Locking In The Profits Or Putting It All On Black? An Empirical

Locking In The Profits Or Putting It All On Black? An Empirical
WORKING PAPER
Locking In The Profits Or Putting It All
On Black?
An Empirical Investigation Into The
Risk-Taking Behaviour Of Hedge Fund
Managers
Andrew Clare
&
Nick Motson
July 2009
ISSN
Centre for Asset Management Research
Cass Business School
City University
106 Bunhill Row London
EC1Y 8TZ
UNITED KINGDOM
http://www.cass.city.ac.uk/camr/index
Locking In The Profits Or Putting
It All On Black?
An Empirical Investigation Into
The Risk-Taking Behaviour Of
Hedge Fund Managers
Andrew Clare
&
Nick Motson 1
FME/ESRC Fellow
Faculty of Finance,
Cass Business School,
106 Bunhill Row
London
EC1Y 8TZ
Tel: +44 (0)20 7040 4074
n.e.motson@city.ac.uk.
Abstract
The ideal fee structure aligns the incentives of the investor with those of the fund manager. Mutual
funds typically only charge a management fee which is a proportion of the funds under management.
Hedge funds on the other hand generally change an incentive fee which is a fraction of the fund's
return each year in excess of the high-water mark. The justification generally given for these incentive
fees is that they provide the manager with the incentive to target absolute returns. As these incentive
fees can be considered a call option on the performance of the fund (the fee structure gives the
managers the positive fees with profits but no negative fees with losses), it is possible that the
managers incentives might vary according to the delta of this option. A number of papers have
examined the optimal investment strategies of money managers in the presence of incentive fees within
a theoretical framework with seemingly conflicting results. In this paper, using a large database of
hedge fund returns, we examine the risk taking behaviour of hedge fund managers in response to both
their past returns relative to their high-water mark and their past returns relative to their peer group.
We then attempt to reconcile these results with the theoretical frameworks proposed.
1
Corresponding author Tel: +44(0)20 7040 4074 e-mail: n.e.motson@city.ac.uk
INTRODUCTION
The ideal fee structure aligns the incentives of the investor with those of the fund
manager. Investors will normally be looking to maximise their risk-adjusted return while fund
managers will seek to maximise their fees. Mutual funds typically only charge a management
fee which is a proportion of the funds under management. 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. Hedge funds on the other hand generally charge both a
management fee and an incentive fee which is a fraction of the fund's return each year in
excess of a high-water mark. It is clear that this structure aligns the objectives of these two
parties more closely since they both stand to benefit from incrementally better performance.
However hedge fund 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. For the period 1994 to 2006 Brooks, Clare and Motson
[2008] found fees cost on average 5.15% pa and depending upon the variance of returns
Goetzmann et al [2003] estimate that the performance fee effectively costs investors
between 10 and 20 percent of the portfolio. 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 anyway. On the one hand Anson [2001], 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. This is a view that is partially supported by Goetzmann et al [2003] who state that “the
manager has the incentive to increase risk provided other non modelled considerations are
not overriding”. An opposing view is presented by L’Habitant [2007] who considers the
incentive fee as 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.
Several academic papers have examined the effect that incentive fees have upon the
optimal dynamic investment strategies of fund managers within a theoretical framework.
Typically these papers present a framework with one risky and one riskless asset and then
examine the allocation the manager would make to each asset under various scenarios. The
theoretical results provide a range of possible behaviour depending upon: the assumptions
made about manager preferences’; the possibility of fund liquidation; and the assumed level
of the management’s stake in the fund. Thus the models illustrate the importance of what
Goetzmann et al [2003] describes as “non-modelled considerations”, or what could also be
described as implicit rather than explicit contract terms.
The explicit terms of the compensation contract are that investors agree to pay the
manager a fixed percentage of positive returns while accepting all of the downside, if the
contract was this simple then the manager would, as Anson [2001] describes, simply
possess a call option on the future performance of the fund which would provide the
manager with an incentive to increase risk. However, there are also many implicit terms to
the contract that are more difficult to model, some of which will mitigate this problem and
others that may exacerbate it. For example, investors will expect the hedge fund manger to
invest a substantial percentage of their own net worth in the fund and penalise them for poor
performance (or for excessive risk taking) by withdrawing their funds (just as a mutual fund
client would).
This will mitigate some of this risk taking. However, risk taking might be
exacerbated if as has been illustrated using mutual fund flow data, fund flows are a convex
function of past performance where good performance leads to significant fund inflows, but
where poor performance leads to smaller net outflows.
This results in manager
compensation having a call option-like feature that can induce the manager to indulge in
excessive risk-taking.
In this paper we present empirical evidence of the influence of the hedge fund
industry’s typical fee structure on the risk taking behaviour of hedge fund managers. Our
analysis takes explicit account of the option-like features of the compensation structure. We
also analyse the various hedge fund strategies separately rather than assuming that
manager behaviour is effectively unaffected by their strategies, which is often the implicit
assumption of other work in this area.
Amongst other things, our results enable us to
distinguish between and to say something about the competing theoretical models that seek
to identify the relationship between incentives and hedge fund manager behaviour. To do
this we use a large database of hedge fund returns and identify each fund’s position relative
to its peer group and to its high-water mark. After identifying the position of each fund in each
of these two ways we can then examine whether hedge fund managers adjust the volatility of
their fund in response to their performance relative to other hedge funds or the “moneyness”
of the performance option.
We aim to answer questions of the following kind: do those funds that find that their
incentive option is out of the money “put it all on black” and increase risk; do they maintain
risk levels; or do they reduce them? We then attempt to reconcile these results with the
theoretical frameworks that have been proposed.
A REVIEW OF THE THEORETICAL MODELS OF BEHAVIOUR IN THE PRESENCE OF
INCENTIVE FEES
The conflicting results of theoretical models of fund manager behaviour in the
presence of incentive fees and the importance of the implicit terms is clearly illustrated by
contrasting the findings of Carpenter [2000], Goetzmann et al [2003], Hodder and Jackwerth
[2007] and Panageas and Westerfield [2008]. Carpenter [2000] examined the optimal risk
taking behaviour of a risk-averse mutual fund manager who is paid with a call option on the
assets they control (similar to hedge fund incentive fees). She found that a manager paid
with an incentive fee increases the risk of the fund’s investment strategy if the fund’s return is
below the hurdle rate and decreases the risk if the fund is above the hurdle rate. Carpenter’s
analysis is for a single evaluation period and does not consider the possibility of the fund
being liquidated unless the value goes to zero. Goetzmann et al [2003] provide a closed-form
solution to the cost of hedge fund fee contracts subject to a number of assumptions in a
continuous time framework. They model incentive fees as an option and find that the cost of
the contract rises as the portfolio’s variance rises and hence conclude that the manager has
the incentive to increase risk “provided other non modelled considerations are not
overriding”. The authors include the possibility that the fund can be liquidated if its value falls
below a specified boundary and show that as the fund’s value approaches this boundary the
manager will reduce risk. So whereas Carpenter’s theoretical manager would increase
(decrease) risk as the fund value falls (rises) Goetzmann et al’s would decrease (increase)
risk as it falls (rises).
Hodder and Jackwerth [2007] consider the optimal risk-taking behaviour of an
expected-utility maximising manager of a hedge fund who is compensated by both a
management fee and an incentive fee. The authors also examine the effect of several implicit
terms including the manager’s own investment in the fund, a liquidation barrier where the
fund is shut down due to poor performance and the ability of the manager to voluntarily shut
down the fund as well as to enhance the fund’s Sharpe Ratio through additional effort. Using
a numerical approach they find that seemingly slight adjustments to the compensation
structure can have dramatic effects on managerial risk taking behaviour. Specifically, they
find that the existence of a liquidation barrier and an assumption that the managers own a
percentage of the fund inhibits excessive risk taking as the fund value falls.
Panageas and Westerfield [2008] find that a manager compensated with an incentive
fee and a high-water mark will place a constant fraction in the risky asset if they are
operating in an infinite horizon setting. The intuition behind this is that the manager does not
optimise just one option but an infinite time series of options, a manager who is below the
high-water mark could increase the value of the current option by taking excessive risk today.
However this will decrease the value of future options because it will also increase the
probability of negative returns while the high-watermark is still fixed.
In Exhibit 1 we present a stylised summary of the differences between Carpenter’s
[2000], Goetzmann et al’s [2003], Hodder and Jackwerth’s [2007] and Panageas and
Westerfield’s [2008] models of fund manager behaviour in the presence of incentive fees.
Exhibit 1 clearly illustrates the striking difference between Carpenter’s and
Goetzmann et al’s models of behaviour. Carpenter assumes that the fund will only be
liquidated if the fund value goes to zero hence as the value of the fund falls the manager
increases risk to increase the chance of collecting incentive fees without fearing liquidation.
