Post-Jan. 1, 2003 44,166 3,473 51 45 8

[6.69]***

Panel B: On-the-Run Notes

1999-2008 2,390 1,026 32 32 78

Pre-Jan. 1, 2003 957 407 10 10 93

Post-Jan. 1, 2003 1,433 619 23 23 68

[5.00]***

Panel C: 1st-Off-the-Run Notes

1999-2008 2,390 443 32 29 28

Pre-Jan. 1, 2003 957 151 10 8 33

Post-Jan. 1, 2003 1,433 292 23 22 25

[2.52]***

Panel D: 2nd-Off-the-Run Notes

1999-2008 2,390 175 32 26 9

Pre-Jan. 1, 2003 957 28 10 8 5

Post-Jan. 1, 2003 1,433 147 23 18 10

          [3.48]***

Table 3…Cont’d.

           

No. of Obs. No. of Obs. No. of Unique No. of Unique Mean

    with Specialness Notes Notes with Specialness (incl. zeros)

Panel E: 3rd-Off-the-Run Notes

1999-2008 2,390 137 32 20 7 Pre-Jan. 1, 2003 957 20 10 8 3 Post-Jan. 1, 2003 1,433 117 23 12 9

[4.19]***Panel G: All Deliverables, excluding

On-the-Run, 1st, 2nd, and 3rd

Off-the-Run Notes

1999-2008 14,979 885 37 29 6 Pre-Jan. 1, 2003 4,045 40 15 8 1 Post-Jan. 1, 2003 10,934 845 25 24 8

[13.08]***Panel I: All Non-Deliverables

1999-2008 48,933 1,819 64 43 3 Pre-Jan. 1, 2003 21,157 363 42 25 2 Post-Jan. 1, 2003 27,776 1,456 51 31 4

          [11.43]***

Table 4Determinants of Deviations from SIV

GMM Regressions with Newey-West (1987) standard errors with 30 lags

Panel A: Regressions on Pricing DeviationsVariables All Notes All Notes All Notes

(82,589 obs.) (82,589 obs.) (82,589 obs.)

Intercept 4.79 2.15 51.44(6.22)*** (3.37)*** (52.27)***

Total Issue Size (offered to public) -0.15 -0.46 (linearly de-trended) (4.10)*** (10.88)***

Outstanding Issue Size (offered to public) -0.21(7.13)***

Post-2003 Dummy 4.58 4.23 4.90(10.74)*** (9.92)*** (10.96)***

Deliverable Dummy 43.75 43.57 41.08(68.94)*** (68.97)*** (48.62)***

Age Indicator -2.25(87.08)***

OTR Dummy 140.13 140.39(119.58)*** (118.00)***

1st Off-the-Run Dummy 64.14 64.01(77.69)*** (77.58)***

2nd Off-the-Run Dummy 44.80 44.68(64.31)*** (64.09)***

3rd Off-the-Run Dummy 28.50 28.38(46.62)*** (46.23)***

CTD Dummy -15.61 -15.68 -35.76(21.64)*** (21.69)*** (38.28)***

Deliv. x Post-2003 Period 3.12 2.94 -9.11(3.16)*** (2.99)*** (7.57)***

OTR x Post-2003 Period -69.30 -69.07(51.96)*** (51.40)***

CTD x Post-2003 Period -0.88 -0.83 13.44(0.94) (0.88) (11.48)***

Adj. R2 0.630 0.630 0.510

Auction Cycle

1 2 3 4 5 6 7 8 9 10 11 12 130

20

40

60

80

100

120

0

20

40

60

80

100

120

140

OTR Premium, OTR-SIV Pricing Deviation & Specialness (Auction cycle with a reopening in 1-month)

OTR Premium OTR-SIV Pricing Deviation Fed Lending Rate

7-DAY WEEKS TO ISSUANCE OF NEW NOTE

PR

C. D

EV

IAT

ION

(cen

ts/$

100

par)

FE

D L

EN

DIN

G R

AT

E (b

ps)

Range of Days for the Reopening of Existing Issue)59 to 64 Calendar Days(

Range of Announcement Days for Issuance of NewNote

)12 to 16 Calendar Days(

15-Sep-03

Table 5Determinants of Pricing Deviations & Specialness for the OTR

Note     

Variables OTR Notes OTR Notes OTR Notes OTR Notes OTR Notes OTR Notes OTR Notes OTR Notes

  Av. Prc. Dev. Av. Prc. Dev. Av. Prc. Dev. Av. Prc. Dev. Av. Spc. Av. Spc. Av. Spc. Av. Spc.

