Signal Processing - May 2017 - 25

4 × D/P and Annualized Following Seven-Year Return

Take a Bet Again-Intolerance of Loss?

20
15
10
5

Long-term stock return predictability-efficient
market or behavioral?
Robert Shiller, a prominent behavioral economist who won
the 2013 Nobel Prize in Economics the same year as Fama,
found that long-term stock return is predictable: a higher stock
price (P) to dividend (D) ratio signals a lower expected return,
and vice versa [8], [39]. The following time-series regression
between the portfolio return and the portfolio firm dividendto-price (D/P) ratio has significant nonzero coefficient b:
R t +1 = a + b (D/P) t + f t +1 .
The efficient market economist John H. Cochrane illustrated this well in an op-ed article in the Wall Street Journal at
the end of 2008 [67], the height of the financial crisis, shown in
Figure 5. In hindsight, the article turned out to be an accurate
prediction of the stock market movement.
From the efficient market viewpoint [40], such predictable
long-term stock returns are caused by time-varying risk premia. That is, the utility function is time varying. People are
more risk averse in recessions because they do not have financial security and demand higher risk premia, i.e., lower stock

Following
Seven-Year
Return

19

4
19 5
50
19
5
19 5
6
19 0
65
19
7
19 0
7
19 5
80
19
8
19 5
9
19 0
9
20 5
0
20 0
0
20 5
1
20 0
15

0

Path?

Price

FIGURE 5. The D/P ratio can predict a future seven-year return. (Image
courtesy of John H. Cochrane, a former president of the American Finance
Association, updated from [40]. An earlier version of this figure also
appeared in [67].)

Price

The implication of prospect theory to economics, decision
theory, and business management is profound. However, it is
also all too easy for researchers to attribute any stock return
anomaly found against established asset-pricing models to
behavioral factors. Note that for a purely behaviorally caused
market anomaly to persist over time, one must assume that
even smart investors as a group do not learn over time (or generations) from their psychological mistakes.
It is important to note that most mathematical models in economics are based on the expected utility theory
and EMH. For example, the Black-Scholes option pricing model [38] assumes an efficient market, in that stock
price follows a random walk and there are no riskless arbitrage opportunities. (Both Robert C. Merton and Myron S.
Scholes won the 1997 Nobel Prize in Economics for their
contributions to option pricing.) Behavioral factors in the
market are still difficult to quantify and have not led to
fully developed asset-pricing models that can be tested and
potentially rejected.

4 × D/P Ratio

25

Assume you got a traffic ticket and have the following
two choices:
1) the bet: flip a coin (equal probability on both sides);
heads, you pay a US$2,000 fine, tails, you pay
no fine
2) cash: you pay a US$1,000 fine in cash.
Would you take the bet or pay the US$1,000 cash
fine? Are you loss averse and risk seeking?

News
Time
(a)

News
Time
(b)

FIGURE 6. The information processing in the market: (a) it takes time for
market participants to process complex information and for this information
to reflect in the price, whereas in a mostly pure efficient market, information
is processed immediately and fully reflected in the price (b). (This figure is
modified from a figure in [42]. Image courtesy of John. H. Cochrane.)

prices and higher expected returns. By contrast, people are
more tolerant of risks in economic booms, and therefore stock
prices are high and expected returns (RP) are low. However,
behavioral economists like Shiller believe that people overreact to economic situations, resulting in speculative bubbles in
booms due to irrational exuberance [41] and recessions due to
a lack of psychological confidence. Oftentimes, economists in
both camps agree on the findings from data but dispute the
cause: whether excess returns are indeed RP or psychological mispricing.

Signal and information processing in efficient
markets and traps in data
In the most purely efficient market, information is processed
immediately and fully reflected in the price, as shown in
Figure 6(b). That is, the market moves from one equilibrium to
another equilibrium in no time. SP researchers are more familiar

IEEE Signal Processing Magazine

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May 2017

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25



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

Signal Processing - May 2017 - Cover1
Signal Processing - May 2017 - Cover2
Signal Processing - May 2017 - 1
Signal Processing - May 2017 - 2
Signal Processing - May 2017 - 3
Signal Processing - May 2017 - 4
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Signal Processing - May 2017 - 101
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Signal Processing - May 2017 - 105
Signal Processing - May 2017 - 106
Signal Processing - May 2017 - 107
Signal Processing - May 2017 - 108
Signal Processing - May 2017 - 109
Signal Processing - May 2017 - 110
Signal Processing - May 2017 - 111
Signal Processing - May 2017 - 112
Signal Processing - May 2017 - Cover3
Signal Processing - May 2017 - Cover4
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