Rewarding Trading Skills without Inducing Gambling

• Author: IGOR MAKAROV,GUILLAUME PLANTIN
• Published date: 01 June 2015
• DOI: http://doi.org/10.1111/jofi.12257
• Date: 01 June 2015

THE JOURNAL OF FINANCE •VOL. LXX, NO. 3 •JUNE 2015

Rewarding Trading Skills without

Inducing Gambling

IGOR MAKAROV and GUILLAUME PLANTIN∗

ABSTRACT

This paper develops a model of active asset management in which fund managers may

forgo alpha-generating strategies, preferring instead to make negative-alpha trades

that enable them to temporarily manipulate investors’ perceptions of their skills. We

show that such trades are optimally generated by taking on hidden tail risk, and

are more likely to occur when fund managers are impatient and when their trading

skills are scalable, and generate a high profit per unit of risk. We propose long-term

contracts that deter this behavior by dynamically adjusting the dates on which the

manager is compensated in response to her cumulative performance.

The last 30 years have witnessed two important developments in financial

markets. First, financial innovation has made it possible to slice and combine

a large variety of risks by trading a rich set of financial instruments. Second,

management of large amounts of capital has been delegated to entities such

as hedge funds and bank proprietary desks that are not subject to significant

trading restrictions and not required to disclose publicly the details of their

positions.

The amount of capital available to such entities crucially depends on in-

vestors’ perceptions of their “alpha,” that is, their ability to generate excess

returns above the level of fair compensation for risk. Combined with the rela-

tive opaqueness of these entities and their vast risk-taking opportunities, this

creates pervasive incentives for money managers. In particular, fund managers

running out of alpha-generating strategies may find it tempting to pretend

otherwise, taking risky positions with zero or even negative alpha that may

temporarily improve their perceived reputation in the event of favorable out-

comes. Strategies that generate frequent small positive excess returns that

∗Makarov is with the London School of Economics and Plantin is with the Toulouse School of

Economics. We are most grateful for helpful comments made by the Editor (Cam Harvey) and

two anonymous referees, as well as Gilles Chemla, Zhiguo He, Christopher Hennessy, Roni Kisin,

Peter Kondor, Semyon Malamud, Gustavo Manso, Andrea Prat, Jan Schneider, Lars Stole, Ilya

Strebulaev, and seminar participants at Chicago Booth, Imperial College, Kellogg, LBS, Pompeu

Fabra, Rochester, Queen Mary, University of London, University of Lugano, University of Tokyo,

Vienna University, American Finance Association 2011 Denver meetings, HKUST Finance Sym-

posium, Second Paris Hedge Fund Conference, Third Annual Paul Woolley Centre Conference,

Society for Economic Dynamics 2010 Montreal Meeting, Second Theory Workshop on Corporate

Finance and Financial Markets, New York,and UBC Summer Conference 2010. Plantin benefitted

from a European Research Council Starting Grant (No. 263673 – RIFIFI).

DOI: 10.1111/jofi.12257

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are offset by very rare and large losses seem especially well suited to disguis-

ing luck as skill. As Rajan (2008) puts it, “How can untalented investment

managers justify their pay? Unfortunately, all too often it is by creating fake

alpha – appearing to create excess returns but actually taking on hidden tail

risk.”1Consistent with this view,Jiang and Kelly (2012) show t hat a significant

number of hedge funds are indeed exposed to tail risk.

Creating fake alpha by taking on hidden tail risk does not appear to be lim-

ited to the hedge fund industry. For example, in its 2008 report to shareholders

on the causes of its subprime losses, UBS concludes that “The UBS compensa-

tion and incentivization structure did not effectively differentiate between the

creation of alpha versus the creation of return based on a low cost of funding.”

More generally, Acharya et al. (2010) argue that the manufacture of tail risk

through deliberate retention of senior tranches on poor collateral by U.S. banks

was an important ingredient of the 2008 banking crisis.

The perverse incentives to enter into (at best) zero-alpha gambles are as-

sociated with a number of costs. First, they defeat the purpose of delegated

asset management, which is meant to achieve superior returns by optimally

combining “brains and resources.” Second, they lead to a misallocation of capi-

tal. The manufacture of tail risk also has far-reaching consequences for overall

financial stability when gambling institutions are systemically important.