On the other hand, Goetzmann et al have a fixed liquidation boundary, thus as the fund value
approaches this boundary the manager decreases risk in order to reduce the probability of
liquidation. In the model of Panageas and Westerfield the manager holds a constant level of
risk. Hodder and Jackwerth’s model lies somewhere between the other three.
However, even in the absence of incentive fees there are implicit terms to the
compensation contract that could encourage excessive risk taking. Chevalier and Ellison
[1997] showed that if fund flows are a convex function of past performance, that is to say that
more money flows into strong performers than out of weak performers, because the
management fees are a fixed percentage of assets under management they will display call
option like features. This in turn creates incentives for fund managers to increase or
decrease the risk of the fund that are dependent on the fund's year-to-date return. Sirri and
Tufano [1998] and others have confirmed that flows in and out of mutual funds do exhibit this
convexity, superior relative performance leads to the growth of assets under management
while there is no substantial outflow in response to poor relative performance. This
flow/performance relationship was investigated for hedge funds by Agarwal, Daniel and Naik
[2004] who find that funds in the top quintile of performers exhibit an inflow of 63%, while the
bottom quintile exhibits an outflow of only 3%.
An empirical investigation of the risk taking behaviour of mutual funds for the 16 year
period from 1976 to 1991 was undertaken by Brown, Harlow and Starks [1996]. Using a
contingency table approach they showed that mutual fund managers undertake what they
termed as “tournament behaviour”, with funds whose mid-year returns were below the
median (losers) increasing volatility in the latter part of the year by more than those funds
whose mid-year returns were above the median (winners). The authors concluded that this
behaviour was a direct consequence of the adverse incentives described above. Managers
who have performed poorly by mid-year have incentives to increase their risk level to try and
improve their ranking by the year-end; whereas managers with strong mid-year performance
appeared to reduce risk in order to maintain their ranking.
Empirical research on the relationship between risk taking and incentives in hedge
funds is sparse. Using a regression approach Ackermann, McEnally and Ravenscraft [1999]
found a positive and significant relationship between the Sharpe ratio and the level of
incentive fees but no statistically significant relationship between the level of risk (as
measured by the standard deviation of returns) and the level of incentive fees. The authors
concluded that this was evidence that the incentive structure was effective because it
attracted top managers while not increasing their propensity to take on risk. Brown,
Goetzmann and Park [2001] showed that survival probability depends on absolute and
relative performance, excess volatility, and on fund age. Perhaps not surprisingly the authors
found that excess risk and poor relative performance substantially increased the probability
of termination which they argue is a cost sufficient to offset the adverse incentive of
excessive risk taking provided by the fee contract. Using a contingency table approach
similar to Brown, Harlow and Starks [1996] they found that funds tend to increase (decrease)
their risk in response to poor (strong) relative performance but not in response to their
absolute performance.
DATA
A major limitation of earlier studies is that they implicitly assume that hedge funds are
a homogenous asset class. In practice however, the term “hedge fund” refers to the structure
of the investment vehicle rather than the investment strategy being followed. Different
strategies have varying levels of risk and historic return which makes a strategy level
comparison essential if the results are to be meaningful. The data that we use in this study
has been extracted from the TASS live and graveyard databases from January 1994 through
to December 2007. More specifically, we extract monthly Net Asset Values (NAV), strategy
details and inception dates for all hedge funds that are denominated in US Dollars, that
report monthly and that have reported for at least one full calendar year over this sample
period. These criteria result in a total sample of 4,990 funds of which 2,449 are currently
reporting and 2,541 are no longer reporting. The data are summarised in Exhibit 2.
The total number of funds has increased rapidly over time from just over 500 in 1994
to approximately 2,500 in 2007, of which the long/short equity category comprised 950. The
mean and median fund sizes have also increased over time, the difference between these
two statistics indicate that the sample is dominated by smaller funds. There is a similar but
less pronounced pattern in the fund age.
Using the net asset values (NAVs) of each fund as reported in the TASS database we
calculate the monthly gross returns for each hedge fund over time using the algorithm
outlined in Brooks, Clare and Motson [2008]. We use gross rather than net returns in order to
isolate changes in risk that are a result of manager behaviour rather than being due to the
mechanics of the incentive contract since because as demonstrated in Brooks, Clare and
Motson [2008] incentive fees can have the effect of lowering the standard deviation of
observed net returns when a fund is above its high-water mark which could clearly bias the
results.
Calculation of the exact delta of the fee option is problematic because we do not have
an appropriate model or a true estimate of the implied volatility, so instead we use the
“moneyness” of the option as a proxy for delta. Moneyness is defined as:
Moneyness fMy =
NAV fMy
HighWaterMark fMy
(1)
where Moneyness fMy defines fund f’s value after M months of year y relative to its
previous maximum value as represented by its high water HighWaterMark fMy .
METHODOLOGY
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.
Exhibit 3 (taken from Brooks et al [2008]) shows the distribution of hedge fund returns
conditional upon the moneyness of the incentive option for three sub-samples defined as “at
the money” (ATM), “in the money” (ITM) and “out of the money” (OTM) using the data
described above.
The standard deviation of both the OTM and the ITM samples are
statistically larger than for the ATM sample, which could support the hypothesis that hedge
funds increase their risk when they are significantly below or above their high-water mark as
defined in expression (1).
However there is an alternative explanation for the above result: funds that produce
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 investigate this we calculate the annualised standard
deviation of gross returns for the funds in our sample for each calendar year as well as the
moneyness of the incentive option at the end of the year. we then split the sample into 12
sub-samples based on levels of moneyness between 0.70 and 1.30 and calculate the
median standard deviation for each sub sample. The results are presented in Exhibit 4.
The “V” shape of Exhibit 4 illustrates that the alternative explanation of the earlier
result is extremely possible. Those funds with historically lower standard deviation are 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.
In order to examine whether funds adjust the risk of their portfolios in response to
their performance we need to examine the standard deviation of returns before and after a
specific assessment point in time.
Using gross monthly hedge fund returns we calculate the annualised performance of
fund f between January and month M. Specifically, for each fund f in a given year y, we
calculate the M-month cumulative return as follows:
[
]
ReturnfMy = (1+ rf 1y ) + (1+ rf 2 y ) + ......(1+ rfMy)
12
M
−1
(2)
where rf is the monthly gross return for hedge fund f. In our initial analysis we set M to
6 (June), but we also allow month M to vary between April and August so that the return is
measured over periods ranging from four to eight months. We refer to this period as the
“assessment period”, that is, the period over which we assess the performance of each fund.
In order to analyse whether hedge funds adjust the risk of their portfolios in the post
assessment period, that is from month M to December, we follow Brown et al [1996] and
calculate the Risk Adjustment Ratio (RAR) using the following expression:
RAR fy =
2
⎛ ∑12
⎜ m = M +1 (r fmy − r f (12 − M ) y )
⎜
(12 − M ) − 1
⎝
⎛ ∑ M (r fmy − r fMy )2
⎜ M =1
⎜
M −1
⎝
⎞
⎟
⎟
⎠
⎞
⎟
⎟
⎠
(3)
where RARfy represents the RAR of fund f in year y. Expression (3) is simply the ratio
of the standard deviation of returns for the post assessment period to the standard deviation
of returns over the assessment period. In our base case the assessment period is from
January to June (M=6). This analysis is conducted using non-overlapping assessment and
post assessment periods.
As well as assessing the performance of the fund from January to month M, we also
calculate the moneyness of the incentive fee option at the end of month M. The performance
of any fund over the assessment period might be above the median return for its strategy,
but still may not be sufficient to lift the fund’s performance above its high water mark and
therefore may not be enough for the manger to be able to claim a performance fee. By using
moneyness as a way of categorising the position of the fund and therefore the fund
manager’s attitude to risk, we can assess the influence not only of relative performance, but
also the value of the incentive option on manager behaviour.
We analyse the post-assessment performance of fund f relative to the performance of
the hedge fund strategy to which it belongs. We therefore ask whether the funds adjust their
behaviour relative to their peer group. We normalise the post assessment return and the
RAR by using the following expressions:
[
]
[
]
Normalised Re turn fMy = Re turn fMy − Median Re turnsMy
Normalised RAR fMy = RAR fMy − Median RAR sMy
(5)
(6)
where s is one of the ten individual strategies being considered such that Normalised
Return and Normalised RAR are measures of how fund f either performed or changed risk
relative to other funds following the same strategy for a particular period. A value greater
(less) than zero for each expressions (5) and (6) should therefore be taken to indicate that
the fund in question has either outperformed (underperformed) its peer group, or increased
(decreased) its risk by more (less) than its peer group for the particular period in question.
