High Water Marks - William N. Goetzmann

High Water Marks
William N. Goetzmann
Jonathan Ingersoll Jr.
Stephen A. Ross
Yale School of Management
July 9, 1997
Incentive fees for money managers are frequently accompanied by high water mark
provisions which condition the payment of the incentive upon exceeding the
maximum achieved share value. In this paper, we show that these high water mark
contracts are valuable to money managers, and conversely represent a claim on a
significant proportion of investor wealth. We provide a closed-form solution to the
high water mark contract under certain conditions. This solution shows that
managers have an incentive to take risks.
We conjecture that the existence of high water mark compensation is due to
decreasing returns to scale in the industry. Empirical evidence on the relationship
between fund return and net money flows into and out of funds suggest that
successful managers, and large fund managers are less willing to take new money
than small fund managers.
Please direct correspondence to:
William N. Goetzmann
Yale School of Management
Box 208200
New Haven, CT 06520-8200
See http://viking.som.yale.edu for a current version
I. Introduction
The growth of the hedge fund industry over this past decade has brought an unusual form of
incentive contract to the attention of the investment community. Hedge fund managers typically
receive a proportion of the fund return each year in excess of the portfolio’s previous high water
mark, i.e. the maximum share value since the inception of the fund. These incentive fees generally
range from 15% to 25% of the return of new profits each year and managers also charge an
additional fixed fee of 1% to 2% of portfolio assets. For example, George Soros’ Quantum Fund
charges investors an annual fixed fee of 1% of net asset value, and a high water mark based incentive
fee of 20% of net new profits earned annually. As a result, the Quantum Fund returned 49% (prefee) in 1995 on net assets of $3.7 billion resulting in an estimated total compensation of $393 million
for that year, most of which was due to the incentive terms.1 Of course, when the high water mark
is not achieved, manager returns are substantially reduced. In 1996, the Quantum fund lost 1.5%,
and thus earned only their fixed fee on $5.4 billion--$54 million. While the Quantum fund stands
out as an unusually good performer over the past decade, its compensation terms are typical of the
hedge fund industry. High water mark contracts have the appealing feature of paying the manager
a bonus only when the investor makes a profit, and in addition, requiring that the manager make up
any earlier losses before becoming eligible for the bonus payment. On the other hand, their optionlike characteristics clearly induce risk-taking behavior when the manager is below the high
watermark, and the large bonus of 20% above the benchmark clearly reduces long-run asset growth.
In this paper we examine the costs and benefits of high-water mark compensation to the
investor. To do so, we develop a valuation equation which allows us to estimate the division of
wealth that an investor implicitly makes with the portfolio manager, upon entering into a such a
contract. We find that the manager receives as much as 40% of investor wealth for reasonable
parameters of the valuation equation. A significant proportion of this compensation is due to the
incentive feature of the contract, however the tradeoff between fixed fees and high water mark fees
depends upon the volatility of the portfolio and the investor withdrawal policy. We find that this
proportion is high when money is “hot” i.e. when the probability of investors leaving the fund is
high, and when the volatility of the assets is high. In contrast, when investors are likely to remain
for the long term, and when volatility is low, the fixed-fee portion of the contract provides the
greatest value to the manager.
We also consider why high water mark contracts exist, and in particular, why they are used
by hedge fund managers as opposed to, say, mutual funds. While their prevalence in the hedge fund
industry might be an accident of history, the high water mark compensation contract may have
features particularly suited to the types of investment strategies employed by hedge funds. The role
of volatility and investor withdrawal, for example, may account for why we find high water mark
incentives are used in “speculative” asset classes such as hedge funds, commodity funds and
venture capital funds. In these asset classes, investor payoff is presumably based more upon
expectations of superior manager skill and less upon the expected returns to an undifferentiated or
passively managed portfolio of assets. Given that hedge fund investment is, in a sense, a pure bet
on manager skill, our analysis provides a framework for considering how much skill a hedge fund
manager must have to justify earning such high fees.
