## _wp15198 - References ## Source details **Canonical URL:** [_wp15198 - References](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15198.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15198.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15198.pdf.json) --- ### Introduction and motivation - Professional portfolio managers (mutual, pension, and hedge fund managers) are largely ignored in standard portfolio choice theory, which assumes direct household management. - Direct holdings of corporate equity by the household sector: fell from 99 percent in 1945 to 47 percent in 2010. - According to Investment Company Institute, 67 percent of individual investors seek services of financial advisors when making their decisions. - Two strands of recent literature highlighted: - Optimal contracts to solve the agency problem between manager and investor (performance relative to a benchmark). - Whether relative performance induces managers to change fund risk exposure and how this links to compensation. ### Model and approach - Paper takes optimal contracts as given (reflecting properties commonly observed in practice) and analyzes the effects of relative performance pay for fund managers. - Model features: - Two investment funds in a market for an asset. - Each fund manager observes a signal concerning the profitability of the risky asset. - Markets operate in a Kyle (1985)-type framework with two insiders and noisy signals. - Each manager’s payoff depends on his own performance and the performance of the other manager. - Fund owners, fund investors, and owners of the funds split proceeds according to the model’s specification. - Extensions considered: - Two separate markets for two assets (cross-market correlation). - Two assets traded in the same market (benchmark inclusion effects on individual stock volatility). - Endogenous information acquisition with costly signals under two information structures: public costly information (all or none informed) and private costly information (independent acquisition decisions). ### Main findings - Relative performance pay for fund managers can have deleterious effects for investors, translating into a lower expected utility. - If information is free: - Markets will typically be more informative. - Markets will typically be deeper (more liquid). - When the decision to acquire information is endogenized (information is costly): - Incentives to acquire information may be hindered by relative performance contracts. - This reduction in information acquisition can, ex-ante, reduce the informativeness and depth of the market. - The result that prices are more informative holds only for the case of free information; it is reversed when information is costly. - The result that markets are deeper holds for free information and for public costly information, but may or may not hold under private costly information. ### Mechanisms and channels - Increased relative performance weight: - Raises managers’ trading aggressiveness (place more weight on their signal), making prices reflect signals more prominently when information is acquired. - Can increase cross-market price correlation through more aggressive use of signals tied to correlated asset payoffs. - Raises volatility for assets included in benchmarks; the more heavily a compensation package relies on a stock, the higher the variance of that stock price. - Information acquisition effects: - Higher relative-performance emphasis reduces managers’ expected pay conditional on relative performance, making information acquisition less attractive when costly. - Less information acquisition decreases the probability of informative prices ex-ante, potentially reversing benefits of relative performance on price informativeness. - Under private costly information, equilibrium outcomes (zero, one, or two informed managers) depend on the information cost c relative to threshold expressions in the model; these endogenous outcomes make effects on market depth and informativeness parameter-dependent and sometimes ambiguous. ### Additional implications and comparative results - Cross-market contagion: presence of relative performance contracts in at least one market can increase price correlation across markets. - Benchmark inclusion: including a stock in a benchmark increases its price variance; heavier weighting in the benchmark raises that variance further. - Home bias: benchmarking against an exogenous, domestic