SOME LESSONS FROM CAPITAL MARKET HISTORY

Chapter 12

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Chapter OverviewReturn of an investment: arithmetic

and geometric

The variability of returns

Efficiency of capital markets

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Return from a Security (1)Dollar return vs. percentage

returnTwo sources of return

◦dividend income◦capital gain (loss)

realized or unrealized

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Dividend Payout Capital Gain

t

tt

ti P

PPPDivR

1

MeanAssume the distribution is normal

Mean return - the most likely return

A measure of centrality

Best estimator of future expected returns

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The First LessonThe difference between T-bills and

other investment classes can be interpreted as a measure of the excess return on the risky asset

See Excel spreadsheet in “Discussions” folder 5

Risk premium = the excess return required from an investment in a risky asset over a risk-free investment

Arithmetic vs. Geometric Averages (1)

Geometric return = the average compound return earned per year over multiyear period

Arithmetic average return = the return earned in an average (typical) year over a multiyear period 6

Geometric average return = 1)1(*...*)1(*)1( 21 T

TRRR

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

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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 ReturnsVariance = the average squared

deviation between the actual return and the average return

Standard deviation = the positive square root of the variance

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2

1)(

)(

T

RRRVar i

Var

Standard DeviationMeasure 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

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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)

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Z-scoreFor any normal random variable:

Z – z-score (see “Supplements” folder)

X – normal random variable - mean

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X

Z

Yet Another Measure of Risk

• How much can a bank lose during one year?

• Usually reported at 5% or 1% level

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VaR = statistical measure of maximum loss used by banks and other financial institutions to manage risk exposures

The Second LessonThe 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 EfficiencyEfficient 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 EfficiencyWeak 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 EfficiencyCurrent stock price reflects all security

market informationYou 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 EfficiencyMutual 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 20

Strong Form EfficiencyNo 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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