Transparency and Talent Allocation in Money Management Simon Gervais∗ Gu¨nter Strobl† June 25, 2015 Abstract Weconstructandanalyzeamodelofdelegatedportfoliomanagementinwhichmoneymanagers signal their investment skills via their choice of transparency for their fund. We show that a natural equilibrium is one in which high- and low-skill managers pool in opaque funds, while medium-skill managers separate in transparent funds. In this equilibrium, high-skill managers rely on their eventual performance to separate from low-skill managers over time, saving the costs associatedwithtransparency. Incontrast,medium-skill managersrely ontransparencyto separate from low-skill managers, especially when it is difficult for investors to tell them apart throughperformancealone. Low-skillmanagersprefermimickinghigh-skillmanagersinopaque funds in the hope of replicating their performance and compensation. The model yields several novel empirical predictions that contrast transparent funds (e.g., mutual funds) and opaque funds (e.g., hedge funds). ∗Fuqua School of Business, Duke University, 100 Fuqua Drive, Durham, NC 27708-0120, [email protected], +1 919 660 7683. †Frankfurt School of Finance and Management, Sonnemannstrasse 9–11, 60314 Frankfurt, Germany, [email protected], +49 69 154 008 445. 1 Introduction Starting with Bhattacharya and Pfleiderer (1985), the canonical model of delegated portfolio man- agement has been that of an investor (the principal) hiring a fund manager (the agent) to make investments on his behalf. Several paperswithin this class of models investigate the possibility that managers signal their skills to investors via the various decisions they make in this context. For example, Huberman and Kandel (1993) and Huddart (1999) show that fund managers increase the risk of their investment strategy in order to signal their ability to gather information that enables them to control and profit from this risk. Similarly, Das and Sundaram (2002) study the joint role of performance-based compensation as an incentive and a signaling device. Finally, Stein (2005) develops a model that explains the prevalence of open-end funds, as such funds do not insure the manager against liquidation risk and so provide a natural signaling avenue for skilled managers. Our model complements this literature by introducing an important signaling dimension that is available to managers at the inception of their fund: the transparency of the fund. As documented by Almazan et al. (2004), mutual funds differ widely in the constraints that they impose on their manager in an effort to monitor their investment activities and performance. In our model, we assume that transparency allows investors to learn more quickly and more precisely about the skills of the agents they hire to manage their portfolio. That is, investors have access to more than just the historical fund performance to update their beliefs about the manager’s ability to invest profitably on their behalf. At the same time, however, we assume that this extra source of information is costly, creating a natural tradeoff: skilled managers want their competence revealed quickly in order to attract more capital to their fund, but take the cost of doing so into account. For example, the decision to operate under the umbrella of a mutual fund family may increase the amountof informationthat gets communicated toinvestors aboutthefundover time(e.g., Gervais, Lynch and Musto, 2005), but producing this information requires time and effort that can erode trading profits. Similarly, the communication of a manager’s trading strategy helps investors in their assessment of the manager’s skill, but may inadvertently encourage competitors to employ the same strategy, reducing the profitability of the strategy in the process (e.g., Frank et al., 2004). In this context, we establish that a natural equilibrium for the money management industry is one in which the most and least talented managers make their fund relatively opaque, while managers with moderate abilities make theirs more transparent. The intuition for this result essentially amounts to managers choosing the route that most efficiently facilitates the discovery of their skills by investors. Two instruments are at every manager’s disposition: performance and transparency. The fund’s performance represents the smallest information set about the manager’s skills that emanates from the fund over time. The fund’s transparency is chosen at the inception 1 of the fund, and serves to affect the speed at which information about the manager’s skill publicly flows to investors. Because the most skilled managers know that their performance