index can lead to overexposure to domestic assets (demand for a domestic asset increases with its weight in the benchmark), providing a mechanism for home bias. - Comparison with literature: - Results are consistent with empirical/theoretical findings that managers tend to over-bear risk to beat benchmarks (more aggressive trading under stronger relative performance incentives). - Differs from Palomino (2005) by assuming fixed market structure (no entry), homogeneous ability, and endogenous informational asymmetries; here, stronger relative performance leads to lower expected returns for investors. - Relative to Cuoco and Kaniel (2011), both find higher and more volatile prices for benchmarked stocks; differences stem from market structure assumptions (perfect competition vs. imperfect competition) and focus on market microstructure (liquidity, price informativeness, cross-market correlation, information acquisition). ### Policy-relevant implications - Trade-off for regulators: - Aligning principals’ and agents’ interests via relative performance pay can generate adverse effects: increased contagion, higher volatility for benchmarked stocks, and possible reductions in ex ante informativeness and market depth. - Net welfare effect of promoting relative performance pay is ambiguous and depends on: - Whether information is effectively free or costly. - Whether information is public or private. - Open regulatory questions for future research: - What frameworks for setting fund managers’ incentives and disclosure requirements could limit contagion and excessive volatility while maintaining price informativeness? - Designing contracts that mitigate the adverse ex-ante effects on information acquisition is a direction for future research. ### Appendix: Key derivations and quantitative results (selected expressions preserved as in source) - Conjectured linear price and demand functions: P = ( 1 + 2 + u); i = i es i. - Conditional moments: - E[s j js i] = E[v j s i] = 2 v 2 v + 2 " s i := D. - E[ j js i] = j 2 v 2 v + 2 " s i. - E[ j v j s i] = j C, where C := 2 v 4 v 2 v + 2 " + D2. - E[ 2 j js i] = 2 j (C+2 "). - Manager objective (conditional on s i): - Ef[( i j) (v( i + j + u))] js i g = i D  2 i  i j D j C +  i j D +  2 j C + 2 ". - First-order condition: - i = D / (2) (1  j (1 )). - Symmetry i = j = leads to 2 = [1  (1 )] 2 v 2 v + 2 ". - Solved values (closed-form expressions recalled): - = s 2 u 2 (1 ) 2 v + 2 2 ". -  = 2 2 v q 2 u 2 (1 ) 2 v + 2 2 " (2 2 v + 2 ") / (2 u (1 ) 2 v + 2 " + 2 u). - Expected payoff to investors of fund i: - E[( )] = & 2 v 2 2 2 v 2 2 " = & (2 v  22 v + 2 "). - Re-expressed in closed form (as in Appendix B and C) and shown that d/d E[( )] < 0: higher relative performance parameter reduces ex-ante expected profits of fund investors. - Liquidity and adverse selection: - Adverse selection cost L( ) = 2 E[( )] = 2 2 v r 2 u 2 p 2 " + (1 )2 v 2 (2 v + 2 ") + (1 )2 v !; since d/d E[( )] < 0, d/d L( ) < 0 — liquidity traders are better off with more relative performance pay when information is free. - Cross-market correlation: - Correlation coefficient  depends on 1 only through 1 and satisfies @/@1 > 0 when @/@ 1 > 0 and @ 1/@1 > 0; identical result for 2. - Endogenous information acquisition: - Expected manager profit when both informed: E[( i j) (v P)] =  (1 ) 2 v 2 " + (1 )2 v 2 (2 v + 2 ") + (1 )2 v. - Derivative with respect to is negative: d/d E[( i j) (v P)] < 0. If equilibrium with both informed requires E[( i j) (v P)] > c, there can exist a threshold above which no information is acquired. - Under certain public-costly-information assumptions, expected conditional variance of prices is increasing in — prices are less informative as increases in that setting. ### Figures and simulation notes (parameter settings reported as in source) - Figures illustrate numerical simulations of price informativeness and expected conditional variance as a function of relative performance concerns , with parameters: - Costs uniformly distributed on unit interval;  set to 0.1. - Variance of payoffs 2 v set to values including 0.01, 0.05, 0.08, 0.15 in different panels. - Noise variance 2 u varied across ranges (e.g., from 0.0025 to 0.034; 0.0025 to 0.3175; 0.05 to 0.0815; 0.1 to 0.1315). - Expected conditional variance rescaled to equal 1 when is 0 and noise variance is at its minimum of its set range. - Figures 2–4 (“Expected Price Response to Trades” as a function of ) parameter cases: - Figure 2: varying 2 u from 0.6 to 0.6315, with 2 v = 0:15 and  = 0:1. - Figure 3: varying 2 u from 0.2 to 0.2315, with 2 v = 0:15 and  = 0:1. - Figure 4: varying 2 u from 0.0005 to 0.032, with 2 v = 0:15 and  = 0:1. *Source: _wp15198 - References.