Chacko Slides

8/8/2019 Chacko Slides

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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



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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



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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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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



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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



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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


Optimizing on Credit Risk

Sub-Optimal Sharpe: 0.19Sharpe 1: 0.72 Sharpe 2:0.84

Documents

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