will be difficult to imitate, especially in the long run, they do not see the point of incurring the monitoring and strategy leakage costs that come with transparency. Thatis, they useperformanceas their main instrument to separate from lesser skilled managers. Managers with more moderate skills face a more subtle tradeoff. Theycan poolinan opaquefundwiththehigh-skillmanagers (andthelow-skill managers who then have no choice but to also pool) in the hope that they will be able to mimic their performance (and compensation) for a long time. The problem is that the medium-skill managers thenalsofacethepossibilitythattheywillbemimicked bylow-skillmanagers, therebyreducingthe price that investors are willing to pay for their services. Alternatively, the medium-skill managers can choose to operate afundthatis sufficiently transparentto separate from thelow-skill managers who fear the rapid termination of their fund in a transparent environment. This strategy readily conveys their (medium) skill to investors, which is especially beneficialwhen it is unlikely that they can mimic high-skill managers and likely that they will appear unskilled when pooled with low types. That is, for these medium-skill managers, the immediate convergence of investors’ beliefs to their true skill is worth the cost of transparency. Several empirical implications emanate from this partial-pooling equilibrium, in which opaque funds are run by managers with extreme skills, high and low, while transparent funds are run by managers with more average talent. First, because skill levels are endogenously more dispersed in opaquefunds,weexpectthe cross-sectional performanceof opaquefundsto also bemoredispersed. Second, this dispersionof skills in opaque fundsimplies that fundperformanceshould play a bigger role in the learning process of investors about the skill of these funds’ managers. In particular, the sensitivity of flow to performance and the attrition rate are predicted to be higher in opaque funds. Third, because learning and attrition eventually improve the quality of the pool of opaque-fund managers, the contrast between high- and low-transparency fundsevolves over time. That is, while fundsof various degrees of transparency may beexpected to performsimilarly whenthey arenewly established, we show that the screening of opaque funds will lead the surviving funds to eventually outperform their more transparent counterparts. In a similar vein, funds of the same vintage (i.e., funds that survive a given number of years) are expected to be larger and to pay their managers more if they choose to remain opaque at the outset. One natural interpretation of the model’s endogenous emergence of opaque and transparent funds is the coexistence of hedge funds and mutual funds. As Brown and Goetzmann (2003) write, “hedge funds are best defined by their freedom from regulatory controls stipulated by the InvestmentCompanyActof 1940” (p.102). Mutualfunds,ontheother hand,areheavily regulated 2 and must frequently report detailed information about their positions and strategies to investors. Hedgefundmanagersarealsoknowntouseawiderarrayoffinancialinstrumentsthanmutualfund managers in order to capitalize on their investment skills (e.g., Fung and Hsieh, 1997; Bookstaber, 2003). In contrast, Koski and Pontiff (1999) document that mutual fund managers make little use of complex securities in their trading. Inthis light, theaforementioned partial-pooling equilibriumsuggests thathedge fundswilltend to attract the best and worst managers, whereas mutual funds will tend to attract more middle-of- the-road managers. In particular, the model’s implications can be used to contrast mutual funds and hedge funds in terms of their attrition rate, excess returns, fund flows and size, and manager compensation. For example, Brown et al. (2008) empirically investigate the relationship between the disclosures of hedge funds and their operational risk. One of their findings is that hedge funds are more likely to disclose information about their fund following good performance, leading the authors to conclude that filing may be a signal of quality. Viewed through the lens of our model, their results may indicate that the early lack of filing is used by managers to signal their skills which subsequently get revealed through the good performance of their fund. Importantly, the predictions of our model are not limited to a comparison of mutual funds and hedgefunds. Indeed,sincethesetypesofmoneymanagementvehicles candifferinmoredimensions than just their transparency, an empirical strategy that more explicitly controls for other factors is one that contrasts the low- and