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 shares or one or more funds of hedge funds. CEO = Collateralized Equity Obligation, the underlying pool consists of a portfolio of individual , preferred , 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 (1) SPV/Trust 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 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

1000 90

80 800 …As a result, correlation started to drop sharply 70 600 Ford 60 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 . Simulations give us a range of prices for the CFO tranches.