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Collateralized Fund Obligations Pricing and Risks

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Collateralized Fund Obligations Pricing and Risks Collateralized Fund Obligations Pricing and risks Luis A. Seco Sigma Analysis & Management University of Toronto RiskLab Collateralized Debt Obligation (CDO) Absorbs Debt Pool first % defaults Absorbs second % defaults Absorbs third % of defaults (3) CEO’s and CFO’s CFO = Collateralized Fund Obligation, much like a CDO, but the underlying pool are hedge fund shares or one or more funds of hedge funds. CEO = Collateralized Equity Obligation, the underlying pool consists of a portfolio of individual stocks, preferred stock, stock ETFs, indexes, or equity derivatives. Anatomy of a CFO The CFO’s dream $1 $1.15 $1 $1.2 $4 5 years later $1 $1.35 $6 $1 $2.3 CFO’s as principal protection Bond Investor (1) SPV/Trust Bond Investor (2) Bond Investor (3) Guarantees principal Fund Pool Bond defaults CFO’s history Diversified Strategies CFO SA, launched in 2002. Issued $250M in five tranches, AAA, AA, A, BBB and the equity tranche. Also in June 2002, MAST-1 (“Man-Glenwood Alternative Strategies I”) issued $374M in rated notes and $176M in non-rated notes and shares. In 2003 Moodys began to use a MC-based model to rate CFO tranches. CFO’s Advantages Disadvantages Equity investors find a way Hard to value to obtain leverage. Very dependent on Debt holders find an correlations amongst the uncorrelated asset class to funds constituents invest in. Expensive structuring fees Tranches can be packaged makes it difficult to find the by volume and credit rating. equity investor sometimes. Risk focus: Correlation breakdown Correlation breakdown (google-earth view) Correlation breakdown in GM and Ford 1-Year Rolling Correlation of Ford and GM CDS Spread Indices 1200 100 90 1000 80 800 …As a result, correlation started to drop sharply 70 600 60 Ford Correlation CDS Spread, bps Spread, CDS 400 GM 50 200 40 0 30 Jul-03 Jul-04 Jul-05 Jan-04 Jan-05 Mar-04 Mar-05 Nov-03 Nov-04 Sep-03 Sep-04 May-03 May-04 May-05 Underlying asset process X=ln(S) follows a covariance-switching process: The time discretized leads to a gaussian-mixture distribution The equivalent martingale We assume the jump does not change with the change in measure (Merton 1974) The equivalent measure is then Conditional on the history of the jumps, the distribution of X is a multivariate gaussian which can be computed explicitly. The equivalent martingale (2) Conditional on the history of the jumps, the distribution of the hedge fund portfolio is a multivariate gaussian which can be computed explicitly. Simulating the jumps, we obtain the distribution of portfolio returns, under the risk-free equivalent measure. The quantiles of the distribution gives us the probabilities of default of each of the bond tranches. Pricing Merton 74 Arbitrage-free process for the underlying hedge funds Process for the underlying hedge funds Conditional on a historical path of J (n jumps at times t) X is a multivariate Gaussian with: is distributed as a gaussian Simulating J Prob default of each tranche Yield/default sensitivities Conclusions CFO’s are instruments of great investor value. CFO’s are sensitive to correlation motion or uncertainty, specially in situations where the underlying funds are uncorrelated on average. Pricing is highly sensitive to a switching variable, which cannot be priced in the market. Simulations give us a range of prices for the CFO tranches..
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