The Cross-section of Managerial Ability and Risk Preferences

Transcription

1 The Cross-section of Managerial Ability and Risk Preferences Ralph S.J. Koijen Chicago GSB October 2008

2 Measuring managerial ability Mutual fund alphas from a performance regression using style benchmarks R A it r f = α i + β i ( R B t r f ) + ε it

3 Measuring managerial ability Mutual fund alphas from a performance regression using style benchmarks R A it r f = α i + β i ( R B t r f ) + ε it Reduced-form approach ignores that fund returns are the outcome of a portfolio-choice problem Brennan (1993), Becker et al. (1999), Cuoco and Kaniel (2007), Basak, Pavlova, and Shapiro (2007), Binsbergen, Brandt, and Koijen (2007), Yuan (2007), Wermers, Yao, and Zhao (2007)

4 Measuring managerial ability Mutual fund alphas from a performance regression using style benchmarks R A it r f = α i + β i ( R B t r f ) + ε it Reduced-form approach ignores that fund returns are the outcome of a portfolio-choice problem Brennan (1993), Becker et al. (1999), Cuoco and Kaniel (2007), Basak, Pavlova, and Shapiro (2007), Binsbergen, Brandt, and Koijen (2007), Yuan (2007), Wermers, Yao, and Zhao (2007) Often leads to dynamic strategies that could induce to misspecifications

5 New approach: Portfolio choice theory Consider an active portfolio manager s problem Manager dynamically selects portfolio to maximize utility

6 New approach: Portfolio choice theory Consider an active portfolio manager s problem Manager dynamically selects portfolio to maximize utility Two basic components: 1 Managerial ability (λ Ai ): shapes the investment opportunity set 2 Risk preferences (γ i ): determine which portfolio is selected along this set

7 New approach: Portfolio choice theory Consider an active portfolio manager s problem Manager dynamically selects portfolio to maximize utility Two basic components: 1 Managerial ability (λ Ai ): shapes the investment opportunity set 2 Risk preferences (γ i ): determine which portfolio is selected along this set Main idea: Use restrictions from structural portfolio management models to estimate the cross-section of managerial ability and risk preferences Analogy: Use household s Euler condition to estimate preference parameters Hansen and Singleton (1983), Vissing-Jorgensen and Attanasio (2003), and Gomes and Michaelides (2005)

8 Main economic questions Main economic questions: 1 Which economic restrictions follow from portfolio choice theory 2 What can we learn about the dynamics of mutual fund strategies? 3 Does heterogeneity matter?

9 Main economic questions Main economic questions: 1 Which economic restrictions follow from portfolio choice theory 2 What can we learn about the dynamics of mutual fund strategies? 3 Does heterogeneity matter? Main answers: 1 Economic restrictions can be used to disentangle both attributes 2 Fund alphas reflect both ability and risk preferences 3 Second moments of fund returns contain information about the manager s attributes 4 Structural model captures important dynamics of fund strategies 5 Heterogeneity matters: utility costs up to 4% per annum by ignoring heterogeneity

10 Main economic questions Main economic questions: 1 Which economic restrictions follow from portfolio choice theory 2 What can we learn about the dynamics of mutual fund strategies? 3 Does heterogeneity matter? Main answers: 1 Economic restrictions can be used to disentangle both attributes 2 Fund alphas reflect both ability and risk preferences 3 Second moments of fund returns contain information about the manager s attributes 4 Structural model captures important dynamics of fund strategies 5 Heterogeneity matters: utility costs up to 4% per annum by ignoring heterogeneity Main methodological contribution: Develop econometric framework to enable likelihood-based inference in continuous-time, dynamic optimization models

11 Modeling managerial preferences Model I: preferences for assets under management Basak, Pavlova, and Shapiro (2007a, 2007b), Chapman, Evans, and Xu (2007) Model features managerial incentives: 1 Fund flows that depend on past performance 2 Promotion/demotion risk that depends on past performance

