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Correlation Breakdown in the Valuation of Collateralized Fund Obligations

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Correlation Breakdown in the Valuation of Collateralized Fund Obligations Correlation Breakdown in the Valuation of Collateralized Fund Obligations UNAI ANSEJO, MARCOS ESCOBAR, AITOR BERGARA, AND LUIS SECO UNAI ANSEJO ollateralized Debt Obligations have an AAA-rated tranche, an AA-rated is a doctoral student at Uni- (CDO) are structured credit vehi- tranche, a single A tranche, a BBB rated verisdad del Pais Vasco in cles that redistribute credit risk to tranche and an equity tranche. Exhibit 1 shows Bilbao, Spain. [email protected] meet investor demands for a wide a schematic prototype of a CFO structure. A Crange of rated securities with scheduled interest CFO can be regarded as a financial structure MARCOS ESCOBAR and principal payments. CDOs are securitized with equity investors and lenders where all the is an assistant professor in by diversified pools of debt instruments. assets, equity and bond are invested in a port- the Department of Mathe- Recent developments in credit structuring folio of hedge funds. The lenders earn a spread matics at Ryerson Univer- technology include the introduction of Collat- over interest rates and the equity holders, usu- sity in Toronto, Ontario, Canada. eralized Fund Obligations (CFO).The capital ally the manager of the CFO, earn the total [email protected] structure of a Collateralized Fund Obligation return of the fund minus the financing fees. is similar to traditional CDOs, meaning that As pointed out in recent articles on this AITOR BERGARA investors are offered a spectrum of rated debt topic (Mahadevan and Schwartz [2002] and is professor in the Depart- securities and equity interest. Although any Stone and Zissu [2004]), both investors and ment of Physics at Uni- verisdad del Pais Vasco in managed fund can be the source of collateral, issuers find CFO securitizations attractive. Bilbao, Spain. the target collateral in these structures tends Investors, because a triple-A-rated bond will [email protected] to be hedge funds, such as relative value hedge have a yield similar to that of a triple-A col- funds, event-driven hedge funds or com- lateralized debt obligation plus a premium, LUIS SECO modity trading advisors (CTAs), along with because with this structure they gain expo- is professor in the Depart- funds that finance the needs of growing com- sure to a diverse collection of hedge funds ment of Mathematics at University of Toronto in panies, such as private equity and mezzanine through a fund of funds manager. And issuers, Toronto, Ontario, Canada. funds. Often, a special purpose entity pur- because securitization is a convenient vehicle [email protected] chases the pool of underlying hedge fund for raising funds for an otherwise relatively investments, which are then used as collateral illiquid product. Stone and Zissu [2004] pro- to back the notes. vide a detailed overview of the first securiti- These asset-backed notes are also called zation of a fund of funds, the Diversified tranches. The most senior tranche is usually Strategies CFO SA, launched in June 2002. rated AAA and is credit-enhanced due to the This CFO issued US$251 million in five subordination of lower tranches. This means tranches, rated AAA, AA, A, BBB and the that the lowest tranche, which is typically the equity. Also in June of 2002, lawyers from equity tranche, absorbs losses first. When the the Structured Products Group completed the equity tranche is exhausted, the next lowest second Collateralized Fund Obligation backed tranche begins absorbing losses. A CFO may by hedge fund portfolios and assigned ratings WINTER 2006 THE JOURNAL OF ALTERNATIVE INVESTMENT 1 E XHIBIT 1 Schematic Prototype of a CFO Structure. Typical Maturities 3–7 Years by Moody’s Investors Service, Inc. and Standard & Poor’s The credit rating of a CFO tranche depends directly Rating Services. The CFO, titled Man Glenwood Alter- on the mark-to-market value of the pool of hedge funds. native Strategies I or “MAST I,” issued rated notes Collateralized fund obligations tend to be structured as totaling US$374 million and nonrated notes and prefer- arbitrage market value CDOs, meaning that the fund of ence shares totaling US$176 million. As the first of their funds manager focuses efforts on actively managing the kind, these CFOs were viewed as a cutting edge trans- fund to maximize total return while restraining price action within the industry and attracted considerable volatility within the guidelines of the structure. The diver- attention in the financial press. sity of hedge fund investment strategies and the active As far as valuation is concerned, Moody’s in August management of portfolio positions among strategies ensure 2003, began to use HedgeFund.net data to evaluate the that hedge fund risk and return characteristics are dif- risks of the underlying collateral in order to develop an ferent from those of traditional assets (equities, bonds or accurate Montecarlo-based rating model for