Transcript
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FIXED INCOME
George Chacko
Harvard Business School & IFL
Liquidity Risk In CorporateBond Markets
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Roadmap Introduction
Liquidity Risk Research Motivation Liquidity Measurement Liquidity Factor Construction Empirical Results for Liquidity Risk Practical Implications of Liquidity Risk
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Capital Structure
Arbitrage
Worldcom Risk-Neutral Default Probability
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
J S D J S D J
Probability
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Worldcom 6.95 30Y
Issuance Date: Aug-1998 Amount: $1.75 BB Callable
0
2
4
6
8
10
12
14
16
J
ul-00
O
ct-00
J
an-01
A
pr-01
J
ul-01
O
ct-01
J
an-02
A
pr-02
Spreadove
rbenc
hmarkTreasu
ryStrip
(%)
Forecast Spread
Actual Traded Spread
Baa2
Ba2
Caa
Capital Structure
Arbitrage
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Corp Bond Market
LiquidityIssue Trading Frequency -
Median bond trades less than once a quarte
100.00%
3.58%
13.40%
39.23%
24.33%
0
2000
4000
6000
8000
10000
12000
14000
16000
1 Trade/Week 1 Trade/M 1 Trade/Qtr > 1 Trade/Qtr No Trades
Trading Frequency
Nu
mberofIssues
(Total:24170)
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
Cumula
tivePercentIssues
ource: State Street Global Markets
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Liquidity Trend in Bond
MktAverage Trade Size Percentiles (millions of US dollars):
YR94 YR95 YR96 YR97 YR98 YR99 YR00 YR01 YR02 YR03 YR04
MIN 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
10% 0.36 0.44 0.43 0.48 0.50 0.43 0.40 0.42 0.37 0.35 0.28
20% 0.75 0.83 0.84 0.94 0.97 0.82 0.72 0.73 0.67 0.66 0.55
30% 1.06 1.11 1.18 1.23 1.32 1.12 1.01 1.03 0.94 0.91 0.78
40% 1.43 1.50 1.63 1.68 1.78 1.54 1.38 1.43 1.22 1.16 1.03
50% 1.84 2.02 2.09 2.16 2.34 2.08 1.93 1.98 1.66 1.52 1.30
60% 2.30 2.63 2.71 2.85 3.10 2.88 2.56 2.65 2.21 1.97 1.65
70% 3.02 3.59 3.61 3.72 4.15 3.89 3.45 3.59 2.99 2.50 2.17
80% 4.10 4.99 4.97 5.06 5.56 5.31 5.02 5.12 4.30 3.46 2.88
90% 6.20 7.22 7.33 8.00 9.16 8.93 8.23 8.42 7.06 5.75 4.55
MAX 100.31 99.92 100.67 111.99 224.98 249.93 152.53 199.98 271.99 199.98 100.28
ource: State Street Global Markets
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TRACE
ComparisonCUSIP 172967BC4 (CITIGROUP), 4/14/2004 -- 1
99
101
103
105
107
109
111
113
115
4/14/2004
4/21/2004
4/28/2004
5/5/2
004
5/12/2004
5/19/2004
5/26/2004
6/2/2
004
6/9/2
004
6/16/2004
6/23/2004
6/30/2004
7/7/2
004
7/14/2004
7/21/2004
7/28/2004
8/4/2
004
8/11/2004
8/18/2004
8/25/2004
9/1/2
004
9/8/2
004
9/15/2004
9/22/2004
9/29/2004
TRACE High (via Bloomberg)
TRACE Low (via Bloomberg)
TRACE 1MM+ HighTRACE 1MM+ Low
ource: State Street Global Markets
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Limitations of Liquidity
Measures
Conventional Measures of Liquidity:
Trading Volume
Bid-Ask Spread
However, if securities are extremely illiquid,
conventional measures dont work well
Rather than looking at actual trading, onesolution is to look at a securitys propensity totrade.