In addition to valuation of the high water mark contract, we explore the question of whether
the high water mark compensation is due to the fact that hedge fund technology may have
diminishing returns to scale. Most hedge fund managers are engaged in some form of “arbitrage
in expectations,” in the domestic and global debt, equity, currency and commodities markets. By
its very nature, arbitrage returns may not be scaled up as investors purchase more fund shares. To
test whether the high water mark contract may be a substitute for increasing compensation through
fund growth, we examine the empirical relationship between hedge fund investor cash-flows and
performance. In contrast to similar studies in the mutual fund industry, we find that large funds, and
funds with superior performance, do not issue new shares — indeed we find evidence that they
experience net reclamations. This is consistent with the hypothesis that the hedge fund industry
itself has important limits to growth. This has implications for investors seeking alternative
investments to equities and debt. While hedge fund performance over the past seven years has been
strong on a risk-adjusted basis, this performance may be in part due to the relatively small size of
the hedge fund sector. The unwillingness of successful funds to accept new money may be
indicative of diminishing returns to the industry as a whole as investment dollars flow in. We
conjecture that the option-like fees commanded by hedge funds exist because managers cannot
expect to trade on past superior performance to increase compensation through growth.
The paper is structured as follows. Section II develops a valuation equation for the
manager’s contract. Section III provides some comparative statics and discusses the implications
of our results. Section IV estimates parameters for the model, using empirical data on hedge funds.
Section V presents evidence on hedge fund performance, size and fund flows. Section VI
II. The cost of the management contract
The hedge fund management contract has interesting option-like characteristics. It is a
potentially perpetual contract with a path-dependent payoff. The payoff at any point in time depends
on the high-water mark which is related to the maximum asset value achieved. As such the contract
can be valued using option-pricing methods. We begin our analysis under the simple null hypothesis
that the manager provides no additional component of return; i.e., there is no manager skill in
predicting excess returns or timing the market.
We work in a continuous-time framework and assume that, in the absence of payouts, the
assets of the fund, S, follow a lognormal diffusion process with expected rate of return µ and
. H is the current high-water mark; it is the highest level the net asset value has reached
subject to certain adjustments. The client makes regular withdrawals from the fund at the rate W(S,
H, t).2 The fund has operating expenses, including, a regular management fee which must be paid
from the assets. We assume these expenses are proportional to the value of the fund, cS per unit
time. When the asset price moves above the high-water mark, the manager also collects an extra or
incentive fee equal to the fraction k of this return. In the stylized setting of the model, the incentive
fee is earned continuously. In practice, the incentive fee is usually accrued on a monthly basis with
H being reset on an annually or quarterly. F(S, H, t) is the present value of future fees and operating
The evolution of the assets of the fund are
dS '
µS ! W(S, H, t) ! cS dt % S d
The high-water mark is the highest level the asset value has reached net of any withdrawals and
certain expenses allocated to its reduction. If the withdrawals and allocated expenses are a fraction
a of the asset value, then the high-water mark is also adjusted down by the fraction a, that is, dH =
!aHdt. So the evolution of H is
dH ' !
W(S, H, t) % cNS
H dt
where cNS are the costs and fees allocated to reducing the high-water mark.
While the fund’s assets are below the high-water mark, i.e., S < H, the cost function satisfies
the option-like partial differential equation
1 2 2
% [rS ! W(S, H, t) ! cS]FS !
W(S ,H, t) % cNS
HFH % Ft ! rF % cS ' 0 .
This equation has the standard Black-Scholes interpretation. The expected rate of return on S has
been risk-neutralized to r. The change in H requires no similar adjustment since it is locally
deterministic and therefore free of risk. The term cS is the flow rate of costs whose present value
we are determining. It is like a dividend to the derivative asset in the Black-Scholes model.
Three boundary conditions are required to solve this equation. Two of the boundary
conditions for the problem are
F(0, H) ' 0
FH(S, 4) ' 0 .
The first condition says if the asset value falls to a zero, then there are no further costs. The second
condition says if the high-water mark is very high (relative to the asset value), then we can ignore
the present value of the incentive fees so a change in the high-water mark will not affect the value.
