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 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 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 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 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 Line Deviation from the perfect hedge line represents residual P/L of the hedged portfolio

5 Different Hedging Intervals 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 This observation is consistent to the stability of the hedging ratio shown in previous slide.

6 How about a smaller portfolio? 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… 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… 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(s i )=log spread change of CDS contract i, Δln(s M )=log spread change of market benchmark, and Log CDS Beta – Statistical Definition E[.] denotes exponentially weighted expectation. (In our implementation, we use decay factor with 6- month half-life.) Portfolio beta β p is calculated as By construction, market beta is equal to 1.

11 MTM change of CDS contract i, Δv i, 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 Δv i Index Equivalent for the portfolio is simply the sum of individual H i Portfolio index equivalent is interpreted as the notional of index contract to hedge portfolio systematic risk. Index Equivalent

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

13 Index Intrinsic Value 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.