Using the variables calculated above we construct 2x2 contingency tables in order to
test whether hedge funds adjust their risk in response to either their relative performance or
the moneyness of their incentive option. Specifically we construct two 2x2 tables where we
split the funds into those with high (Normalised RAR>0) or low (Normalised RAR<0) Risk
Adjustment Ratios conditioned upon either past performance or moneyness. The null
hypothesis in each case is that the percentage of the sample population falling into each of
the high or low RAR categories is independent of either the return or the moneyness. The
statistical significance of these frequencies is tested in 2 ways:
i)
a chi-square test having one degree of freedom (though this might be misspecified as it assumes the cell counts are independent); and
ii)
the log odds ratio, which is robust to the misspecification of the chi-square test
and also provides additional information regarding the direction and level of
dependence.
Although the contingency table approach will identify whether there is any directional
relationship between the Risk Adjustment Ratio and either past performance or the
moneyness of the incentive option, this approach assumes that the relationship is linear. In
order to examine further this relationship we construct tables where Normalised RAR is
conditioned upon either:
i)
12 levels of moneyness between 0.70 and 1.30, and
ii)
10 Deciles of relative performance
For each of these sub-samples we then test whether the median Normalised RAR is
significantly different from zero using the Wilcoxon Signed Rank test.
RESULTS
In panel A of Exhibit 5 we present summary statistics of the median annualised return
for each strategy and for all funds on an annual basis using a 6 month assessment period; in
Panel B we present the median moneyness for the same break down of funds over the
assessment period; while in Panel C we present the RAR for the assessment period for the
same stratification.
These results clearly illustrate the heterogeneous nature of the ten hedge fund
strategies being examined. For example consider a global macro hedge fund in 1994 that
produced an annualised return of 1% in the first half of the year and had a RAR of 0.80.
Treating hedge funds as one homogenous group would classify this as being below the 1.5%
median return and below the 0.85 median RAR, yet it is considerably above the median
return of -8.3% and above the median RAR of 0.74 for funds following the same strategy,
namely global macro. Additionally market conditions at particular points in time can affect
different strategies in different ways, for example the median RAR for fixed income arbitrage
funds during the 1998 LTCM/Russian debt crisis was 2.93, but it was only 1.33 for global
macro funds and 1.84 for all hedge funds.
Although we do calculate the performance statistics described above treating all
hedge funds as one group, we believe that the results are more meaningful when they are
considered by strategy.
CONTINGENCY TABLES
Exhibit 6 shows the contingency table results using the period from January to the
end of June in each full year as the assessment period (M=6) categorised by their returns
over the assessment period (Panel A) and by moneyness at the end of June (Panel B), and
therefore the period from July to December as the post assessment period.
Panel A shows that over the full sample period we can reject the null hypothesis of
independence between the relative return and RAR. More specifically, the Low Return/High
RAR and High Return/Low RAR cells have statistically significantly larger frequencies than
the other two outcomes. This result is in line with the findings of Brown et al [1996] for mutual
funds: those funds that have generated returns that are below the median for their strategy
over the first six months of the year are likely to increase risk more than the median fund
possibly in order to try and improve their whole-of-year ranking; while those funds that have
achieved above median returns for their strategy are more likely to decrease risk, possibly in
order to protect their returns and relative performance rankings. Taking each year
individually, relationship is in the same direction for 12 out of the 14 years in the sample and
is statistically significant for ten of these years.
Panel B shows that for the full 14 year sample period we can reject the null
hypothesis of independence between moneyness and the subsequent RAR with the Below
HW Mark/High RAR and Above HW Mark/Low RAR cells having statistically significant and
larger frequencies than the other two outcomes implying that those funds that find
themselves below their high-water marks after six months increase risk relative to the median
risk during the post assessment period, and those funds above it decrease risk. When we
look at individual years, the log odds ratio shows that the relationship is only in the same
direction for 11 out of the 14 years in the sample and significant for 5 of them. In fact in 2005
the relationship is statistically significant and in the opposite direction – implying that in these
years funds that were below their high water mark after 6 months reduced their risk relative
to the median risk during the post assessment period.
These results imply that although hedge fund managers adjust their risk in response
to both their relative returns and according to the moneyness of the incentive option the
effect is more pronounced in the former rather than the latter case. This is borne out by the
fact that the log odds ratio of 0.2708 is greater overall when performance is benchmarked
against the median performance (last row, column (7) of Exhibit 6, Panel A) compared with a
logs odds ratio of 0.0997 when performance is assessed as a function of the moneyness of
the fund at the start of the post assessment period (last row, column (7) of Exhibit 6, Panel
B).
After considering the case of M=6 we now consider other assessment and post
assessment periods. Our original choice of M=6 was a relatively arbitrary one. It may be
that funds change their risk exposures in response to their performance relative to their
peers, or because of the moneyness of the incentive option earlier, or later in the year. In
Exhibit 7 we present results analogous to those in Exhibit 6 but with M=4, 5, 6, 7 and 8. Our
assessment periods are therefore either from January to April (M=4) or from January to May
(M=5) etc; and we calculate the moneyness of the fund at the end of April (M=4) or at the
end of May (M=5) etc. The results are all for the full 14 year sample rather than for individual
years.
Panel A in Exhibit 7 shows that for all assessment periods the effect of relative return
on normalised RAR is statistically significant but at a declining rate, as evidenced by the
declining value of the log odds ratio that falls from 0.2401 to 0.1597. This result suggests that
fund managers are more likely to change their risk taking behaviour earlier on in the year
rather than later in the year – and most likely halfway through the year. The effect of
moneyness (presented in panel B) appears to be only statistically significant for M=6 and
M=8, with the log odds ratio increasing from -0.0024 to 0.0931 as we move from M=4 to
M=8.
These results imply that hedge fund managers care more about relative return early
in the year but more about the value of their incentive option (absolute return) later on in the
year. One possible explanation for this is that as the year moves towards its end managers
have less chance or opportunity to improve their ranking but can attempt to maximise the
fees they will receive by increasing risk, though the data does not support this. The
proportion of funds that are below their high-water mark that increase risk actually falls from
15.81% over the (4,8) assessment period to 15.21% over the (8,4) assessment period.
Rather the result appears to be driven by the proportion of funds that are above their highwater mark who reduce risk which increases from 34.22% to 35.82%.
DISAGGREGATED ANALYSIS
Having ascertained that there appears to be a relationship between the risk taking
decisions of hedge fund managers and both their relative performance and the value of their
incentive option using 2x2 contingency tables we now examine the relationship across a
broader cross-section of relative returns and moneyness.
Exhibit 8 presents the results for the effect of relative performance on Normalised
RAR for M=6, these results are shown graphically in Exhibit 9. Although the funds in the top
four performance deciles reduce risk this reduction is only statistically significant for the first
and fourth deciles. Meanwhile there is a statistically significant increase in risk for the fifth to
the ninth performance deciles. This confirms our previous results and is consistent with the
mutual fund literature that shows that fund managers react to their implicit incentives to
increase (decrease) risk in order to improve (maintain) their ranking by year end.
Exhibit 10 presents the results for the effect of the moneyness of the incentive option
(absolute performance) on subsequent Normalised RAR for M=6, these results are shown
graphically in Exhibit 11. Here we see that there is evidence of a statistically significant
change in risk behaviour across the moneyness categories. For moneyness above 1.15, that
is for fund’s that are 15% above the high-water mark half way through the year, there
appears to be a statistically significant risk reduction, this is in line with the theoretical models
presented by Carpenter [2000] and Hodder and Jackwerth [2007] who describe this as
“locking in” behaviour. However for moneyness between 1.05 and 0.90 that is 5% above to
10% below the high - water mark after six months there is a statistically significant increase
in risk. More interestingly we can see that for funds that are more than 10% below their high
water mark after the first half of the year there is a reduction in risk taking behaviour and this
reduction in risk is statistically significant for levels of moneyness down to 0.80. These
results clearly do not support Carpenter’s model [2000] but are much closer to the model
proposed by Hodder and Jackwerth [2007].
VARYING THE ASSESSMENT PERIOD
Exhibit 12 presents the results for the effect of relative performance on Normalised
RAR for a assessment periods ranging from (4,8) to (8,4). The results are broadly consistent
across all assessment periods with a large negative and significant normalised RAR for the
top performing decile and smaller positive normalised RAR for lower deciles.
Exhibit 13 presents the results for the effect of moneyness on Normalised RAR for a
assessment periods ranging from (4,8) to (8,4). In contrast to the results for the response to
relative performance, here we find significant changes in response as we vary the
assessment period. As the assessment period increases from M=4 to M=8, although the
results for above 1.10 moneyness are broadly consistent, with a normalised RAR
significantly below zero, managers that are below their high-water mark appear to change
their behaviour. In the early part of the year normalised RAR is below zero for levels of
moneyness below 0.85 (in some cases this is statistically significantly), however as we move
towards August (8,4) there is a significant increase in risk, in fact for the (8,4) assessment
period the median normalised RAR is significantly above zero for all levels of moneyness
below 1.15.
