Coupon Spreads, Limits to Arbitrage Treasury Market Christopher G. Lamoureux & George Theocharides March 8, 2013
Coupon Spreads 700 600 C e n t s p e r 500 400 300 $ 1 0 0 p a r 200 100 0 5/15/1997 2/9/2000 11/5/2002 8/1/2005 4/27/2008 1/22/2011 100 Non deliverable On the run Note First off the run note Non deliverable note 200
On-the-Run Premia & 590 490 390 290 190 90 10 4/29/1999 9/10/2000 1/23/2002 6/7/2003 10/19/2004 3/3/2006 7/16/2007 11/27/2008 4/11/2010 110 210 (basis points) On the Run Premium (cents per $100 par)
3500000 30000 3000000 20000 Dealers' Repo Positions ($ millions) 2500000 2000000 1500000 1000000 10000 0-10000 -20000-30000 -40000 Dealers' Net Inventory ($ millions) 500000 Term Repo -50000 0 8/1/2001 8/1/2002 8/1/2003 8/1/2004 8/1/2005 8/1/2006 8/1/2007 8/1/2008 8/1/2009 8/1/2010 Date Overnight Repo Term Repo Net Inventory -60000
Auction & Formats Generally quarterly issuances: Feb,... cycle. Structurally missing data in our panel from the July and October 2006 notes. No format prior to September 2003. Prior to this no off-cycle reopenings and arbitrary on-cycle reopenings. Aug 2003 Sept 2008: New note each quarter. Reopening in following month. November 2008 Present: New note each quarter. Reopening in each of next two months.
Sub-periods We split our data into 3 subperiods: 1. May 1997 - December 2002 (Pre-Electronic) 2. January 2003 - June 2008 (Increased Risk Capital) 3. July 2008 - March 2011 (Crisis) Per./Form. % Dlr. % Foreign. Size ($b.) 1/O 78 7 14 1/R 82 6 11 2/O 61 20 17 2/R 84 6 9 3/O 54 24 25 3/R 60 19 20
1. Repo specialness leads to violations of the Law of One Price. Also risk of call to cover. Duffie (1996). Storied 3Com / Palm episode. Krishnamurthy (2002); Nashikkar (2007). Sluggish adjustment of Risk Capital: Duffie (2010). Price pressure (microstructure); Grossman & Miller (1988). Nagel (2011). Note that the effects of more risk capital are not unambiguous, suggesting the need to explore multiple dimensions of coupon spread dynamics.
2. The turmoil in the wholesale funding markets, which started in 2007, is a rich source of data relating to limits to arbitrage (optical arbitrage): 1. August 2007 - September Euro/$ Covered Interest Parity Violation (Baba, Packer, Nagano (2008): $ shortage). 2. Convertible Bond Arbitrage (Mitchell and Pulvino (2011)). 3. CDS-Bond Basis: US Corporate Bonds (Bai and Collin-Dufresne (2010), Mitchell and Pulvino (2011). European Sovereign Debt (Foley-Fisher (2010). 4. 30-year swap rates 50 bp lower than 30-year US Treasury in late November 2008. 5. Buraschi, Sener, and Menguturk (2012) Sovereign debt in different currencies: August 9, 2007 March 31, 2009.
3. Also, Mitchell & Pulvino (2011) document a high correlation between arbitrage errors in the CDS/Bond basis and convertible bonds, which is normally 0, is 91% during the crisis. Why? Lack of Risk Capital and collapse of repo market (two sides of the same coin). We add to the mix evidence from 10-year US Treasury market, including the effects of Fed policy. We complement other examples, since coupon spreads are true arbitrage trades.
4. Important Related paper: Hu, Pan, and Wang (2012) Noise t deviations of all Treasury securities maximal 10 year terms. Argue that this captures the liquidity or level of risky capital in markets (One-dimensional). Hu, Pan, and Wang claim that their Noise t measure is a summary of the liquidity in the overall market, which is the level of arbitrage capital. However, they have no direct evidence of this.
