CHAPTER 13 EXPERIMENT: Predicting the Next Price Change by Looking at
Past Price Changes
This experiment is based on Bloomfield, R., and J. Hales, 2002, “Predicting the
next step of a random walk: Experimental evidence of regime-shifting beliefs,”
Journal of Financial Economics 65, 397-414. The point is to see if people are prone
to make the judgment errors suggested by Barberis, N., A. Shleifer, and R.
Vishny, 1998, “A model of investor sentiment,” Journal of Financial Economics 49,
307-44 (BSV). In particular, do people believe that stocks follow one of two
regimes: mean-reversion, when the past shows frequent reversals; and
continuation, when the past shows a pronounced tendency to trend?
Subjects are shown price paths for 16 hypothetical stocks. Eight of them
are mirror images of the other eight. Each graph shows the last eight price
changes (i.e., up or down, without indication of magnitude) for the 16 stocks.
The idea is to see whether people think that the next stock change is more likely
to be an increase or a decrease. This is done indirectly by asking subjects how
many shares they would like to buy or sell, and at what price. They are told that
if the next price change is positive the stock pays a $100 dividend, and if the next
price change is negative the stock pays no dividend. If a subject thinks the two
outcomes are equiprobable, he would be inclined to think that the stock is worth
$50. On the other hand, if a subject thinks that a price increase/decrease is more
likely, the stock would be worth more/less than $50.
What should people think? The instructions make it clear that stock price
changes follow a random walk.
The point is to see if subjects, even when
confronted with such statements, still exhibit BSV preferences.
The exact transaction/payoff mechanism is somewhat subtle. Subjects are
instructed to provide a share price for each price change sequence as follows. “If
you specify $51, you are buying one share at $51. If $52 you are buying two
shares: one at $51 and one at $52. If $53 you are buying three shares: one at $51,
one at $52, one at $53, and so on. If you specify $49, you are selling one share at
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$49. If $48 you are selling two shares: one at $49 and one at $48. If $47 you are
selling three shares: one at $47, one at $48, one at $49, and so on. If you do not
want to buy or sell, just write down $50.” Payoffs in each case are calculated as
dividends minus expenditure for purchases, and as sale proceeds minus
dividends for sales. The overall payoff is the summation of the 16 individual
payoffs.
Some of the price paths have a low number of reversals (0 or 1), others
have a moderate number (3 or 4), while still others have a high number (6 or 7).
BSV predicts that after looking at a low-reversal (trending) sequence people
typically expect continuation.
This means that if the latest price change is
positive/negative the subject would buy/sell at a price above/below $50. On
the other hand, BSV predicts that after looking at a high-reversal sequence
people typically expect another reversal. This means that if the latest price
change is positive/negative the subject would sell/buy at a price below/above
$50. To test this, take a subject’s price, subtract $50, and change the sign of this
difference if the last price change was negative. Let’s call these “net prices.” If
people’s beliefs conform to BSV, net prices should on average be positive after
people see a low-reversal sequence. On the other hand, after people see a highreversal sequence, net prices should on average be negative.
Instructions for the students, the 16 price change graphs, and an answer
sheet follow.
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duplicated, or posted to a publicly available website, in whole or in part.
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STUDENT INSTRUCTIONS: “What do you think the stock is worth?”
•
You will be shown 16 graphs.
•
Each graph shows the last 8 price changes for different stocks.
•
We will show you the first of the 16 now to get you thinking about the
process.
•
The x-axis shows periods (0 to 8, since there are eight price changes). The
y-axis is an index of price changes (not actual price changes). The index
always starts at 10, and price changes are always +1/-1 (up/down).
–
If 2 more price increases than decreases, ends at 12 (as in graph)
–
If 4 more price increases than decreases, ends at 14
–
ETC.
–
If 2 fewer price increases than decreases, ends at 8
–
If 4 fewer price increases than decreases, ends at 6
–
ETC.