The third condition applies along the boundary S = H. Suppose the asset value rises from S
= H to S = H + . The the high water mark is reset to H + , and an incentive fee of k is paid
reducing the asset value to H + (1 ! k). Therefore
F(H % , H) ' k % F(H % ! k , H % )
. k
In the limit as 6 0 this is exact giving our third boundary condition
' k .
MH /0S'H
We first consider the special case when withdrawals are proportional to asset value W(S, H,
t) = wS. Since withdrawals were the only time-dependent feature of the problem, the cost function
F does not depend on time under this assumption, and Ft = 0. Furthermore, it is clear by inspection
and the economics of the problem that F is now homogeneous of degree one in S and H, so the
solution has the form F(S, H, t) = HG(x) with x / S/H. Substituting this into ? gives an ordinary
differential equation
1 2 2
x G xx%
(r % cN ! c)xG x ! (r % cN % w)G % cx ' 0 .
The solution to this equation is G(x) = c/(w + c)x + Ax where A is a constant of integration
and is the positive root of the quadratic equation. 3
Q( ) /
1 2 2
% r % cN ! c !
1 2
! (r % cN % w) ' 0
1 2
% c ! r ! cN %
1 2
% c ! r ! cN
% 2 2(r % cN % w)
Note that must be bigger than 1 since the quadratic form, Q( ), is convex and Q(1) < 0 implying
the positive root must exceed 1.
In terms of the original variables, S and H, the solution is
S % AH 1! S
F(S, H) '
The only remaining task is to determine the second constant of integration A. Applying the third
boundary condition (6) gives
(1 % k) ! 1 w % c
A '
So the present value of all future fees is
F(S, H) '
S %
· (k, )H 1! S
(k, ) /
(1 % k) ! 1
1 2
% c ! r ! cN %
1 2
% c ! r ! cN
III. Interpretation
% 2 2(r % cN % w)
The first term of the solution cS/(w + c) is the present value in perpetuity of the regular fees.
Since the investor withdraws funds at the rate w and costs occur at the rate c, the present value of all
future costs is the proportion c/(w + c) of the asset value.
The second term is the present value of the incentive fees. It can be expressed as a product
of three factors:
Present Value of Incentive ' F(S, H) !
S '
S· (k, )· S/H
The first factor, wS/(w + c), is the present value of the assets net of the future regular costs. The
factor (k, ) measures the present value of the incentive fees as a fraction of this “remaining” value,
wS/(w + k), at the inception of the contract (or whenever the asset value is at the high-water mark).
The final factor (S/H) !1 is the reduction in the present value of future incentive fees due to the extra
time required before the asset value hits the high-water mark again.
Figure 1 plots the manager’s fraction for a range of values for the incentive fee, given the
high water mark equal to the asset value, a volatility of the assets equal to 20%, a short-term rate
equal to 5%, a withdrawal policy equal to 5% and a fixed fee equal to 1%. In addition, we have
assumed that there is no “value added” by the manager. Even without an incentive fee, the fraction
of wealth given to the manager is surprisingly high. For instance, in the simple case where the
incentive fee is zero, the manager claims a percentage of the assets in proportion to his claim on the
future payouts of the fund. With a 5% payout and a 1% fixed fee, this is 16.7%. Presumably, this
fixed fee is not all profit to the manager. It must cover management expenses. For active managers,
these costs may be high, however even a low-cost equity index fund may have expenses of 40 basis
points. With the payout rule of 5%, index fund fees translate into a 7 ½ % fraction of investor
wealth. With a payout ratio equal to current dividend yields, this fraction increases to 13%. Thus,
our analytical framework demonstrates that even low fixed fees claim a non-trivial proportion of
investment assets. 3 As the incentive fee rises, the proportion of assets it represents increases -rapidly at first. Given a volatility of 20% and incentive fees of 20%, the incentive fees amount to
a fraction of assets between 10% and 15%.
Due to the perpetual nature of the investment problem, the manager fraction is very sensitive
to the withdrawal policy, w.
Figure 2 shows the ratio of the fixed fee value to the incentive fee
value for ranges of asset volatility
and the withdrawal policy w. Notice that for low withdrawal
rates and low asset volatility, the fixed fee portion of the compensation is the dominant source of
value. This is not surprising, since the option value is increasing in
and the present value in
perpetuity of the regular fees is decreasing in w. For asset volatility over 10% and withdrawal
policies over 20%, the high water mark compensation has the greatest manager value. This suggests
that manager compensation contracts may separate according to the volatility of the strategies and
investment outflows.