CFOs (see ETFs), as illustrated by numerous articles in the literature Moody’s [2003]). Although CDOs have attracted much (e.g., Moody’s [2003] and CISDM [2006]). The unique attention in the academic literature (Hull and White return and risk characteristics of hedge funds are better [2004]; Li [2000], and Laurent and Gregory [2003]), no characterized by more general distributions than the usual effort has been made to develop an analytical rating model multivariate Gaussian approach. Therefore the probability for CFOs. of default of the different tranches will be also more 2 CORRELATION BREAKDOWN IN THE VALUATION OF COLLATERALIZED FUND OBLIGATIONS WINTER 2006 volatile. In addition, lack of transparency within hedge about future cash flows to be generated by the fund may funds in general makes it more difficult to obtain high- be closely guarded. Hedge funds are largely unregulated frequency historical data which leaves investors with no because they are typically limited partnerships with fewer choice but to calibrate rather complex valuation models than 100 investors, which exempts them from the Invest- including the typical non-Gaussian behavior of hedge ment Company Act of 1940. Offshore hedge funds are funds with monthly data. non-U.S. corporations and are not subject to SEC regu- With the ultimate aim of assessing the model and cal- lation. This limited regulation allows hedge funds to be ibration risk incurred by CFOs, we develop in this article extremely flexible in their investment options. Hedge funds an analytical procedure for valuing the different tranches can use short selling, leverage, derivatives, and highly con- of a CFO by calculating the probability of default and the centrated investment positions to enhance returns or reduce credit spreads from the bonds, and analyzing the pricing systematic risk. They can also attempt to time the market sensitivities to changes in parameters. When calculating by moving quickly across diverse asset categories. Hedge the probabilities of default and the credit spreads of the funds attract mainly institutions and wealthy individual different tranches of a CFO, one should take into con- investors, with minimum investments typically ranging sideration the non-Gaussian behavior of the returns from from $250,000 to $1 million. Additionally, hedge funds the pool of hedge funds. As we shall show later, those often limit an investor’s liquidity with lock-up periods of credit spreads are directly related to the percentiles of the one year for initial investors and subsequent restrictions underlying portfolio distribution. on withdrawals to certain intervals. Specific investments In our pricing model we will assume that returns made by hedge funds are often carefully guarded secrets. from the pool of hedge funds follow a Covariance- This lack of transparency may make it difficult for a fund Switching (CS) Stochastic Process which is defined in the of hedge funds manager to assess the fund’s aggregate expo- Appendix. This framework allows us to incorporate two sure to a particular investment on a portfolio basis. It also well known characteristics from the return series of hedge presents a challenge to the fund manager attempting to funds: first, the skewed and leptokurtic nature of the mar- monitor a particular hedge fund’s adherence to its adver- ginal distribution functions, and second, the asymmetric tised style or investment approach. However in certain correlation or correlation breakdown phenomenon cases the transparency issues indicated above can be alle- (Longin and Solnik [2001]). As we will later prove, the viated if the manager allows separate accounts. In order to correlation between the different hedge funds depends account for the plethora of hedge fund and CTA strate- on the direction of the market. For instance, correlations gies and the speed at which a given fund’s composition tend to be larger in a bear market than in a bull market. can be changed, we model the alternative assets to exhibit The structure of this article is as follows. Providing more exotic distributions than the Gaussian one, displaying empirical evidence of the existence of correlation regimes, asymmetric and leptokurtic returns. in Section 2 we present the Covariance-Switching process As is the case with most diversified portfolios, fund as the model for the profit and loss function for a pool of of hedge funds reduce the numerous types of risks arising hedge funds and we outline some of their properties. The from individual hedge funds by diversifying both across model for valuing a CFO is presented in Section 3, and strategies as well as the number of funds in each strategy. in Section 4 we illustrate the strong parameter depen- Both types of diversification reduce risk, but because of dence with an example of a hypothetical CFO based on the potential for style drift and a rapid total loss of value the S&P CTA index. This methodology can be applied in a single fund, diversification across funds is especially to other daily hedge fund indexes such as the Dow Jones important.
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