# Performance Analysis of a Collateralized Fund Obligation (CFO) Equity Tranche

HEC Montréal

^{1}TL;DR: This article examined the performance of the junior tranche of a Collateralized Fund Obligation (CFO), i.e. the residual claim (equity) on a securitized portfolio of hedge funds.

Abstract: This article examines the performance of the junior tranche of a Collateralized Fund Obligation (CFO), i.e. the residual claim (equity) on a securitized portfolio of hedge funds. We use a polynomial goal programming model to create optimal portfolios of hedge funds, conditional to investor preferences and diversification constraints (maximum allocation per strategy). For each portfolio we build CFO structures that have different levels of leverage, and analyze both the stand alone performance as well as potential diversification benefits (low systematic risk exposures) of investing in the Equity Tranche of these structures. We find that the unconstrained mean-variance portfolio yields a high performance, but greater exposure to systematic risk. We observe the exact opposite picture in the case of unconstrained optimization where a skewness bias is added, thus proving the existence of a trade-off between stand alone performance and low exposure to systematic risk factors. We provide evidence that leveraged exposure to these hedge fund portfolios through the structuring of CFOs creates value for the Equity Tranche investor.

## Summary (2 min read)

Jump to: [1. INTRODUCTION] – [2. METHODOLOGY] – [3. DATA] – [4. EMPIRICAL RESULTS] and [5. CONCLUSION]

### 1. INTRODUCTION

- In 2002, structured finance and hedge funds merged together for the first time.
- On the one hand it provides investors with a new vehicle through which to obtain exposure to hedge fund returns, and on the other hand offers to the financial engineers a new and quite unique pool of assets that they could securitize.
- This article provides a thorough analysis of the factors that might influence the performance of various hypothetical CFO Equity Tranches.
- In order to investigate the impact of strategy selection and diversification in the underlying hedge fund portfolio, the authors implement an optimization model that allows us to specify preferences for higher moments.
- Section 3 describes and analyzes the data and Section 4 focuses on the empirical results.

### 2. METHODOLOGY

- The methodology is comprised of three steps.
- The authors also perform constrained optimizations for each set of preferences, with maximum allocation to each strategy limited to 10%, 15%, 20%, 25% and 50%.
- Finally, given the recent empirical evidence supporting equally-weighted portfolio (for example DeMiguel, Garlappi and Uppal (2005)) the authors also consider the (1/m) portfolio allocation.
- Therefore, the greater the number of tranches, the greater the structure’s financing costs.
- 2.1 Evaluating the Equity Tranche Given the 31 hedge fund portfolios and 20 possible CFO structures, the authors obtain 620 series of returns (31 × 20 CFO structures) containing 84 observations each.

### 3. DATA

- The hedge fund data was provided by Desjardins Global Asset Management and includes HFR and TASS databases.
- Firstly, 2,523 funds of hedge funds were withdrawn because they are not strategy-specific funds.
- In order to circumvent the issue of relative size of the strategies, avoid working with 4,146 assets and further counter the issue of survivorship bias, an equally-weighted index is constructed for each strategy.
- This result can mainly be explained by the fact that period 1 witnessed a very bullish market while period 2 was more unpredictable and generated less value on the financial markets4 .
- Several other financial time series covering the period over which the CFO structures are distributed (2001-2008) are required to perform all the necessary calculations.

### 4. EMPIRICAL RESULTS

- The authors observe, conditional on the diversification constraint imposed, the weight yi assigned to each strategy.
- 1.1 Performance Analysis Table 6 presents the descriptive statistics, the tests of normality and the performance measures attributable to the returns of the portfolios examined in period 2.
- The mean-variance optimal portfolio (preference set E1) no longer outperforms.
- This supports the existence of an optimal debt level from the equity owner’s viewpoint, the merit of CFOs and thus, the added-value of the latter for the investor.
- This is indeed very interesting as CFOs are flexible instruments, meaning that it is possible to choose the types of underlying portfolio according to one’s need for diversification and the extent of leverage based on one’s appetite for risk.

### 5. CONCLUSION

- The objective was to assess the performance of the Equity Tranche of CFOs both in terms of risk-adjusted return as well as systematic risk exposures.
- For this purpose, 30 optimal portfolios (each conditional to a set of preferences and weight constraints) and an equally-weighted portfolio were constructed using 16 hedge fund strategy indexes.
- Interestingly, the authors observe that if they consider the overall distribution of returns of a CFO Equity Tranche in analyzing the performance, securitizing and tranching the underlying portfolio of hedge funds adds value for the end investor.
- Thus, these conclusions suggest that market participants might have been too hasty in dismissing CFOs, and not taking greater advantage of the benefits offered by these investment vehicles.
- Since it is only a matter of time before financial markets have had the chance to digest the consequences of the current crisis, it is relevant to pursue this research further.

