Signal Processing - November 2017 - 171

PERSPECTIVES

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but can they be a crystal ball to predict
the stock market and earn a large excess
return? Before we dream of the AlphaGo for market prediction, let us review
a few basic principles on asset pricing
to better understand the role AI could
play. I refer to the stock market in this
discussion, but the same applies to other
assets and securities such as currencies,
commodities, and bonds.

Stock price reflects a market
equilibrium when supply meets
demand, a state in which sellers
and buyers agree

result, no one can make profit from a
known prediction.
An informal way to think about it is
that today's price is the average price
of the many possible prices we think
we might see tomorrow, the "expected"
price. And furthermore, when determining today's price, people discount tomorrow's expected price because, in general,
people have an aversion to future uncertainty. The dark shadow curves
in Fig--ure 1 represent another possibility tomorrow.
When no one else but one person,
say, Alice, has this magic AI tool, then
there are two kinds of people trading.
Alice, who knows the future price, and
ignorant people trading at the wrong
price today (see the aforementioned first
argument) but will gain this knowledge
tomorrow. So if Alice buys the stock today, she would make a free profit when
the price rises to where she knows it will
be tomorrow. Note that as Alice buys
the stock, the price would be moving up
along the supply curve, and the demand
curve would be moving slightly right toward its correct place. The more Alice is
buying, the more the demand curve will
move to the right. Another compounding effect would be that, though other
people (suppliers) do not have Alice's
information, they may quickly infer
from Alice's order for a large quantity

of shares that there is something there
and raise their expected price, moving
the supply curve to the left. In such a
case, the free profit Alice can make is
apparently limited. Of course, if Alice
is not trading in a large quantity and no
one pays attention to her trading, she
may make a one-time profit for herself
by keeping her information secret. Realworld examples such as undetected insider trading, or, arguably, the opaque
strategies employed by Jim Simons at
Renaissance Technologies, can only
profit if others do not know or infer
what they know.

Price

In a free market, the price "clears the
market," which means the price at which
Risks or uncertain future
the quantity people buy and the quantity
outcomes are an inherent nature
they sell are the same. Why do prices
of the financial market and the
move? The basic concept is represented
underlying economic activities
in the supply-demand curves. When the
Stock price is the result of a market
quantity that sellers are willing to sell
equilibrium when market participants
does not meet the quantity that buyers
optimize risk-returns. The current stock
are willing to buy, prices change until a
price represents the best knowledge of
new equilibrium is reached. See Figure 1
sellers and buyers for the expected (averfor the supply-demand curves.
age) future of the stocks/firms. The exNow add this to the mix: assume
cess expected return in the stock market
that an AI tool can predict tomorrow's
comes as the reward of holding market
stock price. Say the price is going to be
risk, also called systematic risk, which
US$10 higher tomorrow, represented
cannot be eliminated.
by the red curves and P(t+1). What
This is a more involved argument that
will happen?
can be best illustrated by the Capital Asset
If everyone in the market has a magPricing Model (CAPM). The argument
ic AI tool or at least knows the tool's
also holds for other asset-pricing modprediction, then today's price
els. A CAPM (see Fig--ure 2)
will immediately rise to the
is an equilibrium relationship
Supply-Demand
predicted point. Why? Bebetween stock prices and the
S (t +1)
cause no one would sell at a
market portfolio. It is oblower price. Indeed, as long
tained when people optimize
S (t )
as a few market participants
the expected return (mean of
have this knowledge, the
the stock return) for a given
price will change immediaterisk represented by volatility,
S
(t
+1)
P (t +1)
ly. There are many examples
i.e., the standard deviation
of this in the real world such
of the stock return. This opas an acquisition announcetimization leads to a market
ment. Company A is trading
equilibrium, i.e., a mean-variP (t )
D (t +1)
at US$25. Company B anance-efficient (MVE) tangennounces it has entered into an
cy portfolio T, such that the
D (t )
P (t +1)
agreement to purchase Comprices
of all stocks satisfy the
D (t +1)
pany A in one month's time
CAPM relationship accordQuantity
for US$35. Company's A
ing to their correlation to the
stock immediately jumps
market portfolio, the optimal
to US$35 in anticipation of
portfolio. A market index,
FIGURE 1. An example of the supply-demand and price equilibrium movement at today (time t) and tomorrow (time t+1).
the deal close price. As a
such as the S&P 500 index,
IEEE SIGNAL PROCESSING MAGAZINE

November 2017

171

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