A new working paper by Andrew Clare and Nick Motson of London’s Cass Business School – “Locking in the profits or putting it all on black? An investigation into the risk-taking behaviour of hedge fund managers” – provides a comprehensive analysis of the influence of the hedge fund industry’s typical fee structure on the risk taking behaviour of hedge fund managers.

The researchers find evidence to suggest that hedge fund managers adjust the risk profile of their funds in response to their relative performance, with managers of relatively poorly (strong) performing funds increasing (decreasing) the risk profile of their funds. “Our results call in to question the idea that hedge funds target absolute returns and suggests instead that hedge funds “target” performance of their peers. This may well be a consequence of the actions of fund of fund managers and other investors who make their own investment decisions based upon the relative performances of the funds in which they seek to invest,” says Clare.

“We found that managers whose incentive option was well in the money reduced the risk profile of their fund. Relatively speaking these managers were protecting the value of this option towards the end of the year. For investors who would like to see their managers taking risk in a consistent manner regardless of the month of the year, this result may come as a bit of a disappointment. It suggests that there is an element of locking in behaviour, particularly towards the end of the calendar year,” said Motson.

But perhaps of particular significance given the performance of the hedge fund industry over 2008,the researchers found that those fund managers whose incentive option was well out of the money, tended not to “put it all on black” as a way of trying to win back up earlier losses. Given that so many hedge fund managers have started 2009 below their high-water marks, this could be good news for hedge fund investors.

The incentive fee debate
Incentive fees are not a new phenomenon, they are as old (if not older) than hedge funds themselves. It is well documented that Alfred Winslow Jones, who is generally considered to be the father of the hedge fund industry, charged a 20% incentive fee when he founded his partnership in 1949. It is less well know that others such as the legendary investor Benjamin Graham who ran investment partnerships from the 1920s to the 1950s also charged an incentive fee, or that even Warren Buffet who is so dismissive of what he calls the “2-and-20 crowd” charged a 25% incentive fee when he formed his first partnerships in the 1950s.

The ideal compensation structure should align the manager’s interests with the interests of the investors. While investors will look to maximise their risk-adjusted return, the fund managers will seek to maximise their fees. As mutual funds typically only charge a management fee (purely a fixed proportion of the funds under management) the manager simply has the incentive to maximise the size of the funds that they manage, rather than the return on those funds. Clearly this traditional fee structure can only align fund manager and investor objectives to a limited degree: if the investor is unsatisfied with the performance of the manager they can usually withdraw their funds thus reducing the fee to zero. Introducing an incentive fee, which is a fraction of the fund’s return each year in excess of a high-water mark could help to align the incentives, since both the investor and the manager stand to benefit from incrementally better performance.

However incentive fees are a contentious issue for two important reasons. First the fees can be very large as a proportion of the fund and can therefore be a drag on the performance of the fund. In an earlier paper the authors found that for the period from 1994 to 2006 fees cost on average 5.15% pa. Clearly investing in a hedge fund would only be rational if they provide a large, positive risk-adjusted return which compensates for these fees.

The second and perhaps more interesting issue is whether the incentive fees provide the manager with the right incentives. On the one hand Anson (2001)[2], who describes incentive fees as a “free option”, argues that the option-like nature of the incentive fee will lead the manager to increase the volatility of returns in order to maximise the value of this option.

An opposing view is presented by L’Habitant (2007)[3] who considers the incentive fee to be analogous to an option premium paid to the hedge fund manager by the investor. This premium ensures that the manager will optimise the size of the fund to keep returns high because the incentives for superior performance can be greater than for asset growth. He argues that the absence of incentive fees (for example in mutual funds) leads the manager to maximise funds under management, which is not necessarily in the interests of the investor who is seeking to maximise risk-adjusted returns.