The previous analysis has shown that managers do appear to change their risk taking
behaviour according to both relative performance and as a function of the value of their
incentive option, with the former having the largest impact. As suggested by the theoretical
literature on this topic, the implicit terms of the compensation contract do appear to inhibit
excessive risk taking by fund managers who find themselves substantially below their highwater mark. Now we examine whether fund characteristics such as size and age have any
impact on risk taking behaviour.
FUND SIZE
Using a Probit regression Liang [2000] shows that fund size is an important factor in
determining fund survival with smaller funds more likely to liquidate. With this in mind we now
examine whether small and large funds differ in their risk taking behaviour in response to
relative performance and dependent upon the moneyness of their incentive option. Using the
fund size data reported in Exhibit 2, we split the sample by defining large funds as those
which are in the top quartile of assets and small funds as in the bottom quartile of assets
under management.
In Exhibits 14 and 15 we present the results for the effect of relative performance on
Normalised RAR for both large and small funds. The pattern of risk taking is similar for both
the large and small fund samples with a normalised RAR of below zero for the first to third
deciles and above zero for the fifth to ninth deciles. It is interesting to note that for the fifth,
sixth, seventh deciles the median normalised RAR for the small fund sample is more
positive, which suggests that smaller funds are more likely to increase risk, however the
difference is not statistically significant.
In Exhibits 16 and 17 we present the results for the effect that the moneyness of the
incentive option has on Normalised RAR for both large and small funds. For the funds that
are significantly above their high-water mark (moneyness greater than 1.15), the median
normalised RAR is more negative for the small fund sample suggesting smaller funds are
more susceptible to “locking in” behaviour though this difference is not statistically significant.
For those funds that are at or slightly below their high-water marks the median normalised
RAR for the small fund sample is more positive than for large funds suggesting smaller funds
are more prone to risk shifting behaviour, however for funds that are significantly below their
high-water mark (moneyness of between 0.80 and 0.90) this patter is reversed. This result
would appear to be consistent with the literature because it could be the possibility of
liquidation that prevents small funds from increasing risk once they are significantly below
their high-water mark.
FUND AGE
Both Liang [2000] and Brown, Goetzmann, and Park [2001] identify age as an
important factor in determining fund survival with younger funds more likely to liquidate. With
this in mind we now examine whether young and old funds differ in their risk taking behaviour
in response to relative and absolute returns. Using the fund age data reported in Exhibit 2,
we split the sample by defining old funds as those which are in the top quartile of fund age
and small funds as in the bottom quartile of fund age.
Exhibits 18 and 19 present the results for the effect of relative performance on
Normalised RAR for both young and old funds. The pattern of risk taking is almost identical
for both the old and young fund samples with a normalised RAR of below zero for the first to
third deciles and above zero for the fifth to ninth deciles and no statistical difference between
the two samples for any decile. It is interesting to note that for the eighth, ninth and tenth
deciles the median normalised RAR for the old fund sample is more positive suggesting that
younger funds are less likely to increase risk following poor relative performance perhaps
because they face a higher probability of liquidation.
Exhibits 20 and 21 present the results for the effect of the moneyness of the incentive
option has on Normalised RAR for both young and old funds. Once again there is no
statistically significant difference between the two samples for any level of moneyness.
However it is worth noting that for both levels of moneyness above 1.20 and below 0.90 the
young fund sample has a more negative normalised RAR, implying that younger funds are
more prone to “locking in” and less prone increasing risk folloing poor performance. Once
again this result is consistent with the literature because if it is the threat of liquidation that is
preventing excess increasing of risk, and younger funds have a higher probability of
liquation, then they are less inclined to increase risk.
CONCLUSIONS
In this paper we have found evidence to suggest that hedge fund managers adjust
the risk profile of their funds in response to their performance relative to their peers, with
managers of relatively poor (strong) performing funds increasing (decreasing) the risk profile
of their funds. This is in line with the findings of Brown, Harlow and Starks [1996] for mutual
funds but somewhat surprising as hedge funds have generally been portrayed as pursuing
absolute returns. 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.
Our 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. Relatively speaking these managers are
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.
We find that these managers do not “put it all on black” in order to “win” back earlier losses
and to increase the value of their incentive option. This should be good news for hedge fund
investors. This conservative behaviour may be due to the implicit terms of the manager’s
contract. As Hodder and Jackwerth [2007] suggest, these implicit terms may include the risk
of liquidation as investors withdraw funds and may also be due to the often substantial
management stake in the fund that discourages the fund manager from “swinging the bat”.
Our results are of significance for the design of 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. It is possible that this locking in
behaviour could be reduced by introducing a rising scale of incentive fees.
REFERENCES
Ackermann, C., R. McEnally, and D. Ravenscraft. “The performance of hedge funds: risk,
return, and incentives”, Journal of Finance, 54 (1999), pp. 833-874.
Agarwal, V., N.D. Daniel, and N.Y. Naik. “Flows, Performance, and Managerial Incentives in
Hedge Funds” EFA Annual Conference Paper No. 501 (2004).
Anson, M.J.P. "Hedge Fund Incentive Fees and the 'Free Option’ " Journal of Alternative
Investments, (2001), 4 (2), pp. 43-48.
Brooks, C., A. Clare, and N. Motson. “The gross truth about hedge fund performance and
risk the impact of incentive fees”, Journal Of Financial Transformation, 24 (2008), pp.
33-42.
Brown, K.C., W.V. Harlow, and L.T. Starks. “Of Tournaments and Temptations: An Analysis
of Managerial Incentives in the Mutual Fund Industry”, Journal of Finance, 51 (1996),
pp. 85-110
Brown, S. J., W.N. Goetzmann, and J. Park. “Careers and Survival: Competition and Risk in
the Hedge Fund and CTA Industry”, The Journal of Finance 56 (2001), pp.1869-1886.
Carpenter, J. N. “Does Option Compensation Increase Managerial Risk Appetite?”, The
Journal of Finance 55 (2000), pp. 2311-2331.
Chevalier, J. and G. Ellison. “Risk Taking by Mutual Funds as a Response to Incentives” The
Journal of Political Economy, 105 (6), (1997), pp. 1167-1200
Goetzmann, W.N., J. E. Ingersoll, and S. A. Ross.”High-Water Marks and Hedge Fund
Management Contracts”, Journal of Finance 58 (2003), pp. 1685-1718.
Hodder, J.E., and J. C. Jackwerth. “Incentive Contracts and Hedge Fund Management”,
Journal of Financial and Quantitative Analysis, 42 (2007), pp. 811-826.
L’Habitant, F.S. “Delegated portfolio management: Are hedge fund fees too high?” Journal of
Derivatives & Hedge Funds, 13 (2007), pp. 220–232.
Liang, B. “Hedge Funds: The Living and the Dead,” The Journal of Financial and Quantitative
Analysis, 35 (2000), pp. 309–326.
Panageas, S., and M. Westerfield. “High-Water Marks: High Risk Appetites? Convex
Compensation, Long Horizons, and Portfolio Choice”, Journal of Finance. 64 . (2009),
pp.1-36.
Sirri, E.R. and P. Tufano. “Costly Search and Mutual Fund Flows”, Journal of Finance, 53
(1998), pp. 1589–1622.
Proportion in Risky Asset
EXHIBIT 1
Comparison of Risk Choices Under Various Theoretical Models of Behaviour
50%
60%
70%
80%
90%
100%
110%
120%
Fund Value
Carpenter
Goetzmann, Ingersoll & Ross
Panageas & Westerfield
Hodder & Jackwerth
This exhibit 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 [2009]
EXHIBIT 2
Summary Statistics for Hedge Fund Sample 1994-2007
EXHIBIT 2
Summary Statistics Of Hedge Fund Sample 1994-2007
Convertible Arbitrage
Dedicated Short Bias
Emerging Markets
Equity Market Neutral
Event Driven
Fixed Income Arbitrage
Global Macro
Long/Short Equity Hedge
Managed Futures
Multi-Strategy
Total
1994
26
11
46
12
63
19
48
175
156
20
576
1995
38
13
72
20
80
30
55
225
175
25
733
1996
40
12
101
31
104
41
61
278
169
36
873
1997
47
14
120
41
134
55
68
375
179
51
1,084
1998
51
17
132
55
162
55
83
468
186
62
1,271
1999
64
17
149
77
174
67
87
554
176
73
1,438
2000
75
22
155
106
194
69
76
659
178
85
1,619
2001
81
18
149
116
215
77
77
762
172
101
1,768
2002
104
18
144
148
233
91
89
840
160
119
1,946
2003
120
19
144
170
273
115
112
899
172
153
2,177
2004
122
20
166
175
314
144
135
968
188
176
2,408
2005
105
19
190
188
341
166
139
1,015
210
192
2,565
2006
97
20
219
194
319
159
147
1,055
217
238
2,665
2007
66
15
228
163
284
132
131
950
214
266
2,449
Median Fund Size ($m)
Mean Fund Size ($m)
6.6
56.4
5.5
46.4
6.1
51.4
8.0
62.2
11.0
79.2
11.3
64.2
15.6
69.8
18.9
79.9
20.0
86.3
20.7
93.3
27.0
127.6
28.9
143.3
31.2
169.5
60.0
250.8
41
56
43
58
45
61
52
68
Median Age (months)
Mean Age (months)
24
37
27
38
29
40
30
41
33
44
36
47
39
49
41
51
41
52
42
54
This exhibit presents summary information for the sample of hedge funds collected from the TASS database. Only funds that are denominated in US Dollars, report monthly performance and that
have a return history spanning at least one full calendar year are included. The statistics for fund size are based on funds that report this information and thus do not represent every fund in the
sample. Fund age is calculated based on the reported inception date of the fund
EXHIBIT 3
The Distribution of Hedge Fund Returns Conditional
upon the Moneyness of The Incentive Option
-20%
-16%
-12%
-8%
-4%
ATM
0%
ITM
4%
8%
12%
16%
20%
OTM
This exhibit presents the distribution of returns at time t+1 conditional upon the moneyness of the incentive option at time t for three sub samples of the data. These sub-samples are defined as “At
The Money” (ATM) where moneyness is greater than 95% and less than 105%, “In The Money” (ITM) where moneyness is greater or equal to 105% and “Out Of The Money” (OTM) where
moneyness is less than or equal to 90%
Median Annualised Standard Deviation
.