high-transparency funds from a specific industry. For example, we know from Aggarwal and Jorion (2012) that hedge funds vary in their degree of transparency. A test of our model would then dictate a comparison between transparent and opaque hedge funds of the same vintage in terms of the cross-sectional variability of their performance, their attrition rate, and their average performance.1 Similarly, Agarwal, Boyson and Naik (2009) document that some mutual funds adopt strategies that are similar to those of hedge funds. If these strategies include transparency choices, then the universe of mutual funds alone should allow a test of our model. Our model builds on Berk and Green’s (2004) insight that capital should rapidly flow to funds that experience high returns, as investors update about the fund manager’s skill for investing profitably. In equilibrium, the marginal benefit of investing in a fund is equal to the marginal cost, funds do not generate any excess (net) returns, and the entire economic surplus accrues to the manager in the form of compensation for his services. Like Dangl, Wu and Zechner (2008), we add the possibility that the fund controls the speed at which investors learn the manager’s skills. In their model, this is done privately by the fund’s management company which strategically times 1NotethatAggarwalandJorion’s(2012)studydoesnotreadilyconstituteanempiricaltestofourmodel,astheir methodology pools all thehedge fundsof all vintages. 3 the replacement of the manager in order to positively influence the updating process of investors about the quality of the fund. In our model, this is done publicly by the manager himself who self-selects into a transparency level that subsequently impacts the updating process of investors. As such, the choice of transparency acts as a signal in our model, whereas it creates a moral hazard problem in theirs. Our results relate to a recent paper by Daley and Green (2014). They show that the addition of independent signals about skills (which they call “grades”) in Spence’s (1973) seminal model of job-market signaling makes high-skill and low-skill workers more likely to pool in equilibrium. The analogy to grades in our model is the fund manager’s performance, which cannot be controlled. When the performance of high types cannot be easily imitated, they are more than happy to rely exclusively on their performance in order to separate from other fund managers in the long run. That is, they do not mind pooling in the short run, as their performance will eventually speak for itself. A similar result is obtained by Al´os-Ferrer and Prat (2012) in a job-market signaling model with dynamic learning. As in our model, the receiver (employer) learns about the sender’s (worker’s) type over time and, when learning is fast and accurate, a pooling equilibrium emerges. Our paper differs from these two papers in that the high type is not endowed with a lower cost of signaling. Instead, in our money-management context, the cost of signaling through higher levels of transparency is (endogenously) higher for high types, as transparency comes with valuableinformationleakages andthuserodesmorevalueforthosemanagerswhohavethepotential to generate consistently good performance. That is, for highly skilled managers, separation is cheaper to achieve via long-run performance than via the extra information about their type that is facilitated by transparency. Inadditiontohighandlowtypes,ourpaperconsidersathird(medium)typewhoisnotasskilled as the high type but, unlike the low type, can create some value. This consideration makes our results more similar to those obtained by Feltovich, Harbaugh and To (2002), and Araujo, Gottlieb and Moreira (2007) in the context of job-market signaling with three worker types.2 As we show, the partial-pooling equilibrium that we derive is often the Pareto-dominant equilibrium, in that it makes all money managers better off. Our results are also reminiscent of Zwiebel’s (1995) partial- pooling results for the innovation choices made by three types of firm managers with reputation concerns. Besides the fact that our focus is on transparency choices, our modeling approach differs from his in that the managers’ actions are public and thus serve as a signal of their skill. More generally, our paper contributes to the literature on the organization of the money man- agement industry,especially as itpertainsto theallocation, performance, andstrategies of talented 2DaleyandGreen’s(2014)appendixshowsthattheirresultsextendtothecaseofN typesandtherebyencompass those in theseearlier papers. 