#### Transcript Chapter 12

```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
5
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
6
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
8
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
9
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
11
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

13
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
16
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.
security price rapidly to reflect the
effect of new information
17
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
18
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
19
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
20
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
21
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