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Aboul-Enein: Alternative Investment Research Group, Desjardins Global Asset Management and HEC Montréal

Dionne: Professor of Finance and Canada Research Chair in Risk Management, HEC Montréal and CIRPÉE.

Corresponding author: HEC Montréal, Research Chair in Risk Management, 3000, Chemin de la Côte-Sainte-

Catherine, Montréal, (QC) Canada H3T 2A7. Phone: +514 340-6596; Fax: +514 340-5019

georges.dionne@hec.ca

Papageorgiou: Professor of Finance, HEC Montréal, Director of Research, Desjardins Global Asset Management

and CIRPÉE

We thank P. Ali, M. Crouhy, J. Grenier, A. Hocquard, V. Kapoor, E. Lefort and F. Longstaff for their comments and

support. Claire Boisvert and Lewina Giles improved the presentation of this article. This research was financed by

the Canada Research Chair in Risk Management and the Alternative Investment Research Group, Desjardins Global

Asset Management.

Cahier de recherche/Working Paper 09-31

Performance Analysis of a Collateralized Fund Obligation (CFO)

Equity Tranche

Shady Aboul-Enein

Georges Dionne

Nicolas Papageorgiou

Août/August 2009

Abstract:

This article examines the performance of the junior tranche of a Collateralized Fund

Obligation (CFO), i.e. the residual claim (equity) on a securitized portfolio of hedge

funds. We use a polynomial goal programming model to create optimal portfolios of

hedge funds, conditional to investor preferences and diversification constraints

(maximum allocation per strategy). For each portfolio we build CFO structures that have

different levels of leverage, and analyze both the stand alone performance as well as

potential diversification benefits (low systematic risk exposures) of investing in the Equity

Tranche of these structures. We find that the unconstrained mean-variance portfolio

yields a high performance, but greater exposure to systematic risk. We observe the

exact opposite picture in the case of unconstrained optimization where a skewness bias

is added, thus proving the existence of a trade-off between stand alone performance

and low exposure to systematic risk factors. We provide evidence that leveraged

exposure to these hedge fund portfolios through the structuring of CFOs creates value

for the Equity Tranche investor.

Keywords: Collateralized Fund Obligation (CFO), hedge funds, structured finance,

portfolio optimization, performance analysis, multivariate linear regression, systematic

risk.

JEL Classification: G11, G23

Performance Analysis of a CFO Equity Tranche

2

1. INTRODUCTION

In 2002, structured finance and hedge funds merged together for the first time. This

union gave birth to Collateralized Fund Obligations (CFO) which consists in the

securitization of hedge fund portfolios.This new category of asset seems to offer the

best of both worlds. On the one hand it provides investors with a new vehicle through

which to obtain exposure to hedge fund returns, and on the other hand offers to the

financial engineers a new and quite unique pool of assets that they could securitize. The

variety of strategies and low correlations with traditional assets make hedge funds an

ideal candidate as collateral for securitization transactions. Although the theoretical

justification of CFOs has been firmly established in financial literature (See Cheng

(2002), Mahadevan and Schwartz (2002), Stone and Zissu (2004) and Missinhoun and

Chacowry (2005)), there are still many misgivings as to their practical pertinence.

Thus, despite the rapid growth of the CDO market over the past two decades, there

were no more than 20 CFO transactions prior to 2008. A lack of interest by investors in

the Equity Tranche of these structures seems to be the source of the slow proliferation.

The perception of low added-value and high inherent leverage, made it difficult to

solicitate interest in the junior tranche of CFOs. That said, given the novelty and the

complexity of these products, which belong to a vast family of derivatives, it is logical to

suppose that the distinctive fundamental characteristics and benefits of the exposure to

a CFO Equity Tranche have yet to be carefully scrutinized. This article provides a

thorough analysis of the factors that might influence the performance of various

hypothetical CFO Equity Tranches. Using data on historical hedge fund returns, the goal

is to structure various CFOs based on a variety of underlying portfolios and investigate

the returns of the Equity Tranche both in terms of stand alone performance and in terms

of potential diversification benefits.

