Wealth Manager

A world where alpha sums to zero implies
a particular set of laws that constrain
the productivity of investment strategies
overall. One example is the expectation
that indexing will fare reasonably well
over time compared to a relevant pool of
active funds. Owning beta for the long run,
in other words, looks like a compelling alternative
if zero sum alpha is the rule.

But what if alpha doesn’t sum to zero?
What if it sums positively? Or negatively?
Is it possible that, say, 80 percent of managers
can beat their benchmark? If so, how
does that alter the outlook for indexing
relative to active management? Or, more
ominously, what if 80 percent of managers
could fall short of the market’s return over
some time frame?

Clearly, whether investing is, or isn’t, a
zero sum game matters. A casual review of
the topic turns up an abundance of opinion,
with most of it arguing that zero summing
reigns supreme. A widely quoted
source for this claim is “The Arithmetic
of Active Management,” a 1991 article by
Nobel Laureate William Sharpe. He explained
that simple mathematics offer
the proof, which leads to some fairly basic
and enduring principles in the business of
money management.

“Properly measured,” Sharpe wrote, “the
average actively managed dollar must underperform
the average passively managed
dollar, net of costs.” The reason is that
“the market return must equal a weighted
average of the returns on the passive and
active segments of the market.”

By that standard, the index is destined
for above-average performance relative to
the appropriate universe of active managers.
Yes, some managers will win
the race, but the victories will be
offset by the relative-performance
losers. So it goes when alpha adds
up to naught.

You would expect indexing’s
disciples to say as much. But active
managers and their supporters
generally agree, too. Does that
mean the subject is closed? Yes
and no. The issue is being debated
anew in the 21st century. Helping
stoke the fires of deliberation
is an intriguing paper by Joanne
Hill of Goldman Sachs. In a 2005
research report, “Alpha as a Net Zero-Sum
Game,” she laid out a case for why the
alpha pie is not as limited as Sharpe and
others would have us believe.

No, Sharpe isn’t wrong, at least as he
defined the terms. Rather, Hill and others
question Sharpe’s underlying assumptions
as the one and only way to consider
alpha. “The alpha game in practice (rather
than theory) is not a closed system, where
there are a set of identical and finite chips
available at the start and end, so that the
returns delivered by winners must come at
the expense of losers,” Hill wrote. The reason
is that investors in the aggregate have
different time horizons, behavioral biases,
risk preferences, capital constraints, skill
levels and so on, she explained—none of
which are addressed in Sharpe’s article.
In other words, the rules required for zero
sum alphas give way after you factor in the
complexities of the real world.

Alpha may not sum to zero once you
consider risk in context with return, says
Max Darnell, chief investment officer and
partner at First Quadrant, a money manager
in Pasadena, Calif.

Yes, returns alone sum to zero, he concedes,
but risk-adjusted returns are another
matter. “If you’re living in a return-only
world and ignore the differences between
investors, which are risk differences, then
return is a zero sum game,” Darnell tells
Wealth Manager. But assuming that everyone
shares the same tolerance and objectives
for risk doesn’t match reality. “It’s on
the risk side that we all distinguish ourselves.”

As an example, Darnell points to this
past summer’s liquidity crisis, which triggered
a sharp sell off in the stock market.
Reaction to the crisis varied, depending
on risk tolerance, investment horizon, etc.
Some hedge funds were selling because of
short-term trading mandates that prevented
them from sitting idle during a surge in
market volatility driven by falling prices.
Such hedge funds are a natural seller to
pension funds, which often have long term
horizons and look to raise risk exposure
at moments of crisis. In other words,
sellers and buyers can both be “winners”
in risk-adjusted terms even though one or
even both may have losses for a moment
in time.

Thinking of alpha in risk-adjusted terms
can trace its intellectual origins to 1738,
when Dutch mathematician Daniel Bernoulli
laid out the foundations of expected
utility theory. As he put it, “...the value
of an item must not be based on its price,
but rather on the utility it yields. ...the
utility...is dependent on the particular
circumstances of the person making the
estimate.” That leads to the notion that
people may place a diminishing value on
additional wealth under risky conditions,
as the graph below illustrates.

Bernoulli’s hypothesis challenged the
era’s conventional wisdom for making decisions
under conditions of uncertainty.
Rather than picking the strategy that offered
the highest expected value, Bernoulli’s
model favored the highest expected
utility. As a result, two people faced with
the same decision and looking at the same
data could reasonably come to different
conclusions in Bernoulli’s world. Why? Because
expected utility varies depending on
a person’s preferences.

