Anchoring Credit Default Swap Spreads to Firm...

Anchoring Credit Default Swap Spreads toFirm Fundamentals

Jennie Bai and Liuren Wu

NY Fed & Baruch College

October 11, 2011Baruch Brown Bag

Liuren Wu (Baruch) WCDS 10/11/2011 1 / 24

Objective

Examine the capability of structural models, and more generally firmfundamental characteristics, in explaining the cross-sectional variation ofcredit default swap (CDS) spreads across different firms.


Literature

The performance of structural models and firm fundamentals has beenexamined from several angles:

1 Average bias: All models are biased one way or the other.Huang&Huang (2003), Eom, Helwege, Huang (2004), ...

2 Time-series regressions on monthly changes: Low R2 (Collin-Dufresne,Goldstein, and Martin (2001),...)

3 Hedging performance: Schaefer & Strebulaev (2008)

4 Default probabilities: KMV, Bharath & Shumway (2008)

Implications on their cross-sectional explanatory power on CDS:1 Average bias (non-zero intercept) can co-exist with high R2 in a

cross-sectional level regression.

2 Short-term movements can be driven by supply-demand shocks insteadof changes in fundamentals. Low time-series R2 on short-term changescan co-exist with high cross-sectional R2 on levels.

3 Change regressions generate the right slope but low R2?

4 It is easier to link fundamentals to CDS than to actual defaults.Liuren Wu (Baruch) WCDS 10/11/2011 3 / 24

Overview

Explain the cross-sectional CDS variation with firm fundamentals

CDS: Take five-year credit default swap spread from Markit as thebenchmark credit spreads.

MCDS: Propose a new implementation of the Merton model to explain thecross-sectional variation of five-year CDS spreads.

WCDS: Propose a Bayesian shrinkage methodology to combine a long list offinancial variables with the Merton prediction to enhance the cross-sectionalexplanatory power.

Performance metrics:

1 Cross-sectional correlation between CDS and MCDS/WCDS.→ square root of the R2 from a cross-sectional regression

2 Cross-sectional correlation between current market-model deviationsand future market movements,Corr (ln(CDSt+h/CDSt), ln(CDSt/FCDSt)), FCDS=MCDS, WCDS.


Why do we focuse on cross-sectional variation?

If a model prediction can explain a high proportion of the cross-sectionalvariation, the model can be applied in at least two areas:

1 Interpolation/extrapolation (for market makers/broker dealers):

There are thousands of companies in the U.S. non-financial universewith fundamental information publicly available.

Less than 500 of them have valid CDS quotes.

If a model can differentiate the CDS level difference across differentfirms based on fundamental information, one can calibrate the modelto the 500 companies with CDS quotes to generate CDS quotes on theother thousands of companies.

Average bias is removed by design (via cross-sectional fitting).

Robustness can be measured by an out-of-sample analysis: Calibratethe model using half of the universe with CDS, and verify the CDSprediction on the other half.


Why do we focuse on cross-sectional variation?

1 Interpolation/extrapolation (for market makers/broker dealers):

2 Alpha generation (for investors/hedge funds):

In this case, the criterion for a good model is not to generate smallpricing errors, but to generate large, transient errors.

A market-neutral strategy would ask for a model that does notgenerate an average bias cross-sectionally.

The low R2 from time-series change regression suggests the possibleexistence of short-term transient supply-demand shocks.

The model valuation can be used to separate the permanentcomponent from the transient component.

Use current market deviations from model valuation to predict futuremarket movements.

In a cross-sectionally calibrated model, the forecasting correlation is anout-of-sample measure and can be used to hedge against in-sampleover-fitting.


Data collection and sample construction

Create a weekly (Wednesday) sample date list from January 8, 2003 toSeptember 30, 2009, 351 weeks.

At each date, identify a list of U.S. non-financial, public companies with

Five-year CDS observation from Markit.Total debt from Capital IQ.One year stock market history from CRSP.

Most analyses are cross-sectional.

579 companies are selected, with 138,200 week-company observations.

Each day, the number of available firms ranges from 246 to 474.


