Why do bad hedge-fund managers survive?

Why do bad hedge-fund managers

survive?

Candidato: Gabriele Macci

Relatore: Prof. Giulio Bottazzi

Tesi Diploma Magistrale, A.A. 2018/19

Contents

Why do bad hedge-fund managers survive?

Gabriele Macci

The relationship between the performance of a hedge fund and the qual-ity of its portfolio managers is hardly simple or easy to judge; in other words, it is not easy to distinguish between “bad” and “good” managers. One common belief is that judging the quality of a fund manager is easier when the financial market environment is positive and stable than when it is negative and volatile. Contrary to this belief, preliminary observa-tion of empirical data shows that the distribuobserva-tion of fund performance and the ratio between “good” and “bad” managers stay relatively stable with time, even when the market conditions change substantially. This paper, after describing the empirical data, introduces a model attempt-ing to interpret the observed invariance. The adopted model is based on a modified principal agent scheme where each manager is an agent and each fund investor is a principal. The developed model, which takes into account the different levels of turnover present in bull and bear periods, justifies the invariance between “good” and “bad” managers.

1

Introduction

The performance of a hedge fund is not perfectly correlated with the qual-ity of its portfolio management. For instance, although the acquisition of a company might have been carefully planned, a bad unpredictable event might still depress the profitability of the transaction. Alternatively, even though some commodity price shifts might have been forecast incorrectly, a hedge fund could still make a fortune just because of sheer luck. However, despite the absence of perfect correlation between performance and management qual-ity, still the former can represent a (noisy) signal for the latter. This signal is valuable to hedge fund investors because, if they believe management is not

good enough, they can ask a replacement1.

The relationship between performance and manager quality is also influ-enced by external factors such as the financial cycle. During bear periods, the market is usually more volatile and consequently the above relationship is weaker. Similarly toKhorana(1996), this weakness reduces the chances of ob-serving high turnover levels in managers positions because investors are more uncertain about manager quality. The fact that “bad” managers can better hide behind “good” managers during bear than bull periods, could then in-duce one to believe that a higher proportion of “bad” managers is present in industry during bear periods. Contrary to this belief, preliminary observation of empirical data shows that the distribution of fund performance along with the ratio between “good” and “bad” managers stay relatively stable with time, even when the market conditions change substantially.

This finding calls for further study, especially when discussing the per-formance dynamics of this industry. Broadly speaking, in the case of the hedge fund industry, one can imagine to decompose the variations of perfor-mance into two sources: endogenous to the sector - as a change in the average quality of portfolio managers - or exogenous - as a variation in financial mar-kets fundamentals. In this sense, finding an answer to the question of how much portfolio manager quality varies in time sheds new light on how much endogenous forces account for the change in the industry performance. An implication of finding that the proportion of “bad” managers is stable with time is, then, that most of the variation is generated exogenously to the in-dustry2_.

1_{The typical case considered in this paper are single-manager hedge funds. In these}

funds, the number of investors per fund is restrained so that investors can easily form influ-ential coalitions advancing their requests to the fund. These funds employ just one portfolio manager with a small staff of analysts. Therefore the notion of “change in management” simplifies into “manager substitution” from here onward.

2_{This is not to exclude that the industry performance depends on endogenous factors}

- such as the quality of their service providers or of their internal organization. The paper just argues that “composition effects”, due to shifts in the average quality of management, should be downplayed.

The key contribution of this paper is to present a model justifying the find-ing that the proportion of “bad” managers does not fluctuate when financial markets conditions change. To show this, a “principal-agent” model has been developed. The model identifies three different elements potentially causing a fluctuation: the first one is that the investors (the principals) can decide at any moment to substitute the portfolio managers (the agents); the second is that the relationship between fund performance and manager action varies in intensity with financial markets conditions; the third is the types of managers themselves — there are managers with different capabilities. The “good” managers are better able to anticipate opportunities on (exogenous) financial markets than “bad” managers. This quality is not immediately visible to the investors who can only try to infer it from the funds performances.