* ### References ............................................................................................................. ### _wp15198 - References ..................................................................................................... ### Introduction and motivation - Professional portfolio managers (mutual, pension, and hedge fund managers) are largely ignored in standard portfolio choice theory, which assumes direct household management. - Direct holdings of corporate equity by the household sector: fell from 99 percent in 1945 to 47 percent in 2010. - According to Investment Company Institute, 67 percent of individual investors seek services of financial advisors when making their decisions. - Two strands of recent literature: - Optimal contracts to solve the agency problem between manager and investor (performance relative to a benchmark). - Whether relative performance induces managers to change fund risk exposure and how this links to compensation. ### Paper focus and approach - The paper takes optimal contracts as given (reflecting properties commonly observed in practice) and analyzes the effects of relative performance pay for fund managers. - Model features: - Two investment funds in a market for an asset. - Each fund manager observes a signal concerning the profitability of the risky asset. - Markets operate in a Kyle (1985)-type framework with two insiders and noisy signals. - Each manager’s payoff depends on his own performance and the performance of the other manager. - Fund owners, fund investors, and owners of the funds split proceeds according to the model’s specification. - Extensions considered: - Two separate markets for two assets (cross-market correlation). - Two assets traded in the same market (benchmark inclusion effects on individual stock volatility). - Endogenous information acquisition with costly signals under two information structures: public costly information (all or none informed) and private costly information (independent acquisition decisions). ### Main findings and mechanisms - Investor welfare and markets: - Investors have lower expected utility under relative performance pay for managers. - Conditional on information being acquired (i.e., information is free or agents pay cost and choose to be informed), markets tend to be more informative and deeper. - An increase in the importance of relative performance raises correlation between two separate markets (contagion effects). - Inclusion of a stock in the benchmark increases that stock’s price volatility. - Manager behavior: - Managers trade more aggressively (place more weight on their signal) as the importance of relative performance increases; this can be interpreted as increased risk-taking for a given signal. - Information acquisition and equilibrium informativeness: - When information acquisition is endogenous and costly, an increase in the importance of relative performance probabilistically reduces the availability of an informed equilibrium (lower probability that any manager decides to acquire information). - Thus, although conditional on being informed prices become more informative with stronger relative performance incentives, ex ante the overall informativeness and market depth can be attenuated or cancelled because fewer agents choose to acquire information. ### Comparisons with related literature - Relation to empirical and theoretical results on risk-taking: - Consistent with literature that managers tend to over-bear risk to beat benchmarks; model’s mechanism yields more aggressive trading under stronger relative performance incentives. - Comparison with Palomino (2005): - Palomino finds relative performance objectives can lead to survival of better-quality funds and higher expected investor returns when entry and heterogenous ability are present. - This paper differs by assuming fixed market structure (no entry), homogeneous ability, and endogenous informational asymmetries; here, stronger relative performance leads to lower expected returns for investors. - Comparison with Cuoco and Kaniel (2011): - Both papers find higher and more volatile prices for stocks included in benchmarks; differences