EXHIBIT 4
Median Annualised Standard Deviation by Moneyness of Incentive Option
25%
24%
23%
22%
21%
20%
19%
18%
17%
16%
15%
14%
13%
12%
11%
10%
9%
8%
7%
6%
5%
0.70-0.75
0.75-0.80
0.80-0.85
0.85-0.90
0.90-0.95
0.95-1.00
1.00-1.05
1.05-1.10
1.10-1.15
1.15-1.20
1.20-1.25
Moneyness
This exhibit shows the median historical annualised standard deviation of returns versus various levels of moneyness measured at the end of each calendar year.
1.25-1.30
EXHIBIT 5
Summary Statistics Return, Moneyness and Risk Adjustment Ratio (RAR)
1994-2007
Panel A: Median (Annualised) Gross Return
Convertible Arbitrage
Dedicated Short Bias
Emerging Markets
Equity Market Neutral
Event Driven
Fixed Income Arbitrage
Global Macro
Long/Short Equity Hedge
Managed Futures
Multi-Strategy
All Funds
1994
-5.4%
57.1%
-5.0%
6.9%
9.7%
9.5%
-8.3%
-0.3%
2.7%
-2.5%
1.5%
1995
18.6%
-8.7%
-0.8%
17.4%
23.8%
17.6%
19.9%
32.6%
22.1%
18.6%
21.6%
1996
24.9%
-4.7%
38.5%
23.0%
25.5%
20.3%
13.5%
35.6%
4.7%
20.5%
23.7%
1997
1998
1999
2000
19.3% 14.4% 19.9% 28.2%
2.7% -2.6% -14.5% -16.1%
51.5% -19.2% 47.2%
8.4%
20.6% 14.5% 12.7% 20.5%
20.1% 17.8% 23.6% 21.6%
21.2% 11.7% 19.6% 12.1%
14.1%
8.5%
4.7%
6.3%
27.7% 24.5% 42.0% 20.2%
16.4%
4.9%
7.4% -3.0%
21.1% 16.7% 23.0% 28.1%
22.5% 15.2% 24.3% 15.8%
2001
22.4%
7.2%
15.5%
12.8%
11.5%
15.8%
11.3%
8.2%
5.1%
14.9%
11.3%
2002
2003
11.3% 16.5%
39.9% -18.5%
20.7% 42.3%
6.9%
7.6%
4.2% 23.5%
15.7% 12.8%
11.9% 18.5%
2.5% 18.1%
13.0% 22.3%
6.6% 14.8%
7.3% 17.5%
2004
1.4%
-4.3%
7.3%
5.1%
10.3%
9.1%
1.0%
6.8%
-8.3%
6.2%
5.9%
2005
-7.3%
7.8%
12.0%
7.8%
8.1%
7.7%
6.2%
6.1%
-0.5%
4.1%
6.3%
2006
17.4%
-0.3%
17.3%
14.5%
17.7%
12.9%
7.6%
14.2%
15.8%
14.5%
14.5%
2007
12.5%
-8.1%
29.8%
13.3%
18.2%
11.9%
15.2%
24.1%
12.4%
18.9%
18.9%
1994
0.97
1.11
0.97
1.01
1.02
1.03
0.92
1.00
0.98
1.00
1.00
1995
1.04
1.00
0.96
1.04
1.06
1.05
1.00
1.06
1.03
1.02
1.04
1996
1.07
0.83
1.06
1.06
1.07
1.05
1.05
1.13
1.00
1.06
1.07
1997
1.05
0.96
1.09
1.05
1.05
1.06
1.03
1.07
1.03
1.06
1.05
1998
1.05
0.96
0.90
1.04
1.06
1.03
1.03
1.07
1.00
1.05
1.04
1999
1.06
0.93
0.83
1.03
1.06
1.04
0.99
1.08
0.99
1.05
1.04
2000
1.08
0.91
0.92
1.07
1.05
1.02
1.00
1.03
0.97
1.07
1.03
2001
1.07
0.89
0.97
1.03
1.04
1.04
1.02
1.01
1.01
1.04
1.03
2002
1.03
0.98
1.04
1.02
1.02
1.04
1.01
1.01
0.97
1.02
1.02
2003
1.06
0.89
1.07
1.01
1.06
1.03
1.04
1.01
1.10
1.04
1.03
2004
1.01
0.71
1.02
1.01
1.02
1.02
1.00
1.01
0.98
1.01
1.01
2005
0.94
0.65
1.02
1.02
1.01
1.02
0.99
1.00
0.96
1.00
1.00
2006
1.04
0.61
1.06
1.04
1.06
1.04
1.02
1.05
1.04
1.05
1.05
2007
1.04
0.53
1.08
1.04
1.07
1.04
1.03
1.08
1.02
1.06
1.06
1994
1.00
0.92
0.89
0.96
0.85
0.88
0.74
0.87
0.80
0.82
0.85
1995
0.78
1.09
0.59
1.25
0.97
0.86
0.97
1.31
0.85
1.07
0.97
1996
1.14
1.59
0.72
0.96
0.97
1.00
0.98
1.15
1.01
0.85
1.00
1997
1.27
0.92
1.65
0.97
1.02
1.14
0.99
1.08
1.36
1.33
1.17
1998
2.09
2.06
1.75
1.65
2.58
2.93
1.33
1.78
1.81
1.97
1.84
1999
1.03
1.24
1.02
0.87
0.93
1.09
1.14
1.02
0.96
1.07
1.01
2000
0.90
1.01
0.74
0.75
0.70
0.84
0.89
0.66
1.50
0.79
0.76
2001
0.67
1.19
1.29
0.80
1.09
1.24
0.87
0.92
1.10
0.86
0.97
2002
1.84
1.39
0.94
1.44
1.20
1.14
0.99
1.25
1.17
1.35
1.24
2003
0.89
0.84
0.86
1.01
0.77
1.20
0.98
0.88
0.68
0.90
0.86
2004
0.59
1.50
0.70
0.99
1.10
0.81
0.93
1.09
0.74
0.89
0.95
2005
0.72
1.18
1.18
1.05
1.08
0.87
1.09
1.06
1.02
1.14
1.05
2006
0.54
0.88
0.51
0.83
0.85
0.92
0.72
0.65
0.83
0.66
0.71
2007
2.18
1.34
1.68
1.40
1.62
1.93
1.87
1.68
1.33
2.13
1.68
Panel B: Median Moneyness
Convertible Arbitrage
Dedicated Short Bias
Emerging Markets
Equity Market Neutral
Event Driven
Fixed Income Arbitrage
Global Macro
Long/Short Equity Hedge
Managed Futures
Multi-Strategy
All Funds
Panel C: Median RAR
Convertible Arbitrage
Dedicated Short Bias
Emerging Markets
Equity Market Neutral
Event Driven
Fixed Income Arbitrage
Global Macro
Long/Short Equity Hedge
Managed Futures
Multi-Strategy
All Funds
This exhibit presents median values for various statistics for both individual strategies and for all funds in the sample using a 6
month assessment and post assessment period. Panel A presents the median annualised return for M=6 calculated from
equation (2) in the text. Panel B presents the median moneyness for M=6 calculated from equation (4). Panel C presents the
median risk adjustment ratio calculated from equation (3) for M=6.