Fast forward several centuries and utility
theory figures prominently in the explanation
of why tactical asset allocation
(TAA) holds out the potential for raising
expected returns with little or no corresponding
rise in expected volatility. At
first glance, the apparent free lunch appears
to run afoul of modern portfolio
theory, which equates higher return with
higher risk. But here’s where utility theory
steps in.

“The linkage between risk and reward
is not inviolate [in TAA] if a higher-return
strategy has lower ‘utility’ than a more
comfortable but less-rewarding strategy,”
wrote Robert Arnott (head of Research Affiliates
and Darnell’s predecessor at First
Quadrant) in The Portable MBA in Investment
(1995, Wiley). TAA doesn’t offer the so-called
free lunch, but it “succeeds because
total return and investor utility are not one
and the same thing. When wealth is declining,
most investors seek the solace of
lower risk, hence lower exposure to risky
markets,” Arnott advised. “Tactical asset
allocation potentially enhances long-run
returns without increasing portfolio risk,
but at a cost of lower comfort, hence lower
utility, for many investors.”

Explained another way, raw performance
numbers and risk-adjusted returns
exist in parallel universes. Each has a distinctive
set of rules and the two measures
are related. But the calculus of investing
that works smoothly in one universe can
malfunction in the other.

That, at least, is part of the explanation
for the reason why alpha may not sum
to zero. Yes, alpha ultimately balances
out in the world laid out in Sharpe’s 1991
paper. But if you consider a more nuanced
framework, the standard assumptions
may not hold.

Even so, the notion of alpha summing
to zero in the return-only space provides
a powerful warning that’s not easily dismissed.
“When Bill Sharpe wrote ‘The
Arithmetic of Active Management,’ the
way he said it is indisputable: The average
manager can’t outperform the average,”
asserts Ronald Kahn, global head of advanced
equity strategies at Barclays Global
Investors in San Francisco.

Kahn’s view is notable for several reasons.
First, he and Richard Grinold share
billing for the creation of the so-called
fundamental law of active management,
which quantifies the idea that generating
alpha is dependent on opportunity plus
skill and the frequency of its application.
Although Kahn works at Barclays, the
world’s largest indexer, he oversees research
for the firm’s nearly $500 billion in
active quantitative strategies.

Kahn, in short, is a card-carrying believer
in active management. Yet he also
recommends caution for thinking that
alpha’s supply may be greater than tradition
suggests. In fact, he warns that after
adjusting returns by some measure of risk,
alpha probably sums to a negative number.
The odds of producing positive alpha,
in other words, may be less favorable than
is widely assumed—even among the zero sum
crowd. “I think that’s a healthy way to
think about it,” he says.

Another veteran investment strategist
agrees. “You can have academic debates
about whether alpha’s a zero sum game,”
says Robert Jaeger, chief investment officer
of EACM, a division of BNY Mellon that
oversees $5 billion for institutional investors—
more than half allocated to hedge
funds. “But my working assumption and
a guiding principle is that it is a zero sum
game.” The hedge fund business, Jaeger
adds, is no exception.

Steven Foresti echoes Jaeger’s caution. “I
wouldn’t be persuaded to abandon the zero-
sum game idea,” says the managing director
of research for Wilshire Consulting,
a unit of Wilshire Associates. “I suppose
you can make theoretical arguments that
investors have different objectives. Some
are laying off risk while others are trying
to beat the market, for example. But in the
aggregate, it really does come back to the
‘Arithmetic of Active Management.’”

Foresti argues too, that the more competitive
markets become, the more likely
that alpha will sum to zero— especially
over time. That doesn’t invalidate active
management, but it does help keep investors
sober about the nature of the game,
he says.

Recognizing that returns-based alpha
sums to zero boils down to common
sense, suggests Laurence Siegel, director of
research in the investment division of the
Ford Foundation, which favors active management
for its $13 billion-plus portfolio.
“You should know the rules of the game
before you start to play,” he says. Otherwise,
you shouldn’t be playing, he adds.

But which set of rules? Each one is valuable
for thinking about the limits and opportunities
of investment strategy. One
reminds that everyone can’t be above average;
the other asserts that risk matters.
Giving up one or the other seems hopelessly
misguided. Alas, the two principles
aren’t easily reconciled into one strategic
vision. Perhaps one day a brainy financial
economist will win a Nobel by figuring out
how to integrate them.