arise from market structure assumptions (perfect competition vs. imperfect competition) and focus (this paper emphasizes market microstructure: liquidity, price informativeness, cross-market correlation, information acquisition). ### Policy-relevant implications - Potential trade-off for regulators: - Aligning principals’ and agents’ interests via relative performance pay can generate adverse effects: increased contagion, higher volatility for benchmarked stocks, and possible reductions in ex ante informativeness and market depth. - Open regulatory questions for future research: - What frameworks for setting fund managers’ incentives and disclosure requirements could limit contagion and excessive volatility while maintaining price informativeness? ### Paper organization (as provided) - Section II: Model basics. - Section III: Effects of relative performance contracts when managers have free access to information; main results. - Section IV: Effects of relative performance on the decision to acquire information and differences emerging from endogenizing information acquisition. *Source: _wp15198 - References .....................................................................................................* ### Section V concludes. ### Section V concludes. ### Main findings on relative performance pay - Relative performance pay for fund managers can have deleterious effects for investors, translating into a lower expected utility. - If information is free: - Markets will typically be more informative. - Markets will typically be deeper (more liquid). - When the decision to acquire information is endogenized (information is costly): - Incentives to acquire information may be hindered by relative performance contracts. - This reduction in information acquisition can, ex-ante, reduce the informativeness and depth of the market. - The result that prices are more informative holds only for the case of free information; it is reversed when information is costly. - The result that markets are deeper holds for free information and for public costly information, but may or may not hold under private costly information. ### Mechanisms and channel summaries - Increased relative performance weight: - Raises managers’ trading aggressiveness, which can make prices reflect signals more prominently when information is acquired. - Can increase cross-market price correlation through more aggressive use of signals tied to correlated asset payoffs. - Raises volatility for assets included in benchmarks; the more heavily a compensation package relies on a stock, the higher the variance of that stock price. - Information acquisition effects: - Higher relative-performance emphasis reduces managers’ expected pay conditional on relative performance, which can make information acquisition less attractive when costly. - Less information acquisition decreases the probability of informative prices ex-ante, potentially reversing the apparent benefits of relative performance on price informativeness. - Under private costly information, equilibrium outcomes (zero, one, or two informed managers) depend on the information cost c relative to threshold expressions in the model; these endogenous outcomes make the effects on market depth and informativeness parameter-dependent and sometimes ambiguous. ### Additional implications identified in the analysis - Cross-market contagion: presence of relative performance contracts in at least one market can increase price correlation across markets. - Benchmark inclusion: including a stock in a benchmark increases its price variance; heavier weighting in the benchmark raises that variance further. - Home bias: benchmarking against an exogenous, domestic index can lead to overexposure to domestic assets (demand for a domestic asset increases with its weight in the benchmark), providing a mechanism for home bias. ### Policy and regulatory considerations - There is a trade-off between aligning managers’ incentives with principals’ interests and the potential adverse effects on contagion, volatility, and market informativeness when information acquisition is costly. - From a regulator’s perspective, the net welfare effect of promoting relative performance pay is ambiguous and depends on whether information is effectively free or costly and whether information is public or private. - Addressing this trade-off and designing contracts that mitigate the adverse ex-ante effects on information acquisition is a direction for future research. *Content unit: _wp15198 - Section V concludes.