In this paper, we develop a new framework for the study of these risk-taking

incentives. We study situations in which managers find it optimal to fake their

alpha and propose a new class of contracts that eliminate incentives to employ

such strategies.

Our model builds upon the frictionless benchmark of Berk and Green (2004),

who study career concerns in delegated fund management. In their model, a

fund manager and investors discover the manager’s alpha-generating skill by

observing her realized returns. The excess returns that a manager is expected

to generate increase with her skill, but decrease in the number of funds under

her management. Competitive investors supply funds to the manager until they

earn a zero net (after fees) expected return. At the beginning of each period, the

manager sets fees that enable her to reach the optimal fund size, and extracts

the entirety of the surplus that she generates. Learning and competition among

investors imply that both fund flows and managerial compensation strongly

depend on the manager’s record.

We extend this model by allowing the manager to secretly enter into zero-

alpha trades with the sole purpose of manipulating investors’ perceptions of

her skill. In what follows, we refer to this opportunistic behavior as inefficient

risk shifting or gambling. In contrast to earlier papers on risk shifting, we

propose a general setting in which the fund manager can secretly choose to

take on positions with arbitrary payoff distributions. This captures the large

set of trading opportunities available to modern managers, and is therefore an

important case to consider.

1Raghuram Rajan, “Bankers’ pay is deeply flawed,” Financial Times, January 9, 2008.

Rewarding Trading Skills without Inducing Gambling 927

We first study the impact of this friction in the case in which the manager and

investors sign only short-term contracts. Three factors conducive to inefficient

risk shifting emerge from our analysis. The first is the size of the alpha per unit

of risk that can be generated by a skilled manager. If it is large, the history of

returns has a large impact on investors’ beliefs about the manager’s ability to

generate future excess returns. The second factor is the scalability of trading

skill, that is, the sensitivity of expected excess returns to fund size. If trading

skill is scalable, a good reputation translates into a large future fund size

and in turn large future profits. Third, because the manager can manipulate

her reputation only temporarily, it is more valuable for her to do so when

she is more impatient. These three factors determine the convexity of future

expected gains as a function of realized returns, and thus affect inefficient risk-

shifting incentives. In particular,the model predicts that “fallen star” managers

(those who show high initial potential but realize disappointing returns) are

particularly prone to gambling. For a calibration consistent with Berk and

Green (2004), we find that their efficient equilibrium with short-term contracts

breaks down in the sense that any equilibrium must involve some degree of

risk shifting.

We are able to fully characterize such equilibria with risk shifting in a sim-

plified version of the model where the manager maximizes both her expected

current return and the expected reputation that results from it. Interestingly,

even though we impose no restriction on the risk profiles available to the man-

ager, we show that she optimally manufactures hidden tail risk. In other words,

she sells disaster insurance, adding some noisy payoff to the collected premium

so that investors cannot discover the exact nature of the trade.

We next consider long-term contracts. Here we follow two distinct lines of in-

quiry.First, we consider a contract popular in the hedge fund industry, namely,

a contract in which the manager’s profits are given by a performance fee above

a high-water mark. Similar to Panageas and Westerfield (2009), we find that,

without new inflows or outflows triggered by realized performance, the perfor-

mance fee based on a high-water mark does not induce inefficient risk shifting.

In the presence of fund flows, however, we show that the high-water mark

contract does not generally solve the risk-shifting problem.

Second, we consider an optimal contract that fully eliminates risk-shifting

incentives. This contract is designed to discriminate between skill and luck,

exploiting the fact that the impact of gambling on investors’ beliefs vanishes

in the long run, when true skill is eventually revealed. The contract defers

payments to the manager at dates that vary depending on her cumulative

performance. The promised payment also evolves such that it always at least

matches the manager’s outside options, so she does not renegotiate the contract.

As we detail in Section II, this mechanism is highly reminiscent of recent

proposals for bankers’ compensation reforms issued by both public authorities

and the industry itself. All such proposals consist of a bonus deferral together

with a clawback mechanism that revises the initial promised payment with

the benefit of hindsight. We offer theoretical foundations for these proposals.

More importantly, we qualify them, suggesting that it is important to adjust