Risk and Return –
Introduction
For 9.220, Term 1, 2002/03
02_Lecture12.ppt
Student Version
Outline




Introduction
What is risk?
An overview of market performance
Measuring performance
 Return and risk measures
 Summary and Conclusions
Introduction
 It is important to understand the relation
between risk and return so we can
determine appropriate risk-adjusted
discount rates for our NPV analysis.
 At least as important, the relation between
risk and return is useful for investors (who
buy securities), corporations (that sell
securities to finance themselves), and for
financial intermediaries (that invest,
borrow, lend, and price securities on behalf
of their clients).
What is risk?
 Definition: risk is the potential for
divergence between the actual
outcome and what is expected.
 In finance, risk is usually related to
whether expected cash flows will
materialize, whether security prices
will fluctuate unexpectedly, or
whether returns will be as expected.
An overview of market performance
– is there risk?
DJIA (Dow 30)
January 1930 to October 2002
12000
10000
8000
6000
4000
2000
Jan-00
Jan-95
Jan-90
Jan-85
Jan-80
Jan-75
Jan-70
Jan-65
Jan-60
Jan-55
Jan-50
Jan-45
Jan-40
Jan-35
Jan-30
0
An overview of market performance
– is there risk?
Monthly % Change in DJIA (Dow 30)
January 1930 to October 2002
40%
30%
20%
10%
0%
-10%
-20%
-30%
Jan-00
Jan-95
Jan-90
Jan-85
Jan-80
Jan-75
Jan-70
Jan-65
Jan-60
Jan-55
Jan-50
Jan-45
Jan-40
Jan-35
Jan-30
-40%
An overview of market performance
– is there risk?
NASDAQ Composite Index
November 1984-October 2002
Nov-00
Nov-98
Nov-96
Nov-94
Nov-92
Nov-90
Nov-88
Nov-86
Nov-84
5200
4700
4200
3700
3200
2700
2200
1700
1200
700
200
An overview of market performance
– is there risk?
Monthly % Change in
NASDAQ Composite Index
October 1984 to October 2002
30%
20%
10%
0%
-10%
-20%
Nov-00
Nov-98
Nov-96
Nov-94
Nov-92
Nov-90
Nov-88
Nov-86
Nov-84
-30%
An overview of market performance
– is there risk?
Apr-02
Apr-01
Apr-00
Apr-99
Apr-98
Apr-97
Apr-96
Apr-95
Apr-94
Apr-93
Apr-92
Apr-91
Apr-90
Apr-89
Apr-88
Apr-87
Apr-86
Apr-85
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
Apr-84
S&P/TSX Composite Index
April 1984 - October 2002
An overview of market performance
– is there risk?
Monthly % Changes of
S&P/TSX Composite Index
April 1984-October 2002
20.0%
10.0%
0.0%
-10.0%
-20.0%
May-02
May-01
May-00
May-99
May-98
May-97
May-96
May-95
May-94
May-93
May-92
May-91
May-90
May-89
May-88
May-87
May-86
May-85
May-84
-30.0%
Measuring Performance: Returns
 Dollar return (over one period):
= Dividends + End of Period Price – Beginning of Period Price
 Percentage return (over one period):
=Dollar return/Beginning of Period Price
=(Dividends + End of Period Price)/Beginning of Period Price -1
 Examples: calculate both $ and % returns
1.
2.
3.
4.
P0=$50, Div1=$2, P1=$55.50
P0=$20, Div1=$0.25, P1=$12.75
P0 = $30, Div1=$1, Capital Gain=$5
P0 = $130, Div1=$0, Capital Loss=$128
Holding Period Returns
 Let Rt be the observed
return earned in year t,
then the holding period
return over a T-period
time frame is as follows:
T
1  HPR 1 to T   1  R t 
t 1
 The average compound
rate of return or geometric
average rate of return
(GAR) just converts the
HPR to an equivalent
effective annual rate:
1  GAR 1 to T   1  HPR 1 to T 
1
T
 T

   (1  R t ) 
 t 1

1
T
Mean returns
 The mean return is the
arithmetic average
rate of return and is
calculated as follows:
T
Mean return  R 
R
t 1
T
t
The risk premium
 Definition: the risk premium is the return
on a risky security minus the return on a
risk-free security (often T-bills are used as
the risk-free security)
 Another name for a security’s risk premium is
the excess return of the risky security.
 The market risk premium is the return on
the market (as a whole) minus the risk-free
rate of return.
 We may talk about the past observed risk
premium, the average risk premium, or the
expected risk premium.
Risk Measures
 Studies of stock returns indicate they are
approximately normally distributed. Two statistics
describe a normal distribution, the mean and the
standard deviation (which is the square root of the
variance). The standard deviation shows how spread
out is the distribution.
 For stock returns, a more spread out distribution
means there is a higher probability of returns being
farther away from the mean (or expected return).
 For our estimate of the expected return, we can use
the mean of returns from a sample of stock returns.
 For our estimate of the risk, we can use the standard
deviation or variance calculated from a sample of
stock returns.
Sample standard deviation and variance
 Sample variance is
a measure of the
squared deviations
from the mean and
is calculated as
follows:
 Sample standard
deviation is just
the square root of
the sample
variance:

T
1
s 2  Var 
Rt - R

T  1 t 1
and
s  SD  Var

2
How to interpret the standard deviation
as a measure of risk
 Given a normal distribution of stock returns …
 there is about a 68.26% probability that the
actual return will be within 1 standard deviation
of the mean.
 there is about a 95.44% probability that the
actual return will be within 2 standard deviations
of the mean.
 There is about a 99.74% probability that the
actual return will be within 3 standard deviations
of the mean.
Summary and conclusions
 We can easily calculate $, %, holding
period, geometric average, and mean
returns from a sample of returns data.
 We can also do the same for a security’s
risk premium.
 The mean and standard deviation
calculated from sample returns data are
often used as estimates of expected returns
and the risk measure for a security or for
the market as a whole.