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Chapter 12
SOME LESSONS FROM
CAPITAL MARKET
HISTORY
1
Chapter Overview

Return of an investment: arithmetic and
geometric

The variability of returns

Efficiency of capital markets
2
Return from a Security (1)
Dollar return vs. percentage return
 Two sources of return

◦ dividend income
◦ capital gain (loss)
 realized or unrealized
Div Pt 1  Pt
Ri 

Pt
Pt
Dividend Payout
Capital Gain
3
Mean

Assume the distribution is normal

Mean return - the most likely return

A measure of centrality

Best estimator of future expected returns
4
The First Lesson

The difference between T-bills and other
investment classes can be interpreted as a
measure of the excess return on the risky asset
Risk premium = the excess return
required from an investment in a risky
asset over a risk-free investment
See Excel spreadsheet in “Discussions” folder
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Arithmetic vs. Geometric
Averages (1)

Geometric return = the average
compound return earned per year over
multiyear period
Geometric average return =
 T (1  R1 ) * (1  R2 ) *... * (1  RT ) 1

Arithmetic average return = the return
earned in an average (typical) year over a
multiyear period
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Arithmetic vs. Geometric
Averages (2)

The geometric average tells what an investor
has earned per year on average, compounded
annually.

The geometric average is smaller than the
arithmetic (exception: 0 variability in returns)

Geom. average ≈ arithmetic average – Var/2
7
Which Average to Use?

Geometric mean is appropriate for making
investment statements about past performance
and for estimating returns over more than 1
period

Arithmetic mean is appropriate for making
investment statements in a forward-looking
context and for estimating average return over
1 period horizon
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The Variability of Returns

Variance = the average squared deviation
between the actual return and the
average return
(R  R )

Var ( R) 
2
i
T 1

Standard deviation = the positive square
root of the variance
  Var
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Standard Deviation

Measure of dispersion of the returns’
distribution

Used as a measure of risk

Can be more easily interpreted than the
variance because the standard deviation is
expressed in the same units as
observations
10
The Normal Distribution (1)

A symmetric, bell-shaped frequency
distribution

Can be completely described by the mean
and standard deviation
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The Normal Distribution (2)
12
Z-score

For any normal random variable:
X 
Z

Z – z-score (see “Supplements” folder)
 X – normal random variable

- mean


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Yet Another Measure of Risk
VaR = statistical measure of maximum
loss used by banks and other financial
institutions to manage risk exposures
•
How much can a bank lose during one
year?
•
Usually reported at 5% or 1% level
14
The Second Lesson

The greater the potential reward the
greater the risk

Which types of securities have higher
potential reward?
See Excel spreadsheet in “Discussions” folder
15
Capital Market Efficiency

Efficient capital market - market in
which security prices reflect available
information

Efficient market hypothesis - the
hypothesis that actual capital markets are
efficient
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What assumptions imply efficient
capital market?
1.
Large number of profit-maximizing
participants analyze and value securities
2.
New information about the securities
come in random fashion
3.
Profit-maximizing investors adjust
security price rapidly to reflect the
effect of new information
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Forms of Market Efficiency

Weak form – the current price of a
stock reflects its own past prices

Semistrong form – all public
information is reflected in stock price

Strong form – all information (private
and public) is reflected in stock prices
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Weak Form Efficiency
Current stock price reflects all security market
information
 You should gain little from the use of any trading
rule that decides whether to buy/sell security
based on the passed security market data
 Major markets (TSX, NYSE, NASDAQ) are at
least weak form efficient

January
effect
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Semistrong Form Efficiency

Mutual fund managers have no special ability to
beat the market

Event studies (IPO, stock splits) support the
semistrong hypothesis
Quarterly
earnings surprise – test results
indicate abnormal returns during 13-26 weeks
following the announcement of large
unanticipated earnings change (earnings
surprise) in a company
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Strong Form Efficiency

No group of investors has access to private
information that will allow them to consistently
experience above average profits
Evidence
shows that corporate insiders and
stock exchange specialists are able to derive
above-average profits
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