The model first defines the objectives driving each involved actor (the portfolio managers and the investors); it then attempts to characterize the equilibrium describing which actions will be taken by the various actors to achieve their goals. The resulting model dynamics has been supported by a numerical simulation showing that the ratio between “good” and “bad” managers does not fluctuate in time. Some possible justifications for this finding are presented at the end of section 4; the preliminary empirical data is presented in section3.

2

Literature review

Previous studies on quality of fund managers have concentrated on the em-pirics of topics like position stability and mobility. Building on those studies, this paper proposes a model and derives some conclusions on the aggregate pattern deriving from those studies.

Brown et al.(2001) collected data on managers from major offshore hedge funds from 1989 to 1995. “Of the 715 managers that appeared in the database over the seven-year period, we identified 2,221 separate engagement-years. An engagement for a manager is an employment contract with a single fund. An

engagement-year is one completed year of this contract. Out of 715 managers, [...] 373 disengagements” were found. These data suggests that turnover rates were on average very high in that period. Even if no similar studies have analyzed recent data, working for a hedge fund is still nowadays considered as a largely unsecured position (see, for instance, Forbes article by Gray, 2016).

Deuskar et al. (2011) studied the probability for a manager of joining a hedge fund conditional on the performances achieved in the past when man-aging a mutual fund portfolio. They discovered that less performing mutual fund managers have a higher probability to completely shift and go to work for a hedge fund. On the other hand, talented mutual fund managers tend either to remain in the mutual industry or to manage a new hedge fund to-gether with the current mutual one. These findings provide some preliminary evidence that hedge funds do not always acquire talented managers.

Khorana(1996) performed empirical analysis on mutual funds which, with the necessary adjustments, can also be applied to the hedge fund industry. He found that low fund performance are associated with a higher probability of the manager being fired. This risk may be reduced when there is a high level of volatility in the manager’s portfolio. Khorana explained this finding by saying that investor advisors have more difficulties in extracting the proper information, i.e. the actual manager responsibility, when the portfolio is highly volatile. This paper mutuates this idea to the hedge fund industry where investors, contrary to mutual funds investors, have a sizeable dimension and can directly control their own investments.

3

Empirical analysis

Financial markets condition may affect hedge fund returns both directly, by influencing portfolio returns, and indirectly, by causing some changes in the way a hedge fund is organized (who is employed, which are its service providers and so on). The aim of this section is to present some preliminary observations on the relationship between those indirect effects and the distri-bution of hedge fund performance.

At the moment no data on individual hedge funds is available, so no study on individual funds is feasible. However Hedge Fund Research Inc. (HFR) release on a monthly basis and with a lag of three months aggregated data on the hedge fund performance in the form of indices. These indicators, a.k.a. HFRI indices, differentiate the hedge funds based on their style3_{. For instance,}

a hedge fund with focusing on currency exchange rates is classified as “macro” and, more specifically, as “macro currency” if at least 35% of its portfolio is dedicated to currency exposure over a given market cycle. There are four general classifications for fund strategies: event-driven, equity hedge, macro and relative value. Each of these strategies has sub-strategies, for a total of 27 different indices4_{. The data used in this paper range from January 2008 to}

August 2018.

Each index aggregates the average return rate of all those funds mainly adopting the index sub-strategy . However, comparing an index with another can be misleading because their underlying compositions are/might be differ-ent. To partially address this issue, each time-series is normalized by its stan-dard deviation; this way, two indices reflecting the same average performance but different volatility levels become similar for the next steps of the analysis5. In order to study how the distribution of performance depends on indi-rect effects, two assumptions are made on diindi-rect effects: 1) it is possible to find an indicator that influences all the funds in the same way; 2) financial markets conditions only directly affect the mean and variance of fund

perfor-3_{Each index is built according to the methodology described inHFR(2018).}

4_{Event driven sub-strategies are: activist, credit arbitrage, distressed/ restructuring,}

merger arbitrage, multi-strategy and special situation. Equity hedge sub-strategies are: equity market neutral, fundamental growth, fundamental value, quantitative / directional, energy / basic materials, healthcare, technology and multi-strategy. Macro sub-strategies are active trading (only available since Jan 2009), commodity, currency, discretionary, multi-strategy and systematic diversified. Relative value sub-strategies are: fixed income-asset backed, fixed income-convertible arbitrage, fixed income corporate, fixed income sovereign (only available since Jan 2009), multi-strategy, volatility and yield alternatives.