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Latent Liquidity Latent liquidity: a quantitative measure of propensity to
trade for individual securities
Rationale:
For a bond dealer, it is easier to access a bond issue ifit is held in high-turnover portfolios
If a bond issue is held by high-turnover funds, it islikely that security has a higher propensity to trade.
So, a securitys propensity to trade can be constructedby looking at the aggregate trading characteristics ofowners of that security
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Latent Liquidity PropertiesLatent Liquidity vs. Principal Issued
1.0
2.0
3.0
4.0
5.0
$0.0 $0.5 $1.0 $1.5 $2.0
Principal amount ($ Billion)
L
atentLiquidityBuck
HigherLiquidity
Lower
Liquidity
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Latent Liquidity PropertiesLatent Liqudity vs. Age of Bond
1
2
3
4
5
0 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
Age - (Years Since Issuance)
LatentLiquidityBuc
HigherLiquidity
LowerLiquidity
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Latent Liquidity PropertiesLatent Liquidity Bucket vs. Time To Maturity
1
2
3
4
5
- 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0
Average Time To Maturity (Years)
Averge
LatentLiquidityBu
HigherLiquidity
Lower Liquidity
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Liquidity Risk Factor
Construction We sort the US corp bond universe into 3x3x3 = 27
buckets
Duration
Credit Risk Latent Liquidity
We then form three portfolios:
HML Duration
LMH Credit Risk LMH Latent Liquidity
These portfolios represent interest rate, credit, andliquidity risk factors
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Liquidity Risk Factor
Time Series
8 0
9 0
1 00
1 10
1 20
1 30
1 40
11/27/19934/11/1995 8/23/1996 1/5/1998 5/20/19991 0/1/2000 2/13/2002 6/28/2003D at
Liquidity
Index
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Factor Regressions With these factors, we can now do factor
regressions to compute individual security betas.
We first compute credit, duration, and liquidity
betas for the US corp bond universe. We then do a 5x3x3 sort of these securities based
on these betas 5 liquidity portfolios, 3 creditportfolios, and 3 duration portfolios
Using these 45 portfolios, we then conduct a seriesof tests to check the importance of the liquidity risk
factor.
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Empirical ResultsLiquidity Risk Alpha
L M/L M H/M H H - L
CAPM -0.54% 0.71% 1.25% 1.94% 2.36% 2.90%
Duration -0.36% 0.69% 1.31% 2.13% 2.78% 3.14%
Duration, Credit -0.56% 0.63% 1.09% 1.68% 2.15% 2.71%
Alphas of Portfolios Sorted on Liquidity Betas
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Empirical ResultsContribution of Liquidity: 1
Incremental R2 of Liquidity Factor
Liquidity Portfolios
H H/M M M/L L
Credit H 5% 12% 18% 23% 30%
Portfolios M 5% 13% 21% 25% 32%
L 4% 13% 22% 26% 34%
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Empirical ResultsContribution of Liquidity: 2
Incremental R2 of Liquidity Factor
Liquidity Portfolios
H H/M M M/L L
Duration L 4% 14% 21% 27% 36%
Portfolios M 3% 16% 20% 28% 37%
H 6% 17% 23% 30% 39%
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Practical ImplicationsConvertible Arbitrage
