Risks and Portfolio Decisions Involving Hedge Funds

Motivation(s)

Hedge funds have become the vehicle for investors wishing to earn risk premia. Due to the complex nature of hedge fund strategies and limited disclosure requirements, only two strategies have been analyzed in terms of risk: trend following and risk arbitrage. However, earlier theories on asset pricing (e.g. capital asset pricing model, arbitrage pricing theory) inaccurately constrain the relation between risk factors and returns to be linear. This prompted some new studies to approximate the asymmetric nonlinear payoffs with a collection of options on a selected number of benchmark index returns.

Proposed Solution(s)

The authors extend the contingent claim-based model to include call and put options on the market index. Since options are frequently traded assets whose payoff relates in a nonlinear way with the market return, their market prices can be used to approximate nonlinear payoffs. Their inclusion of exchange traded options

  • helps capture the hedge fund risk in an intuitive manner,

  • embeds investor preferences, information, and market conditions,

  • and enables replication of hedge fund payoffs.

Evaluation(s)

The analysis focused on equity-oriented hedge fund strategies since there are plenty of high quality data (e.g. S&P 500). The following strategies were of interest since they have payoffs that arises primarily from relative mispricings of securities rather than the movement of the market as a whole: event arbitrage, restructuring, event driven, relative value arbitrage, convertible arbitrage, and equity hedge. The authors also investigated equity non-hedge and short selling (dedicated short-bias) strategies whose payoffs arises from taking directional bets.

Two separate databases, HFR spanning 1990 to mid-2000 and CSFB/Tremont spanning 1994 to mid-2000, were analyzed to mitigate the 3% survivorship bias and 1.4% backfilling bias. To estimate how hedge funds would have performed during past extreme events, the authors constructed a theoretical return series using Black and Scholes’ formula i.e. they assumed current hedge funds were bearing the same systematic risk exposures as those in the desired time period.

The results illustrate that a wide range of hedge fund strategies exhibit returns similar to those from writing a put option on the equity index. The observed nonlinearities across multiple strategies suggest these events represent risks borne by hedge fund investors. The nonlinear risk exposures also appear in the size, value, and momentum factors.

Since hedge funds exhibit significant left-tail risks, the authors used conditional value-at-risk (CVaR) to account for negative tail risk. CVaR is the statistical mean of the losses exceeding the VaR. VaR focuses only on the frequency of extreme events while CVaR focuses on both the frequency and size of losses. This approach is more appropriate than traditional mean-variance analysis since the latter underestimates tail losses, which is most severe for portfolios with low volatility. Across the hedge fund indexes, long-run returns are lower, long-run volatilities are higher, and long-run tail losses are larger compared with hedge funds during the recent period.

Although the statistics on out-of-sample test data spanning mid-2000 to 2001 for both databases were not statistically significant, the magnitudes were economically significant.

Future Direction(s)

  • Instead of using stepwise regression deal with limited returns data, how would one go about deriving a generative model that is reflective of a hedge fund’s SEC (e.g. F13) filings?

  • The common advise is to focus on the top 30 holdings of net long domestic equity fund managers with low turnover. How would one robustly track a hedge fund’s strategy?

  • How can one synthesize an options strategy to reproduce hedge fund strategies?

Question(s)

  • Did the authors actually have an options strategy or were solely looking at the magnitude of the options regression coefficient?

Analysis

CVaR is an appropriate measure of nonlinear risks for a wide range of hedge fund strategies. The authors should have tried to determine the composition of the nonlinear risks (e.g. capital adequacy). In addition, more validations are needed to verify whether constructing a theoretical return series using Black and Scholes’ formula to analyze long-run performance with limited data is accurate. It is worthwhile to mention that this study found hedge fund strategies exhibit returns similar to writing options. The only annoying issue is the structure of the paper: it’s not laid out for easy reading and the paper could have been more succinct.

References

AN04

Vikas Agarwal and Narayan Y Naik. Risks and portfolio decisions involving hedge funds. Review of Financial studies, 17(1):63–98, 2004.