Money management in equilibrium

MONEY MANAGEMENT IN EQUILIBRIUM

JONATHAN BERK

STANFORD UNIVERSITY


UNDERLYING RESEARCH

▸ Joint with Richard Green

▸ Mutual Fund Flows and Performance in Rational Markets

▸ Joint with Jules van Binsbergen

▸ Measuring Skill in the Mutual Fund Industry

▸ Assessing Asset Pricing Models using Revealed Preference

▸ Overview paper joint with Jules van Binsbergen

▸ Mutual Funds in Equilibrium


RATIONAL, COMPETITIVE MARKETS (AKA, EFFICIENT MARKETS)

▸ Markets are so competitive that the quality of the company is

reflected in the VALUE of the company

▸ Consequently, the expected return of the company is just a

function of its risk, it tells you nothing about the quality of the

company.

▸ This idea is so well accepted as an explanation of equity

prices that it is acceptable as evidence in a court of law


THE INCONSISTENCY

▸ Historically, the rational competitive market concept has

been inconsistently applied to money management

▸ Equity

The value (size) of a stock reflects its quality. The expected return reflects its risk

▸ Money Management

The size (total AUM) of a fund is random. The quality of the fund (manager) is

reflected in the fund’s expected return (alpha)


NET ALPHA

▸ Using the Net Alpha to measure the quality of the manager is

akin to using a stock’s return to measure the quality of the

company

▸ Like a stock, the expected return of a fund is determined by its

risk, so the net alpha of every fund is zero.

▸ Hard not to see the irony that Fama himself did not correctly

apply his own “theory.” That should be a warning for us all. If

we want to be a scientific based discipline we need to take the

science seriously.


HOW DOES THIS WORK?

▸ Like every industry in the economy, mutual funds face

decreasing returns to scale

▸ Assume that there was a manager who provided his

investors with a positive alpha. What would happen?

▸ The size of the fund adjusts to ensure that net alpha is zero.


DYNAMICS

▸ Start with a mutual fund market in equilibrium so all net

alphas are zero.

▸ Now new information arrives, say the manager outperforms

his benchmark

▸ People update, if nothing else happened this manager would

have a positive net alpha in equilibrium

▸ Result: Inflow of funds until the net alpha is again zero


WHAT DO WE LEARN FROM NET ALPHA

▸ The same thing we learn when we study the net alpha of

stocks

▸ Net alpha tells us about investors, not managers

▸ Positive: Markets are not fully competitive

▸ Negative: Some investors are irrational (too much money

is being allocated to money management)

▸ Zero: Markets are competitive and investors rational


GROSS ALPHA

▸ You cannot use the gross alpha either

▸ What you rather have, a 100% return on $1 or a 10% return

on $1 Billion?

▸ Size matters in money management, you cannot use a

measure that ignores it.


IN FACT ...

▸ Gross alpha isn’t necessarily even positively correlated with skill if

investors are rational and markets are competitive

▸ Why? Because in competitive, rational markets (aka, efficient

markets)

▸ Net alpha is zero

▸ Gross alpha is just net alpha plus the percentage fee

▸ That is, gross alpha is equal to the fee, which is a choice variable!

▸ For gross alpha to even be positively correlated to skill requires

additional assumptions


FEES ARE IRRELEVANT

▸ Managers can charge a high fee and manage a small fund

or a low fee and manage a large fund

▸ The fee only determines the size of the fund

▸ Either way, managers will always choose to actively manage

the amount of capital that maximizes the value they add


CORRECT MEASURE OF SKILL

▸ Value Added: the total amount of money the manager extracts

from markets:

q is AUM

f is the percentage fee

is the expected outperformance


VALUE ADDED ESTIMATES

(in Y2000 $ millions/month)

About $2 million/year!


PERSISTENCE

▸ We first sort stocks into deciles based on t-stat of value

added up until time t

▸ We then measure performance over horizons of 3 to 10

years by recording the average value added in each decile in

each month

▸ We repeat this procedure at the end of each horizon

providing a single value added time series for each decile.

