Institutional investors are invariably confronted with numerous challenges when attempting to construct a diversified portfolio of hedge funds. While too abundant to list, some of these challenges include governance issues, such as cumbersome and inefficient internal contracting processes for hiring external managers or various regulatory requirements, and resource constraints, for example limited in-house staff and modest administrative budgets. In addition to these operational considerations, there are of course direct investment challenges in hiring hedge funds such as acquiring or accessing the requisite specialised skills to decide upon strategy allocations as well as to vet and select individual managers across areas as diverse as correlation/dispersion trading or Japanese cross-holding activism.

One of the challenges which investors face that may seem relatively mundane in comparison is also a highly critical and often overlooked concern: how many hedge funds in a direct portfolio is the right number? Of course, there is no one-size-fits-all answer to such a broad question. While finding the optimal amount of concentration versus diversification is an investment puzzle that has confronted practitioners since well prior to the institutionalisation of the hedge fund industry,[1] there are a number of considerations specific to hedge funds that impact the number of line items an investor should target.

Outside of the typical issues of asset size of the intended portfolio, the number of internal staff supporting the process, access to consultants and other strategic partners, the risk/return objectives of the portfolio are perhaps most important in such a heterogeneous investment arena. For instance, for a portfolio intended to outperform a broad hedge fund index such as the HFRI Fund Weighted Composite (arguably a naïve objective), the a priori motive is to access idiosyncratic risk. Unlike traditional capital markets, where diversification is intended to eliminate idiosyncratic risk in favour of systematic risk (i.e., beta), there should be an upper bound on diversification within hedge funds, as increased diversification mathematically reduces the possibility of idiosyncratic outperformance (i.e., alpha). To the extent that hedge funds would be considered expensive active management, an allocation to hedge funds should be intended to outperform some less expensive comparable return stream. If you want to simply be the market in hedge funds perhaps the capital could be better allocated elsewhere to begin with.

Further, selecting too many managers carries several additional explicit negatives as well. There are actual costs with performing due diligence on hedge funds such as travel expenses, background checks, legal fees, investment staff man-hours as well as ongoing resources needed to monitor the portfolio. Obviously, an investor should only expend these additional incremental costs if they can reasonably expect to be compensated for it.

Conversely, a certain minimum number of managers is needed in order to ensure basic strategy and underlying asset class diversification.[2] Concentration is a double-edged sword which increases the probability for outperformance as well as underperformance. Again, unlike liquid capital markets, volatility may not be the best proxy for risk in this context. Hedge fund returns are non-normal, but also investing in limited partnerships requires foregoing custody and day-to-day oversight of the actual assets. These are real risks.

One particular real risk of more (or perhaps less, as the case may be) concern to institutional investors which actually materially increases with each additional manager added to the portfolio is headline risk, or the probability that one of the managers in the portfolio appears in the financial media related to accusations of untoward activity. The cumulative probability of having such an event in your portfolio increases with each additional line item. Taken to the logical extreme, if an investor becomes the market, every single headline event in the industry will thus occur in their portfolio. For institutional investors, such an outcome may not have an immediate monetary or returns-based impact on the portfolio, but it often can invite regulator ire or the erosion of goodwill from their constituents. Such a perception of weak due diligence efforts can ultimately alter the governance structure and investment processes of an institutional investor, and not always for the better. It’s not a surprise then that steps are often taken to proactively reduce such adverse consequences.

Undoubtedly, not all headline events are created equal, and avoiding them should not be the preeminent concern of building a portfolio. However, certain headline scenarios can actually result in catastrophic investment losses, notably operational blow-ups or outright frauds. Obviously, robust due diligence and manager selection processes are intended to prevent such managers from entering the portfolio in the first place. But to be honest, one cannot completely eliminate the possibility of this occurring short of simply not investing in hedge funds. However, the potential impact of possible catastrophic losses on the portfolio can be mitigated through position sizing, which is directly related to number of positions.

It is thus with the objective of balancing the outperformance potential of concentration with the risk mitigation characteristics of diversification that we conducted a simple sensitivity analysis investigating the impact of additional managers to a portfolio of hedge funds which has suffered a blow-up.