5_{Normalizing to zero also the average return associated to every index does not affect}

mance. The first assumption means that it is possible to identify the notion of “financial markets conditions” with a certain indicator. The second assump-tion excludes that financial markets condiassump-tions have other direct effects on performance distribution (such as asymmetric effects on winners and losers). The indicator identified for assumption 1) is the monthly change in the Standard and Poor 500 index (S&P500). The choice of this indicator re-lies on two observations. First, it is highly correlated (0.749) with the HFR index that describes performance of hedge fund industry overall. Secondly, S&P500 is not substantially affected by changes in hedge fund performance because it is based on a broad and diversified portfolio of companies. In line with assumption 2), every cross-section of data is standardized in its mean and variance. Lastly, a time series for each percentile is derived from these standardized distributions. The result of these normalizations is that any ad-ditional variation in performance distributions from one period to another can only be attributed to a change internal to the hedge fund industry. Summing up, by calculating the correlation coefficient between S&P500 and each per-centile time series, it is possible to study the relation between the change in S&P500 and performance distributions after controlling for direct effects. The results are reported in figure figure 1.

First, though some residual variation is still present, the magnitude of the correlation coefficient is very low for most of the percentiles. Under the two above assumptions, this finding would suggest that, after controlling for di-rect consequences of changes in financial markets conditions, factors internal to hedge fund industry play a minor role in affecting the cross-sectional dis-tribution of hedge fund performance. Consequently, three hypotheses can be formulated: a. internal factors influence little performance distribution; b. they counterbalance each other; c. they just remain unvaried. Supposing the only internal factor is the manager quality (or the most relevant), then the last hypothesis would be the most plausible. This empirical analysis would then support the thesis that average quality of managers remains largely stable with time despite substantial changes in financial markets conditions.

0 10 20 30 40 50 60 70 80 90 100 -0.3 -0.2 -0.1 0 0.1 0.2 0.3

Figure 1: this figure show the correlation coefficient between the monthly returns of S&P500 index and each percentile in the distribution of hedge fund returns from January 2008 to August 2018. Hedge fund returns are proxied by HFRI indices as explained in the text. Note that any cross-sectional distribution contains only 27 elements so that missing percentiles are computed through linear interpolation.

Secondly, the presence of some negative values for the correlation coeffi-cient of the lowest percentiles is counter-intuitive to the belief that the average quality of the managers increases during bull periods. According to this belief those values should have been positive because in bull periods investors should be better able to substitute “bad” managers. In other words, poor-performing funds should benefit the most out of these periods because more-performing funds already had “good” managers. This argument also seems to support the thesis that average manager quality might remain unchanged with time.

4

The model

Timing: time is infinite and discrete, divided into one month periods. Actors: There is a fix 0.5 mass of funds, each fund has just one investor. Fixing the number of funds together with assuming no-entry implies no-exit, i.e. investors cannot exit from their investment; this sounds reasonable be-cause, at least in the short run, investments are usually subjected to lock-up periods. The simplification of just one investor per fund is in line with the

discussion in footnote 1about single-manager hedge funds.

There is a unit mass of potential hedge fund managers; they are “poten-tial” because they can either be employed or unemployed in any period. It is assumed that employed managers cannot move from a fund to another and, due to capacity constraints, they cannot manage more than one fund. Since the number of funds is fixed, then also the mass of unemployed managers is constant and equal to 0.5. Given by definition that the mass of unemployed managers and funds is equal, it is feasible to substitute all managers in a single period without any friction6_{. Each manager has a fixed-type and this}

type can either be good, g, or bad, b, depending on manager’s forecast ability of the financial markets conditions (see below for the formal definition). The overall proportion of good managers is β. The proportion of good managers among employed managers is βe and βu among unemployed, then βe+β₂ u = β.