Explicit and implicit terms
In their paper Clare and Motson contrast four untested academic views of the impact of incentive fees on fund manager behaviour[4]. Fig.1 presents a stylised summary of the differences between the competing theories. It shows the relationship between the proportion of risky assets held (on the vertical scale) and the value of the fund. According to Carpenter, as the value of the fund falls the manager increases holdings of risky assets; Goetzmann, Ingersoll and Ross’s model suggests that as the value of the fund falls the manager reduces these holdings; Panageas and Westerfield suggest that the manager maintains a constant level of risk; while Hodder and Jackwerth’s model lies somewhere between the other three.

This figure shows how the optimal proportion of assets held in the risky asset varies with fund value under four different theoretical models of behaviour, Carpenter (2000), Goetzmann, Ingersoll and Ross (2003), Hodder and Jackwerth (2007) and Panageas and Westerfield (2008).
Although the explicit terms of the compensation contract are quite straightforward to model, the implicit terms such as the manager’s own investment in the fund, the risk of liquidation due to poor performance and reputation/career concerns are extremely difficult to model. “Rather than trying to build yet another theoretical model of manager behaviour, we decided to try and measure the actual behaviour of hedge fund managers so that we could see whether any of the models were capturing reality,” said Clare.

Why use gross rather than net returns?
To reconcile theory and reality Motson and Clare examined the performance of a sample of almost 5,000 hedge funds over the period from January 1994 through to December 2007. But rather than simply using the net returns provided by the TASS database they instead extracted the Net Asset Values and fee details from the database then used a simple algorithm to calculate the monthly gross returns.

According to Motson, “It is important to use gross returns because we need to isolate changes in risk that are a result of manager behaviour rather than those that are due to the mechanics of the incentive contract. For example, suppose there are two funds, both charging a 20% incentive fee (and no management fee), but one of the funds is above its high-water mark and the other is below. If both funds make a gross return of 1% in a month and then lose 1% gross over the next month, the fund that is above its high-water mark will report net returns of +0.8% and then -0.8%, while the fund that is below its high-water mark will report net returns of +1% and then -1%. Thus using net returns would lead us to inappropriate conclusions about their performance, that is, the fund that is below its high-water mark is more volatile than the other. In fact they both have identical gross returns and identical volatility.”

“Moneyness” as a proxy for delta
Although it is widely accepted that incentive fees are an option (or a series of options), modelling this option presents a number of challenges, the most important of which is that there is no reliable estimate of the implied volatility. Motson and Clare sidestep this problem by using what they term “moneyness” as a proxy for the delta of the option. They define moneyness as:

where MoneynessfMy defines fund f’s value after M months of the year y relative to its previous maximum value as represented by its high water mark HighWaterMarkfMy. The moneyness measure is relatively intuitive; a value of above (below) 1.0 implies that the fund is above (below) its high-water mark. For example, a moneyness value of 1.1 shows that the fund is 10% above its high-water mark while a value of 0.9 shows that the fund is 10% below its high-water mark.

Beware of jumping to conclusions
But one has to be extremely careful when interpreting the relationship between the risk choices of a fund manager in response to returns because the two are inherently linked. In an earlier research paper[1] Clare and Motson examined the distribution of hedge fund returns conditional upon the moneyness of the incentive option, splitting them into three sub-samples defined as “at the money” (ATM), “in the money” (ITM) and “out of the money” (OTM).

Fig.2 taken from this earlier work illustrates the difference between the three sub-samples.The standard deviation of both the OTM and the ITM samples are statistically larger than for the ATM sample, which could be interpreted as evidence that hedge funds increase their risk when they are significantly below or above their high-water mark.

This figure taken from Brooks, Clare and Motson (2008) shows the distributions of return at time t+1 conditional upon the moneyness at time t. The three distributions are defined as: At the Money (ATM) where moneyness is between 0.95 and 1.05, In the Money (ITM) where moneyness is greater than 1.05 and Out of the Money (OTM) where moneyness is smaller than 0.95.