* ### References ### _wp15198 - References ### References (bibliography) - [1] Admati, A.R., and P. Páeiderer (1997). ìDoes It All Add Up? Benchmarks and the Compensation of Active Portfolio Managers,î Journal of Business 70, 323ñ350. - [2] Bagnoli, M., and S. Watts (2000). ìChasing Hot Funds: The E§ects of Relative Performance on Portfolio Choice,î Financial Management 29 (3), 31ñ50. - [3] Benartzi, S., and R. Thaler (2001). ìNaive DiversiÖcation Strategies in Retirement Saving Plans,î American Economic Review 91, 79ñ98. - [4] Berk, J. B., and R. C. Green (2004). ìMutual Fund Flows and Performance in Rational Markets,î Journal of Political Economy 112 (6), 1269ñ1295. - [5] Broner, F. A., R. G. Gelos, and C. M. Reinhart (2006). ìWhen in peril, retrench: Testing the portfolio channel of contagion,î Journal of International Economics 69 (1), 203ñ230. - [6] Brennan, M. J. (1993). ìAgency and Asset Pricing,î working paper, UCLA. - [7] Brown, K., W. Harlow, and L. Starks (1996). ìOf Tournaments and Temptations: An Analysis of Managerial Incentives in the Mutual Fund Industry,î Journal of Finance 51, 85ñ110. - [8] Chen, H.-L., and G. Pennacchi (2009). ìDoes Prior Performance A§ect a Mutual Fundís Choice of Risk? Theory and Further Empirical Evidence,î Journal of Financial and Quantitative Analysis 44 (4), 745ñ775. - [9] Chevalier, J., and G. Ellison (1997). ìRisk Taking by Mutual Funds as a Response to Incentives,î Journal of Political Economy 105, 1167ñ1200. - [10] Coval, J., and T. Moskowitz (1999). ìHome Bias at Home: Local Equity Preference in Domestic Portfolios,î Journal of Finance 54 (5), 2045ñ2074. - [11] Cuoco, D., and R. Kaniel (2011). ìEquilibrium Prices in the Presence of Delegated Portfolio Management,î Journal of Financial Economics 101, 264ñ269. - [12] Das, S., and R. Sundaram (1998a). ìOn the Regulation of Mutual Fund Fee Structures,î NBER Working Paper 6639. - [13] Das, S., and R. Sundaram (1998b). ìFee Speech: Adverse Selection and the Regulation of Mutual Fund Fees,î NBER Working Paper 6644. - [14] Dybvig, P., H. Farnsworth, and J. Carpenter (2010). ìPortfolio Performance and Agency,î Review of Financial Studies 23 (1), 1-23. - [15] Eichberger, J., S. Grant, and S. P. King (1999). ìOn Relative Performance Contracts and Fund Managerís Incentives,î European Economic Review 43, 135ñ161. - [16] Goriaev, A., F. Palomino, and A. Prat (2000). ìMutual Fund Tournament: Risk Taking Incentives Induced By Ranking Objectives,î Working Paper CentER, Tilburg University, No 2000ñ94. - [17] Grinblatt, M., and S. Titman (1989). ìAdverse Risk Incentives and the Design of Performance-Based Contracts,î Management Science 35, 807ñ822. - [18] Heinkel, R., and N. M. Stoughton (1994). ìThe Dynamics of Portfolio Management Contracts,î Review of Financial Studies 7, 351ñ387. - [19] Koski, J., and J. Ponti§ (1999). ìHow are Derivatives Used: Evidence from the Mutual Fund Industry,î Journal of Finance 54 (2), 791ñ816. - [20] Ippolito, R. A. (1992). ìConsumer Reaction to Measures of Poor Quality: Evidence from the Mutual Fund Industry,î Journal of Law and Economics 35, 45ñ70. - [21] Kyle, P. (1985). ìContinuous Auction and Insider Trading,î Econometrica 53 (6), 1315ñ1336. - [22] Lettau, M. (1997). ìExplaining the Facts with Adaptative Agents: The Case of Mutual Fund Flows,î Journal of Economic Dynamics and Control 21, 1117ñ1147. - [23] Ou-Yang, H. (2003). ìOptimal Contracts in a Continuous-Time Delegated Portfolio Management Problem,î Review of Financial Studies 16, 173ñ208. - [24] Palomino, F. (2005). ìRelative Performance Objectives in Financial Markets,î Journal of Financial Intermediation 14, 351ñ375. - [25] Pinheiro, M., (2008). ìLoyalty, peer group e§ects, and 401(k),î Quarterly Review of Economics and Finance 48 (1), 94ñ122. - [26] Sensoy, B. (2009). ìPerformance evaluation and self-designated benchmark indexes in the mutual fund industry,î Journal of Financial Economics 92 (1), 25ñ39. - [27] Shelef, O. (2013). ìIncentive Thresholds, Risk Taking, and Performance: Evidence from Hedge Funds,î working paper, Haas School of Business. - [28] Sirri, E. R., and P. Tufano (1998). ìCostly Search and Mutual Fund Flows,î Journal of Finance 53, 1589ñ1622. - [29] Starks, L. T. (1987). ìPerformance Incentive Fees: An Agency Theoretic Approach,î Journal of Financial and Quantitative Analysis 22, 