12 Modeling managerial preferences Model I: preferences for assets under management Basak, Pavlova, and Shapiro (2007a, 2007b), Chapman, Evans, and Xu (2007) Model features managerial incentives: 1 Fund flows that depend on past performance 2 Promotion/demotion risk that depends on past performance Model II: preferences for returns relative to the benchmark Brennan (1993), Becker et al. (1999), Chen and Pennacchi (2007), Binsbergen, Brandt, and Koijen (2007) Advantage: Derive cross-equation restriction analytically

13 Modeling managerial preferences Model I: preferences for assets under management Basak, Pavlova, and Shapiro (2007a, 2007b), Chapman, Evans, and Xu (2007) Model features managerial incentives: 1 Fund flows that depend on past performance 2 Promotion/demotion risk that depends on past performance Model II: preferences for returns relative to the benchmark Brennan (1993), Becker et al. (1999), Chen and Pennacchi (2007), Binsbergen, Brandt, and Koijen (2007) Advantage: Derive cross-equation restriction analytically Unfortunately, cross-equation restriction for fund alphas strongly rejected Analogy: CRRA preferences cannot match consumption and asset pricing data Requires a generalization of preferences Hansen and Singleton (1983), Vissing-Jorgensen and Attanasio (2003), and Gomes and Michaelides (2005)

14 Modeling managerial preferences Model points to a desire for underdiversification: managers overinvest in the active portfolio Generalize the manager s preferences: quest for status as a motive for underdiversification The manager has preferences for: 1 Assets under management 2 Fund status: relative position in cross-sectional asset distribution

15 Modeling managerial preferences Model points to a desire for underdiversification: managers overinvest in the active portfolio Generalize the manager s preferences: quest for status as a motive for underdiversification The manager has preferences for: 1 Assets under management 2 Fund status: relative position in cross-sectional asset distribution Different curvature parameters for: 1 Assets under management: controls passive risk taking 2 Fund status: controls active risk taking Standard models nested

16 Conventional approach to measure ability Mutual fund alphas from a performance regression using style benchmarks R A it r f = α i + β i ( R B t r f ) + ε it α i

17 Conventional approach to measure ability Mutual fund alphas from a performance regression using style benchmarks R A it r f = α i + β i ( R B t r f ) + ε it α i Cross-sectional distribution displays heterogeneity and estimation error

18 Economic restrictions and efficiency The impact of imposing the economic restrictions Performance regressions Structural model α i The variance of alphas is three times smaller

19 Main empirical results Managerial ability and risk aversion are highly positively correlated Managerial ability (λ A ) Coefficient of relative risk aversion (RRA(a 0 ))

20 Outline 1 Data 2 Financial market and preferences 3 Cross-equation restrictions 4 Status model 5 Novel econometric approach to estimate dynamic models of delegated portfolio management by maximum likelihood 6 Main empirical results 7 Economic costs of heterogeneity

21 Data Manager-level database based on CRSP data from to Assign each manager-fund combination to one of nine styles reflecting size and value orientation

22 Data Manager-level database based on CRSP data from to Assign each manager-fund combination to one of nine styles reflecting size and value orientation 3,694 unique manager-benchmark combinations consisting of 3,163 different managers and 1,932 different funds

23 Data Manager-level database based on CRSP data from to Assign each manager-fund combination to one of nine styles reflecting size and value orientation 3,694 unique manager-benchmark combinations consisting of 3,163 different managers and 1,932 different funds Construct returns before fees and expenses

24 Data Manager-level database based on CRSP data from to Assign each manager-fund combination to one of nine styles reflecting size and value orientation 3,694 unique manager-benchmark combinations consisting of 3,163 different managers and 1,932 different funds Style composition (R. = Russell) Mutual fund style Selected benchmark Fraction of Number of observations (%) observations Large/blend S&P Large/value R Value Large/growth R Growth Mid/blend R. Mid-cap Mid/value R. Mid-cap Value Mid/growth R. Mid-cap Growth Small/blend R Small/value R Value Small/growth R Growth Total ,694

25 Financial market The manager can trade 3 assets:

26 Financial market The manager can trade 3 assets: 1 Cash account: ds 0 t = S 0 t r f dt

27 Financial market The manager can trade 3 assets: 1 Cash account: ds 0 t = S 0 t r f dt 2 Style benchmark portfolio: ds B t = S B t (r f + σ B λ B )dt + S B t σ B dz B t

