CDS Beta Hedge Back-testing

2

CDS Back-test Portfolio – Base Case

The back-test portfolio consists of 131 CDS names selected on the basis of liquidity and continuous data availability.

All CDS contracts are of 5 years.

Because of the selection criteria, the portfolio covers most headline names, such as AIG, Ambac, MBIA, FSA, etc.

The portfolio is beta-hedged with 5Y on-the-run CDX IG index, rebalanced every 2 days.

The hedged and unhedged portfolio P/L is tracked from Jan 2008 to Mar 2009.

The period covers 2 major stress events – Bear Sterns merged to JP Morgan in March and Lehman bankruptcy in September, and subsequent market dislocation after that.

All CDS quotes are sourced from MarkIt Partners.

3

Back-test Result

-10%

-8%

-6%

-4%

-2%

0%

2%

2008

0104

2008

0204

2008

0304

2008

0403

2008

0501

2008

0530

2008

0627

2008

0728

2008

0825

2008

0923

2008

1023

2008

1121

2008

1222

2009

0122

2009

0220

Cum

ulat

ive

P/L

Unhedged LogSpread Beta Hedged Level Spread Beta Hedged

Prior to September 2008, the hedged portfolio generally kept cumulative P/L below 1% of portfolio notional.

While the performance deteriorated after Lehman’s bankruptcy, the (log spread) beta hedged portfolio can still limit the cumulative loss to 2% up to mid March 2008. During the same period, the unhedged portfolio incurred a 8% loss.

Log spread beta hedge is more effective than level spread beta.

* Cumulative P/L calculation is described in Appendix.

4

The hedge size is reasonably stable, except during the month of Sept 2008.

As a word of caution, daily P/L swing of the beta hedged portfolio could still be large, even though these fluctuations tend to cancel out over time.

How stable is the hedge ratio?

Perfect Hedge LineDeviation from the perfect hedge line represents residual P/L of the hedged portfolio

0%

20%

40%

60%

80%

100%

120%

140%

160%

2008

0102

2008

0131

2008

0229

2008

0401

2008

0429

2008

0528

2008

0625

2008

0724

2008

0821

2008

0919

2008

1021

2008

1119

2008

1218

2009

0120

2009

0218

2009

0318

Hed

ge A

mou

nt (a

s %

of p

ortf

olio

not

iona

l)

-3%

-2%

-1%

0%

1%

2%

3%

-3% -2% -1% 0% 1% 2% 3%

Index 2-day P/L

Unh

edge

d Po

rtfo

lio 2

-day

P/L

5

Different Hedging Intervals

-10%

-8%

-6%

-4%

-2%

0%

2%

Cum

ulat

ive

P/L

Unhedged log Spread Beta Hedged

-10%

-8%

-6%

-4%

-2%

0%

2%

2008

0109

2008

0207

2008

0307

2008

0408

2008

0506

2008

0604

2008

0702

2008

0731

2008

0828

2008

0926

2008

1028

2008

1126

2008

1226

2009

0127

2009

0225

Cum

ulat

ive

P/L

Unhedged log Spread Beta Hedged

Rebalance Daily

Rebalance Weekly

We don’t observe significant difference in hedging performance as changing to 1-day or 5-day hedging intervals, especially prior to September 2008.

This observation is consistent to the stability of the hedging ratio shown in previous slide.

6

How about a smaller portfolio?

-12%

-10%

-8%

-6%

-4%

-2%

0%

2%

4%

2008

0104

2008

0204

2008

0304

2008

0403

2008

0501

2008

0530

2008

0627

2008

0728

2008

0825

2008

0923

2008

1023

2008

1121

2008

1222

2009

0122

2009

0220

Cum

ulat

ive

P/L

Unhedged log Spread Beta Hedged

We randomly selected 40 names from the universe tested in the base case*. (It includes financial names, such as AIG, Ambac.)

We observed slightly higher volatility of the hedged portfolio, but it is still substantially lower than un-hedged.

* The random names are chosen based on alphabetical order of respective CDS tickers

7

Introducing Tenor Mismatch…

-16%

-14%

-12%

-10%

-8%

-6%

-4%

-2%

0%

2008

0104

2008

0204

2008

0304

2008

0403

2008

0501

2008

0530

2008

0627

2008

0728

2008

0825

2008

0923

2008

1023

2008

1121

2008

1222

2009

0122

2009

0220

Cum

ulat

ive

P/L

Unhedged log Spread Beta Hedged

In real CDS portfolios, contracts may have tenors different from the hedging index.

We created a portfolio of the same 131 names in the universe, but with 10-year maturity. We beta-hedged with 5-year index.

At the end of the back-testing period, the cumulative P/L of the hedged portfolio is -2% vs. -10% of the unhedged portfolio.

8

Stress Test…

-20%

-15%

-10%

-5%

0%

5%

10%

15%

2008

0104

2008

0204

2008

0304

2008

0403

2008

0501

2008

0530

2008

0627

2008

0728

2008

0825

2008

0923

2008

1023

2008

1121

2008

1222

2009

0122

2009

0220

Cum

ulat

ive

P/L

Unhedged log Spread Beta Hedged

We created a small portfolio using 23 financial names (e.g. Ambac, AIG, CIT, etc.)

Not surprisingly, the hedge deteriorated after watershed event of Lehman bankruptcy.

It seems to suggest that financials, as a group, are subject to additional common factor other than the index after Sept 2008.

Appendix

10

Beta of CDS contract i is defined as

where Δln(si)=log spread change of CDS contract i,

Δln(sM)=log spread change of market benchmark, and

Log CDS Beta – Statistical Definition

2)]ln([)]ln()ln([)]ln([)]ln([)]ln()ln([

MMM

MiMii sEssE

sEsEssE

iii

iiii

M DVw

sDVws

01

01

iiii

iiiii

p sDVw

sDVw

01

01

E[.] denotes exponentially weighted expectation. (In our implementation, we use decay factor with 6-month half-life.)

Portfolio beta βp is calculated as

By construction, market beta is equal to 1.

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MTM change of CDS contract i, Δvi , can be expressed as

Index Equivalent (H) represents the notional amount of benchmark index contract (CDX IG 5Y in our case) that can offset the MTM change Δvi

Index Equivalent for the portfolio is simply the sum of individual Hi

Portfolio index equivalent is interpreted as the notional of index contract to hedge portfolio systematic risk.

Index Equivalent

MiM

iii

iiii

sssDVN

sDVNv

01

01

MM

iiiii

MMiMiM

iii

sDVsDVNH

sDVHsssDVN

0101

0101

12

P/L over a fixed interval (e.g. daily) of contract i is calculated by

Thus, cumulative P/L from time 0 to time T (non-overlapping) is

where

P/L Calculation

iiiiittttsDVsNPnL

01

kt

PnL

k

Tt

t

it

n

k

1

13

Index Intrinsic Value

0

50

100

150

200

250

300

350

-60

-40

-20

0

20

40

60

80

100

120

140

160Composite Spread

Intrinsic Spread

Dif ference

Index Roll Index Roll

Source: MarkIt

The correlation between single name and index decreases after September 08.

In fact, the index trading level started to deviate from its intrinsic value (calculated by MarkIt) from almost 0 to 50 bp since then.

This discrepancy introduces additional volatility to the hedged portfolio.