4 agents withinit. Animportantpaperinthisliterature is thatofChevalier andEllison (1999) which empirically establishes a relationship between fund performance and fund manager characteristics, most notably the school that the manager attended. More recent papers empirically investigate the form of money management that skilled fund managers tend to favor. For example, Kostovet- sky(2011)documentsa“braindrain”wherebythemostskilledmutualfundmanagersleave tostart hedge funds. Cheng et al. (2012) document that mutual fund families allocate their most skilled managers to funds that can best lever their skills through various mechanisms. Similarly, Berk, van Binsbergen, and Liu (2015) show that mutual fund companies efficiently allocate internal cap- ital to match their managers’ talent. Finally, Guerrieri and Kondor (2012) and Di Maggio (2015) model the investment choices that managers of different skills make in order to enhance or preserve their reputation with investors. As in our model, the managers care about the investors’ percep- tion of their skill; in contrast, the investment strategies that managers use in these models remain private and so do not directly signal skill. The rest of the paper proceeds as follows. In section 2, we introduce the model. Section 3 contains our equilibriumanalysis. Theempiricalpredictions of themodelare derived anddiscussed insection4. Finally, section 5summarizesandconcludes. Allproofsarecontained intheAppendix. 2 The Model We consider an N-period economy populated with risk-neutral money managers and investors who discount future cash flows at a rate normalized to zero. Money managers (or just managers for short) have no wealth, but potentially have some investment skills. Investors are wealthy, but have no investment skills. Each money manager can open an investment fund (or just fund for short), and investors must decide on how much capital A to allocate to each fund at the beginning of n every period n ∈{1,...,N}. Money managers come in three different types, high, medium or low, that correspond to their ability to generate investment profits. Specifically, the manager’s type is drawn from the following distribution: h, prob. λ h τ˜= m, prob. λ (1) m  ℓ, prob. λ ,  ℓ where λ +λ +λ = 1. The manager privately observes his own type at the outset. This type h m ℓ determines the distribution of the nth-period excess return r˜ (τ˜) that his fund will generate. We n assumethat theseexcess returns(or justreturns forshort)areindependentlydrawnacross periods. The performance of high types first-order stochastically dominates that of medium types, which in turn first-order stochastically dominates that of low types. Although any first-order stochastic 5 ordering is sufficient to generate our results, the analysis is greatly simplified by assuming three- point distributions (good, average, and bad) for the various types’ returns. Specifically, for the low types, we assume that r , prob. p G G r˜ (ℓ) = r , prob. p (2) n  A A r , prob. p ,  B B where p +p +p = 1, r > r > r , and µ ≡ p r +p r +p r = 0. That is, on average, the G A B G A B ℓ G G A A B B low types do not generate any excess returns, and so investors do not benefit from their investment services.3 The medium types’ returns in period n are given by r , prob. pG r˜n(m)= ( rG, prob. pGp+ApA, (3) A pG+pA and their expected returns are µ ≡ pGrG+pArA > 0. Finally, the high types’ return in period n m pG+pA are assumed to be equal to r ≡ µ > µ with probability one. These distributions, although G h m somewhat specific, capture the notion that the one-period performance of low and medium types will match that of high types with some probability (p and pG , respectively), and the low G pG+pA types’ performance will match that of medium types with probability p + p . The advantage, G A which will become more apparent later, comes from the fact that skilled managers can never be mistaken for less skilled managers, which greatly simplifies the analysis. At the outset, managers choose the transparency t ∈ [0,1] of their fund. This choice, which is publicly observable by investors, can be used by managers to signal their type to investors in equilibrium. A fund’s transparency is meant to capture the possibility that money management vehicles can take different forms, and our assumption is that these various forms are indexed by their transparency. For example, hedge funds are known to be more opaque about their operations than mutual funds, and some hedge funds are less open to divulging their strategies to potential investors than other hedge funds. This, we assume, translates into various degrees of screening by investors: more transparent funds allow investors to better sort managers with respect to their skills. That is, the possibility of looking at more than just the return history of a fund allows investors to determine with more accuracy whether a manager’s performance is due to his skill or to (bad) luck. In terms of the model, we assume that a more transparent fund allows investors to identify early the money managers who do not have the ability to generate any excess returns (i.e., the low types). Specifically, we assume that, before the fund is open for potential investment, investors 3Ourresults are unaffected if we assume more generally that µℓ ≤0. 