Coupon Spreads: Periods 1 & 2 Coupon Spread (cents) 0 100 200 300 On each date we sort all notes by age with the on the run note being Note 1, the first off the run note Note 2, etc. For each note on each day we measure its coupon spread as the price deviation from a replicating portfolio of coupon STRIPS. We measure these spreads in cents, when the note price is expressed as % of par. (So a value of 100 corresponds to 1% of the price of a note selling at par.) This plot shows the inter quartile range (box), the median (bar inside the box), and 95%ile bands (the whiskers) of the coupon spreads for Notes 1 31. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Note (by age) May 1997 December 2002 Coupon Spread (cents) 50 0 50 100 150 200 250 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Note (by age) January 2003 June 2008
Coupon Spreads: Period 3 Coupon Spread (cents) 0 100 200 300 400 500 600 On each date we sort all notes by age with the on the run note being Note 1, the first off the run note Note 2, etc. For each note on each day we measure its coupon spread as the price deviation from a replicating portfolio of coupon strips. We measure these spreads in cents, when the note price is expressed as % of par. (So a value of 100 corresponds to 1% of the price of a note selling at par.) This plot shows the inter quartile range (box), the median (bar inside the box), and 95%ile bands (the whiskers) of the coupon spreads for Notes 1 31. 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 Note (by age) July 2008 March 2011
Principal Components Analysis We use the Gibbs sampler to integrate over the uncertainty in the first two moments and missing data. Consider that the coupon spread for Note j on day t is missing. Then x j,t N (ˆµ j, ˆσ 2 j ). ˆµ j = µ j + Σ 12 Σ 1 22 (X t, j µ j ) (1) ˆσ 2 j = Σ 11 Σ 12 Σ 1 22 Σ 21 (2) Here, µ j is the unconditional mean of the j th coupon spread. µ Σ N( x, T 1 Σ) (3) Σ µ IG(ˆΣ, T ) (4) Here ˆΣ is the maximum likelihood estimator of Σ (which is conditional on µ), and x is the sample mean. IG refers to the inverse gamma distribution.
Principal Components Analysis 2. Once we have a draw from Σ, we form the correlation matrix, and its eigenvalues and eigenvectors. Armed with these, we form the PC scores. Identification (Aliasing Problems): Switching rank of eigenvalues from one draw to the next. Change in sign of eigenvector from one draw to the next.
First eigenvector Loading Loading 0.00 0.05 0.10 0.15 0.20 0.05 0.10 0.15 0.20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Note (by age) May 1997 December 2002 All notes are sorted by age with the on the run note being Note 1, the first off the run note Note 2, etc. For each note on each day we measure its coupon spread as the price deviation from a replicating portfolio of coupon strips. We use the Gibbs sampler to construct the posterior distribution of the eigenvectors from the correlation matrix. This plot shows properties of the posterior distribution on the first eigenvector (or the loadings of Notes 1 31 on the first principal component). We show the inter quartile range of the posterior (box), the median (bar inside the box), and 95% confidence interval (the whiskers). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Note (by age) January 2003 June 2008
First eigenvector Period 3. Loading 0.10 0.05 0.00 0.05 0.10 0.15 0.20 All notes are sorted by age with the on the run note being Note 1, the first off the run note Note 2, etc. For each note on each day we measure its coupon spread as the price deviation from a replicating portfolio of coupon strips. We use the Gibbs sampler to construct the posterior distribution of the eigenvectors from the correlation matrix. This plot shows properties of the posterior distribution on the first eigenvector (or the loadings of Notes 1 31 on the first principal component). We show the inter quartile range of the posterior (box), the median (bar inside the box), and 95% confidence interval (the whiskers). 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 Note (by age) July 2008 March 2011
Second eigenvector Loading Loading 0.0 0.2 0.1 0.0 0.1 0.2 0.3 0.4 0.3 0.2 0.1 0.1 0.2 All notes are sorted by age with the on the run note being Note 1, the first off the run note Note 2, etc. For each note on each day we measure its coupon spread as the price deviation from a replicating portfolio of coupon strips. We use the Gibbs sampler to construct the posterior distribution of the eigenvectors from the correlation matrix. This plot shows properties of the posterior distribution on the second eigenvector (or the loadings of Notes 1 31 on the second principal component). We show the inter quartile range of the posterior (box), the median (bar inside the box), and 95% confidence interval (the whiskers). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Note (by age) May 1997 December 2002 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Note (by age) January 2003 June 2008
Second eigenvector Period 3. Loading 0.0 0.2 0.4 0.6 All notes are sorted by age with the on the run note being Note 1, the first off the run note Note 2, etc. For each note on each day we measure its coupon spread as the price deviation from a replicating portfolio of coupon strips. We use the Gibbs sampler to construct the posterior distribution of the eigenvectors from the correlation matrix. This plot shows properties of the posterior distribution on the second eigenvector (or the loadings of Notes 1 31 on the second principal component). We show the inter quartile range of the posterior (box), the median (bar inside the box), and 95% confidence interval (the whiskers). 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 Note (by age) July 2008 March 2011
Cumulative % Explained Component Period 1 Period 2 Period 3 1 43.1 52.6 81.0 (0.9) (0.9) (0.06) 2 59.3 62.9 88.8 (0.8) (0.8) (0.05) 3 68.1 68.6 91.7 (0.6) (0.7) (0.04) 3F 71.6 79.0 96.3 (0.3) (0.2) (0.04) It appears that the slope factor is unique to the first period.