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This analysis assumed an individual hedge fund generated a one-month loss ranging from -25% to -90%, a fairly broad range that should encompass all definitions of a blow-up. The other N number of managers in the portfolio were then assumed to generate an average rate of return for the period between -3% and 3%, a range that captures nearly 90% of the historical monthly return distributions of any hedge fund index. Holding the returns constant in a given scenario (for instance, a -50% blow-up return and 1% average return), the number of managers N was increased to 50, thus isolating the incremental impact on portfolio return of an additional line item.[3] Table 1 summarises the results.

As should be obvious in Fig.1, at some point, adding more and more managers to the portfolio has little to no effect on reducing the impact of the blow-up on the portfolio return. Also readily apparent is the implication that across most scenarios, having fewer than 10 managers results in the blow-up significantly impacting the portfolio return. The slope of the curve for most functions below 10 is still quite steep, suggesting significant marginal diversification utility from an additional manager. In scenario 8 for example (-75% blow-up, average return of 3%), the portfolio would lose 5% with 10 managers but only 1% with 20 managers. Without unnecessarily complicating the discussion with additional formulas, this analysis suggests that anywhere between 15 and 30 managers may be a prudent number of line items for typical institutional investors.

Correspondingly, in our customised fund of one portfolios, KRS has decided to reduce the allowable number of individual hedge funds to a range of 15 to 35 line items from the previous higher range of approximately 25 to 55 managers. Additionally, our investment committee has approved a direct portfolio target of approximately 20 managers to fill out over the next two years. While it is absolutely incumbent upon investment professionals to do everything possible to ensure that the ex ante possibility of a significant loss does not accompany an investment in a hedge fund, prudent portfolio construction can serve to mitigate the effects of such an unfortunate outcome on the overall fund should it occur. Although the above analysis focused on equal weighted, or naïve diversification, position sizing paradigms – a discussion for another day – can also serve to further reduce portfolio risk.

Christopher M. Schelling is Deputy CIO, Director of Absolute Return, Kentucky Retirement Systems and Adjunct Professor of Finance, Gatton School of Business, University of Kentucky.

Footnotes

1. For instance, see Markowitz (1959), Lintner (1965), or Elton and Gruber (1977). These studies, as well as a multitude of others, although sometimes contradictory, have in the aggregate suggested the optimal number of individual line items in a portfolio lies somewhere between 8 and 40. Above this point, idiosyncratic or unsystematic risk is substantially reduced and additional positions contribute little incremental portfolio-level volatility reduction.
2. Research by Lhabitant and Learned [(2002), (2004)] constructed equally weighted hedge fund portfolios from N (number of managers) = 1 to 50 by randomly selecting hedge funds from a data set of nearly 7,000 funds. At each point N, the random sampling was conducted for 1,000 trials, creating 50,000 portfolios. The authors demonstrated certain risks such as skewness and volatility were already reduced by approximately 75% at only five managers. Marginal diversification benefits were negligible by 30 to 35. Worse, some risks were actually shown to have increased with the addition of new managers, such as correlation to equities and kurtosis. The authors ultimately concluded that the optimal number of hedge funds that provided most of the benefits of diversification without the added risks of additional managers was roughly 10.
3. For the more algebraically inclined, the formula was Portfolio Return = [(1/ N) * CBlow-up Return] + [(N -1)/ N * CAverage Return). Note that as N approaches infinity, Portfolio Return approaches CAverage Return asymptotically. The intention was to measure the rate of flattening of the slope of the function for all realistic values of CBlow-up Return and CAverage Return. We omit this additional analysis in the interest of simplicity.

References

Elton E., Gruber M. (1977), ‘Risk Reduction and Portfolio Size: An Analytical Solution’, Journal of Business, (Oct. 1977), 415-437
Lhabitant F.S., Learned M. (2004), ‘Finding the Sweet Spot of Hedge Fund Diversification’, EDHEC White Paper, (April 2004)
Lhabitant F.S., Learned M. (2002), ‘Hedge Fund Diversification: How Much is Enough?’, FAME Research Paper, (July 2002), No. 52
Lintner J. (1965), ‘Security Prices, Risk, and Maximal Gains from Diversification’, The Journal of Finance, 20, 587-615
Markowitz H.M. (1959), ‘Portfolio Selection: Efficient Diversification of Investment’, John Wiley & Sons, New York, YK