IV. Model parameters
What are reasonable parameter values for the valuation equation? To address this we
turn to the database of hedge fund returns used in Brown, Goetzmann and Ibbotson (1997) [BGI].
The data are annual returns and fund characteristics gathered from the 1990 through 1996 volumes
of the U.S. Offshore Funds Directory, the only publically available source of information about
hedge funds that includes defunct as well as surviving funds. Offshore funds in the directory
represent a substantial portion of the hedge funds in operation, and include most of the major
IV.1 Fund volatility
To estimate the fund volatility, we calculate the sample standard deviation for all funds. Of
610 hedge funds in the sample, 229 have return histories exceeding two years. Of this group, the
median and mean sample standard deviation is 18.7% and 23.0% per year, respectively. There are
two reasons why such a small percentage of funds have enough data to calculate volatility. First,
many funds have started recently, so a large number of the extant funds have only a short track
record. Second, the attrition rate for funds is relatively high — about 20% of funds fail each year.
Since we are effectively conditioning upon fund survival we are presumably losing the funds which
had such poor returns that they failed in their second year. This may bias our volatility estimate
IV.2 Withdrawal rate, w
In our model, the payout policy w is a flow, however it is unlikely that all hedge fund
investors conceive of it that way. A constant payout ratio is a reasonable assumption for certain
institutional investors such as university endowments and charitable foundations which choose
payout ratios as a matter of policy, however it may not be a reasonable assumption for the most
common type of hedge fund investor – traditionally a high net worth individuals. modeling the
conditional probability of withdrawal may be useful in determining a realistic value for w.
valuation equation can be adjusted to use a probability of a 100% withdrawal of funds in any year.
This may be a more realistic framework for the analysis, since hedge funds shut down with relatively
high frequency. In a study of offshore funds from 1989 through 1995, BGI found about a 20%
attrition rate. Although small funds are more likely to shut down than large funds, this still means
that the effective withdrawal rate due to closure is high and this translates into a high corresponding
value for w. To investigate this issue, we use a simulation in a later section to demonstrate how
varying the probability of fund shut down can affect the manager’s wealth. Another issue is whether
or not the withdrawal rate is conditional upon performance. Certainly we would expect poor
performers to shut down more frequently, and this would translate into a w that depends upon past
performance. This is also succeptible to simulation, but has not been completed at the time of
IV.3 Incentive fee, k and fixed fee c
Figure 3 is a histogram of the incentive fees and the fixed fees for the BGI data. 15% is the
most common incentive fee, and Figure 4 indicates that 2% is the most common fixed fee. A natural
question is what factors differentiate funds on the basis of fees. We tried volatility, past performance
and fund size as predictors, and found none to explain differences in incentive fees.
IV.4 Fixed fee vs. performance fee
How does a high water mark contract compare to a simple fixed fee contract? Absent any
incentive differences implied by the contracts, it is possible to characterize the trade-off between a
higher fixed fee and the incentive fee, conditional upon a given value, F. To do this, we assume that
investors are indifferent among contracts that cost the same in terms of the manager’s fraction.
Solving for different values of the incentive fee in terms of the contract value as a fixed point
provides a measure of the trade-off. Figure 5 shows the tradeoffs for a representative set of
parameters. For a benchmark contract of 20% performance fee and 1% fixed fee, w=5%, =20%
the figure shows that the manager fraction would be preserved at the same value by a fixed fee of
3 % with no incentive fee. This trade-off is dramatically affected by the volatility of the assets, but
not so much by the withdrawal policy w. With asset volatility at 50%, the investor is willing to pay
a 6% incentive fee to eliminate the incentive fee of 20%.
III. Positive risk-adjusted returns
III.1 Required alphas
Thus far we have not addressed the question of positive risk-adjusted returns. How high does
the manager’s rate of return have to exceed the drift of the passively managed assets in order to
justify the fee structure?