Correlation with Hu, Pan and Wang s Noise Component Period 1 Period 2 Period 3 1 30.8 83.4 94.0 (0.4) (0.1) (0.04) 2-40.0 1.6-22.5 (1.2) (2.5) (3.8) 3-1.9-27.2 NI (3.4) (2.3) ( ) R 2 25.7 77.1 94.7 (0.6) (0.5) (0.7) F-1 50.8 74.4 95.0 (0.6) (0.6) (0.2)
Correlation with on-the-run premia Component Period 1 Period 2 Period 3 1-18.1 15.5-22.2 (0.4) (0.3) (0.1) 2-8.8-17.6 28.8 (0.9) (1.4) (1.3) 3 7.4 8.9 NI (1.9) (1.2) ( ) R 2 4.7 8.9 19.2 (0.3) (1.2) (6.4) F-1-10.0-1.4-23.4 (0.8) (0.6) (0.5)
Non-On-the-Run Specials Little if anything is known about specials for non-on-the-run notes. % of possible times on special Note(s) Period 1 Period 2 Period 3 1 42.5 43.2 57.6 2 15.8 20.4 22.1 3 2.9 10.3 10.6 4 2.1 8.2 9.3 All Del. 8.4 12.3 19.6 All Non-del. 1.7 5.2 17.4 From Period 1 to 2: Consistent with flattening out of the on-the-run premium seen in Slide 11.
Non-On-the-Run Specials 2. Little if anything is known about specials for non-on-the-run notes. Mean Spreads above Minimum Lending Fee (bps) Note(s) Period 1 Period 2 Period 3 1 89 73 20 2 77 42 2 3 56 20 9 4 18 25 3 All Del. 77 37 6 All Non-del. 2 2 2 Interesting general decline in special rates, even during the crisis, and after fails penalty imposition.
5 3 4 % August 2010 Note; May 2004 May 2007 Cents/$100 par value 200 150 100 50 0-50 -100-150 Coupon Spread Reconstitution Spread 112 110 108 106 104 102 100 98 96 Basis Points -200 5/17/04 7/6/04 8/23/04 10/12/04 12/1/04 1/20/05 3/10/05 4/28/05 6/16/05 8/4/05 9/22/05 11/10/05 1/3/06 2/22/06 4/11/06 5/31/06 7/19/06 9/6/06 10/25/06 12/13/06 2/2/07 3/23/07 5/11/07 Date Reconstitution Spread (right axis) Coupon Spread (right axis) (left axis) 94
Delivery Fails (All Treasuries) 3000000 2500000 2000000 Fails ($ millions) 400000 350000 300000 250000 200000 150000 100000 50000 0 Eight-Month Period A round the May 1, 2009 300bp Fee Fails ( $ millions) 1500000 1000000 Date 500000 0 Date A 300bp fails penalty fee was implemented on May 1, 2009 by TPMG and SIFMA
New 10-year Note: QE-I 600 2200 Cents per $100 par value/basis Points 500 400 300 200 2000 1800 1600 1400 1200 1000 800 600 Fed Purchases ($ millions) 100 Coupon Spread 400 200 0 2/17/09 3/17/09 4/17/09 5/17/09 6/17/09 7/17/09 8/17/09 9/17/09 10/17/09 Date 0 Y T M on 20 year old 30-year bond (left axis) Coupon spread on new 10-year note (left axis) Fed purchases of new 10-year note (right axis) Y T M on new 10-year note (left axis) Fed purchases of 20 year old 30-year bond (right axis)
The Speed of Capital The spike in the on-the-run note s coupon spread on the announcement on March 18 (it was 491 on 3/17, and 370 on 3/19), is relevant to understanding the speed of arbitrage capital. This convergence was not the result of gradual restoration of risky balance sheets. The Fed s announcement changed the risk profile and capital moved in. And the effect occurred before the Fed bought a single US Treasury security. Most significant effect of QE-I as the effect on coupon spreads is permanent.
New 10-year Note: QE-II 900 New 10 year note Yield-to-Maturity (basis points) / Coupon Spread (cents per $100 par) 350 300 250 200 150 100 800 700 600 500 400 300 200 Fed Purchases ($ Millions) 50 8/16/2010 10/5/2010 11/24/2010 1/13/2011 3/4/2011 Date 100 Y T M on new 10-year note (left axis) Coupon Spread on new 10-year note (left axis) Y T M on 20 year old 30-year bond (right axis) Fed purchases of 20 year old 30-year bond (right axis)
What s Next? I like Buraschi, Sener, and Menguturk (2012). Studies spreads between Mexican, Brazilian, and Turkish sovereign debt in $ and euro. These spreads also explode during the financial crisis. They regress the spreads on proxies for risk factors that might drive the financial frictions. Like Mitchell & Pulvino they find strong correlations between their empirical measure of during the crisis and usual suspects. They infer e.g.: Closed End Fund Discount risk... accounts for a majority of the explanation.