Money management in equilibrium
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Transcript of Money management in equilibrium
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MONEY MANAGEMENT IN EQUILIBRIUM
JONATHAN BERK
STANFORD UNIVERSITY
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT 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
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MONEY MANAGEMENT IN EQUILIBRIUM
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)
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MONEY MANAGEMENT IN EQUILIBRIUM
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.
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MONEY MANAGEMENT IN EQUILIBRIUM
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.
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
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.
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
VALUE ADDED ESTIMATES
(in Y2000 $ millions/month)
About $2 million/year!
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
PERSISTENCE IN VALUE ADDED
Vanguard Benchmark
The 10th decile is always the highest decile and almost always is statistically positive
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MONEY MANAGEMENT IN EQUILIBRIUM
PERSISTENCE IN VALUE ADDED
FFC Risk Adjustment
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MONEY MANAGEMENT IN EQUILIBRIUM
OUT OF SAMPLE PERFORMANCE OF THE TOP DECILE
Note how much capital is concentrated in the 10th decile
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MONEY MANAGEMENT IN EQUILIBRIUM
OUT OF SAMPLE COMPENSATION
Vanguard is stronger than FF
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MONEY MANAGEMENT IN EQUILIBRIUM
PREDICTABILITY IN VALUE ADDED USING COMPENSATION
Vanguard Benchmark
The predictability is stronger and more monotone than when we
sorted on past value added!
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MONEY MANAGEMENT IN EQUILIBRIUM
NET ALPHA ESTIMATES
(in b.p./month)
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MONEY MANAGEMENT IN EQUILIBRIUM
There is no obvious evidence of any predictability
OUT OF SAMPLE NET ALPHA
Vanguard Benchmark
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MONEY MANAGEMENT IN EQUILIBRIUM
OUT OF SAMPLE NET ALPHA
FFC Risk Adjustment
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OUT-OF-SAMPLE NET-ALPHA OF THE TOP DECILE
A little evidence of predictability Strong evidence of predictability
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
MUTUAL FUNDS
▸ New information is the return the manager earns.
▸ Only two ways to eliminate a positive NPV investment
opportunity
▸ Investor flows
▸ Fee changes
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
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%
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MONEY MANAGEMENT IN EQUILIBRIUM
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.
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MONEY MANAGEMENT IN EQUILIBRIUM
1977-2011
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MONEY MANAGEMENT IN EQUILIBRIUM
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!
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MONEY MANAGEMENT IN EQUILIBRIUM
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?
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
FACTOR MODELS
▸ Here there is no theory
▸ They appear to just be the result of overfitting to the data
▸ Finance equivalent of epicycles
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MONEY MANAGEMENT IN EQUILIBRIUM
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
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MONEY MANAGEMENT IN EQUILIBRIUM
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MONEY MANAGEMENT IN EQUILIBRIUM
JONATHAN BERK
STANFORD UNIVERSITY