Intercept 207.48 218.91 199.92 247.37 474.38 474.38 376.63 354.24

(3.24)*** (3.51)*** (3.92)*** (3.69)*** (3.33)*** (3.32)*** (3.48)*** (3.80)***

Auction Size (offered to public) 5.66 5.90 4.90 -18.10 -18.10

(2.90)*** (3.18)*** (2.17)** (4.07)*** (4.05)***

Auction Size (total) 6.61 -14.34 -12.92

(5.04)*** (4.99)*** (4.62)***

Post-2003 Dummy -57.65 -57.03 -51.74 -51.16 -32.70 -32.69 -49.85 -50.53

(6.72)*** (6.66)*** (6.23)*** (6.45)*** (2.32)** (2.35)** (3.60)*** (3.89)***

Bid-to-Cover Ratio -58.87 -60.26 -61.85 -65.83 -14.92 -14.94 -1.69 -0.70

(6.30)*** (6.49)*** (6.93)*** (6.35)*** (1.15) (1.13) (0.13) (0.06)

% of Issuance Awarded to Dealers/Brokers -0.48 0.83

(1.49) (1.37)

% of Issuance Awarded to Foreigners 0.72 -0.94

(1.32) (0.85)

Average % of Issuance Awarded to Dealers/Brokers -0.31 -0.41 -0.50 0.04 0.04 0.80

(per note) (0.71) (0.94) (1.19) (0.04) (0.04) (0.98)

Average % of Issuance Awarded to Foreigners 2.12 1.20 1.29 0.40 0.39 -0.28

(per note) (3.33)*** (1.71)* (1.93)* (0.29) (0.22) (0.17)

Yield Difference 8.04 24.61 24.82 14.73 16.24 16.46 16.51 34.37

(2.03)** (3.39)*** (3.56)*** (2.41)** (2.11)** (0.68) (0.73) (2.93)***

Average % of Issuance Awarded to Foreigners -2.02 -2.03 -0.02 -0.06

x Yield Difference (2.97)*** (3.15)*** (0.01) (0.03)

% of Issuance Awarded to Foreigners -0.93 -2.50

x Yield Difference (1.47) (2.26)**

Periods (2-weeks) until Off-the-Run 5.83 5.67 7.09 6.84 -18.64 -18.64 -21.16 -21.92

(3.80)*** (3.70)*** (4.59)*** (4.37)*** (5.20)*** (5.19)*** (5.87)*** (6.26)***

Reopened Issue Dummy 35.51 41.76 51.17 43.70 -137.64 -137.59 -129.86 -125.32

(2.03)** (2.52)*** (3.32)*** (2.49)*** (3.40)*** (3.42)*** (4.11)*** (4.00)***

Future Reopening Issue Dummy 0.60 7.01 -2.24 -7.42 35.61 35.66 65.97 87.48

(0.05) (0.54) (0.19) (0.49) (1.23) (1.22) (2.62)*** (3.62)***

Adj. R2 0.524 0.534 0.560 0.519 0.264 0.261 0.286 0.305

                 

Table 6PCA

Panel A: PCA (May 1997 - December 2002), (1,466 obs., 31 Notes)

PC Mean Std. Dev.

     

1 52.69% 1.00%

2 65.56% 0.76%

3 71.83% 0.64%

4 77.16% 0.52%

5 81.42% 0.43%

6 85.07% 0.35%     

Panel C: PCA (January 2005 - June 2008), (910 obs., 31 Notes)

PC Mean Std. Dev.

     

1 80.27% 0.86%

2 86.42% 0.58%

3 89.37% 0.46%

4 91.15% 0.38%

5 92.59% 0.32%

6 93.77% 0.27%     

Eigenvector for the 1st Factor

2/17/20053/9/2005

3/29/2005

4/18/20055/8/2005

5/28/2005

6/17/20057/7/2005

7/27/2005

8/16/20059/5/2005

-10

0

10

20

30

40

50

60

70

0

50

100

150

200

250

300

350

400

June 2005 10-year U.S. Treasury Futures Contract

Pricing Deviation Gen. Coll. Rate Fed Lending Rate

DATE

PR

C. D

EV

IAT

ION

(cen

ts/$

100

par

)

LE

ND

ING

RA

TE

(b

ps)

End of March 2005 futures contract

31-March-05Beginning of June 2005 fu-

tures contract1-June-05

End of June 2005 futurescontract

30-June-05

0

50

100

150

200

250

300

-120

-70

-20

30

80

LE

ND

ING

RA

TE

(bp

s)

PR

C. D

EV

IAT

ION

(cen

ts/$

10

0 p

ar)

DATE

Summer & Fall 2003 Delivery Fails Episode

OTR Premium Gen. Coll. Rate Fed Lending Rate

Issue Off-the-Run 15-Aug-03

Issue Off-Off-the-Run17-Nov-03

Reopening of Aug-2013 Issue

Reopening of Nov-2013 Issue15-Dec-03

Conclusions

• Market is becoming less segmented in recent years.• The on-the-run premium is not an idiosyncratic feature of the most recently

auctioned note.• Despite the fact that the introduction of electronic trading should have resulted

in a greater distinction in liquidity between the on-the-run note and older notes, their relative pricing deviations has shrunk.

• We show that the pricing deviations we document may not imply that an arbitrage opportunity exists.

• Price premia, repo specialness, and liquidity are at least partially distinct phenomena.

• We show that being deliverable against the 10-year note futures contract is valuable.

Thank You!