Do Leveraged Credit Derivatives Modify Credit Allocation ?

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J.F. Boulier, M. Brière & J.R. Viala

Crédit Agricole Asset Management, Université Libre de Bruxelles

EDHEC Symposium « Risk and Asset Management », Nice, April 19, 2008

Do Leveraged Credit Derivatives Modify Credit

Allocation ?

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Introduction

5 000 10 000 15 000 20 000

25 000 M arché G lobal des D érivés du C rédit en M ds $ (source: B B A )

O bligations G lobales C orporate en souffrance en M ds $ (indice M L global broad corporate)

Exponential expansion of credit derivatives markets

The fastest growing part of the global financial derivatives

Driven by :

Need of higher yielding investments in a context of low yields Need of hedging or gaining exposure to credit without funding Strong interest by some market participants in leveraging

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Introduction

0% 10% 20% 30% 40% 50% 60% Single-name CDSs Full index trades Tranched index Synthetic CDO's Credit linked notes Basket products 2004 2006 A strong product innovation

Initial growth began with single names CDS market

Development of synthetic CDO, index tranches, CDO² (CDO of CDO), CPPI, CPDO…

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Introduction

Our questions :

Does this new “asset class” change the strategic global allocation for an asset manager ?

What happens if we replace the investment in traditional corporate bonds in credit derivatives ?

How much should be invested in this new asset class ? How much should we optimally leverage this asset class ?

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This work:

Builds efficient frontiers in a mean/variance framework

based on long term assumptions on expected returns and covarariances

Compares efficient frontiers

traditional corporate bonds (IG and HY) or credit derivatives with different degrees of leverage

The analysis requires long samples on all asset classes

Credit derivatives : analysis of CDS market (deepest) CDS indices begin in 2004

Approximation to recover a “simulated” longer history

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Methodology

Approximation of CDS returns

A CDS is an agreement between 2 parties to exchange credit risk of a reference entity

The seller of a CDS sells protection

He receives periodic fee if the credit of the reference stable or improves

He pays a compensation to the buyer in case of credit event

CDS premium approximated by the bond credit spread over swap

Theoretically, funding at libor, buying protection through CDS and entering an asset swap is fully hedged in any state of the world (Hjort et al. (2002))

In practice, difference between the 2 : the “basis” (De Wit (2006)) Relatively good approximation to use the credit spread

cf empirical tests : Blanco, Brennan and Marsh (2003), Houweling and Vorst (2002), Hull, Predescu and White (2004)

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Methodology

This was true before the Subprime crisis !

CDS monthly returns (iTraxx, source JPMorgan)

Corporate bond – swap rate +3M cash rate monthly returns

-0.8% -0.4% 0.0% 0.4% 0.8% 1.2% 1.6% 02 /07/20 04 02 /09/20 04 02 /11/20 04 02 /01/20 05 02 /03/20 05 02 /05/20 05 02 /07/20 05 02 /09/20 05 02 /11/20 05 02 /01/20 06 02 /03/20 06 02 /05/20 06 02 /07/20 06 02 /09/20 06 02 /11/20 06

itraxx unfunded Merrill 5-7Y IG - sw ap 5Y

-3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% 02/ 07/ 2004 02/ 10/ 2004 02/ 01/ 2005 02/ 04/ 2005 02/ 07/ 2005 02/ 10/ 2005 02/ 01/ 2006 02/ 04/ 2006 02/ 07/ 2006 02/ 10/ 2006 02/ 01/ 2007 02/ 04/ 2007 02/ 07/ 2007 02/ 10/ 2007 02/ 01/ 2008 02/ 04/ 2008

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Data

Traditional asset classes returns

Weekly returns of gvt bonds, IG and HY bonds, equities in USD April 1995-June 2007

Data source : Datastream for equity and govies (10Y benchmark) indices, Merrill Lynch for corporate bonds indices

100 150 200 250 300 350 400 450 27 /03/95 27 /03/96 27 /03/97 27 /03/98 27 /03/99 27 /03/00 27 /03/01 27 /03/02 27 /03/03 27 /03/04 27 /03/05 27 /03/06 27 /03/07

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Data

Credit derivatives returns

IG and HY CDS indices approximation Swap rates from Datastream

50 100 150 200 250 300 350 400 450 27 /0 3 /1 9 9 5 27 /0 3 /19 96 27 /0 3 /19 9 7 27 /0 3 /19 98 27 /0 3 /19 9 9 27 /0 3 /20 00 27 /0 3 /20 0 1 27 /0 3 /20 02 27 /0 3 /20 0 3 27 /0 3 /20 04 27 /0 3 /20 0 5 2 7 /0 3/20 06 27 /0 3 /20 0 7

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Historical risk / return tradeoff

Gvt Bonds IG bonds IG spreads HY bonds HY spreads Equities

Excess return 1.3% 2.5% 0.7% 3.4% 1.7% 7.2%

Volatility 7.2% 5.1% 3.1% 4.9% 6.4% 17.4%

Sharpe ratio 0.18 0.49 0.22 0.69 0.26 0.41

Historical volatility

Low level of volatility of corporate bond indices (especially HY) compared to govies