Financial ratios

For each company, collect/compute the following additional variables whenavailable:

Leverage: (i) The ratio of (current liability + 0.5 long-term liability) tomarket capitalization (LM), (ii) Debt to asset ratio (DA)Coverage: EBIT to Interest expense ratio (EE)Liquidity: Working capital to total asset ratio (WA)Profitability: EBIT to total asset (EA)Investment: Retained earning to total asset (RA)Size: Log market capitalization (MC)Options: One-year option implied volatility to realized volatility ratio(IV)Momentum: One year stock return (MM).

Timing: We use a 45-day rule to match the quarterly financial statementinformation with market data.

Example: Match market data between May 15 to August 14 with theQ1 balance sheet, market data between August 15 to November 14with Q2 balance sheet, ...


MCDS: A new implementation of the Merton model

Inputs: total debt (TD), the one-year realized volatility on the stock return(RV ), and the market capitalization (MC ).

Outputs: Firm value FV and firm volatility σF :

MC = FV ·N(d + σF√

T )−TD ·N(d), RV = N(d + σF√

T )σFFV /MC ,

Compute the standardized leverage metric — distance to default:

DD =ln(FV /TD)− 1

2σ2FT

σF√

T.

Convert the distance to default into a raw CDS spread, RCDS,

RCDS = −6000 · ln(N(DD))/T . (1)

Remove systematic bias and nonlinearity in the raw model prediction viacross-sectional monotone, local quadratic regression,

ln(CDS) = f (ln(RCDS)) + R.

We label the bias-corrected Merton model prediction as MCDS:ln(MCDS) = f̂ (ln(RCDS)).Liuren Wu (Baruch) WCDS 10/11/2011 9 / 24

Structural model implementation variations

The implementation differs from general practices in several aspects to enhancethe cross-sectional explanatory power.

Many academic papers follow KMV practices.

KMV sets T = 1 to match the forecasting horizon, we set T = 10 to becloser to the average maturity of the debt. ⇒ Volatility plays a bigger rolewith a longer maturity.

KMV uses current liability plus half of long-term debt as the debt principal.We use total debt.

Some assume that equity is a knock-out call option instead a European call:FV = TD + MC (← Bharath& Shumway’s “naive” measure).

Instead of focusing on DD, or a raw CDS prediction, we remove the averagebias and nonlinearity via a local quadratic regression. This procedure allowsus to focus on the model’s capability in differentiating the CDS levels acrossdifferent firms.

Some transform an estimated default probability into a CDS number byadding a risk premium, it is easier & more accurate the other way around.


WCDS: A Bayesian approach to include additional variables

Define the MCDS’ deviation from market as R = ln(CDS)− ln(MCDS).

Orthogonalize each variable F of its contribution to MCDS:

F kk = f k(ln(MCDSt)) + xk

t , k = 1, 2, · · · ,K .

Map the deviation to each orthogonalized variable x ,

Rt = f k(xkt ) + ek

t , k = 1, 2, · · · ,K .

Stack the contribution from all variables, Xt = [R̂1t , R̂

2t , · · · , R̂K

t ].

Replace missing values with the average prediction from other variables.

R ijt =

K̃∑k=1

wk R̂ i,kt , wk = e>(ee′ + diag〈1− R2〉)−1,

Bayesian shrinkage to maintain intertemporal stability of weights,

B̂t = (X>t Xt+Pt−1)−1(

X>t Rt + Pt−1B̂t−1

),Pt = diag〈(X>t Xt+Pt−1)φ〉.

Generate the WCDS prediction: ln(WCDS)t = ln(MCDS)t + XtB̂t .


Discussions on WCDS implementation details

One can in principle directly add the Merton model inputs into the WCDSconstruction.

We use MCDS to serve as a benchmark and examine the additionalcontribution of other variables.

The univariate nonlinear mapping removes the potential nonlinearity in themarginal contribution.

It does not adjust for nonlinearity in interactions.

Bates& Granger (69) find that simple equal weighting of many predictorscan generate an enhanced aggregate predictor — can be better thanweighted average with regression estimated weights due to overfitting issues.

Our Bayesian shrinkage approach takes equal weighting as a prior atthe beginning.

It corrects potential multi-collinearity with a ridge regression analog.

It is a little smarter than simple average, but a lot more conservativethan unconstrained regression.