All the analysis thus far has been based upon a model in which the
manager has no extra information, and thus adds no value. Indeed, nowhere in the valuation
equation does the drift of the assets appear. Consequently it is difficult to incorporate positive riskadjusted returns into our analytical framework. Investors use hedge funds precisely because they
anticipate high returns. Thus, we would like to understand how high the expected return to the fund
must be in order to justify the manager fees.
To address this issue we use numerical simulation methods as a substitute for analytical
The simulation is set up as follows. A fifty year horizon is chosen, and returns to
portfolio are randomly generated from the log normal distribution. Since the classic hedge fund is
market neutral, we set the expected return on a benchmark portfolio return equal to the return of the
riskless asset, and the asset volatility equal to 20%. We set the fixed fee d to 1%. We treat the
withdrawal policy in two ways. First, we consider a range of fixed withdrawal rates, and calculate
the ratio of the present value of the investor’s portion of the active investment to the value of the
passively managed investment [ i.e. (S-F)/S ]. Depending upon the manager’s “value-added” this
ratio is either above or below 1 in simulation. Figure 7 plots this ratio for a range of manager alpha
levels, allowing for differing withdrawal rates. We find that the break-even point is not sensitive to
the withdrawal policy -- for 2%, 10% or 20% annual withdrawal rates, the break-even alpha is about
150 basis points.
Our second simulation sets w to zero, substituting fund attrition withdrawal. We when a
fund closes, we calculate the value of the active and passive investments at the time of closure, and
then discount this value to the present. We consider a range of probabilities of fund closure, with
annual attrition rates varying from 5% to 35%. These results are reported in Figure 8. The basic
result is the same. Fund attrition does not matter so much to the break-even point which is about 300
basis points.Taken together, these two simulations suggest that the high water mark provision of the
contract is worth 1.5% to 3.0% per year in fees, depending upon the way money is withdrawn from
the fund.
Although it seems natural to identify the manager’s contribution in terms of a positive
additional rate of return — an alpha — this might not be the appropriate way of considering the
benefits to investing in a hedge fund. The benefits expressed by alpha are linear in the capitalization
of the fund, but hedge funds might in fact provide decreasing returns to scale. An alternative way
of thinking of hedge funds is that they are firms that can capture a fixed amount of “arbitrage” profits
in the economy. In other words, they have a limited net present value. The choice of how to finance
this venture is a capital structure decision. From this perspective, the issuance of additional shares
has a diluting effect on the outstanding claims — investors simply divide a fixed pie of arbitrage
gains. In this framework, new money, i.e. a positive flow of funds into the account from new
investors, has only limited attraction to the hedge fund manager. It benefits him only to the extent
that he is unable to borrow fully what his activities require, or to the extent that he fears bankruptcy
through a margin call.
V. Incentives and new money
Do hedge funds take new money when they do well? If the manager’s technology were
linear, then on balance, more money would be welcome. If not, then new money, at least for large
funds, would be accepted when the fund decreased in scale, rather than when it grew. To test the
hypothesis that hedge fund managers do not accept new money when they do well, we examine the
relationship between flow of funds and past performance for hedge funds by regressing net fund
growth on lagged return in cross section. If managers accept new money after a good year, and/or
investors pull out of poorly performing funds, we would expect to find a positive regression
coefficient. On the other hand, if managers refuse new money after a good year, and seek additional
funding after a bad year , then we would expect to find negative a regression coefficient on past
We define net fund growth as the increase in net asset value of the fund due to the
purchase of new shares, as opposed to the investment return of the fund. This requires us to make
the simplifying assumption that new shares are purchased only at the beginning of the year —
purchases during the year will be interpreted as investment return. 5 Another problematic issue is
survivorship. Although we have defunct fund data, we must make some assumption regarding the
fund outflow in the year of its disappearance. We address survival issues by assuming a 100%
outflow for the year a fund closes. We control for year effects by performing the regression
separately for each year, and also by including year dummies for the stacked regression.
