The role of market impact and investor behavior on fund flows Yoni and Doyne 9/2/09

Aim of work To understand how market impact affects the dynamics of mutual funds. Does it impose a size limit? What role does investor behavior play? What role does managerial skill play?

Outline Describe (our) past work on size distribution. Discuss past work on mutual fund investors. Propose a new behavioral model.

Past Work We investigated the growth dynamics as an Entry/Exit process where funds just diffuse in size. Mutual fund size distribution evolves from a log normal to a power law. We observed no market impact affect. We observe no size limit.

The exit/entry process Funds enter with a constant rate and are created with a size with probability. Each fund exits with a rate.

The exit/entry process We modeled size change as the size change can be decomposed to performance and investor money flux and the return (performance) is given by

The exit/entry process The average monthly return and its volatility, and the money flux and its volatility, are plotted as a function of the fund size (in millions) for the year The data are binned based on size, using bins with exponentially increasing size. The average monthly return is compared to a constant return of and the monthly volatility is compared to The average monthly flux is compared to a slope of -0.5 and the money flux volatility is compared to a linear slope of

The exit/entry process The number density of funds with size where the mean and variance depend on size as

The exit/entry process The model is compared to the empirical distribution at different time horizons. The left column compares CDFs from the simulation (full line) to the empirical data (dashed line). The right column is a QQ-plot comparing the two distributions. In each case the simulation begins in 1991 and is based on the measured parameters. The first row corresponds to the years and the second row to the years (in each case we use the data at the end of the quoted year).

Size distribution model Implications We managed to model the size dynamics with no impact term. Size distribution is lognormal->Zipf. There is no apparent size limit. We used no investor behavior.

How can we reconcile? Two approaches are currently advocated: Fama and French “no skill and no impact” approach. Berk and Green rational solution for skill and impact.

No skill approach Fama and French [2009] estimated after transaction cost over performance. After transaction performance is size independent and below market. No impact -> after transaction cost corresponds to skill. Conclude, skill is narrowly distributed around 0.

No skill approach Equilibrium accounting dictates no impact: You win some you lose some. We show that under equilibrium accounting liquidity providers gain on the expense of liquidity takers. Mutual funds act as liquidity takers -> pay impact!

No skill approach - conclusions Agrees with our dynamic growth model. If impact increases with size, Does skill increase with size?

Rational approach Berk and Green [2004] proposed a rational model Managers posses skill to create before transaction performance the after transaction cost performance is given as represents the fund fees and is the cost function.

Rational approach Investors are Bayesian updaters and they estimate and invest such that Investors choose the optimal size at each time

Implications of BG -size The size of a fund corresponds to skill where For This corresponds to a fund of size 100 billion usd. Heavy tailed size distribution -> Heavy tailed skill.

Implications of BG -size Infinite investor pockets? BG industry size for 1000 funds trading assets and turnover rate we rewrite cost as which corresponds to (in millions) Compare to industry size of 10 trillion

Implications of BG - performance The expected return is size independent The variance decays with size Investors should prefer larger funds as sharp ratio decreases with size!

Implications of BG - growth BG model - average fund size is independent of age. Empirically

BG - conclusions Incorporates impact in a widely acceptable fashion. Has behavioral components (makes economists happy). Model does not agree with observations!

New approach We offer a new model that interpolates between the previous approaches.

New approach Define the size of the industry at time t In BG Q depends on the priors on all managerial skill. We model Q as an exogenous variable.

New approach In the past two decades industry grew more than ten folds. At each time step investors choose to invest in the industry. Investors choose a fund to invest in such that

New approach Investors are Bayesian updaters. Choose such that. where

The overall performance is given such that as increases decreases. For the constant is given by such that New approach

Implications of new approach Both and are size independent. Sharp ratio is size independent! Investor flux decays with size as In agreement with observations of growth dynamics.

Implications of new approach Works with finite investor pockets for any investor flux. Decouples (partially) skill from size. Size can be described by our exit/entry process.

Implications of new approach Size of a fund grows with age even under infinite pockets. For finite pockets depends on

Equilibrium? Money flux drives the industry out of equilibrium. Money flux decreases overall fund performance.

Thank you