EXHIBIT 6
Contingency Tables of Relative Returns, Moneyness and Risk Adjustment Ratio
Panel A
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
1994-2007
Observations
576
733
873
1,084
1,271
1,438
1,619
1,768
1,946
2,177
2,408
2,565
2,665
2,449
23,572
Below Median Return
Lower RAR
Higher RAR
25.69%
23.96%
21.96%
26.74%
20.39%
27.26%
21.86%
27.86%
23.92%
25.18%
20.38%
27.96%
22.30%
26.25%
23.53%
25.57%
22.51%
26.16%
20.26%
28.25%
22.84%
25.71%
25.03%
22.92%
22.78%
26.38%
23.23%
24.50%
22.68%
25.91%
Above Median Return
Lower RAR
Higher RAR
24.65%
25.69%
28.38%
22.92%
29.90%
22.45%
28.41%
21.86%
26.28%
24.63%
29.83%
21.84%
27.86%
23.59%
26.64%
24.26%
27.60%
23.74%
29.86%
21.64%
27.20%
24.25%
25.07%
26.98%
27.35%
23.49%
26.87%
25.40%
27.47%
23.94%
576
733
873
1,084
1,271
1,438
1,619
1,768
1,946
2,177
2,408
2,565
2,665
Below High-Water Mark
Lower RAR
Higher RAR
25.52%
25.17%
15.14%
18.01%
9.51%
11.68%
8.39%
9.32%
14.63%
14.24%
11.89%
15.79%
16.12%
17.11%
17.48%
18.55%
20.40%
20.91%
12.68%
15.34%
16.74%
19.27%
18.87%
15.36%
7.69%
10.81%
Above High-Water Mark
Lower RAR
Higher RAR
24.83%
24.48%
35.20%
31.65%
40.78%
38.03%
41.88%
40.41%
35.56%
35.56%
38.32%
34.01%
34.03%
32.74%
32.69%
31.28%
29.70%
28.98%
37.44%
34.54%
33.31%
30.69%
31.23%
34.54%
42.44%
39.06%
Log Odds Ratio
-0.1113
0.4103
0.5769
0.5044
0.1162
0.6283
0.3293
0.1764
0.3007
0.6547
0.2329
-0.1613
0.2992
0.1093
0.2708
Std Error Log
Odds
0.1667
0.1486
0.1369
0.1225
0.1123
0.1068
0.0998
0.0952
0.0910
0.0869
0.0817
0.0791
0.0777
0.0809
0.0261
t-value
Chi-Square
-0.67
2.76
4.21
4.12
1.04
5.88
3.30
1.85
3.31
7.53
2.85
-2.04
3.85
1.35
10.37
0.45
7.65**
17.87**
17.06**
1.07
34.87**
10.91**
3.43
10.95**
57.24**
8.14**
4.16*
14.85**
1.82
107.61**
t-value
Chi-Square
0.00
1.78
1.66
0.88
-0.22
3.39
0.93
1.05
0.54
2.83
2.62
-3.67
4.19
0.00
3.16
2.76
0.77
0.05
11.55**
0.87
1.10
0.29
8.04*
6.87*
13.50**
17.68**
Panel B
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Log Odds Ratio
0.0004
0.2795
0.2759
0.1401
-0.0272
0.4027
0.0984
0.1039
0.0494
0.2712
0.2228
-0.3066
0.4229
Std Error Log
Odds
0.1667
0.1574
0.1664
0.1593
0.1238
0.1188
0.1056
0.0991
0.0921
0.0958
0.0851
0.0836
0.1010
Proportions in the body of the exhibit give the proportion of funds that fall into each classification. Each fund was required to have a complete return history for each calendar year. Above and below
median measures are defined as Normalised Return or RAR greater or less than zero. The log odds ratio is the log of the ratio of the product of the second and third columns to the product of the
first and fourth with standard error and the t-value measures the significance of this ratio. The chi-square number represent the statistics from the 2x2 contingency tables with 1 degree of freedom.
Values significant at the 5% level are denoted with * and those significant at 1% by **.
EXHIBIT 7
Contingency Tables of Relative Returns, Moneyness and Risk Adjustment Ratio Varying the Assessment Period
Panel A
Assessment Period
(4,8)
(5,7)
(6,6)
(7,5)
(8,4)
Obs
23,574
Below Median Return
Lower RAR
Higher RAR
22.82%
25.68%
22.64%
25.88%
22.68%
25.91%
23.31%
25.44%
23.56%
25.41%
Above Median Return
Lower RAR
Higher RAR
27.32%
24.18%
27.50%
23.98%
27.47%
23.94%
26.83%
24.42%
26.59%
24.44%
Below High-Water Mark
Lower RAR
Higher RAR
15.92%
15.81%
14.94%
15.52%
13.85%
14.78%
14.40%
14.94%
14.33%
15.21%
Above High-Water Mark
Lower RAR
Higher RAR
34.22%
34.05%
35.20%
34.34%
36.30%
35.07%
35.74%
34.92%
35.82%
34.64%
Log Odds Ratio Std Error Log Odds t-value
0.2401
0.2704
0.2708
0.1819
0.1597
0.0261
0.0261
0.0261
0.0261
0.0261
Chi-Square
9.20
10.35
10.37
6.97
6.13
84.65**
107.34**
107.61**
48.63**
37.54**
Log Odds Ratio Std Error Log Odds t-value
Chi-Square
Panel B
Assessment Period
(4,8)
(5,7)
(6,6)
(7,5)
(8,4)
Obs
23,574
-0.0024
0.0633
0.0997
0.0599
0.0931
0.0280
0.0283
0.0288
0.0286
0.0286
-0.08
2.24
3.46
2.09
3.26
0.01
5.01
11.96**
4.38
10.62**
Proportions in the body of the exhibit give the proportion of funds falling into each classification. Each fund was required to have a complete return history for each calendar year. Above and below
median measures are defined as Normalised Return or RAR greater or less than zero. The log odds ratio is the log of the ratio of the product of the second and third columns to the product of the
first and fourth with standard error and the t-value measuring the significance of this. The chi-square number represents the statistics from the 2x2 contingency tables with 1 degree of freedom.
Values significant at the 5% level are denoted with * and those significant at 1% by **.
EXHIBIT 8
1
Median Normalised Risk Adjustment Ratio by Performance Decile
Assessment
Period
(6,6)
Performance Decile
10
Observations
2,132
Median Normalised RAR -0.0088**
Wilcoxon Statistic -2.9985
p-Value 0.0027
9
8
7
6
5
4
3
2
1
2,275
0.0726**
-10.3075
0.0000
2,304
0.0475**
-9.2600
0.0000
2,378
0.0624**
-10.6714
0.0000
2,363
0.0470**
-9.5400
0.0000
2,427
0.0441**
-8.6747
0.0000
2,397
-0.0036**
-5.2503
0.0000
2,438
-0.0397
-0.6152
0.5384
2,432
-0.0484
-0.3410
0.7331
2,426
-0.1449**
-8.1947
0.0000
This exhibit presents the normalised risk adjustment ratio by performance decile as well as the test statistics for a Wilcoxon signed rank test of this median. Values significant at the 5% level are
denoted with * and those significant at 1% by **.
2
EXHIBIT 9
Median Normalised Risk Adjustment Ratio by Performance Decile
0.08
Normalised RAR
.
0.04
0.00
-0.04
-0.08
-0.12
-0.16
10
9
8
7
6
5
4
3
2
1
Performance Decile
This exhibit shows the median normalised risk adjustment ratio by performance decile with statistically significant values in black and others in grey
3
EXHIBIT 10
Median Normalised Risk Adjustment Ratio by Moneyness
Assessment
Period
(6,6)
Moneyness
Observations
Normalised RAR
Wilcoxon Statistic
p-Value
0.70-0.75
0.75-0.80
0.80-0.85
0.85-0.90
0.90-0.95
0.95-1.00
1.00-1.05
1.05-1.10
1.10-1.15
1.15-1.20
1.20-1.25
1.25-1.30
244
-0.0037
-1.1305
0.2583
300
-0.0332
-0.4416
0.6588
460
-0.0171*
-2.0408
0.0413
810
-0.0074*
-2.5126
0.0120
1,358
0.0207**
-4.7442
0.0000
2,796
0.0481**
-9.4457
0.0000
6,292
0.0437**
-15.7107
0.0000
5,140
0.0133**
-9.3987
0.0000
2,420
-0.0678
-0.3358
0.7370
1,197
-0.0665*
-1.9776
0.0480
691
-0.1334**
-3.9762
0.0001
342
-0.1387**
-2.9477
0.0032
This exhibit presents the normalised risk adjustment ratio by level of moneyness as well as the test statistics for a Wilcoxon signed rank test of this median. Values significant at the 5% level are
denoted with * and those significant at 1% by **.
4
EXHIBIT 11
Median Normalised Risk Adjustment Ratio by Moneyness
0.08
.