Smaller vol for credit derivatives than corporate bonds for IG Higher vol for credit derivatives than corporate bonds for HY

Historical returns

120 bp credit spread for IG over govies, 70 bp over swap 210 bp credit spread for HY over govies, 170 bp over swap

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Historical risk / return tradeoff

Discrepancy in the Sharpe ratios for all asset classes

Attractive Sharpe ratios for IG (0.49) and HY bonds (0.69)

Less attractive picture for credit derivatives (0.22 and 0.26), but still more interesting than govies

0% 1% 2% 3% 4% 5% 6% 7% 8% 0% 5% 10% 15% 20% volatility e xcess r e tu rn HY bonds IG bonds Gvt bonds Equities 0% 1% 2% 3% 4% 5% 6% 7% 8% 0% 5% 10% 15% 20% volatility excess r e tu rn HY spreads IG spreads Gvt bonds Equities

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Correlations

Much weaker (even negative) correlation of credit spreads with Treasuries

Similar correlation with equities

Credit derivatives have a strong diversifying power in a global portfolio

Gvt bonds IG bonds HY bonds Equities Gvt bonds 100.0% 94% 16% -7% IG bonds -33.8% 100.00% 38% 2% HY bonds -62.8% 37.90% 100.00% 30% Equities -6.6% 8.4% 25.7% 100.0% Gvt bonds IG spreads HY spreads Equities Gvt bonds 100.0% -34% -63% -7% IG spreads -33.8% 100.0% 64% 8% HY spreads -62.8% 63.8% 100.0% 26% Equities -6.6% 8.4% 25.7% 100.0%

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Portfolio construction

Classic mean variance optimization with no short selling constraint

Historical VCV matrices on the studied period

Historical expected returns lead to inconsistent efficient frontiers

We suppose a constant Sharpe ratio at 0.3 for each asset class Intermediate level between historical levels for Treasuries 0.18 and equities 0.41, close to credit spreads 0.22-0.26

This makes portfolio composition depend only on the risk profile Optimal weights independant of the level of the Sharpe ratio

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Results

Efficient frontiers : traditional credit compared to credit derivatives (no

leverage) 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% Risk E xce ss Re tu rn

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Results

Improvement in the efficient frontier by investing in credit derivatives

Including IG credit derivatives, we can achieve much less volatile portfolios than with traditional corporate bonds

At higher risk level, IG spreads disappear in favor of HY spreads Credit derivatives offer strong decorrelation and allow to introduce more risky assets (equities) for same level of portfolio risk

Portfolio Risk 3.0% 5.0% 7.0% Excess Return - 2.3% 3.1% Optimal Weights Gvt bonds - 43% 59% IG bonds - 0% 0% HY bonds - 42% 8% Equities - 15% 32% Portfolio Risk 3.0% 5.0% 7.0% Excess Return 2.1% 2.8% 3.2% Optimal Weights Gvt bonds 45% 45% 44% IG spreads _{4% 0% 0%} HY spreads _{47% 32% 20%} Equities _{5% 23% 37%}

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Traditional credit compared to leveraged credit derivatives

Influence of leverage

No change in the Sharpe ratio

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% Risk Ex c e s s R e tu rn

leverage=1 leverage=2 leverage=3 ) ( * ) (L r_f L r r_f r = + − σ σ(L) = L* σ σ σ ) ( * ) ( * ) ( ) ( ) ( f f r rf L r r L L r L r L SR = − = − = −

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Traditional credit compared to leveraged credit derivatives

Influence of leverage

Leveraging increases portfolio risk and allows higher returns

At identical risk level, the higher the leverage, the more we can

reduce the share of risky assets in the portfolio in favour of Treasuries

Optimal allocations contain majority of Treasuries, HY and then equities Portfolio Risk (L=2) 3.0% 5.0% 7.0% Excess Return - 3.2% 3.7% Optimal Weights Gvt bonds - 50% 35% IG bonds - _{0% 0%} HY bonds - 35% 36% Equities - 16% 29% Portfolio Risk (L=3) 3.0% 5.0% 7.0% Excess Return - 3.5% 4.0% Optimal Weights Gvt bonds _{- 62% 46%} IG spreads _{- 0% 0%} HY spreads _{- 28% 34%} Equities _{- 10% 20%}

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We examine how credit derivatives change the construction of an efficient portfolio

We compare 2 types of credit instruments included in a US global portfolio (including gvt bonds and equities)

conventional corporate bonds credit derivatives

Credit risk component has :

very low risk for IG, medium risk (smaller than govies) for HY strong diversifying power relative to traditional asset classes (negative correlation with govies)

Efficient frontiers in a mean variance framework show

the advantage of credit derivatives for portfolio diversification usefulness of leveraging to allow flexible risk modulation

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Directions for future research

Expected returns hypothesis

Strong hypothesis of constant Sharpe ratio

Asymetric nature of credit spreads distribution short spikes and long periods of low values

Mean variance framework problematic for credit spreads : use VaR, conditional VaR ?

Analysis of crisis episodes

Credit derivatives performances / risk in times of stress Consequence for asset allocation