Finally, managers receive a constant wage when working7 _{and prefer staying}

employed to unemployed.

Actions: In every period, each manager actions consists in setting up a portfolio strategy, a, which is either long, l, or short, s. Each investor ob-serves his own fund return but manager actions are unobservable8. Every investor decides to keep (δ = 0) or fire (δ = 1) his manager based on: i) his belief about the manager quality, after observing the hedge fund return and ii) his belief to be able to find a better replacement. His decisions constitute a firing rule.

Exogenous state: the conditions of financial markets (from now on

mar-6_{Working for a hedge fund is usually very remunerative so that no-shortages of labor}

supply should be expected.

7_{I abstract away from optimal compensation schemes such as incentive fees or high}

watermarks. There is no problem of moral hazard in this model, then the only function of contingent compensation schemes could be in screening the right type of managers, but this possibility has not been explored at the moment.

8_{Despite due diligence of investors, investors do not receive reports of the trading}

po-sitions. Portfolio managers do not usually disclose their trading strategies but only their underlying “principles”.

ket state), S, are exogenous and summarized by the type of market period: a bull period if the market is up-trending, U , or bear period if the market is down-trending, D. The market state follows a first-order Markov process. The transition matrix Π is stochastic and its realization Π in each period can be either Π+_{with frequency f}+ _{or Π}− _{with frequency f}−_{. The expected value}

of the transition matrix is ¯Π. The persistency of any market state is higher when Π+ _{realizes. By denoting with π}

S,S0 the probability of reaching state S0

from state S, we have π_SS− < ¯πSS < π_SS+ .

Managers are good when they have a superior knowledge about the evolution of market states. In line with this, the g-types observe the realization of Π in every period while b-types only know ¯Π, f+ _{and f}−_{. As an assumption,}

investors do not to have any superior knowledge, so that they know as much as b-types know.

Returns: The period return, r, takes either value −1 or +1. The proba-bility of r = +1 is r(a, S0), a function of the action of the portfolio manager and the next realization of market state. The complement, 1 − r(a, S0), is the probability of r = −1. The function r(a, S0) is such that having a short portfolio in bear periods yields higher expected returns than a long portfolio, r(s, D) > r(l, D). Vice versa for bull periods, r(l, U ) > r(s, U ). Fund returns are independent from each other.

In every one month period there are two stages:

Stage 1: Each investor announces a firing rule. Good managers observe the realiza-tion Π of Π. Each manager adopts a short or long strategy, a ∈ {l, s}. Stage 2: Market state S0 realizes and it is observed by every actor. After observing

his own fund performance, r, each investor either keeps or fires the manager according to the rule announced in Stage 1. Any fired manager is replaced by a random manager from the unemployed pool9_.

Strategies: The strategy of a g-type manager is a function ag(S, Π, βe) →

9_{The assumption of randomness can be interpreted as the investor not being able to}

{l, s} and the strategy of a b-type manager is a function ab(S, βe) → {l, s}.

Note that b-type cannot condition their actions on Π since their information set is coarser than g-types.

Investors firing rule is a function δ : [0, 1]2 _{→ {0, 1} that specifies for each}

possible pair of prior and posterior beliefs, (βe, βe,rP ), whether the investor will

substitute the manager (δ = 1) or keep him (δ = 0); posterior beliefs will be formally defined in equation (1).