Mean bias of the raw Merton prediction

A. Mean percentage bias B. Weekly mean percentage bias

3 3.5 4 4.5 5 5.5 6 6.5 7−0.5

0

0.5

1

1.5

2

2.5

ln(C

DS

/RC

DS

)

ln(CDS)

03 04 05 06 07 08 09 10−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

ln(C

DS

/RC

DS

)

25%

50%

75%

Merton model under-predicts market CDS, especially for investment-gradecompanies and under booming market conditions.

The mean biases are much smaller during recessions and for high-yieldcompanies.

Similar to literature findings.


The cross-sectional explanatory power

Corr(CDS, MCDS) and Corr (CDS, WCDS)

Statistics MCDS WCDS Diff Z

Panel A: In-sample performance from full-sample estimationMean 0.81 0.88 0.07 3.29Std 0.05 0.02 0.03 1.14t-stats 44.43 109.58 5.84 8.58

Panel C: Out-of-sample performance from half-sample estimationMean 0.80 0.86 0.06 1.95Std 0.06 0.03 0.04 0.88t-stats 61.26 163.39 6.98 10.03

MCDS works well as its cross-sectional correlation with market averages at81%, corresponding to an R2 of 65%, higher than findings in the literature.

WCDS significantly improves upon MCDS in its cross-sectional explanatorypower.

Out-of-sample statistics from half-sample estimation show little deterioration⇒ WCDS can serve the first application (extrapolation) well.Liuren Wu (Baruch) WCDS 10/11/2011 14 / 24

The cross-sectional explanatory power

The time series of the cross-sectional correlation between market andfundamental-based predictions:

03 04 05 06 07 08 09 100.7

0.75

0.8

0.85

0.9

0.95C

ross

−sec

tiona

l Cor

rela

tion

WCDS

MCDS

MCDS works better during recessions than during economic booms.

By incorporating a long list of additional variables via a Bayesian shrinkagemethod, WCDS not only performs better than MCDS, but its performancealso shows more stability/uniformity across different sample periods.


When model deviates from market, which one is right?

When model deviates from market, several possibilities exist:

1 Model deficiency: The model does not include all credit-informativevariables.

2 Information asymmetry: CDS market investors know more (faster)about credit risk than do the fundamental-based predictions.

⇒ Current deviation predicts future change in model value.Corr(ln(CDSt/FCDSt), ln(FCDSt+1/FCDSt)) > 0.

3 Information asymmetry: Fundamental-based predictions containinformation not yet embedded in the CDS market (Markit).

⇒ Current deviation predicts future change in market CDS.Corr(ln(CDSt/FCDSt), ln(CDSt+1/CDSt)) < 0.

4 Permanent v. transient shocks: Firm fundamentals capture thepermanent component of the credit risk. Deviations from fundamentalsare mainly driven transient supply-demand shocks.

⇒ Current deviation predicts future change in market CDS.Corr(ln(CDSt/FCDSt), ln(CDSt+1/CDSt)) < 0.

“FCDS” denotes fundamental-based predictions, either MCDS or WCDS.


One-week ahead forecasting correlations

Forecasting market movements Forecasting prediction changes

03 04 05 06 07 08 09 10−0.12

−0.1

−0.08

−0.06

−0.04

−0.02

0

Corr

(ln(C

DS

t/FC

DS

t),∆

ln(C

DS

t+1)

WCDS

MCDS

03 04 05 06 07 08 09 100.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Corr

(ln(C

DS

t/FC

DS

t),∆

ln(F

CD

St+

1)

WCDS

MCDS

There is two-way information flow between Markit CDS quotes andfundamental-based predictions.

These are purely out of sample estimates — estimation of MCDSt andWCDSt does not depend on any information at time greater than t.


Forecasting correlations over different horizons

Horizon MCDS WCDS WCDS-MCDSh Mean Std t-stats Mean Std t-stats Mean Std t-stats

Panel A: Corr(ln(CDSt/FCDSt), ln(CDSt+h/CDSt)1 -0.06 0.08 -12.46 -0.07 0.08 -17.57 -0.02 0.04 -6.612 -0.08 0.09 -15.36 -0.10 0.08 -21.85 -0.02 0.05 -7.463 -0.09 0.10 -17.12 -0.11 0.08 -24.74 -0.02 0.05 -8.124 -0.10 0.10 -18.53 -0.12 0.09 -26.90 -0.02 0.05 -8.13

Panel B: Corr(ln(CDSt/FCDSt), ln(FCDSt+h/FCDSt)1 0.04 0.06 11.45 0.06 0.07 16.28 0.02 0.08 5.042 0.05 0.06 16.33 0.07 0.06 21.31 0.02 0.07 4.923 0.07 0.06 19.46 0.08 0.06 24.14 0.02 0.07 4.464 0.08 0.06 21.85 0.09 0.07 25.86 0.01 0.07 3.72

Deviations from WCDS forecast future market movements significantlybetter than deviations from MCDS.