V.1 New money regression results
Besides estimating a single linear response, we also consider how the response differs
depending upon past fund performance. Following Sirri and Tufano (1996) and Goetzmann and
Peles (1997) we examine the differential response of new money to past returns via a piece-wise
linear regression. We separate fund return in cross section into quintiles each year, and allow the
coefficients to differ across quintile. We test for the equality of the coefficients across quintiles via
a Chow test. The results for the single response regression are reported in panel 1 of Table I and the
results for the piece-wise regression are reported in panel 2 of Table 1. The year-by year results for
the piecewise regression are reported in Table 2.
The results from panel 1 indicate that new money responds negatively to past positive
The response differs across quintile of lagged returns, however. The best and worst
performers have quite different coefficients. Panel 2 shows that new money responds by flowing
out of poor performers, but does not flow into good performers as one might expect. These results
are quite different from the pattern observed in mutual funds. Sirri and Tufano (1992), Chevalier
and Ellison (1995) and Goetzmann and Peles (1997), for example, all find a positive response to
superior performance. The negative response to top performance we find in the hedge fund universe
provides some support for the hypothesis that good performers may not readily accept new money.
V.2 Sorting on size
Another approach to the issue of whether the technology of hedge funds is linear is to test
whether larger funds continue to take new money. We can address this question simply by sorting
on size, and then averaging a measure of new money. Table 3 reports the results of this exercise.
We break funds into size quintiles in the first period, and then we average the net growth of the fund
in the following period for each quintile. We define growth slightly differently, under the
assumption that money flows in at the end of the period. As in the previous test, we find this change
make no difference our results. Table 3 shows that the largest size funds have net cash outflows,
while the smallest performers have net cash inflows. This pattern is consistent throughout the
period, with negative flows for large funds and positive flows for small funds each year. The second
panel of the table shows the results of t-tests for each group, annually as well as in the aggregate
- the extreme quintiles
have means different from 0.
As in the previous test, this pattern is
consistent with the story that well-capitalized funds avoid taking new money. It differs in that it is
also consistent with the hypothesis that smaller funds raise capital. Since we did not sort on
performance, many of the funds in the first quintile may be good performers, and thus able to raise
new money, or stop funds from flowing out.
Taken together, the empirical tests suggest that hedge fund managers behave differently than
mutual fund managers with respect to accepting new money. While mutual funds demonstrate
dramatic positive inflows into superior performers, this appears not to be the case with hedge funds.
In addition, large funds do not seem to grow at a rate as high as smaller funds — even when
growth is measured in dollar terms rather than percentage terms. We conjecture that this may be due
to the limits of the investment strategies employed by hedge fund managers. To the extent that they
engage in “arbitrage in expectations,” success creates its own limitations. Million dollar winning
positions may not be possible when the assets grow to billions of dollars.
VI. Conclusion
Hedge funds are an interesting new investment class with an unusual form of manager
compensation. In this paper, we provide a closed-form expression for the value of a hedge fund
manager contract. We also provide estimates of the typical parameter values for the equation, and
we examine its implications to both the manager and the investor. The high water mark provision
creates a distinct option-like feature to the contract. As such, it is clear that the value of the contract
to the manager increases in the variance of the portfolio. As a result, the manager has an incentive
increase risk. Depending upon the variance, the incentive fee effectively “costs” the investor 10%
to 15% of the portfolio. With fixed fees, the total percentage of wealth claimed by the hedge fund
manager can be between 30% and 40%. Investing with a hedge fund manager would only appear
to be rational if he or she provided a large positive risk-adjusted return in compensation. When we
consider the possibility that managers are able to create value, i.e. provide a positive alpha in return
for the incentives, we find that investors would accept 200 to 500 basis points of additional fixed
fee per year to forego the incentive feature of the contract. Put another way, if managers are able to
provide positive alphas, we find that rational investors would expect 200 to 900 basis point is
additional risk-adjusted return when they enter into a hedge fund contract. Interestingly, BGI report
that alphas for hedge funds over the 1989 through 1995 period are positive, and range from 4% to
8% annually. Consequently, hedge fund contracts may be priced about right.
The closed-form valuation equation demonstrates the crucial role that the withdrawal policy
plays in the valuation of the manager contract. The most common type of manager fee is a fixed
percentage of assets. When assets are placed with a manager (or a class of managers with the same
fee structure) for the long term, then the implicit cost to the investor can be high, when the
withdrawal policy is low. The manager’s percentage fees are like an additional discount applied
to the future cash flows from the fund.
