Topic 3
Risk and Return – part 1
Reading : Chapter 13
Share Market Downturns?
What was the most significant crash of the
Australian share market in recent history?
On October 20 1987, the Australian All
Ordinaries Index fell by approx. 30%
By the end of October 1987, the index fell by
approx 40%
Monthly Performance of Australian Sharemarket
Dec 1979 - May 2003 (accum. index)
20000
18000
16000
14000
12000
Jan 1990
10000
8000
Jan 1987
6000
4000
Dec 1990
2000
Oct 1987
281
273
265
257
249
241
233
225
217
209
201
193
185
177
169
161
153
145
137
129
121
113
105
97
89
81
73
65
57
49
41
33
25
17
9
1
0
Share Market Downturns
 Investors purchasing shares in the Aust. All
Ordinaries index on January 1 1987 and selling
these shares on December 31 1987
lost 7.9% ….the year of the “crash”
 Investors purchasing shares in the Aust. All
Ordinaries index on January 1 1990 and selling
these shares on December 31 1990
lost 17.5% …. No mention of any”crash”
The year following a fall in the market tends to be very strong
Returns from Australian shares for the calendar years 1981-2003
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
-12.9%
-13.9%
66.8%
-2.3%
44.1%
52.2%
-7.9%
17.9%
17.4%
-17.5%
34.2%
-2.3%
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
45.4%
-8.7%
20.2%
14.6%
12.2%
11.6%
16.1%
3.6%
10.1%
-8.1%
15.9%
What are investment returns?
Investment returns measure the
financial results of an investment.
Returns may be historical or
prospective (anticipated).
Returns can be expressed in:
Dollar terms.
Percentage terms.
Dollar Returns
 The gain (or loss) from an investment.
 Made up of two components:
 income, eg dividends, interest payments,
 capital gain (or loss).
 Total dollar return = dividend income + capital
gain (or loss).
Percentage Returns
Dividends paid at
Change in market
+
end of period
value over period
Percentage return =
Beginning market value
Percentage Return Example
Pt = $37.00
Pt+1 = $40.33
Dt+1 = $1.85
$1.85  $40.33 - $37.00
% Return 
$37.00
 0.14 or 14%
Per dollar invested we get 5% in dividends ($1.85/$37)
and 9% in capital gains ($3.33/$37)
- a total return of 14%.
Inflation and Returns
 Real return is the return after taking out the effects
of inflation.
 Nominal return is the return before taking out the
effects of inflation.
 The Fisher effect explores the relationship between
real returns, nominal returns and inflation.
1  R   1  r   1  h
nominal
real
inflation
What is investment risk?
Typically, investment returns are not
known with certainty.
Investment risk pertains to the
probability of earning a return
different from that expected.
The greater the chance of a return far
different from the expected return,
the greater the risk.
Probability distribution
Stock X
Stock Y
-20
0
15
50
Rate of
return (%)
 Which stock is riskier? Why?
Average Returns: The First
Lesson
Risky assets on average earn a risk
premium, ie there is a reward for
bearing risk.
Average Return & standard Deviation
Example
ABC Co experienced the following returns in the last
five years:
Year
1999
2000
2001
2002
2003
Returns
-10%
5%
30%
18%
10%
Calculate the average return and the standard deviation.
Example … continued
Year
1999
2000
2001
2002
2003
Actual
Return
-0.10
0.05
0.30
Average
Return
0.106
0.106
0.106
Deviation
-0.206
-0.056
0.194
Squared
Deviation
0.042436
0.003136
0.037636
0.18
0.10
0.53
0.106
0.106
0.074
-0.006
0
0.005476
0.000036
0.088720
Example (continued)
0.08872
Variance 
 0.02218
5 - 1 
Std deviation  0.02218  0.1489 or 14.89%
The Normal Distribution
Return
-3
-2
-34.07% -19.18%
-1
0
+1
-4.29% 10.6% 25.49%
+2
+3
40.38% 55.27%
Average return = 10.6% Std deviation = 14.89%
Expected Return & Std Deviation
 Expected return - the weighted average of the
distribution of possible returns in the future.
 Std deviation of returns - a measure of the dispersion
of the distribution of possible returns.
 Rational investors like return and dislike risk.
 The quantification of risk and return is a crucial aspect
of modern finance - need to understand the
relationship between risk and return in order to make a
“good” investment.
Example: Calculating
Expected Return
State of
Economy
Boom
Normal
Recession
Pi
Probability
of State i
0.25
0.50
0.25
Ri
Return in
State i
35%
15%
-5%
Expected return  0.25  35%  0.50  15%  0.25  - 5%
 15%
Example: Calculating Std Deviation
Deviation
State of
Economy
Boom
Normal
Recession
(Ri – R)
0.20
0
-0.20
Squared deviation
(Ri – R)2
0.04
0
0.04
2=
  0.02
 0.1414 or 14.14%
Pi x (Ri – R)2
0.01
0
0.01
0.02
Range of Probable Returns
68 %
95 %
-13.28%
0.86%
15%
Mean
return
29.14%
43.28%
Coefficient of Variation
Share A
Share B
Expected Return
8%
15%
Std Deviation
7%
12%
Which asset is preferable?
