Sigma Analysis and Management Ltd. University of Toronto - RiskLab

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1 Correlation breakdown for hedge fund structures Luis A. Seco, Sigma Analysis and Management Ltd. University of Toronto - RiskLab

2 What Is a Hedge Fund? A hedge fund is a business that: can take both long and short positions use arbitrage, leverage buy and sell undervalued (overvalued) securities trade options, bonds, OTC, weather derivatives, film scripts, etc. invest in almost any opportunity in accordance with the Offering Memorandum- in any market where it foresees inefficiencies and/or substantial gains at reduced risk.

3 Hedge Funds asset growth Hedge Funds Assets (billions USD)

4 Hedge Funds and HF structures Regulation: Risks: certain clients in certain jurisdictions cannot invest in hedge funds. PP structures are often available to a wide variety of investors Structures allow for risk transfer No transparency Little liquidity Minimum investment levels among investors with different views on the risks. Costs Rewards (I don t mean fees) Due diligence Legal overhead Uncorrelated returns Many hedge fund risks are diversifiable Structures add to the costs, but investors seem to think they are worth their price. Structures can enhance returns, but create new risks.

5 Hedge fund diversification Hedge funds are uncorrelated to traditional markets, and internally uncorrelated also. Frequency Sigma Analysis and Management Ltd Bin 120 Correlation histogram for Dow stocks Frequency Frequency 20 Correlation histogram for hedge funds Bin More

6 Normal correlations

7 Distressed correlations

8 Correlation breakdown (google earth view) This is an example of how individual managers change correlations during distress, and how to use this information to classify them into coherent groups

9 Correlation breakdown in GM and Ford Year Rolling Correlation of Ford and GM CDS Spread Indices May-03 Jul-03 Sep-03 Nov-03 Jan-04 Mar-04 May-04 Jul-04 Sep-04 Nov-04 Jan-05 Mar-05 May-05 Jul-05 CDS Spread, bps Correlation As a result, correlation started to drop sharply Ford GM

10 New portfolio theory These regime switching situations cannot be treated just with volatility at the portfolio level. We need a new type of portfolio theory that allows us to account for both types of fund dependence, and perhaps also different return and risk parameters. We are going to choose a mixture of multivariate gaussians, as the probabilistic setting model the returns of the portfolio constituents: ) det(2 ) (1 ) det(2 ) ( ) ( 2 1 ) ( ) ( B e p A pe M X B M X M X A M X t t π π +

11 A generlized Markowitz picture

12 Hedge Fund structures Leveraged products Non-recourse loans Traditional options CPPI options Guaranteed notes Credit derivatives Collateralized Fund Obligations (CFO s)

13 Leveraged products: loans Investors are given loans with the fund investment as only collateral. Example: Investor provides $25M. Lender provides $75M. $100M is invested in a hedge fund portfolio. The investment pays interest to the lender, and returns the principal at maturity. The investor keeps the rest. If returns are good, everyone is happy, specially the investor. If returns are not good, the investor will absorb first losses. The lender can lose too. This is a simple credit derivative.

14 Leveraged products: options Investors purchase a call option, with a reference hedge fund portfolio as underlying They offer non-path dependent returns Assets actually invested in hedge funds vary with the delta of the option Hedge fund shares are unlisted. Illiquidity of the hedge fund portfolio gives rise to higher implied volatilities, which are hard to value. Hedging becomes very difficult.

15 CPPI options An easier alternative to the underwriter, who does not need to worry about interest rate evolution, liquidity or fund volatility. The underwriter has the ability to modify the strike price as interest rate oscillate, or fund performance deviates from expectations. The objective is to re-leverage or de-leverage the underlying portfolio investment as market conditions change. These are path dependent options. If interest rates increase, strike price increases. If they decrease, strike price decreases too. If fund performance decreases, strike price increases; if performance continues, strike price decreases. The strike price change can be monitored with respect to a reference curve, or by keeping the implied leverage of the option constant.

16 CPPI vega sensitivities Note vs. FoF Value Days CPPI value Value of equity of straight investment

17 CPPI correlation breakdown sensitivities Value Note vs. FoF Pre-Iraq Oil Katrina Days CPPI value Value of equity of straight investment

18 Guaranteed notes There are two main reasons for a guarantee: Regulatory environments (Case: NUMA Protector Fund, Peru) Risk perceptions (investors perceive hedge funds to be risky, insurers don t). Guarantees are obtainable by setting aside an interest-earning portion of the assets, and investing the remainder at higher levels of leverage, through a variety of different instruments. Some guarantees are provided by top-rated corporations. Others are not (Case: Portus Asset Management, Canada). We will be assuming a AAA-rated guarantee

19 Anatomy of a guarantee A maturity date. A portion of the investor s assets Guarantees principal in the future: How much is needed is determined by Interest rates Maturity date of the note Obtains exposure to the Hedge Funds Secure debt Investment are used to purchase a zero coupon bond, maturing at the note expiration. The remaining assets are invested, with leverage, to obtain full exposure to a hedge fund portfolio. This can be achieved through A (non-recourse) loan A call option A CPPI option

20 Examples: two cases Consider Interest rates at 25bps per month A 5 year note that guarantees principal No management or performance fees 1. A non-volatile portfolio, which produces 60bps/month 2. A volatile portfolio (S&P Managed Futures Index): its volatility arises from severe correlation breakdown inside the trend-following sector of the managed futures industry.

21 Guaranteed notes on good portfolios Note vs. FoF About 2% per year cost Equivalent to a BB rated bond Value Month Value of equity of guaranteed note Value of equity of straight investment

22 Guaranteed notes on volatile portfolios Note vs. FoF Value Month Value of equity of guaranteed note Value of equity of straight investment

23 CPPI: low volatility underlying Note vs. FoF Value Month Value of equity of guaranteed note Value of equity of straight investment

24 CPPI: vega sensitivity Note vs. FoF Value Month Value of equity of guaranteed note Value of equity of straight investment

25 CPPI Note on a volatile portfolio Note vs. FoF Value Month Value of equity of guaranteed note Value of equity of straight investment

26 Credit derivatives: CFO Avoid the option structure by issuing debt (defaultable bonds) side by side with secured debt (riskless bonds) It provides a risk transfer mechanism between counterparties with different risk views: the investor, who places higher risk on the hedge fund investment the bond holder, who place lower risk on the investment

27 Collateralized Fund Obligation (CFO) Investor s capital Trust Fund Pool Bond Investor (1) Bond Investor (2) Bond Investor (3)

28 Collateralized Fund Obligation (CFO) Investor s capital Receives fund value net of bond liabilities Trust Fund Pool Bond Investor (1) Bond Investor (2) Receive Interest and principal Bond Investor (3)

29 CFO s as principal protection Trust Bond Investor (1) Guarantees principal Fund Pool Bond Investor (2) Bond Investor (3)

30 Default sensitivities to correlations We model inter-manager returns with a mixture of multivariate gaussians, with switching parameter p: and we want to obtain an idea of the sensitivity of the default probabilities of the different CFO tranches to p: Default in this context is used to denote the event in which investors lose money (bond or equity investors alike) ) det(2 ) (1 ) det(2 ) ( ) ( 2 1 ) ( ) ( B e p A pe M X B M X M X A M X t t π π + p (default probability)

31 S&P CTA CFO. A case study. Default Probability ( 1 Yr Maturity) Historical probabilities default probability Stressed probabilities 0% 10% 20% 30% 40% 50% 60% % 80% % 100% BA BB BC Equity Tranche Infra-stressed probabilities