Lecture 7
Introduction to Risk, Return, and the
Opportunity Cost of Capital
Managerial Finance
FINA 6335
Ronald F. Singer
Topics Covered
 72
Years of Capital Market History
 Measuring Risk
 Portfolio Risk
 Beta and Unique Risk
 Diversification
7-2
The Value of an Investment of $1 in 1926
5520
Index
1000
S&P
Small Cap
Corp Bonds
Long Bond
T Bill
1828
55.38
39.07
14.25
10
0.1
1925
1933
1941
1949
1957
1965
1973
1981
1989
1997
Year End
7-3
The Value of an Investment of $1 in 1926
613
203
Index
1000
Real returns
S&P
Small Cap
Corp Bonds
Long Bond
T Bill
10
0.1
1925
6.15
4.34
1.58
1933
1941
1949
1957
1965
Year End
1973
1981
1989
1997
7-4
Rates of Return 1926-1997
Percentage Return
60
40
20
0
-20
Common Stocks
Long T-Bonds
T-Bills
-40
-60 26
30
35
40
45
50
55
60
Year
65
70
75
80
85
90
95
7-5
Measuring Risk

Variance - Average value of squared
deviations from mean. A measure of
volatility.

Standard Deviation - Average value of
squared deviations from mean. A
measure of volatility
7-6
Measuring Risk
Coin Toss Game-calculating variance and standard deviation
(1)
(2)
(3)
Percent Rate of Return Deviation from Mean Squared Deviation
+ 40
+ 30
900
+ 10
0
0
+ 10
0
0
- 20
- 30
900
Variance = average of squared deviations = 1800 / 4 = 450
Standard deviation = square of root variance =
450 = 21.2%
7-7
1
2
-30 to -20
3
2
50 to 60
4
40 to 50
13
30 to 40
20 to 30
11
10 to 20
12
0 to 10
-10 to 0
-20 to -10
1
-40 to -30
13
12
11
10
9
8
7
6
5
4
3
2
1
0
-50 to -40
Measuring Risk
# of Years
13
10
Return %
7-8
Measuring Risk

Diversification: Strategy designed to reduce
risk by spreading the portfolio across many
investments.
 Unique Risk: Risk factors affecting only that
firm. Also called “diversifiable risk.”
 Market Risk: Economy-wide sources of risk
that affect the overall stock market. Also
called “systematic risk.”
7-9
Measuring Portfolio Return
Portfolio rate
of return
=
+
fraction of portfolio
in first asset
fraction of portfolio
in second asset
x
x
rate of return
on first asset
rate of return
on second asset
7-10
Portfolio standard deviation
Measuring Risk
0
5
10
15
Number of Securities
7-11
Portfolio standard deviation
Measuring Risk
Unique
risk
Market risk
0
5
10
15
Number of Securities
7-12
Portfolio Risk
The variance of a two stock portfolio is the sum of
these four boxes:
Stock 1
Stock 1
Stock 2
x 12σ 12
x 1x 2σ 12 
x 1x 2ρ 12σ 1σ 2
Stock 2
x 1x 2σ 12 
x 1x 2ρ 12σ 1σ 2
x 22σ 22
7-13
Example
Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s.
The expected dollar return on your BM is .10 x 55 = 5.50 and
on McDonald’s it is .20 x 45 = 9.00. The expected dollar return
on your portfolio is 5.50 + 9.00 = 14.50. The portfolio rate of
return is 14.50/100 = .145 or 14.5%. Assume a correlation
coefficient of 0.15. Assume the Standard Deviation of BM is
17.1%, and of McD is 20.8%
Bristol - Myers
McDonald' s
x1x 2ρ12σ1σ 2  .55  .45
2 2
2
2
Bristol - Myers x1 σ1  (.55)  (17.1)
 0.15 17.1 20.8
x1x 2ρ12σ1σ 2  .55  .45
2
McDonald' s
x 22 σ 22  (.45) 2  (20.8)7-14
 0.15 17.1 20.8
Example
Portfolio Variance  [(.55) 2 x(17.1) 2 ]
 [(.45) 2 x(20.8) 2 ]
 2(.55x.45x 0.15x17.1x 20.8)  202.5
Standard Deviation  352.1  14.2 %
Compare this Standard Deviation to that of the individual securities
Expected Portfolio Return  (x 1 r1 )  ( x 2 r2 )
Portfolio Variance  x12σ 12  x 22σ 22  2( x1x 2ρ 12σ 1σ 2 )
7-15
Portfolio Risk
The shaded boxes contain variance terms; the remainder contain
covariance terms.
1
2
3
To calculate
portfolio
variance add
up the boxes
4
STOCK
5
6
N
1
2
3
4
5 6
STOCK
N
7-16
Beta and Unique Risk
1. Total risk =
diversifiable risk +
market risk
2. Market risk is
measured by beta,
the sensitivity to
market changes.
Expected
stock
return
beta
+10%
-10%
- 10%
+10%
-10%
Expected
market
return
7-17
Beta and Unique Risk
 Market
Portfolio - Portfolio of all
assets in the economy. In practice a
broad stock market index, such as
the S&P Composite, is used to
represent the market.
- Sensitivity of a stock’s return
to the return on the market portfolio.
 Beta
7-18
Beta and Unique Risk
 im
Bi  2
m
Covariance with the
market
Variance of the market
7-19