28 Financial market The manager can trade 3 assets: 1 Cash account: ds 0 t = S 0 t r f dt 2 Style benchmark portfolio: ds B t = S B t (r f + σ B λ B )dt + S B t σ B dz B t 3 Idiosyncratic technology of the manager (Active portfolio): dsit A = SA it (r f + σ Ai λ Ai ) dt + Sit A σ AidZit A, where λ Ai measures managerial ability, with [ Z B,Z A i ] t = 0

29 Standard model of preferences Preferences for returns relative to the benchmark: ( ) max E t 1 R A 1 γi it (x it ) t [0,T] 1 γ i RT B x it = (x B it, xa it ) : fractions invested in benchmark and active portfolio Optimization subject to the dynamic budget constraint

30 Standard model of preferences Preferences for returns relative to the benchmark: ( ) max E t 1 R A 1 γi it (x it ) t [0,T] 1 γ i RT B x it = (x B it, xa it ) : fractions invested in benchmark and active portfolio Optimization subject to the dynamic budget constraint Optimal strategy: x i = 1 ) Σ 1 γ i Λ i + (1 1γi e 1, i with Σ i = diag(σ P, σ Ai ), Λ i = (λ P, λ Ai ), and e 1 = (1, 0)

31 Implications of the cross-equation restriction Asset dynamics: da it A it r f dt = (x A it σ Ai λ Ai + x B it σ Bλ B ) dt + x B it σ BdZ B t + x A it σ AidZ A it

32 Implications of the cross-equation restriction Asset dynamics: da it A it r f dt = (x A it σ Ai λ Ai + x B it σ Bλ B ) dt + x B it σ BdZ B t + x A it σ AidZ A it Substitute the optimal strategy: ( da it r A f dt = λ2 Ai λb dt + + γ i 1 ) ( dst B it γ }{{} i γ i σ B γ }{{ i S } t B α i β i r f dt ) + λ Ai γ i }{{} σ εi dz A it

33 Implications of the cross-equation restriction Substitute the optimal strategy: ( da it r A f dt = λ2 Ai λb dt + + γ i 1 ) ( dst B it γ }{{} i γ i σ B γ }{{ i S } t B α i β i λ Ai and γ i follow from: β i = λ B + γ i 1 γ i σ B γ i σ εi = λ Ai /γ i r f dt ) + λ Ai γ i }{{} σ εi dz A it

34 Implications of the cross-equation restriction Substitute the optimal strategy: ( da it r A f dt = λ2 Ai λb dt + + γ i 1 ) ( dst B it γ }{{} i γ i σ B γ }{{ i S } t B α i β i λ Ai and γ i follow from: β i = λ B + γ i 1 γ i σ B γ i σ εi = λ Ai /γ i r f dt The cross-equation restriction on the fund s alpha, α i : ( ) λb /σ B 1 ) + λ Ai γ i }{{} σ εi dz A it α i = λ 2 Ai /γ i = σ 2 εi β i 1

35 Implications of the cross-equation restriction Substitute the optimal strategy: ( da it r A f dt = λ2 Ai λb dt + + γ i 1 ) ( dst B it γ }{{} i γ i σ B γ }{{ i S } t B α i β i λ Ai and γ i follow from: β i = λ B + γ i 1 γ i σ B γ i σ εi = λ Ai /γ i r f dt The cross-equation restriction on the fund s alpha, α i : ( ) λb /σ B 1 ) + λ Ai γ i }{{} σ εi dz A it α i = λ 2 Ai /γ i = σ 2 εi β i 1 Main conclusion: Fund alphas 1 Reflect ability and risk preferences 2 Can be estimated from information in second moments

36 Empirical results: Preferences for returns rel. to benchmark Model-implied Performance regr. γ i λ Ai α i β i σ εi α i β i σ εi S&P 500 Mean % % 0.82% % St.dev % % 2.98% % β i = λ ) B + (1 1γi γ i σ B σ εi α i = λ Ai /γ i = λ 2 Ai /γ i