“This result was the motivation for our current research,” Motson said, “though the bulk of the previous paper was about how using net rather than gross returns would lead to biased results in factor models, the section on manager risk appetite received the most attention. We also struggled to explain why funds that were well above their high-water marks tended to increase their risk”.

The alternative explanation for the above result: is that funds with high return volatility are more likely to have extremely positive (or negative) performance and hence more likely to be classified as in (or out) of the money. Whereas funds with low return volatility are less likely to have had extreme return outcomes and hence are more likely to be classified as at the money.

In order to illustrate this, Clare and Motson calculated the annualised standard deviation of gross returns for the funds in their sample for each calendar year, along with the moneyness of the incentive option at the end of the year. They then split the sample into 12 sub-samples based on levels of moneyness between 0.70 and 1.30 and calculated the median standard deviation for each sub-sample. Figure 3 presents the results.

The resulting “V” shape in Fig.3 shows that the alternative explanation of their earlier results was extremely plausible. Those funds that had historically lower standard deviation were more likely to be closer to “at the money” whereas those with higher standard deviation are more likely to be significantly in or out of the money.

The risk adjustment ratio
Given the issues raised above, the research drew on the mutual fund literature in order to assess more accurately whether hedge funds adjusted the risk in their portfolios in response to either their relative performance or the moneyness of their incentive option, using a measure called the Risk Adjustment Ratio (RAR). The RAR is calculated using the following expression:

where RARfy represents the RAR of fund f in year y, M is the month chosen for analysis, rfmy is the monthly gross return for fund f in year y and rfMy is the mean gross return of f in year y up to month M.

Although this expression appears complex, it is simply the ratio of the standard deviation of fund returns between a chosen month M and the end of the calendar year to the standard deviation of returns from the beginning of the year to month M.

Clare and Motson initially chose M=6 months (i.e. June 30) as the break-point though they later examine break-points ranging from April to August so that the volatility is measured over periods ranging from four to eight months.

Finally, rather than treating hedge funds as a homogenous asset class the authors “normalised” the RAR in order to take account of the varying levels of risk and historic return of differentstrategies using the following expression:

where s is one of the 10 individual strategies being considered. The result is that Normalised RAR is a measure of how a particular fund changed risk relative to other funds following the same strategy for a particular period. Once again this measure is relatively intuitive; a Normalised RAR greater (less) than zero indicates that a fund has increased (decreased) its risk by more (less) than the median fund following the same strategy in the particular period in question.

It’s all relative
In order to investigate whether hedge fund managers adjusted their risk in response to their performance relative to their peers, the authors split the funds into performance deciles by strategy. They then calculated the median Normalised RAR for each of the performance deciles and tested whether this median Normalised RAR was significantly different from zero using the Wilcoxon Signed Rank test. Figure 4 presents the results, with values that are statistically different from zero in black and others in grey.

Although the funds in the top four performance deciles reduced risk this reduction was only statistically significant for the first and fourth deciles. Meanwhile the researchers found a statistically significant increase in risk for the fifth to the ninth performance deciles. The authors interpret these results as evidence that “hedge fund managers adjust the risk profile of their funds in response to their relative performance with managers of relatively poor (strong) performing funds increasing (decreasing) the risk profile of their funds.” This in turn meant that “fund managers react to their implicit incentives to increase (decrease) risk in order to improve (maintain) their ranking by year end.”

No evidence of putting it all on black
Using a similar approach the authors also investigated whether hedge fund managers adjusted their risk in response to the moneyness of their incentive option by splitting the funds into 12 levels of moneyness between 0.70 and 1.30. As before they then calculated the median Normalised RAR for each of the sub-samples and tested whether this median Normalised RAR was significantly different from zero using the Wilcoxon Signed Rank test. Figure 5 presents the results, with values that are statistically different from zero in red and others in grey.