More specifically, the first objective, from the viewpoint of a CFO equity owner, is to

define the optimal capital structure(s) as well as the general attributes for the

diversification of the optimal portfolio of hedge funds for the securitization transaction.

Performance Analysis of a CFO Equity Tranche

3

The analysis is therefore far more thorough than that observed in existing literature on

the subject of CFOs. In order to investigate the impact of strategy selection and

diversification in the underlying hedge fund portfolio, we implement an optimization

model that allows us to specify preferences for higher moments. This polynomial goal

programming approach generates optimal allocations conditional to specific investor

preferences. For each “optimal” portfolio, several debt structures are then considered so

as to account for a far broader range of scenarios. This is done in order to identify, on

the basis of a number of performance indicators, the optimal composition of the

collateral and the appropriate leverage to which the exposure should be subjected.

The second objective is to study the exposure of the CFO Equity Tranche to systematic

risk factors, such as market, credit and liquidity. In this sense, the study will determine

the degree to which returns are defined by the returns of readily available risk premia,

and therefore provide a better idea of their risk exposures. This is achieved using a

multivariate linear regression model.

The results indicate that CFOs create value from the equity holder’s perspective.

Nonetheless, there is a trade-off that must be made between the stand alone

performance of a CFO Equity Tranche and its’ systematic risk exposure. We find that the

unconstrained mean-variance portfolio yields a high performance but exhibits greater

exposure to systematic risk factors. We observe the exact opposite in the case of

unconstrained optimization where a preference for skewness is incorporated, thus

proving the existence of a trade-off between performance and low-correlation with the

financial markets. According to our results, an interesting compromise could be obtained

by securitizing a well-diversified (constrained) underlying portfolio of funds.

The article is structured as follows. Section 2 presents the three stage methodology.

Section 3 describes and analyzes the data and Section 4 focuses on the empirical

results. Conclusions are presented in Section 5.

Performance Analysis of a CFO Equity Tranche

4

2. METHODOLOGY

The methodology is comprised of three steps. The first step concerns the allocation of

hedge funds across the different strategies, the second relates to the structuring and

evaluation of the CFO, and the final stage consists in the analysis of the systematic risk

exposures of the resulting Equity Tranche of the CFO.

2.1 Allocation across hedge fund strategies

To decide on the asset allocation between the different investment strategies we use a

polynomial goal programming (PGP) optimization model. This approach was introduced

by Tayi and Leonard (1988), and has been employed by Chunhachinda, Dandapani,

Hamid, and Prakash (1997) and Sun and Yan (2003) to incorporate the effect of

skewness on portfolio allocation decisions. Davies, Kat, and Lu (2009) use this

approach to incorporate investor preferences for higher moments into the construction of

funds of funds. They extend the original model in order to account not only for skewness

but also for the kurtosis that is prevalent in hedge fund return distributions. This

approach incorporates multiple, and often conflicting, objectives and considers the

impact of a change in investor preferences on asset allocation.

2.1.1 The PGP model

Consider an environment with m risky assets, each with random return

~

i

R

, and x

i

being

the percentage of wealth invested in the i

th

asset. The risk free rate r is constant and no

short selling of the risky assets is permitted. The percentage invested in the risk-free

asset is determined by x

m+1

= 1 – I

T

X, where I is an identity vector of dimension m × 1

and X is the vector of dimension m × 1 of percentages of wealth invested in the risky

assets. V is the variance-covariance matrix for

~

R

= (

~

1

R

,

~

2

R

, …,

~

m

R

). This matrix is

positive and of dimension m x m. Thus, the problem of portfolio selection can be defined

using the PGP model:

MIN Z = (1 + d

1

)

α

+ (1 + d

3

)

β

+ (1 + d

4

)

γ

(1)

Subject to E [X

T

~

R

] + x

m+1

r + d

1

=

*

1

Z

, (2)

##### References

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TL;DR: This article used previously developed models to construct asset-based style factors and demonstrate that one model correctly predicted the return behavior of trend-following strategies during out-of-sample periods -in particular, during stressful market conditions like those of September 2001.

Abstract: Asset-based style factors link returns of hedge fund strategies to observed market prices. They provide explicit and unambiguous descriptions of hedge fund strategies that reveal the nature and quantity of risk. Asset-based style factors are key inputs for portfolio construction and for benchmarking hedge fund performance on a risk-adjusted basis. We used previously developed models to construct asset-based style factors and demonstrate that one model correctly predicted the return behavior of trend-following strategies during out-of-sample periods - in particular, during stressful market conditions like those of September 2001.

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