In considering why high water mark contracts exist in the hedge fund industry, we considered
how hedge funds differ in terms of the product they offer. An analysis of the relative benefits of the
fixed fee vs. the incentive fee to the manager suggests that high variance strategies, and strategies
for which the investor may pull out soon, lend themselves to high water mark contracting.
relative value of the fixed fee portion on the contract decreases as the time until the investor
withdraws decreases. Empirical evidence on the short half-life of hedge funds may explain why
hedge fund managers choose to use high water mark contracts.
In has become nearly axiomatic in studies of the investment management industry that
managers seek to increase the size of assets under management. This presumes, however, that the
benefits to investment in the fund can be scaled up with the growth in net asset value. Hedge fund
strategies are fundamentally different from “long” asset portfolio strategies, however. Large sectors
of the hedge fund industry have nearly zero “beta” exposure. Many hedge funds use the invested
money as margin for maintaining offsetting long and short positions. Hedge fund managers are
made up of event arbitrageurs, global debt market speculators, pairs traders and opportunistic
managers exploiting “undervalued” securities.
They use leverage of all types to exploit these
opportunities — from short-selling equities to sophisticated debt repurchase agreements. In this
context, the dollar investment benefits the manager only to the extent that he is credit constrained
in his strategy. By their very nature, arbitrage in expectations are not infinitely exploitable.
Since it is not possible to directly investigate the relationship between scale and strategy
payoff, we use flow of fund, return and size data from the hedge fund industry over the period 1989
through 1995 to explore the issue of linear vs. non-linear returns to scale. Regression of net growth
in fund assets on lagged returns indicates that, unlike the mutual fund industry, the hedge funds
show a net decrease in investment, conditional upon past performance. We conjecture that this is
due to the manager’s unwillingness to increase the fund size. A sort on fund size, however shows
that small funds tend to grow (net of returns), while large funds tend to shrink.
This pattern may help explain the usefulness of the high water mark compensation to the
hedge fund manager. While mutual fund managers and pension fund managers can increase their
compensation by growing assets under management, hedge fund managers cannot. Thus, they must
explicitly build in benefits conditional upon positive returns, since they appear to resist net growth.
The implications of these results extend beyond the issue of the cost of compensation within
an unusual sector of the investment industry. The existence of high water mark contracts may in
fact be a signal to investors that the returns in the industry are diminishing in scale. Option-like
incentive contracts are scarce in the mutual fund industry and pension fund management industry,
but are prevalent in the real estate sector, the venture capital sector and the hedge fund sector.
Perhaps the compensation structure itself is telling us that future returns in these asset classes
depend crucially upon how much money is chasing a limited set of unique opportunities.
Brown, Stephen, William N. Goetzmann and Roger G. Ibbotson, 1997, “Offshore Hedge Funds,
Survival and Performance: 1989 - 1995,” NBER Working Paper no. 5909 and Yale School of
Management Working Paper.
Judith Chevalier and Glen Ellison, 1995, “Risk-Taking by Mutual Funds as a Rseponse to
Incentives,” NBER Wroking Paper no. 5234.
Goetzmann, William N. and Nadav Peles, 1997, “Cognitive Dissonance and Mutual Fund Investors,”
Journal of Financial Research, Summer.
Erik Sirri and Peter Tufano, 1992, “Buying and Selling Mutual Funds: the Impact of Costly Search,”
Harvard Business School Working Paper.
Table 1: Net Fund Growth and Lagged Returns, 1990 - 1995
The table reports the results of two linear regressions of net fund growth on previous year returns. The
growth in net asset value of fund i in year t, N it , is defined as the new dollar cash flow into the fund (in millions) in
the year following the return observation. It is calculated as N it = NAV t-1[ (1+G it)/(1+R it) -1] where NAV it is the fund
net asset value in year t, Rit is the total return for fund i in year t, and Git is the percent change in net asset value for fund
in the year. This assumes that money is only invested at the beginning of the year, and that reinvested dividends are
defined as growth. The form of the regressions are:
(1) Ni t%1 '
% j
(2) Ni t%1 '
% j
Ij %
Ij % j
Ri, t % ei t
Ri, t, q % ei t
Year effects are captured by dummies Ij defined as differing from 1990. Coefficients on returns are allowed to differ
according to quartiles each year: R i, t-1, q where coefficients 6 through 10 capture quartiles 1 through 4. The null
hypothesis is that flows are independent of returns, i.e. 6 and the q ‘s are 1.