0.04
Normalised RAR
0.00
-0.04
-0.08
-0.12
-0.16
0.70-0.75 0.75-0.80 0.80-0.85 0.85-0.90 0.90-0.95 0.95-1.00 1.00-1.05 1.05-1.10 1.10-1.15 1.15-1.20 1.20-1.25 1.25-1.30
Moneyness
This exhibit shows the median normalised risk adjustment ratio by performance level of moneyness with statistically significant values in black and others in grey
5
EXHIBIT 12
Median Normalised Risk Adjustment Ratio by Performance Decile
Varying the Assessment Period
Assessment
Period
Performance Decile
10
9
8
7
6
5
4
3
2
1
(4,8)
Observations
2112
Median Normalised RAR -0.0163**
Wilcoxon Statistic -4.3230
p-Value 0.0000
2293
0.0259**
-8.8680
0.0000
2303
0.0425**
-10.1317
0.0000
2365
0.0593**
-11.3619
0.0000
2361
0.0571**
-11.3571
0.0000
2434
0.0463**
-11.2073
0.0000
2403
-0.0008**
-7.1557
0.0000
2441
-0.0156**
-4.7867
0.0000
2417
-0.0452
-1.6422
0.1006
2445
-0.1382**
-7.1910
0.0000
(5,7)
Observations
2117
Median Normalised RAR -0.0173**
Wilcoxon Statistic -3.2537
p-Value 0.0011
2279
0.0470**
-9.9317
0.0000
2321
0.0603**
-10.8222
0.0000
2382
0.0492**
-10.7923
0.0000
2338
0.0402**
-9.2358
0.0000
2435
0.0397**
-9.6500
0.0000
2416
-0.0001**
-5.4474
0.0000
2422
-0.0253**
-2.8691
0.0041
2434
-0.0585
-0.0705
0.9438
2430
-0.1336**
-7.5317
0.0000
(6,6)
Observations
2132
Median Normalised RAR -0.0088**
Wilcoxon Statistic -2.9985
p-Value 0.0027
2275
0.0726**
-10.3075
0.0000
2304
0.0475**
-9.2600
0.0000
2378
0.0624**
-10.6714
0.0000
2363
0.0470**
-9.5400
0.0000
2427
0.0441**
-8.6747
0.0000
2397
-0.0036**
-5.2503
0.0000
2438
-0.0397
-0.6152
0.5384
2432
-0.0484
-0.3410
0.7331
2426
-0.1449**
-8.1947
0.0000
(7,5)
Observations
2158
Median Normalised RAR -0.0134**
Wilcoxon Statistic -3.7883
p-Value 0.0002
2288
0.0430**
-7.3760
0.0000
2317
0.0354**
-8.3569
0.0000
2371
0.0406**
-8.5266
0.0000
2359
0.0347**
-8.1039
0.0000
2428
0.0364**
-8.1704
0.0000
2391
-0.0011**
-5.2824
0.0000
2427
-0.0053**
-4.1589
0.0000
2412
-0.0412
-1.8652
0.0622
2423
-0.1496**
-7.1575
0.0000
(8,4)
Observations
2199
Median Normalised RAR 0.0323**
Wilcoxon Statistic -7.0864
p-Value 0.0000
2295
0.0288**
-7.5212
0.0000
2328
0.0089**
-6.1737
0.0000
2366
0.0233**
-7.2004
0.0000
2355
0.0450**
-7.8144
0.0000
2417
0.0022**
-5.8398
0.0000
2376
0.0106**
-6.2301
0.0000
2402
0.0113**
-4.5616
0.0000
2423
-0.0420
-1.7225
0.0850
2413
-0.1461**
-4.9008
0.0000
This exhibit presents the normalised risk adjustment ratio by performance decile as well as the test statistics for a Wilcoxon signed rank test of this median. Values significant at the 5% level are
denoted with * and those significant at 1% by **.
6
EXHIBIT 13
Median Normalised Risk Adjustment Ratio by Moneyness
Varying the Assessment Period
Assessment
Period
Moneyness
(4,8)
Observations
Median Normalised RAR
Wilcoxon Statistic
p-Value
0.75-0.80
0.80-0.85
209
-0.0040*
-1.99
0.05
310
-0.0206
-0.45
0.65
498
-0.0643
-0.24
0.81
795
0.0000**
-3.11
0.00
1533
-0.0018**
-5.04
0.00
3347
0.0228**
-9.26
0.00
7943
0.0597**
-21.42
0.00
(5,7)
Observations
Median Normalised RAR
Wilcoxon Statistic
p-Value
246
-0.0392
-0.42
0.68
311
0.0019
-0.64
0.52
479
-0.0277
-1.88
0.06
805
0.0248**
-3.11
0.00
1387
0.0120**
-4.68
0.00
3190
0.0281**
-9.77
0.00
(6,6)
Observations
Median Normalised RAR
Wilcoxon Statistic
p-Value
244
-0.0037
-1.13
0.26
300
-0.0332
-0.44
0.66
460
-0.0171*
-2.04
0.04
810
-0.0074*
-2.51
0.01
1358
0.0207**
-4.74
0.00
(7,5)
Observations
Median Normalised RAR
Wilcoxon Statistic
p-Value
261
0.0395
-1.84
0.07
361
-0.0116
-1.53
0.13
528
0.0507**
-3.62
0.00
828
0.0264**
-3.56
0.00
(8,4)
Observations
Median Normalised RAR
Wilcoxon Statistic
p-Value
284
0.1052**
-2.99
0.00
361
0.1201**
-5.04
0.00
554
0.0158**
-2.72
0.01
829
0.0035**
-3.06
0.00
0.70-0.75
0.85-0.90
0.90-0.95
0.95-1.00
1.00-1.05
1.05-1.10
1.10-1.15
1.15-1.20
1.20-1.25
1.25-1.30
4528
-0.0077**
-8.19
0.00
1828
-0.0713
-0.65
0.52
802
-0.0551
-1.41
0.16
359
-0.1348**
-3.19
0.00
223
-0.1303*
-2.13
0.03
7029
0.0499**
-17.97
0.00
4935
0.0000**
-8.31
0.00
2095
-0.0690
-1.14
0.26
1016
-0.0831*
-2.51
0.01
520
-0.0699*
-2.15
0.03
265
-0.1458**
-3.31
0.00
2796
0.0481**
-9.45
0.00
6292
0.0437**
-15.71
0.00
5140
0.0133**
-9.40
0.00
2420
-0.0678
-0.34
0.74
1197
-0.0665*
-1.98
0.05
691
-0.1334**
-3.98
0.00
342
-0.1387**
-2.95
0.00
1452
-0.0079**
-3.51
0.00
2637
0.0118**
-6.50
0.00
5700
0.0276**
-12.73
0.00
4976
0.0212**
-10.25
0.00
2547
-0.0211**
-2.61
0.01
1314
-0.0436
-0.59
0.55
780
-0.1118
-1.50
0.13
421
-0.1123**
-3.03
0.00
1380
0.0046**
-3.85
0.00
2607
0.0220**
-6.53
0.00
5193
0.0290**
-11.76
0.00
4881
0.0032**
-8.27
0.00
2698
0.0005**
-5.02
0.00
1417
-0.0431
-0.60
0.55
825
-0.0689
-0.42
0.67
504
-0.0863
-1.65
0.10
This exhibit presents the normalised risk adjustment ratio by level of moneyness as well as the test statistics for a Wilcoxon signed rank test of this median. Values significant at the 5% level are
denoted with * and those significant at 1% by **.
7
EXHIBIT 14
Median Normalised Risk Adjustment Ratio by Performance Decile and Size
Performance Decile
10
9
8
7
6
5
4
3
2
1
321
314
303
335
343
356
360
332
350
320
-0.0279
-1.1079
0.2679
0.0917**
-4.1535
0.0000
0.0469**
-3.4364
0.0006
0.0465**
-3.0948
0.0020
0.0333*
-2.2909
0.0220
0.0324**
-3.3899
0.0007
0.0299**
-3.8732
0.0001
-0.0154
-0.4925
0.6224
-0.0045
-1.5033
0.1328
-0.1826**
-5.9635
0.0000
10
9
8
7
6
5
4
3
2
1
Observations
Median Normalised RAR
Wilcoxon Statistic
p-Value
316
0.0282
-1.7392
0.0820
285
0.0758**
-3.3250
0.0009
299
-0.0124
-1.8508
0.0642
296
0.0759**
-3.8803
0.0001
269
0.0814**
-4.1628
0.0000
292
0.0528**
-3.5853
0.0003
300
-0.0141
-1.6791
0.0931
335
-0.0465
-0.2421
0.8087
333
-0.0380
-0.0849
0.9323
335
-0.1553**
-3.3331
0.0009
Wilcoxon Rank Sum Test for
Equal Medians p-value
0.7541
0.6050
0.2444
0.4129
0.1448
0.7060
0.1202
0.4364
0.2374
0.2824
Observations
Large
Median Normalised RAR
Wilcoxon Statistic
p-Value
Performance Decile
Small
This exhibit presents the normalised risk adjustment ratio by performance decile, the test statistics for a Wilcoxon signed rank test of this median as well as the p-values for the Wilcoxon Rank Sum
test of equal medians between the two samples. Values significant at the 5% level are denoted with * and those significant at 1% by **.