37 Empirical results: Preferences for returns rel. to benchmark Model-implied Performance regr. γ i λ Ai α i β i σ εi α i β i σ εi S&P 500 Mean % % 0.82% % St.dev % % 2.98% % β i = λ ) B + (1 1γi γ i σ B σ εi α i = λ Ai /γ i = λ 2 Ai /γ i It requires underdiversification to match the moments of fund returns

38 Managerial preferences: The status model Quest for status as a motive for underdiversification

39 Managerial preferences: The status model Quest for status as a motive for underdiversification Motivation status concerns Hard-wired: Larger funds more visible, higher in ratings,... Evolutionary forces Strategic interaction among fund managers Large literature in economics argues that status concerns are important for financial decision making

40 Managerial preferences: The status model Quest for status as a motive for underdiversification Motivation status concerns Hard-wired: Larger funds more visible, higher in ratings,... Evolutionary forces Strategic interaction among fund managers Large literature in economics argues that status concerns are important for financial decision making Modeling fund status: Total mass of managers normalized to unity, with measure µ( ) Status measured by the percentile rank: ( ) t(a) = µ i A it a, Ā t where Ā T is median fund size

41 Managerial preferences: The status model Manager s objective: [ max E 0 η A1 γ 1i it (x it ) t [0,T] + (1 η) S (1 γ 1 γ 2i ) Ā 1 γ 1i T 1i where: T( ): maps relative fund size to fund status S( ): sign function Restrictions: η [0,1], γ 1i > 1, and T ( ) 0 ( ) ] 1 γ2i AiT T, Ā T

42 Managerial preferences: The status model Manager s objective: [ max E 0 η A1 γ 1i it (x it ) t [0,T] + (1 η) S (1 γ 1 γ 2i ) Ā 1 γ 1i T 1i where: T( ): maps relative fund size to fund status S( ): sign function Restrictions: η [0,1], γ 1i > 1, and T ( ) 0 ( ) ] 1 γ2i AiT T, Ā T Comments: γ 2i can be negative CDF captures the opportunities to improve status Nests standard model of preferences

43 Fund status and risk taking 3.5 Coefficient of relative risk aversion 3 Coefficient of relative risk aversion Rank percentile For most funds, risk aversion and fund size are positively correlated γ 1i controls passive risk taking, γ 2i active risk taking

44 Estimation strategy Define r B t+h = log SB t+h logsb t and r T = {r h,..., r T }

45 Estimation strategy Define r B t+h = log SB t+h logsb t and r T = {r h,..., r T } Two-step maximum-likelihood estimation procedure: 1 Estimate Θ B = {λ B, σ B } using L(r BT ; Θ B ) 2 Estimate Θ Ai = {λ Ai, γ 1i, γ 2i } using L(A T i r BT,A i0 ; Θ Ai, ˆΘ B )

46 Estimation strategy Define r B t+h = log SB t+h logsb t and r T = {r h,..., r T } Two-step maximum-likelihood estimation procedure: 1 Estimate Θ B = {λ B, σ B } using L(r BT ; Θ B ) 2 Estimate Θ Ai = {λ Ai, γ 1i, γ 2i } using L(A T i r BT,A i0 ; Θ Ai, ˆΘ B ) Main complication: computing L(A T i r BT, A i0 ; Θ A, ˆΘ B )

47 Estimation strategy Define r B t+h = log SB t+h logsb t and r T = {r h,..., r T } Two-step maximum-likelihood estimation procedure: 1 Estimate Θ B = {λ B, σ B } using L(r BT ; Θ B ) 2 Estimate Θ Ai = {λ Ai, γ 1i, γ 2i } using L(A T i r BT,A i0 ; Θ Ai, ˆΘ B ) Main complication: computing L(A T i r BT, A i0 ; Θ A, ˆΘ B ) Density of A t+h given A t unknown: da t = A t ( r + x t (A t ) ΣΛ ) dt + A t x t (A t ) ΣdZ t

48 Using the martingale approach in estimation I develop a new approach based on martingale techniques of Cox Huang (1989)

49 Using the martingale approach in estimation I develop a new approach based on martingale techniques of Cox Huang (1989) Main steps of the martingale method:

