Portfolio choices and hedge funds: a disappointment aversion analysis

ABSTRACT

The inclusion of hedge funds in large institutional portfolios is controversial. We use a disappointment aversion utility-based framework to investigate this issue. We empirically model the end-of-period wealth directly as opposed to the joint return distribution. This approach captures the interconnections between different asset categories without resorting to complex modeling. We observe that several hedge-fund strategies produce incremental economic benefits that generally weaken at higher levels of disappointment aversion. Portfolio weights are also constrained to match those of a generic pension fund. Results show that significant economic benefits are possible but only under restrictive conditions.

Keywords:

• Disappointment aversion
• hedge funds
• tail risk
• portfolio choices
• certainty equivalent
• skewed t distribution

JEL CLASSIFICATIONS:

• G4
• G11

Acknowledgments

We acknowledge the comments and suggestions made by the referees and the associate editor, which improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Routledge and Zin (2010) show the concept of generalized DA by introducing an extra parameter that changes the disappointment threshold. With generalized DA, disappointment occurs when bad market states are sufficiently distant from the certainty equivalent. Bonomo et al. (2011) and Delikouras (2017) empirically observe that this extra parameter is very close to 1; an observation that cannot be rejected statistically. Thus we adopt the more parsimonious DA framework, as did Delikouras (2017).

2 See Appendix 1 for the formal approach.

3 See Christoffersen (2012) for further details.

4 The utility maximization problem imposes short-sale constraints because our findings show that in some situations optimal solutions yield negative weights.

5 The number of degrees of freedom emanates from the fragmentation of the targeted wealth series into 10 deciles, from which the number of shape parameters associated with the skewed t distribution is subtracted.

6 To assess the robustness of the conclusions drawn on the basis ${\chi }^2$ test, we also estimated the Kolmogorov–Smirnov test of Diebold, Gunter, and Tay (1998) in the context of Tables 2 and 3. We find that the results are essentially the same.

7 We also perform the out-of-sample analysis using constant, as opposed to expanding, estimation-samples. This alternative methodological choice modifies the results although the general conclusions are relatively robust.

8 The study of Aiken, Clifford, and Ellis (2015), using hand-collected data, finds that a third of the hedge funds in their sample, imposed discretionary liquidity restrictions such as gates during the 2007–2009 crisis hoping to attenuate capital outflows. This phenomenon has an obvious impact on the fluidity by which portfolio rebalancing can be conducted. To assess the impact of such restrictions in our framework, we have rebalanced, ex post, DA portfolios by preventing the holding allocated to the hedge-fund composite index to diminish from the first (just before the crisis) to the third estimation-sample windows. This is a stringent exercise since it implies that all hedge funds within the composite index completely prohibit capital withdrawal. We empirically observe that this gating constraint does not materially affect the out-of-sample estimates of the certainty equivalent measures.

9 We also investigate the magnitude of the transaction costs generated by portfolio rebalancing during the 2007–2009 financial crisis. In response to the severity by which financial markets were hit during this period, augmented portfolios may drastically converge toward very conservative positions in an attempt to reduce tail risk exposure. To investigate this possibility, we proceed as before but this time, we concentrate on the first estimation-sample window that preceded the 2007–2009 period, on the window ending immediately after the crisis, and on the window ending in November 2017. We then compute the differences in the certainty equivalent based on the $w_t$ and $w_t^{\ast }$ series for these three periods. Our evidence does not support the intuition of higher transaction costs around the crisis. In short, average transaction costs seem to progressively increase with length of the estimation-sample.

10 We also computed the Jensen-alpha based on the 7-factor structure of Fung and Hsieh (2001). However, based on the Newey–West standard deviations, only one (two) alpha estimates are significant when A is 0.8 (0.6). Since the null hypothesis is not rejected for almost all cases, the Jensen-alpha estimates are not reported in Table 8.

11 We thank Maher Kooli for granting us access to the BarclayHedge databases.

12 We also perform the analysis when the portfolio weights are set exogenously as in Section 5.3. The findings reveal that in this more rigid framework, none of the augmented portfolios display certainty equivalent measures that outperform those of the benchmark.

Additional information

Funding

Lalancette acknowledges financial support from HEC Montral.