8
EXHIBIT 15
Median Normalised Risk Adjustment Ratio by Performance Decile and Size
0.12
.
0.08
0.04
0.00
Normalised RAR
-0.04
-0.08
-0.12
-0.16
-0.20
-0.24
10
9
8
7
6
5
4
3
2
1
Performance Decile
Large
Small
This exhibit shows the normalised risk adjustment ratio by performance decile and size with statistically significant values in black and others in grey
9
EXHIBIT 16
Median Normalised Risk Adjustment Ratio by Moneyness and Size
Moneyness
Observations
Large
0.75-0.80
0.80-0.85
0.85-0.90
0.90-0.95
0.95-1.00
1.00-1.05
1.05-1.10
1.10-1.15
1.15-1.20
1.20-1.25
1.25-1.30
23
38
55
93
181
363
933
804
350
147
94
40
-0.0918
-0.2433
0.8078
-0.0864
-1.1674
0.2430
-0.0559
-0.2932
0.7693
-0.0007
-0.8138
0.4157
0.0251
-0.9985
0.3180
0.0097*
-2.4175
0.0156
0.0930**
-7.7977
0.0000
0.0133**
-3.7271
0.0002
-0.0513
-0.2035
0.8387
-0.0948*
-1.9724
0.0486
-0.1097*
-2.0646
0.0390
-0.1362
-1.0081
0.3134
0.70-0.75
0.75-0.80
0.80-0.85
0.85-0.90
0.90-0.95
0.95-1.00
1.00-1.05
1.05-1.10
1.10-1.15
1.15-1.20
1.20-1.25
1.25-1.30
Observations
Median Normalised RAR
Wilcoxon Statistic
p-Value
38
0.1699*
-2.1246
0.0336
61
-0.0276
-0.7219
0.4704
67
-0.1402
-0.8808
0.3784
114
-0.0537
-0.0410
0.9673
182
-0.0066
-1.5926
0.1112
399
0.0758**
-3.4845
0.0005
761
0.0536**
-5.9742
0.0000
633
0.0092**
-2.8281
0.0047
306
-0.0246
-1.0474
0.2949
135
-0.1492
-1.4451
0.1484
90
-0.1851**
-2.6000
0.0093
48
-0.2821
-1.7566
0.0790
Wilcoxon Rank Sum Test for
Equal Medians p-value
0.1427
0.5057
0.8209
0.4906
0.5770
0.4436
0.4111
0.5843
0.3613
0.7121
0.4522
0.2872
Median Normalised RAR
Wilcoxon Statistic
p-Value
Moneyness
Small
0.70-0.75
This exhibit presents the normalised risk adjustment ratio by level of moneyness, the test statistics for a Wilcoxon signed rank test of this median as well as the p-values for the Wilcoxon Rank Sum
test of equal medians between the two samples. Values significant at the 5% level are denoted with * and those significant at 1% by **.
10
EXHIBIT 17
Median Normalised Risk Adjustment Ratio by Moneyness and Size
0.20
0.16
.
0.12
0.08
0.04
0.00
Normalised RAR
-0.04
-0.08
-0.12
-0.16
-0.20
-0.24
-0.28
0.70-0.75 0.75-0.80 0.80-0.85 0.85-0.90 0.90-0.95 0.95-1.00 1.00-1.05 1.05-1.10 1.10-1.15 1.15-1.20 1.20-1.25 1.25-1.30
Moneyness
Large
Small
This exhibit shows the normalised risk adjustment ratio by level of moneyness and size with statistically significant values in black and others in grey
11
EXHIBIT 18
Median Normalised Risk Adjustment Ratio by Performance Decile and Age
Performance Decile
10
9
8
7
6
5
4
3
2
1
643
697
680
717
658
686
689
647
594
493
0.1168**
-6.6506
0.0000
0.0555**
-5.5035
0.0000
0.0458**
-4.2515
0.0000
0.0467**
-5.0717
0.0000
0.0798**
-5.2879
0.0000
-0.0140
-1.6818
0.0926
-0.0380
-0.0684
0.9455
-0.0379
-0.2484
0.8038
-0.1492**
-5.2388
0.0000
10
9
8
7
6
5
4
3
2
1
Observations
Median Normalised RAR
Wilcoxon Statistic
p-Value
372
-0.0174
-1.4823
0.1383
360
0.0616**
-3.9925
0.0001
416
0.0487**
-3.7809
0.0002
410
0.0454**
-3.5777
0.0003
412
0.0532**
-5.0333
0.0000
482
0.0748**
-4.4316
0.0000
439
0.0086**
-3.2604
0.0011
485
-0.0474
-1.0448
0.2961
551
-0.0380
-0.3694
0.7118
674
-0.1582**
-4.1649
0.0000
Wilcoxon Rank Sum Test for
Equal Medians p-value
0.6967
0.4473
0.9403
0.6743
0.3229
0.9895
0.1812
0.7059
0.8948
0.7545
Observations
Old
Median Normalised RAR 0.0241**
Wilcoxon Statistic -2.9036
p-Value 0.0037
Performance Decile
Young
This exhibit presents the normalised risk adjustment ratio by performance decile, the test statistics for a Wilcoxon signed rank test of this median as well as the p-values for the Wilcoxon Rank Sum
test of equal medians between the two samples. Values significant at the 5% level are denoted with * and those significant at 1% by **.
12
EXHIBIT 19
Median Normalised Risk Adjustment Ratio by Performance Decile and Age
0.16
.
0.12
0.08
0.04
0.00
Normalised RAR
-0.04
-0.08
-0.12
-0.16
-0.20
-0.24
10
9
8
7
6
5
4
3
2
1
Performance Decile
Old
Young
This exhibit shows the normalised risk adjustment ratio by performance decile and age with statistically significant values in black and others in grey
13
EXHIBIT 20
Median Normalised Risk Adjustment Ratio by Moneyness and Age
Old
Young
Moneyness
0.70-0.75
0.75-0.80
0.80-0.85
0.85-0.90
0.90-0.95
0.95-1.00
1.00-1.05
1.05-1.10
1.10-1.15
1.15-1.20
1.20-1.25
1.25-1.30
Observations
Median Normalised RAR
Wilcoxon Statistic
p-Value
107
0.0009
-1.6122
0.1069
116
0.1208**
-2.8045
0.0050
161
0.0397
-1.9520
0.0509
268
0.0078
-1.7680
0.0771
409
0.0649**
-3.1199
0.0018
780
0.0595**
-5.5015
0.0000
1,666
0.0480**
-8.4206
0.0000
1,388
0.0062**
-3.5949
0.0003
602
-0.0729
-0.2641
0.7917
309
-0.0787*
-1.9637
0.0496
162
-0.1538**
-2.7501
0.0060
75
-0.1415*
-2.2759
0.0229
Moneyness
0.70-0.75
0.75-0.80
0.80-0.85
0.85-0.90
0.90-0.95
0.95-1.00
1.00-1.05
1.05-1.10
1.10-1.15
1.15-1.20
1.20-1.25
1.25-1.30
Observations
Median Normalised RAR
Wilcoxon Statistic
p-Value
21
-0.1298
-0.9559
0.3391
29
-0.2176
-1.7190
0.0856
53
-0.0981
-0.9107
0.3625
119
-0.0580
-0.6205
0.5349
192
0.0000
-1.1812
0.2375
508
0.0382**
-4.2391
0.0000
1,259
0.0666**
-7.8290
0.0000
1,034
0.0607**
-6.0565
0.0000
569
-0.0929
-0.5757
0.5648
277
-0.0552
-0.8951
0.3707
170
-0.1649*
-2.2383
0.0252
91
-0.2061
-1.6304
0.1030
0.1532
0.0019**
0.7089
0.3289
0.6448
0.9980
0.5117
0.0247*
0.3855
0.6031
0.9021
0.6496
Wilcoxon Rank Sum Test for
Equal Medians p-value
This exhibit presents the normalised risk adjustment ratio by level of moneyness, the test statistics for a Wilcoxon signed rank test of this median as well as the p-values for the Wilcoxon Rank Sum
test of equal medians between the two samples. Values significant at the 5% level are denoted with * and those significant at 1% by **.
14
EXHIBIT 21
Median Normalised Risk Adjustment Ratio by Moneyness and Age
0.16
0.12
.
0.08
0.04
0.00
Normalised RAR
-0.04
-0.08
-0.12
-0.16
-0.20
-0.24
0.70-0.75
0.75-0.80
0.80-0.85
0.85-0.90
0.90-0.95
0.95-1.00
1.00-1.05
1.05-1.10
1.10-1.15
1.15-1.20
1.20-1.25
1.25-1.30
M oneyness
Old
Young
This exhibit shows the normalised risk adjustment ratio by level of moneyness and age with statistically significant values in black and others in grey
15
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