Regression 1 Results
coef std.err t.stat p.value
Net Growth
Multiple R-Square = 0.0306 N = 934
Regression 2 Results
20.4 -0.3484
25.1 0.5709
23.4 0.7815
21.9 2.0695
20.9 -0.9116
22.4 -0.0261
Quintile 1 127.621
65.6 1.9450
130.1 0.3272
92.0 0.6601
61.4 0.1541
Quintile 5 -112.260
27.9 -4.0292
Multiple R-Square = 0.0491
Chow test of coefficient equality: F= 5.23, 3,872 p-value= .998
Table 2: Year by Year Regression Results
This table reports the results of year-by-year regressions analogous to those described in Table 1. These are crosssectional regressions in which new money [N] in period t+1 is regressed on period t fund return. Coefficients are
allowed to vary by the quartile of return. New money is denominated in millions of dollars. The year indicates t,
thus the 1990 column shows 1990 new money regressed on 1989 returns.
Int -22.0
47.4 -19.3
Q1 -48.8
56.6 163.6 666.4 -21.5 199.9
Q2 -229.3 245.2 -603.5 -788.1 107.2 146.7
77.5 -416.3 -279.6 197.3
26.0 843.6
67.9 -96.1 -151.1
29.0 -14.6 -149.6
88.3 -164.9 -162.2 -92.7 -164.1 -40.7
Standard Errors
127.5 168.6 377.8
419.2 606.7 942.7
594.3 293.9 404.8
212.8 176.4 239.8
89.1 108.5
-1.823 0.820 1.277 1.500
-0.464 0.444 0.970 1.764
-1.421 0.585 -0.995 -0.836
0.882 -0.701 -0.951 0.487
0.982 -0.452 -0.857 0.121
1.954 -2.257 -1.821 -0.855
-0.819 -0.091
-0.088 2.344
0.403 0.747
0.162 1.474
-0.131 -0.383
-3.132 -0.610
Table 3: Fund Growth Sorted on Size
For each year, funds are sorted on size into quintiles, and
the average net growth for each quintile in the following
year is reported. Net growth is defined as the new money, in
millions, measured for each fund, assuming dolloar flows at
the end of the period. The last row on each panel reports
the results for the aggregate across years. A t-test is
performed for each quintile separately and the t-statistic
is reported in the second panel. The null hypothesis is that
the net growth is different from zero.
Net Fund Growth by Size Quintiles
Yr. Avg
-58.8 -10.82
-148.2 -31.10
-120.6 -29.51
T-statistic for Fund Growth Different From 0
Small Q1
Fixed Fee
For Different Values of w and Std.
Incentive Fee
std = .2 , w = .05, F = .31
std = .5 , w = .05, F = .47
std = .2, w = .2, F = .12
std = .5 , w = .2, F = .21
1. Figures from The U.S. Offshore Funds Directory, 1995 and 1996 editions for the Quantum Fund N.V. Returns assume reinvestment of income, and manager fees calculated from reported changes in net asset value.
2.Since hedge funds generally have no “maturity date” and frequently pay no dividends, a perpetual investment from which only the
manger withdraws cash would be worthless to the investor. The withdrawal of funds ensures the contract has some value to the
3.The boundary conditions for G corresponding to those in (4) are G(0) = 0 and lim x60 G(x) ! xG x(x) = 0. The solution corresponding
to the negative root of the quadratic equation can be eliminated since it gives an unbounded value for G(0).
4. See Brown, Goetzmann and Ibbotson (1997) for a complete discussion of the coverage of the database.
5. When we assumed that money flowed in at the end of the period, the results were essentially the same.
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