On aggregate, every period is described by a 4-tuple, {S, S0, Π, βe}. The

market state S is inherited from the previous period and it is known by every actor. For the managers, S constitutes the basis of the forecasting decision. For investors, S is valuable when they compute the likelihood that a certain strategy was adopted by their own manager conditional on observing the re-turns. The market state S0 determines, in conjunction with the strategies adopted by every manager, what is the distribution of returns during the pe-riod. Π is just observed by g-types. Depending on the realization of Π, the g-types can bet on a switch of the markets state while b-types expect mar-kets state to persist, and vice versa. Finally, βe pins down the probability of

selecting a g-type from the unemployment pool. This is helpful for investors when announcing their firing rule.

In order to guarantee the model is tractable, a no-recall assumption is in-troduced on investors beliefs. In particular, it is assumed that in stage 1 all investors share a common prior belief on having a g-type working for their fund. This assumption imposes no-recall on those investors that decide to keep their manager from previous periods. In other words, investors firing de-cisions only depend on current performance10_{. Imposing rational expectations}

and applying the no-recall assumption, then the prior belief of all investors must be equal to βe.

10_{Relaxing this assumption should not affect the existence of a steady-state for β} e, but

Every fund return represents a signal for the corresponding fund investor. Since at stage 2 each investor knows {S, S0, βe, r}, from Bayes rule the

poste-rior belief of every investor on having hired a g-type is11: β_e,rP (S, S0, βe) = =βe· :=θr z }| { 1 − f+_{· r(a} g(Π+₎, S0) − f−· r(a_g(Π−₎, S0) 1 2(1−r)_·f+_{· r(a} g(Π+₎, S0) + f−· r(a_g(Π−₎, S0) 1 2(1+r) βe· θr+ (1 − βe) · [1 − r(ab, S0)] 1 2(1−r)· [r(a b, S0)] 1 2(1+r) | {z } :=γr = = βe· θr βe· θr+ (1 − βe) · γr for r ∈ {−1, +1} (1)

where ag(Π+₎, a_g(Π−₎ and a_b denote, respectively, the strategy chosen by a

g-type manager with stage 1 information sets at {S, Π+, βe}, {S, Π−, βe} and by

a b-type with information set {S, βe}. Since none of the investors can discern

between a more and a less persistent market, investors do not know which in-formation set was available to g-types and they evaluate the two possibilities with weights {f+_{, f}−_{}. From an investor’s viewpoint, θ}

r and γr represent the

probabilities, respectively for g- and b-types, to obtain return r. Note that if ag(Π+₎ = a_g(Π−₎ = a_b, then θ_r = γ_r for any return level so that prior and

posterior beliefs are identical.

Every investor receiving signal r updates its belief of an amount |βP

e,r− βe|.

Then, from the law of large numbers, the average update of state {S, S0, Π, βe}

can be defined as:

I = |β_e,−1P − βe| ·βe· (1 − r(ag(Π), S0) + (1 − βe) · (1 − r(ab, S0)) +

+ |β_e,+1P − βe| ·βe· (r(ag(Π), S0) + (1 − βe) · r(ab, S0)

 (2)

where the terms in square brackets represent the proportion of funds getting r = −1 and +1, respectively. Hence, I is a measure of how informative a

certain period is.

A pure strategy recursive equilibrium is:

Definition 1. A strategy ag = ag(S, Π, βe) for g-type managers, a strategy

ab = ab(S, βe) for b-type managers, an r-contingent firing rule δ = δ(βe, βe,rP )

for investors and a law of motion, B, for the endogenous state variable βesuch

that:

1. given ab and δ, ag minimizes the probability of g-types of getting fired,

i.e. ag = arg minagPr[δ = 1|ag];

2. given ag and δ, ab minimizes the probability of b-types of getting fired,

i.e. ab = arg minabPr[δ = 1|ab];

3. given ag and ab, δ maximizes expected returns at stage 1, i.e.