Alpha DEF TERM Rm-Rf SMB HML UMD Liq. Adj.R2
0.0029 -0.66 -0.33 0.27 0.3859
1.39 -1.43 -1.21 3.65
0.0011 -0.02 0.09 -0.19 0.07 0.08 -0.02 0.24 0.4897
0.59 -0.13 1.1 -2.45 2.45 1.28 -0.09 2.93
0.0012 -0.19 0.06 0.1 0.01 0.26 0.4565
0.67 -2.58 1.82 1.54 0.24 3.47
0.0004 -0.66 -0.33 0.055
0.58 -1.43 -1.21
0.0026 -0.02 0.08 -0.15 0.07 0.08 -0.03 0.1598
3.51 -0.15 1.08 -2.74 2.44 1.26 -0.09
0.0035 -0.17 0.06 0.09 0.01 0.1566
3.32 -2.07 1.8 1.51 0.25
Benchmark Regressions
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Practical ImplicationsTreasury Yield Curve
Maturity Curvature Term Liquidity
0.5 2 3 5
1 3 7 10
2 7 9 16
3 13 16 27
5 29 37 567 38 46 73
10 21 64 97
Average Contribution of Factors to Bond Yields (RMSE)
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Practical Implications
Back to WorldCom
Worldcom 6.95 30Y
Issuance Date: Aug-1998 Amount: $1.75 BB Callable
0
2
4
6
8
10
12
14
16
Ju
l-00
Oct
-00
Ja
n
-01
Ap
r
-01
Ju
l-01
Oct
-01
Ja
n
-02
Ap
r
-02
Spreadoverbenchma
rkTreasuryStrip(%
)Forecast Spread
Actual Traded Spread
Baa2
Ba2
Caa
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Yield Spread Decomposition for WorldCom(MCIP 8.000 05/15/06)
-
1.00
2.00
3.00
4.00
5.00
6.00
1/1/2001
2/1/2001
3/1/2001
4/1/2001
5/1/2001
6/1/2001
7/1/2001
8/1/2001
9/1/2001
10/1/2001
11/1/2001
12/1/2001
1/1/2002
2/1/2002
Spread(%
Yield Spread Credit Risk Premium Liquidity Risk Premium
Practical ImplicationsCredit vs. Liquidity Spread
1/1/01 -1/1/02: Change in creditspread is minimal
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Practical Implications
Credit vs. Liquidity Spread
Yield Spread Decomposition for Corporate Ba
-
2.00
4.00
6.00
8.00
10.00
12.00
1/1/99
7/1/99
1/1/00
7/1/00
1/1/01
7/1/01
1/1/02
7/1/02
1/1/03
7/1/03
1/1/04
7/1/04
Spread(%)
Yield Spread Credit Risk Premium LiquidityRisk Premiu
Yield Sperad Decomposition for Corporate Baa I
-
1.00
2.00
3.00
4.00
5.00
1/1/99
7/1/99
1/1/00
7/1/00
1/1/01
7/1/01
1/1/02
7/1/02
1/1/03
7/1/03
1/1/04
7/1/04
Spread(%)
RYS YS_duetoCR YS_duetoLR
Baa Index Ba Index
ource: State Street Global Markets
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Practical Implications
Liquidity-Driven Asset Allocation Problem:
Allocate portfolio across a set of Moodys Baa1 orhigher rated long duration securities.
Set: BLS, CAT, BA, CCE, IBM, D,ALL, WFC, PFE, SBC
Scenarios
Scenario 1 (Optimizing on Total Risk)
Scenario 2 (Optimizing on Liquidity risk)
Scenario 3 (Optimizing on Credit risk)
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Liquidity OptimizedEfficient Frontier
0
0.004
0.008
0.012
0.016
0.02
0 0.05 0.1 0.15 0.2 0.25 0.3
Liquidity Risk
R
eturn
Attributable
to
Li
Risk
LR-optimized Sub-optimal Allocation
Practical ImplicationsOptimizing on Liquidity Risk
Sub-Optimal Sharpe: 1.05Sharpe 1: 1.69 Sharpe 2:1.96
ource: State Street Global Markets
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Credit OptimizedEfficient Frontier
0
0.005
0.01
0.015
0.02
0.025
0 0.1 0.2 0.3 0.4 0.5 0.6
Credit Risk
ReturnAttributabletoCr
Credit Risk Optimized Sub-Optimal Credit Allocation
Practical Implications
Optimizing on Credit Risk
Sub-Optimal Sharpe: 0.19Sharpe 1: 0.72 Sharpe 2:0.84
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