50 Using the martingale approach in estimation I develop a new approach based on martingale techniques of Cox Huang (1989) Main steps of the martingale method: 1 Choose optimal year-end asset level (AT ) that solves: Solution: A T = (u ) 1 (ξ ϕ T ) max E 0 [u (A T )] A T 0 s.t. E 0 [ϕ T A T ] A 0

51 Using the martingale approach in estimation I develop a new approach based on martingale techniques of Cox Huang (1989) Main steps of the martingale method: 1 Choose optimal year-end asset level (AT ) that solves: Solution: A T = (u ) 1 (ξ ϕ T ) max E 0 [u (A T )] A T 0 s.t. E 0 [ϕ T A T ] A 0 2 By no-arbitrage, time-t assets under management (At ): [ (u At = E ) 1 t (ξϕt ) ϕ ] T = f (ϕ ϕ t ), t with f ( ) invertible under mild conditions

52 Using the martingale approach in estimation I develop a new approach based on martingale techniques of Cox Huang (1989) Main steps of the martingale method: 1 Choose optimal year-end asset level (AT ) that solves: Solution: A T = (u ) 1 (ξ ϕ T ) max E 0 [u (A T )] A T 0 s.t. E 0 [ϕ T A T ] A 0 2 By no-arbitrage, time-t assets under management (At ): [ (u At = E ) 1 t (ξϕt ) ϕ ] T = f (ϕ ϕ t ), t with f ( ) invertible under mild conditions Key insight: transition density (ϕ t ) known exactly

53 Novel econometric approach using martingale techniques Estimation procedure: 1 Map assets under management (A T ) to the state-price density (ϕ T ) 2 Change-of-variables (Jacobian) formula for random variables ) ) ( l (A t rt B, ϕ t h ; Θ A, Θ B = l (ϕ t rt B A ) 1, ϕ t h ; Θ A, Θ B + log t ϕ t Exact likelihood up to one expectation computed using Gaussian quadrature If u( ) is locally convex, apply concavification techniques Carpenter (2000), Cuoco and Kaniel (2007), Basak, Pavlova, and Shapiro (2007) Enables likelihood-based estimation of a large class of dynamic models

54 Summary statistics ability and risk aversion Summary statistics across all styles γ 1 γ 2 RRA λ A Mean St.dev Coeff. of variation If anything, dispersion in risk aversion higher than in ability

55 Reduced-form α estimates are very noisy Compare implied estimates from structural model to reduced-form performance regression: ˆβ Reduced-form i ˆσ Reduced-form ε,i ˆα Reduced-form i = ˆβ Structural i + u i, R 2 = 97.67% (1) = ˆσ Structural ε,i + u i, R 2 = 98.69% (2) = ˆα Structural i + u i, R 2 = 35.11% (3) To match the unconditional moments: intercept equals zero and slope equals one Low R-squared in (3) reflects estimation error in reduced-form α estimates Variance in fund alphas three times smaller

56 Model specification test Specification test: H 0 : Performance regression with the same distributional assumptions ( ) da it dst r A f dt = α i dt + B β i it St B r f dt + σ εi dzt A H 1 : Status model Likelihood ratio test for (non-)nested models to test hypotheses Vuong (1989) Perform test at manager s level; reject if rejection rate exceeds 5% Rejection rate: 10.3% Status model captures important dynamics of fund strategies

57 Forecasting ability Cross-sectional stability (rank correlation): Risk aversion: 65.0% Ability: 32.9%

58 Forecasting ability Cross-sectional stability (rank correlation): Risk aversion: 65.0% Ability: 32.9% Time-series predictability: Two ways to estimate ability over a 3-year period 1 Appraisal ratio using a performance regression 2 Structural estimation using the status model Estimate appraisal ratio over the consecutive year (works against the structural model) [ ( Compute the RMSE: E λ A i,t+1 ˆλ A ) ] 2 it

59 Forecasting ability Cross-sectional stability (rank correlation): Risk aversion: 65.0% Ability: 32.9% Time-series predictability: Two ways to estimate ability over a 3-year period 1 Appraisal ratio using a performance regression 2 Structural estimation using the status model Estimate appraisal ratio over the consecutive year (works against the structural model) [ ( Compute the RMSE: E λ A i,t+1 ˆλ A ) ] 2 it Using performance regression: RMSE = Using status model: RMSE =

