Correlation breakdown for hedge fund structures Luis A. Seco, Sigma Analysis and Management Ltd. University of Toronto - RiskLab
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.
2004 2003 2002 2001 Hedge Funds asset growth Hedge Funds Assets (billions USD) 1200 1000 800 600 400 200 0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
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.
Hedge fund diversification Hedge funds are uncorrelated to traditional markets, and internally uncorrelated also. Frequency 180 160 140 120 100 80 60 40 20 0 Sigma Analysis and Management Ltd. -1-0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 Bin 120 Correlation histogram for Dow stocks Frequency 100 80 60 40 Frequency 20 Correlation histogram for hedge funds 0-1 -0.7-0.4-0.1 0.2 Bin 0.5 0.8 More
Normal correlations
Distressed correlations
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
Correlation breakdown in GM and Ford 1200 1-Year Rolling Correlation of Ford and GM CDS Spread Indices 1000 800 600 400 200 0 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 100 90 As a result, correlation started to drop sharply Ford GM 80 70 60 50 40 30
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 ) ( ) ( 2 1 2 2 1 1 B e p A pe M X B M X M X A M X t t π π +
A generlized Markowitz picture
Hedge Fund structures Leveraged products Non-recourse loans Traditional options CPPI options Guaranteed notes Credit derivatives Collateralized Fund Obligations (CFO s)
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.
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.
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.
CPPI vega sensitivities Note vs. FoF Value 1.6000 1.5000 1.4000 1.3000 1.2000 1.1000 1.0000 0.9000 0.8000 0.7000 0.6000 0.5000 0.4000 1 26 51 76 101 126 151 176 201 226 251 276 301 326 351 376 401 426 451 476 501 526 551 576 601 626 651 676 701 726 751 776 801 Days CPPI value Value of equity of straight investment
CPPI correlation breakdown sensitivities Value 1.6000 1.5000 1.4000 1.3000 1.2000 1.1000 1.0000 0.9000 0.8000 0.7000 0.6000 0.5000 0.4000 Note vs. FoF Pre-Iraq Oil Katrina 1 26 51 76 101 126 151 176 201 226 251 276 301 326 351 376 401 426 451 476 501 526 551 576 601 626 651 676 701 726 751 776 801 Days CPPI value Value of equity of straight investment
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
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
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.
Guaranteed notes on good portfolios Note vs. FoF 1.6000 About 2% per year cost Equivalent to a BB rated bond 1.5000 1.4000 Value 1.3000 1.2000 1.1000 1.0000 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 Month Value of equity of guaranteed note Value of equity of straight investment
Guaranteed notes on volatile portfolios Note vs. FoF 1.6000 1.5000 1.4000 Value 1.3000 1.2000 1.1000 1.0000 0.9000 1 41 81 121 161 201 241 281 321 361 401 441 481 521 561 601 641 681 721 761 801 Month Value of equity of guaranteed note Value of equity of straight investment
CPPI: low volatility underlying Note vs. FoF 1.6000 1.5000 1.4000 Value 1.3000 1.2000 1.1000 1.0000 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 Month Value of equity of guaranteed note Value of equity of straight investment
CPPI: vega sensitivity Note vs. FoF 1.3000 1.2000 1.1000 1.0000 Value 0.9000 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 0.8000 0.7000 0.6000 0.5000 Month Value of equity of guaranteed note Value of equity of straight investment
CPPI Note on a volatile portfolio Note vs. FoF 1.6000 1.5000 1.4000 Value 1.3000 1.2000 1.1000 1.0000 0.9000 1 44 87 130 173 216 259 302 345 388 431 474 517 560 603 646 689 732 775 818 Month Value of equity of guaranteed note Value of equity of straight investment
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
Collateralized Fund Obligation (CFO) Investor s capital Trust Fund Pool Bond Investor (1) Bond Investor (2) Bond Investor (3)
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)
CFO s as principal protection Trust Bond Investor (1) Guarantees principal Fund Pool Bond Investor (2) Bond Investor (3)
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 ) ( ) ( 2 1 2 2 1 1 B e p A pe M X B M X M X A M X t t π π + p (default probability)
S&P CTA CFO. A case study. Default Probability ( 1 Yr Maturity) 0.6000 Historical probabilities default probability 0.5000 0.4000 0.3000 Stressed probabilities 0% 10% 20% 30% 40% 50% 60% 0.2000 70% 80% 0.1000 90% 100% 0.0000 BA BB BC Equity Tranche Infra-stressed probabilities