6 observe a signal˜ı ∈ {0,1}, which has the following distribution: t Pr{˜ı = 0|τ˜= ℓ} = t = 1−Pr{˜ı = 1|τ˜ = ℓ}, (4) t t Pr{˜ı = 1|τ˜ = m}= Pr{˜ı = 1|τ˜ = h} = 1. (5) t t In effect, therefore, a signal ˜ı = 0 makes it clear to investors that the manager’s type is low and t that they should not hire him, as such a signal can never be observed when the manager’s type is medium or high. Conversely, a signal ˜ı = 1 reduces the possibility that the manager they are t about to hire is a low type, as Pr{˜ı = 1|τ˜= ℓ}Pr{τ˜ = ℓ} (1−t)λ t ℓ Pr{τ˜= ℓ|˜ı = 1} = = (6) t Pr{˜ı = 1|τ˜ = τ}Pr{τ˜= τ} λ +λ +(1−t)λ τ∈{h,m,ℓ} t h m ℓ is decreasing in t. ImplicitlPy, but somewhat deliberately, the assumed distribution for ˜ı implies t that investors cannot distinguish between high types and medium types. That is, high types do not have an obvious advantage over medium types about signaling their skill; investors can only tell whether a manager’s strategy has potential but they cannot tell how profitable it will be. The model’s results hold as long as transparency allows investors to disentangle low types from other types more accurately than medium types from high types. Less critical is the fact that investors do not get to observe an independent draw from ˜ı ’s distribution in every period. This possibility t would certainly allow investors to converge more rapidly on the true type of the manager, but would not affect the main economic forces of the model. The gain in tractability from our one-shot signal assumption is thus warranted. Sincemoretransparencycanonlyeliminatelowtypesfromthepoolofmoneymanagers,medium andhightypes wouldautomatically chooset = 1ifthis choice werenotcostly. Toaddsometension to this choice, we assume that more transparency comes with a higher per-dollar cost of managing a fund’s assets. Following Berk and Green (2004) and in light of Chen et al.’s (2004) empirical findings, we assume that the per-dollar cost of managing a fund is increasing in the size of the fund. In fact, to keep things simple without any loss of generality, we assume that the per-dollar cost of managing a fund of size A in period n is k A , where k > 0. Our innovation over n t n t Berk and Green (2004) is that we assume that k is strictly increasing in t, capturing the idea t that a more transparent fundrequires more costly information to beproduced, moreconstraints on potentialinvestmentstobemade(e.g.,noshort-sellingornoinvestmentinprivatelyheldfirms),and potentially leads to leakages of strategies that reduce their effective profitability. This assumption isalso supportedby theempiricalwork ofBerk andvanBinsbergen(2015), andPa´stor, Stambaugh and Taylor (2015).4 4Wenote,however,thatElton,GruberandBlake(2012),andReuterandZitzewitz(2013) argueagainst theidea that funds experiencedecreasing returns toscale. 7 The manager announces his compensation contract at the beginning of each period n. This contract is represented by the amount w that the manager charges to investors per dollar they n invest in the fund at the beginning of the period.5 Based on this contract, on the history of the fund’s returns, on ˜ı , and on rational equilibrium updates about the manager’s type, investors t choose the amount A of money that they allocate to the fund for this one period. Let us denote n the period-n profits of investors by π˜ ≡ A r˜ (τ˜)−w −k A . As in Berk and Green’s (2004) n n n n t n model, we assume that investors compete for the manager’s scarce talent for investing, and so the (cid:2) (cid:3) equilibrium A always makes them indifferent between investing in the fund and not doing so; that n is, in equilibrium, investors make zero expected profits and managers capture the entire economic surplus that they create. Lemma 1. Suppose that the investors’ information set is I at the beginning of period n. The n amount they invest in the fund in that period is then E r˜ (τ˜)|I −w n n n A = max 0, . (7) n k ( (cid:2) t (cid:3) ) The max operator in (7) simply says that investors are not willing to invest any money when the manager’s compensation exceeds the excess returns that his fund