We report the mean and s.e. of each series in each decile


PERSISTENCE IN VALUE ADDED

Vanguard Benchmark

The 10th decile is always the highest decile and almost always is statistically positive


PERSISTENCE IN VALUE ADDED

FFC Risk Adjustment


OUT OF SAMPLE PERFORMANCE OF THE TOP DECILE

Note how much capital is concentrated in the 10th decile


OUT OF SAMPLE COMPENSATION

Vanguard is stronger than FF


PREDICTABILITY IN VALUE ADDED USING COMPENSATION

Vanguard Benchmark

The predictability is stronger and more monotone than when we

sorted on past value added!


NET ALPHA ESTIMATES

(in b.p./month)


There is no obvious evidence of any predictability

OUT OF SAMPLE NET ALPHA

Vanguard Benchmark


OUT OF SAMPLE NET ALPHA

FFC Risk Adjustment

OUT-OF-SAMPLE NET-ALPHA OF THE TOP DECILE

A little evidence of predictability Strong evidence of predictability


WHAT CAN WE LEARN FROM THE REMARKABLE OBSERVATIONS ABOUT COMPENSATION AND NET ALPHA? ▸ What we saw was that when we used Vanguard, compensation

worked very well. It predicted performance but not net alpha

▸ It did not work well when we used FFC. In fact, net alpha (as

defined by the FFC factor structure) was highly predictable

▸ There are two possible explanations

▸ Investors are happily leaving money on the table

▸ Investors don’t care about the FFC factors


NEO-CLASSICAL ASSUMPTIONS THAT UNDERLIE ALL ASSET PRICING MODELS

▸ Investor compete fiercely with each other chasing positive

NPV investment opportunities

▸ This competition eliminates all such opportunities

▸ Assets are priced to ensure that the expected return is solely

a function of risk

▸ This causes the asset pricing relation to hold


DYNAMICS

▸ What happens when new information arrives?

▸ Again, investor competition instantaneously eliminates any

positive NPV opportunities that may exist at the old prices

(with the new information)

▸ Again, this process implies that the asset pricing condition

continues to hold

▸ This price adjustment process is part of all asset pricing

models


MUTUAL FUNDS

▸ New information is the return the manager earns.

▸ Only two ways to eliminate a positive NPV investment

opportunity

▸ Investor flows

▸ Fee changes


ADVANTAGE OF THIS TEST

▸ It is not subject to the epicycle bias

▸ Current factor models are designed to explain the data, so it

is not surprising that they do a good job of that

▸ Merely explaining the data does not imply the models are

right. Correct models explain must explain new regularities

▸ This test is not something the models were designed to

explain


METHODOLOGY

▸ We will just look at signs

▸ We compute the fraction of times we observe an inflow when the

realized abnormal return is positive

▸ We compute the fraction of times we observe an outflow when the

realized abnormal return is negative

▸ Our measure of model performance is the average of (1) and (2)

▸ We will rank models by this measure

▸ If flows and returns are unrelated the measure will equal 50%


PRACTICAL ISSUES

▸ What time horizon do we measure flows and abnormal

returns over?

▸ We should use the shortest horizon possible

▸ But what if investors don't react immediately

▸ We solve this problem by using horizons from 3 months to 4

years.


1977-2011


Investors do use a risk model They are not risk neutral

MODEL RANKING

Investors do not use the factor models

They adjust for risk using the CAPM beta!


INVESTORS APPEAR TO BE USING THE CAPM

▸ CAPM does better than no model at all

▸ It does better than just adjusting by the market return

▸ Investors are using BETA.

▸ remember, this is theoretical prediction of investor

behavior

▸ how often are economic models able to do this?


TAKE AWAYS

▸ We were very surprised with the finding that people appear

to be using the CAPM

▸ Implied puzzle: Why then does the CAPM not work in the

cross section?

▸ There is also other stuff going on that the paradigm does not

explain


FACTOR MODELS

▸ Here there is no theory

▸ They appear to just be the result of overfitting to the data

▸ Finance equivalent of epicycles


COST OF CAPITAL

▸ Ultimate goal of asset pricing

▸ Method for calculating the cost of capital

▸ What this paper says is the CAPM is still the best we have



JONATHAN BERK

STANFORD UNIVERSITY

Date post:	21-Jan-2018
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Money management in equilibrium

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