Coefficient of variation measures risk per unit
of return.
CVA = 0.07/0.08
CVB = 0.12/0.15
= 87.5%
= 80.0%
Share A is more risky.
Share B has less risk for each unit of expected return
Expected Portfolio Return
Portfolio is a collection of assets or
securities
Portfolio Return:
the weighted average return of the
individual securities, the weight being
the fraction of the total funds invested in
each asset
Expected Portfolio Return
EXAMPLE
E(Rp) =
ASSET
1
2
_
Rp =
=
=
_
R
.10
.15
(.55) .10
.1225
12.25%
weight
.55
.45
+ (.45) .15
Portfolio Risk
(Variance or Std Deviation)
The riskiness of a portfolio depends on
a) The measure of risk of each component asset ()
b) The weight of each asset (w)
c) The measure of "co-movement" between returns
of component assets (covariance = 12 )
The Effect of Diversification
on Portfolio Risk
Portfolio returns:
50% A and 50% B
Asset B returns
Asset A returns
0.05
0.05
0.04
0.04
0.04
0.03
0.03
0.03
0.02
0.02
0.02
0.01
0.01
0.01
0
0
-0.01
-0.01
-0.01
-0.02
-0.02
-0.02
-0.03
-0.03
-0.03
0
-0.04
-0.05
Portfolio Risk
 Covariance => r12 1 2  12
- a statistical measure of the degree to which
two assets "co-vary" or move together
- can be positive or negative
 Correlation Coefficient => r12
- a scaled measure of covariance; a standardised
statistical measure of the covariance
+1 => 0 => - 1
r12
= 12
1 2
Correlation Coefficient
• PERFECTLY POSITIVELY CORRELATED RETURNS
where r12  1
- exact proportional movements in the SAME
direction
• PERFECTLY NEGATIVELY CORRELATED RETURNS
where r12  -1
- exact proportional movements in the OPPOSITE
direction
• ZERO CORRELATION
- where r12  0
- there is no relationship between the returns
Correlation
PERFECTLY POSITIVELY CORRELATED RETURNS
R
A
B
t
PERFECTLY NEGATIVELY CORRELATED RETURNS
R
B
A
t
Correlation
ZERO CORRELATION
R
t
Portfolio Risk
For a two asset portfolio
r2 = w1212 + w2222 + 2 w1 w2 r12 1 2
where
and
r 
r12
 correlation coefficient
r12 1 2  12 (covariance)
w1212 + w2222 + 2 w1 w2 r12 1 2
Portfolio Risk
Example
ASSET
Std deviation 
1
2
weight
. 20
. 28
.55
.45
r12 = 0.3
If we ignore the correlation between Asset 1 and Asset 2, the
weighted average risk of the portfolio is:
p2
p
= (0.55) (0.20) + (0.45) (0.28)
= 23.6%
=
0.236
= 48.58%
Ignoring the correlation between each pair of assets in a portfolio is
INCORRECT
Portfolio Risk
Example – taking into account correlation between each
pair of assets in the portfolio
Std deviation 
. 20
. 28
ASSET
1
2
weight
.55
.45
r12 = 0.3
 p2 = (0.55)2 (0.20)2 + (0.45)2 (0.28)2
+ 2(0.55) (0.45) (0.3) (0.20) (0.28)
p
p
=
=
=
0.0363
0.0363
0.1905
= 3.63%
= 19.05%
Portfolio Risk
- for portfolios with more than two assets, the "comovement" between each set of two assets must be
considered
For a three asset portfolio:
p2 = w1212 + w2222 + w3232
+ 2 w1 w2 r12 1 2
+ 2 w1 w3 r13 1 3
+ 2 w2 w3 r23 2 3
p
=
w1212 + w2222 + w3232
+ 2 w1 w2 r12 1 2
+ 2 w1 w3 r13 1 3
+ 2 w2 w3 r23 2 3
Correlation Coefficient
What is the impact of different r12 on portfolio risk?
ASSET
1
2
p 2
 weight
.20
.55
.28
.45
correlation coefficients r12
-1.0, -0.5, 0, 0.5, 1.0
= (0.55)2(0.20)2 + (0.45)2(0.28)2 + 2(0.55)(0.45)(r12)0.20)(0.28)
r12 =
p =
-1.0
0.016
(min. risk)
-0.5
0.12
0
0.17
+0.5
0.21
+1.0
0.24
(max. risk)
Conclusion: As r12 approaches -1,  p approaches zero.