By incorporating information from more sources, WCDS is also moreresponsive to market CDS levels.


VECM and price discovery

A vector error-correction model (VECM) of Engle and Granger (1987):[∆ ln(CDSt+1)

∆ ln(MCDSt+1)

]=

[α1

α2

]Dt+

[β1β2

]ln (CDSt/MCDSt)+

[e1,t+1

e2,t+1

],

Composition of a permanent component in the CDS-MCDS pair(w1

w2

)=

1

β1 − β2

(−β2β1

)=

(32.06%67.94%

)← Markit← MCDS

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Weeks

Imp

uls

e r

esp

on

se

CDS

MCDS

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Weeks

Imp

uls

e r

esp

on

se

CDS

MCDS


VECM and price discovery

Composition of a permanent component in the CDS-WCDS pair(w1

w2

)=

1

β1 − β2

(−β2β1

)=

(44.72%55.28%

)← Markit←WCDS

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Weeks

Imp

uls

e r

esp

on

se

CDS

WCDS

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Weeks

Imp

uls

e r

esp

on

se

CDS

WCDS

Fundamental-based predictions contribute to a larger proportion of thepermanent component of CDS movements.

WCDS is more responsive to market movements than does MCDS.Liuren Wu (Baruch) WCDS 10/11/2011 20 / 24

An out-of-sample investment exercise

Invest in each CDS contract based on the deviation between marketobservation and fundamental prediction, ni

t = ct(FCDS i

t − CDS it

).

Hold for different horizons (1 to 4 weeks)

Horizon, h Annual. Mean (%) Mean (%) Std (%) Sharpe

A. Investments based on MCDS prediction1 25.25 0.49 2.32 1.512 19.11 0.74 3.14 1.193 14.64 0.84 3.87 0.914 12.63 0.97 4.84 0.73

B. Investments based on WCDS prediction1 32.08 0.62 1.97 2.262 26.98 1.04 2.71 1.953 21.58 1.25 3.33 1.594 18.77 1.44 4.05 1.29

WCDS generates more economically significant predictions than does MCDS.


Time-varying relative contributions

03 04 05 06 07 08 09 10−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

B

LMDA

03 04 05 06 07 08 09 10−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

B

EEWA

03 04 05 06 07 08 09 100.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

B

EARA

03 04 05 06 07 08 09 100.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

B

MCIVMM


Concluding remarks

Fundamental-based predictions can explain a large proportion of thecross-sectional market CDS variation.

An appropriate implementation of the Merton model generates goodcross-sectional explanatory power, despite the average bias of the rawprediction.Incorporating additional fundamental variables via a Bayesian shrinkagemethod can further improve the performance significantly.

When market observations deviate from fundamental-based predictions, it ismore likely that the future market CDS reverts back to the fundamentalprediction than the other way around.

Current market-fundamental deviations forecast future marketmovements.This prediction is significant both statistically and economically.WCDS not only explains more cross-sectional variation, but alsogenerates stronger prediction for future market movements.

A long list of financial variables are found to contribute to the informationaldiscovery of credit risk on top of the Merton model inputs.

We propose a Bayesian approach to combine the predictions from thislong list of variables with the Merton prediction.


After thoughts: What is the purpose of a model?

To reveal average bias and risk premium puzzles (Huang & Huang...)

What risk premiums are we not puzzled by?Cremers, Driessen, and Maenhout: Credit risk premium is consistentwith option risk premium.Carr & Wu: DOOM puts are priced similar to CDS.

To show why & which fundamentals matter.

Fundamentals do not matter much for monthly changes(Collin-Dufresne, Goldstein, Martin).Market level deviations from fundamentals predict future monthlychanges!

To provide an informative anchor for market prices.

Faster is not always better.The fastest movement is bid-ask bounce/noise.

Perfectly matching market prices is not always the goal of modeling.Provided that the model pricing errors are highly transient, the largerthe error, the better!


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