δ = arg max δ βe·f+· πSD+ r(ag(Π+₎, D) + π+_SUr(a_g(Π+₎, U )
+ +f−· π_SD− r(ag(Π−₎, D) + π−_SUr(a_g(Π−₎, U )
 + + (1 − βe) [¯πSDr(ab, D) + ¯πSUr(ab, U )] (3)

4. the endogenous state βe evolves according to the flow equation of

g-types: β_e0 = B(S, S0, Π, βe) = βe  1−Pr[δ = 1]+Pr[δ = 1]·βu−Pr[g-type|δ = 1]  . (4) given this definition of equilibrium, stating that the proportion of good qual-ity managers is stable with time, despite the changes in financial markets conditions, is equivalent to say that in equilibrium there exists a fixed point for equation (4). The fixed point value is unconditional with respect to the realization of S, S0 and Π. Before studying this problem, let us characterize the equilibrium for this economy:

Claim 1 (proof omitted). There exist an equilibrium with the following two properties:

2. g-type and b-type strategies do not depend on βeand they are such that: ag(Π) = arg max ag(Π) πSDr(ag(Π), D) + πSUr(ag(Π), U ) (5) ab = arg max ab ¯ πSDr(ab, D) + ¯πSUr(ab, U ). (6)

Part 1 of the claim can be interpreted as: “any investor prefers g-types to b-types and substitutes the manager whenever he believes that hiring from the unemployed pool increases the chances of hiring a g-type”. Part 2 says that every employed manager tries to maximize the ex-ante fund return given its information set.

Under this claim, it is also possible to reformulate the law of motion B(·) presented in (4). However, the resulting law of motion is not continuous in βe because it “jumps” when, for a certain return r, δ switches from 0 to 1.

Consequently, at this stage it was not possible to apply any theorem to show formally that B(·) has a fixed point.

Therefore, to study the existence of a fixed point, a numerical approach has been used. Figure 2 shows the results of a simulation of the model. The values of parameters have not been calibrated on a particular economy; they have just been chosen so that in equilibrium g- and b-types act differently and investors actively try to hire g-types from the unemployed pool.

The aim of this simulation is to show that the proportion of g-types em-ployed, βe, remains unchanged when the other two exogenous state variables,

S and Π change. As a consequence of S and Π changes, also the mass of fired managers changes with time. Also, since g-types take advantage of their superior knowledge, the average difference between posterior and prior beliefs, I, varies.

A starting point for explaining why βeis constant is computing the sample

mean of I for the case of S = D and S = U . Already in the case of the current simulation, that runs for just 100 periods, we have ¯ID = 0.2939 and

0 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6

Figure 2: this figure show time series for an economy simulated for 100 periods. Note that high and low levels of S stand for S = U and S = D, respectively. High and low levels of Π stand for Π = Π+ _{and Π = Π}−_{, respectively.}

¯

IU = 0.2993. By increasing the length of the simulation, the sample moments

become closer and closer, suggesting that in equilibrium the average of I is also invariant to financial markets conditions.

Despite the current lack of an exhaustive explanation, this finding is a first step in understanding the mechanism leading to a fixed point in B(·). In fact, the interpretation of this finding on I is that investors at stage 1 expect the same average update they got previously, disregarding the markets conditions. What is not clear at the moment is how this makes the realization of S0 at stage 2 impact the mass of fired managers but not their type-composition — probably through the firing rule described in claim 1. Clarifying this last open point, would explain why β_e0 = βe can be part of an equilibrium and is left for

further work on this topic.

5

Conclusions

The key contribution of this paper is to present a model justifying the finding that the proportion of “bad” managers does not fluctuate when fi-nancial markets conditions change. This implies that observing an increase in turnovers is not an indicator per s´e that the managers average quality is changing, not even when such increase is due to investors knowing more clearly

the quality of their own hedge fund manager.

Three steps are left for future research. First, investigating more deeply the mechanism that generates the invariance in the type-proportion of managers. Second, exploring which region of the parameter space yields this invariance. Third, relaxing the assumption that when hiring a manager his previous per-formance is not visible. This simplification makes the model tractable but, without pre-screening of potential managers, too many “bad” candidates may be hired. Finally, considering the manager previous performance would allow to verify if the observed invariance is affected by the investors information structure.

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