is expected to generate. In fact, we assume that the fund closes at that point; that is, the sequence of observable returns r˜ (τ˜) ceases as soon as the manager cannot attract any money into his fund. In this sense, (7) n also highlights the fact that the manager cannot profitably manage a fund once investors reach an information set I such that E r˜ (τ˜)|I ≤ 0. n n n At the beginning of every period n, the manager chooses his contract in order to maximize his (cid:2) (cid:3) expected compensation, U ≡ w A , for that period. In doing so, he takes the investors’ reaction n n n to his choice, (7), into account. The following lemma characterizes his decision. Lemma 2. Suppose that the investors’ information set is I at the beginning of period n, and that n E r˜ (τ˜)|I >0. (8) n n (cid:2) (cid:3) Then the manager’s choice of per-dollar compensation for that period is 1 w = E r˜ (τ˜)|I , (9) n n n 2 (cid:2) (cid:3) 5Notethattheperiod-ncontract couldbemadecontingent onthereturnr˜n(τ˜) ofthefundinthat period. Given thatourmodelabstractsfrommoralhazardproblems,thiswouldhavenoeffectonfundperformanceinthatperiod. It would however allow a skilled manager to capture more of the available surplus than a less skilled manager with the same history, as in Gervais, Lynch and Musto (2005). Since this consideration does not affect our results, we stickwiththesimplerflatper-periodwage. Also,likeBerkandGreen(2004),weruleoutmulti-periodcontractsthat conditiononeverypossiblereturnsequenceandthattherebyallow thehightypetokeepmoreofthesurplusthathe creates. In our context, this is mainly for simplicity, as the result that the high type cannot separate from the low typeholds even when we allow for contracting overa long but finite horizon. 8 the size of his fund is 1 A = E r˜ (τ˜)|I , (10) n n n 2k t and his total compensation is (cid:2) (cid:3) 1 2 U = w A = E r˜ (τ˜)|I . (11) n n n n n 4k t (cid:0) (cid:2) (cid:3)(cid:1) It is clear from (9) and (10) that the manager charges more and that his fund is larger when the investors’ information indicates that he is likely skilled. That is, as documented by Phillips, Pukthuanthong and Rau (2014), the manager reaps the benefit of his reputation by increasing his compensation through fees and flows. Note also that the manager can anticipate the investors’ beliefs and the corresponding amount that they will be willing to invest for every return sequence that his fund generates. Thus, the assumption that he announces his contract only at the beginning of each period is equivalent to him announcing a set of path-dependent contracts for every period n ∈ {1,...,N} at the inception of the fund. From (10) and (11), we can also see that our assumption that transparency affects the per-dollar cost of the fund is equivalent to the alternative assumption that the returns of a fund with transparency t are scaled by a constant of 1. That is, because investors break even in every kt period, it does not matter if the costs of transparency are felt through lower gross fund returns (through strategy leaks, for example) or through more expensive administrative costs.6 Lemma 2 shows that the per-dollar compensation of a manager is proportional to his fund’s expected return, conditional on the investors’ information set. Since a transparency level of t eliminates a fraction t of low-type managers, this implies that the ex ante expected compensation of a manager of type τ˜= ℓ is proportional to (1−t)E r˜ (τ˜)|I . As we show later, this quantity is n n always decreasing in t, despite the fact that E r˜ (τ˜)|I is increasing in t. However, since the fund n (cid:2)n (cid:3) size A is also proportional to E r˜ (τ˜)|I , the total compensation that a low type can expect n n n (cid:2) (cid:3) ex ante is actually a quadratic function of his fund’s expected return and, hence, can be increasing (cid:2) (cid:3) in t. To rule out the economically less sensible case in which all manager types benefit from more transparency, we assume that the cost function k increases sufficiently fast in t. t Assumption 1. dkt ≥ λℓ k , for all t ∈ [0,1]. dt λh t As will become clear in section 3, this assumption ensures that the fund size A , given by (10), n does not increase in t, which further implies that the expected total compensation of a low-type manager decreases in t. 6Theempiricalevidenceabouttheeffectoftransparencyonfundperformanceappearstobemixed. Forexample, while Frank et al. (2004) find that mutualfund disclosures tendto attract investmentstrategy imitators and reduce grossperformance,AggarwalandJorion(2012)findthatmoretransparenthedgefundsdonotseemtounder-perform (and perhaps outperform) their more opaquecounterparts. 9