Insight Summit 2017: Intelligent Risk Taking - Active vs passive investing Money management in equilibrium - Jonathan Berk, A.P. Giannini Professor of Finance, Graduate School of Business, Stanford University Presented at the third annual Insight Summit conference held on 7 November 2017 by London Business School’s AQR Asset Management Institute.

1. MONEY
MANAGEMENT IN
EQUILIBRIUM
JONATHAN BERK
STANFORD UNIVERSITY

2. 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

3. 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

4. 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)

5. 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.

6. 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.

7. 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

8. 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

9. 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.

10. 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

11. 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

12. 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

13. MONEY MANAGEMENT IN EQUILIBRIUM
VALUE ADDED ESTIMATES
(in Y2000 $ millions/month)
About $2 million/year!

14. 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

15. MONEY MANAGEMENT IN EQUILIBRIUM
PERSISTENCE IN VALUE ADDED
Vanguard Benchmark
The 10th decile is always the highest decile and almost always is statistically positive

16. MONEY MANAGEMENT IN EQUILIBRIUM
PERSISTENCE IN VALUE ADDED
FFC Risk Adjustment

17. MONEY MANAGEMENT IN EQUILIBRIUM
OUT OF SAMPLE PERFORMANCE OF THE
TOP DECILE Note how much capital is concentrated in the 10th decile

18. MONEY MANAGEMENT IN EQUILIBRIUM
OUT OF SAMPLE COMPENSATION
Vanguard is stronger than FF

19. 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!

20. MONEY MANAGEMENT IN EQUILIBRIUM
NET ALPHA ESTIMATES
(in b.p./month)

21. MONEY MANAGEMENT IN EQUILIBRIUM
There is no obvious evidence of any predictability
OUT OF SAMPLE NET ALPHA
Vanguard Benchmark

22. MONEY MANAGEMENT IN EQUILIBRIUM
OUT OF SAMPLE NET ALPHA
FFC Risk Adjustment

23. OUT-OF-SAMPLE NET-ALPHA OF THE TOP
DECILE
A little evidence of predictabilityStrong evidence of predictability

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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%

30. 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.

31. MONEY MANAGEMENT IN EQUILIBRIUM
1977-2011

32. 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!

33. 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?

34. 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

35. 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

36. 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

37. MONEY MANAGEMENT IN EQUILIBRIUM

38. MONEY
MANAGEMENT IN
EQUILIBRIUM
JONATHAN BERK
STANFORD UNIVERSITY