Signal Processing - November 2017 - 172

Expected Return (Mean)

Bob uses a wrong AI tool or
is often used as a proxy of the
MVP Efficient Frontier
data and becomes overconfimarket portfolio. Note that
[Rp ]
True MVE
dent that he's the informed
the MVE tangency portfolio
investor in the market, guess
is the optimal portfolio in that
CAPM
what-he becomes the stubit gives maximum expected
born guy holding the wrong
return for a given volatility
A
T
portfolio who's worse off,
and risk-free rate. A CAPM is
Attainable Pool of
Risk Securities
dragging the market portfolio
an equilibrium relationship that
M
and Portfolios
down and hurting all the passtock prices must satisfy with
rf
sive investors. Warren Buffett
regard to their risks and correB
put it this way: "If you've
lations. In a CAPM world, the
been playing poker for half
market portfolio is the MVE
an hour and you still don't
tangency portfolio. No one can
know who the patsy is, you're
hold a better portfolio than the
σRp
O
Standard Deviation (Risk)
the patsy." The caveat is that
market portfolio-the MVE
it's easier said than done: you
tangency portfolio T. Readers
FIGURE 2. Portfolio risk-return optimization and market equilibrium: rf
have to have enough unbican refer to [2] for an introducrepresents the risk-free rate. The risk-free rate is the theoretical rate of
ased data samples to draw
tion to the CAPM with a signal
return of an investment with zero risk. In practice, it is often represented
statistically significant conprocessing perspective as well
by the interest rate on U.S. Treasury bills.
clusion to know who the
as finance jargon I use here.
patsy is.
Of course, such market
My conclusion? AI may provide new
equilibrium and optimal market port■■ The stubborn misinformed Bob's
tools for information. But are you a seafolio will only hold when major market
portfolio underperforms the market.
soned financial professional who works
participants agree on the knowledge,
■■ Note that, if the misinformed invesclosely with the market, or are you a
i.e., mean and covariance, of all stock
tors in aggregate hold the tangency
casual investor? If you are one of us,
returns. If an AI tool provides better
portfolio, the CAPM still holds and
the majority, don't expect AI to bring a
estimate of the knowledge, as long as
no one will outperform the market.
quick buck. If you are the former, you
everyone in the market knows, no one
■■ When the overall weight of the mishave a tough job but there's a chance to
can beat the market portfolio in a riskinformed investors is large enough,
make a fortune.
return sense.
it can drag down the market portfolio.
Now, what if only one group of invesThis may happen in a market with
tors, represented by Alice, has the better
many nonprofessional stubborn
Summary and Q&A
knowledge, and the other group of invesactive investors. But in the U.S. stock
Q: Can AI (or any other technologies)
tors, represented by Bob, disagrees and
market, the institutional investment
help us better evaluate the risk?
stubbornly holds and acts on the wrong
composes the majority. Therefore,
A: Yes, it is possible. But from soknowledge of the firms? In such a case
ciety's perspective, it is not necessarily
M is expected to be similar to the
[3], the informed Alice will hold the true
a good thing. We want smart people to
true tangency portfolio T .
MVE tangency portfolio T, while the miscreate totally new knowledge, prod■■ If the nonprofessional retail investors
ucts, art, etc. that always involve high
informed Bob in aggregate holds a nonare equipped with AI, they would act
risk. Accurate risk evaluation may cause
MVE portfolio B. The market portfolio
more like informed investors that
these high-risk start-ups to find themwill bring the market portfolio closer
M is now the value-weight portfolio of T
selves short of funders, just like an into M, making the market more effiand B. Let w denote the proportion of the
surance company may not want to insure
total value of risk asset owned by Alice,
cient and practically losing less
certain high-risk patients.
and R A and R B denote the expected remoney compared to the informed
Q: Can AI help us better allocate
professional investors.
turns of portfolios A and B, respectively.
capital in a financial market?
Then the market portfolio return R M is
■■ Here's what's interesting: if Bob
A: Yes.
knows that he is not as informed as
Q: Can AI replace some financial
Alice but doesn't know who Alice is
R M = wR A + (1 - w) R B .
analysts?
or what her secret holdings are, his
A: Possibly. That may happen in any
best strategy is to be a passive invesThe relationship among portfolios is ilindustry and has happened before in the
tor holding the market portfolio. If all
lustrated in Figure 2.
stock market. The famed trading pits
misinformed investors know they are
in New York City and Chicago stuffed
misinformed and therefore hold the
Remarks
with floor traders shoving and shouting
market portfolio, the market portfolio
■■ Apparently, Alice's portfolio T has
are no more. They've been replaced by
again becomes the optimal MVE
the highest Sharpe ratio and outperelectronic exchanges. Now automation
tangency portfolio T. However, if
forms the market portfolio M.
172

IEEE SIGNAL PROCESSING MAGAZINE

November 2017

Table of Contents for the Digital Edition of Signal Processing - November 2017