17ñ32. - [30] Taylor, J. (2003). ìRisk-Taking Behavior in Mutual Fund Tournaments,î Journal of Economic Behavior and Organization 50 (3), 373ñ83. - [31] Tesar, L., and I. Werner (1995). ìHome Bias and High Turnover,î Journal of International Money and Finance 14 (4), 467ñ492. ### Appendix: Proofs, key derivations, and quantitative results - Appendix A — Proof of Proposition 1 - Conjectured linear price and demand functions: P = ( 1 + 2 + u); i = i es i. - Conditional moments: - E[s j js i] = E[v j s i] = 2 v 2 v + 2 " s i := D. - E[ j js i] = j 2 v 2 v + 2 " s i. - E[ j v j s i] = j C, where C := 2 v 4 v 2 v + 2 " + D2. - E[ 2 j js i] = 2 j (C+2 "). - Manager objective: Ef[( i j) (v( i + j + u))] js i g = i D  2 i  i j D j C +  i j D +  2 j C + 2 ". - First-order condition gives: - i = D / (2) (1  j (1 )). - Imposing symmetry i = j = leads to 2 = [1  (1 )] 2 v 2 v + 2 ". - Price function: -  = 2 2 v 4 2 2 v + 2 "2 + 2 u [ (s i + s j) + u]. - Solved values: - = s 2 u 2 (1 ) 2 v + 2 2 ". -  = 2 2 v q 2 u 2 (1 ) 2 v + 2 2 " (2 2 v + 2 ") / (2 u (1 ) 2 v + 2 " + 2 u). - Appendix B — Proof of Corollary 1 - Expected payoff to investors of fund i: - E[( )] = & 2 v 2 2 2 v 2 2 " = & (2 v  22 v + 2 "). - Re-expressed: - E[( )] = &2 v s 2 u 2 (1 ) 2 v + 2 2 "1 22 v + 2 "2 (2 v + 2 ") + (1 )2 v = &2 v r 2 u 2 p 2 " + (1 )2 v 2 (2 v + 2 ") + (1 )2 v !. - Appendix C — Proof of Corollary 2 - Shows d/d E[( )] < 0. - Key expression: - E[( )] = &2 v r 2 u 2 p 2 " + (1 )2 v 2 (2 v + 2 ") + (1 )2 v !. - Concludes: higher relative performance parameter reduces ex-ante expected profits of fund investors; investors prefer a manager caring only about absolute performance. - Appendix D — Proof of Corollary 3 - Closed-form expressions recalled: - = s 2 u 2 (1 )2 v + 2 2 ". -  = 2 2 v q 2 u 2 (1 )2 v + 2 2 " (2 2 v + 2 ") / (2 u (1 )2 v + 2 " + 2 u). - Results: - d/d > 0: increases with relative performance pay parameter — managers trade more aggressively as increases. - d/d V ar[v j P] < 0: variance of the asset payoff conditional on price decreases as increases — price informativeness increases with due to increased trading aggressiveness (analogy to Kyle (1985)). - Adverse selection cost L( ) = 2 E[( )] = 2 2 v r 2 u 2 p 2 " + (1 )2 v 2 (2 v + 2 ") + (1 )2 v !; since d/d E[( )] < 0, d/d L( ) < 0 — liquidity traders are better off with more relative performance pay. - Appendix E — Proof of Proposition 2 - Correlation coefficient  depends on 1 only through 1. - Representation: -  = A 1 q (4 2 1 2 1 + 2 2 1 2 "1 + 2 u1). - Shows @/@1 > 0 using @/@ 1 > 0 and @ 1/@1 > 0; identical result for 2. - Appendix F — Proof of Proposition 3 - Expected manager profit when both informed: - E[( i j) (v P)] =  (1 ) 2 v 2 " + (1 )2 v 2 (2 v + 2 ") + (1 )2 v. - Derivative with respect to is negative: d/d E[( i j) (v P)] < 0. - Equilibrium with both informed requires E[( i j) (v P)] > c; if there exists such that E[( i j) (v P)] = c, then for any > no information is acquired. - Appendix G — Proof of Proposition 4 - Under stated assumptions, each manager's expected profit: - E[(1 3) ]  (1 ) 2 v =  q (1 ) 3 3 r 2 u 2 v 2 := E. - Derived expected conditional variance expression and its derivative with respect to : - d/d of expected conditional variance > 0. - Conclusion: expected conditional variance of prices is increasing in — prices are less informative as increases in this setting. ### Figures: simulation notes and empirical illustrations - Figure captions and notes summarize numerical simulations of price informativeness and expected conditional variance as a function of relative performance concerns , with parameters: - Costs uniformly distributed on unit interval;  set to 0.1. - Variance of payoffs 2 v set to values including 0.01, 0.05, 0.08, 0.15 in different panels. - Noise variance 2 u varied across specified ranges (e.g., from 0.0025 to 0.034; 0.0025 to 0.3175; 0.05 to 0.0815; 0.1 to 0.1315). - Calculated expected conditional variance rescaled to equal 1 when is 0 and noise variance is at its minimum of its set range. - Additional figures (Figures 2–4) illustrate "Expected Price Response to Trades" as a function of for parameter cases: - Figure 2: varying 2 u from 0.6 to 0.6315, with 2 v = 0:15 and  = 0:1. - Figure 3: varying 2 u from 0.2 to 0.2315, with 2 v = 0:15 and  = 0:1. - Figure 4: varying 2 u from 0.0005 to 0.032, with 2 v = 0:15 and  = 0:1. *Source: _wp15198 - References* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15198.pdf_