Their results appeared to indicate a marked difference between the results for relative return and for moneyness. For funds that were 15% below their high water marks after the first half of the year, there was a reduction in risk, although this reduction in risk was not found to be statistically significant. For funds that were 15% above their high-water marks after the first half of the year, there did appear to be a statistically significant reduction in the risk of their portfolios. However, for moneyness between 1.05 and 0.85 (funds that were between 15% below and 5% above their high water mark after the first half of the year) there was a statistically significant increase in risk.

“If hedge fund managers typically responded to poor performance by “swinging the bat” we would have found a significant increase in the risk profile of these funds, but instead we found that, if anything, they reduced the risk. To extend the cricket analogy, we found that they tended to try to win back the losses by pinching singles, rather than trying to win it back with sixes”, said Clare.

The implications for investors
Clare and Motson’s findings imply that hedge fund managers adjust the risk profile of their funds in response to their relative performance with managers of relatively poor (strong) performing funds increasing (decreasing) the risk profile of their funds. As Clare points out “the hedge fund industry has always sold itself on the basis that it targets and aims to produce absolute returns for investors. That is, returns that are not benchmarked against specific financial market indices, or against a peer group. These results call in to question this idea and suggest at a minimum that hedge funds pay attention to the performance of their peers. This may well be a consequence of the actions of fund of fund managers and other investors who make their own investment decisions based upon the relative performances of the funds in which they seek to invest. It may well be an unintended consequence of the way in which investors choose to invest in a fund”.

The results with regard to how hedge fund managers adjust the risk profile of their fund given the moneyness of their incentive option are more complex. Managers whose incentive option is well in the money decrease risk. These managers therefore appear to be protecting the value of this option towards the end of the year. For investors who wish their managers to take risks in a consistent manner regardless of the month of the year, this result may come as a disappointment. It suggests that there is an element of “locking in” behaviour, particularly towards the end of the calendar year.

Perhaps of more interest is the risk taking behaviour of those fund managers who find their incentive option to be well out of the money. Here they find that these managers do not “put it all on black” in an attempt to make up earlier losses. This should be good news for hedge fund investors. The authors suggest that this conservative behaviour may be due to the implicit terms of the manager’s contract such as the manager’s own investment in the fund, or the risk to the reputation and career of the manager. These implicit terms should discourage the fund manager from putting it all on black.

In general, Clare and Motson’s results should be interesting to those involved in designing hedge fund manager compensation contracts. It would appear that the concern that incentive fees encourage excessive risk taking behaviour may be misplaced, however there does appear to be an incentive to “lock in” previous gains by reducing the risk profile of the fund. The authors suggest that this locking in behaviour could be reduced by introducing a rising scale of incentive fees.

Clare and Motson plan further research in this area, Motson said: “The Normalised RAR measure could also be implemented as a way to monitor individual fund managers, perhaps as a way of measuring style drift, or alternatively as a way of selecting managers with historically desirable risk characteristics.”

FOOTNOTES

[1] Brooks, Chris, Andrew Clare and Nick Motson (2007), “The gross truth about hedge fund performance and risk the impact of incentive fees”, Journal Of Financial Transformation, Vol. 24 pp 33-42.

[2] Anson, Mark J.P. (2001), “Hedge Fund Incentive Fees and the ‘Free Option’ “ Journal of Alternative Investments, Vol. 4, No. 2 (Fall), pp. 43-48.

[3] L’Habitant, Francois-Serge (2007), “Delegated portfolio management: Are hedge fund fees too high?” Journal of Derivatives & Hedge Funds, Vol. 13, 220–232.

[4] Carpenter, Jennifer N. (2000), “Does Option Compensation Increase Managerial Risk Appetite?”, The Journal of Finance 55, pp. 2311-2331.

Panageas, Stavros, and Mark M. Westerfield (2009),” High-WaterMarks: High Risk Appetites? Convex Compensation, Long Horizons, and Portfolio Choice”, Journal of Finance. Forthcoming.