–
Other price change paths will end up higher and others will end up
lower.
•
After seeing each, you have to decide if you want to buy or sell the stock.
And at what price?
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•
If you buy the stock you will have to pay for it, but you will get the nextperiod dividend. If you sell the stock, you will receive cash for it, but you
will have to pay the dividend.
After the dividend, the stock has no
residual value.
•
The next-period dividend depends on the next-period price change. If
stock price rises next period the dividend is $100. If the stock price falls
next period the dividend is $0.
•
Where do price sequences come from? Researchers have studied large
numbers of publicly traded firms, and constructed models of their
performance patterns. Using these models, researchers created sequences
to represent patterns of “surprises” (actual performance compared to
expected performance).
An upward movement indicates a “positive
surprise,” which means the firm does better than predicted. A downward
movement indicates a “negative surprise,” which means the firm does
worse than predicted. Since performance surprises are unpredictable they
result in a sequence known as a “random walk.” This means statistical
models are unable to predict future surprises from past ones, and on
average there is no upward or downward trend. Random walk sequences
almost always contain intervals of recognizable patterns. But since these
patterns can change greatly at any time, statistical models are still unable
to predict future outcomes.
•
Next we provide more information on transactions and payoffs. After
seeing each price change graph you need to come up with a price. This is
what your price means. If $51, you are buying one share at $51. If $52 you
are buying two shares: one at $51 and one at $52. If $53 you are buying
three shares: one at $51, one at $52, one at $53, and so on. If $49, you are
selling one share at $49. If $48 you are selling two shares: one at $49 and
one at $48. If $47 you are selling three shares: one at $47, one at $48, one at
$49, and so on.
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duplicated, or posted to a publicly available website, in whole or in part.
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•
If you do not want to buy or sell, just write down $50.
•
In making your decision, what should you be considering? You need to
consider the expected value of each stock. You will make the most money
on average if you set a price equal to the expected value of the security.
Assume you believe a stock is worth $60. If you set a price of $60, you will
buy 10 shares at prices $51, $52,…,$60. This is good because you are
buying each share at a price (at or) below expected value, so you expect to
make money on each share. Setting a price higher means you expect you
lose money on some shares. A similar argument holds if you believe that
a stock’s value is below $50.
•
After you make all 16 price decisions, you will be given all 16 next-period
dividends. On this basis you can calculate individual gains and losses.
•
Consider how to calculate gains/losses.
Say your price is $52.
You
bought 2 shares. Your gain/loss will depend on the dividend:
–
DIV = $0
•
–
DIV = $100
•
•
You lose $52 + $51 = $103.
You gain ($100-$52)+($100-$51)=$48+$49=$97.
Now suppose your price is $48. You sold 2 shares. Recall that when you
sell a stock you receive money for the sale but pay dividend.
–
DIV = $0
•
–
DIV = $100
•
•
You gain $48 + $49 = $97
You lose ($100-$48)+($100-$49)=$48+$49=$103.
The overall gain/loss is the sum of these 16 individuals gains/losses.
Track all your gains and losses to see who wins.
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duplicated, or posted to a publicly available website, in whole or in part.
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The 16 PRICE CHANGE GRAPHS
STOCK 1
STOCK 2
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duplicated, or posted to a publicly available website, in whole or in part.
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STOCK 3
STOCK 4
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duplicated, or posted to a publicly available website, in whole or in part.
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STOCK 5
STOCK 6
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STOCK 7
STOCK 8
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STOCK 9
STOCK 10
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11 | P a g e
STOCK 11
STOCK 12
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12 | P a g e
STOCK 13
STOCK 14
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13 | P a g e
STOCK 15
STOCK 16
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14 | P a g e
STUDENT ANSWER SHEET
Stock
Price
Gains/Losses
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
TOTAL
GAINS/LOSSES
©2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or
duplicated, or posted to a publicly available website, in whole or in part.