60 Are managers really skilled? Fraction of alphas that recovers their expense ratio: Reduced-form approach: 46% Structural: 31% Fraction of alphas that significantly exceed their expense ratio: Reduced-form approach: 9% Structural: 13% Structural approach leads to a more positive view on managerial talent

61 Why are ability and risk aversion positively correlated? Managerial ability and risk aversion are highly positively correlated Managerial ability (λ A ) Coefficient of relative risk aversion (RRA(a 0 )) This is consistent with selection effects or reflects career concerns

62 Why are ability and risk aversion positively correlated? Choose between mutual fund industry and savings bank The bank provides a known and constant income O T at t = T Value function mutual fund industry J MF = 1 ( 1 γ exp (1 γ)r + 1 γ ( ) ) λ 2 2γ A + λ2 B Value function bank J OO = 1 1 γ O1 γ T The indifference locus reads λ A (γ) = (log O T r)2γ λ 2 B Fund managers will opt into the industry only if λ A λ A (γ)

63 Heterogeneity in ability and risk aversion Dependent variable Ability (log(λ A )) Risk aversion (log(rra)) Estimate T-statistic Estimate T-statistic Log(TNA) -8.87% % Tenure 7.27% % 1.26 Turnover 6.36% % 0.04 Log(Expenses) 5.04% % Stock holdings -6.37% % Loads -3.41% % B-1 fees 0.04% % 1.07 Log(Family TNA) 0.10% % 1.00 Fund age 3.53% % 0.79 R-squared 13.0% 6.6% Managers of large funds tend to be less skilled, but more aggressive Skilled managers are more experienced and have higher turnover Aggressive managers charge higher expense ratios and hold less cash Substantial unobserved heterogeneity

64 Differences across investment styles Risk aversion Large/value manager Small/growth manager Ability Large/value manager Small/growth manager Density Coefficient of relative risk aversion Density Ability (λ A ) Large/value managers are on average more conservative than small/growth managers Larger fraction of small/growth managers is skilled

65 Does heterogeneity matter? Investor allocates capital to cash, benchmark, and actively-managed funds Three ways to account for heterogeneity: 1 Use performance regressions to estimate cross-sectional distribution 2 Ignore heterogeneity: use average values 3 Use status model to estimate cross-sectional distribution Utility costs (bp) Ignoring heterogeneity Using performance regressions Coefficient of relative risk aversion of the individual investor

66 Variation in risk aversion and expected returns The status model endogenously generates time variation in risk aversion Time series of expected returns from Binsbergen and Koijen (2007) 0.2 Average coefficient of relative risk aversion Expected return Average coefficient of relative risk aversion The correlation is 62%

67 Conclusions Restrictions implied by theory disentangle managerial ability and preferences

68 Conclusions Restrictions implied by theory disentangle managerial ability and preferences Ability and risk preferences estimated using information in second moments

69 Conclusions Restrictions implied by theory disentangle managerial ability and preferences Ability and risk preferences estimated using information in second moments Standard models lead to implausible estimates of ability or risk preferences

70 Conclusions Restrictions implied by theory disentangle managerial ability and preferences Ability and risk preferences estimated using information in second moments Standard models lead to implausible estimates of ability or risk preferences Imputing status concerns in the manager s preferences Delivers plausible estimates of ability and risk aversion Formally favored over other models and reduced-form performance regressions

71 Conclusions Restrictions implied by theory disentangle managerial ability and preferences Ability and risk preferences estimated using information in second moments Standard models lead to implausible estimates of ability or risk preferences Imputing status concerns in the manager s preferences Delivers plausible estimates of ability and risk aversion Formally favored over other models and reduced-form performance regressions New framework to estimate continuous-time, dynamic optimization models

72 Conclusions Restrictions implied by theory disentangle managerial ability and preferences Ability and risk preferences estimated using information in second moments Standard models lead to implausible estimates of ability or risk preferences Imputing status concerns in the manager s preferences Delivers plausible estimates of ability and risk aversion Formally favored over other models and reduced-form performance regressions New framework to estimate continuous-time, dynamic optimization models Ignoring heterogeneity: large welfare losses for individual investors