Investments, tenth edition

Stock Price

Portfolio

$95

$100

$105

$110

$115

$120

Portfolio A: All stock

2

5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

Portfolio B: All options

2

100.0

2

100.0

2

50.0

0.0

50.0

100.0

Portfolio C: Call plus bills

2

7.3

2

7.3

2

2.3

2.7

7.7

12.7

 These rates of return are graphed in  Figure 20.5 .  

 Comparing the returns of portfolios  B  and  C  to those of the simple investment in 

stock represented by portfolio  A,  we see that options offer two interesting features. 

First, an option offers leverage. Compare the returns of portfolios  B  and  A.   Unless 

the stock increases from its initial value of $100, the value of portfolio  B  falls pre-

cipitously to zero—a rate of return of negative 100%. Conversely, modest increases 

in the rate of return on the stock result in disproportionate increases in the option rate 

of return. For example, a 4.3% increase in the stock price from $115 to $120 would 

increase the rate of return on the call from 50% to 100%. In this sense, calls are a 

levered investment on the stock. Their values respond more than proportionately to 

changes in the stock value. 

  Figure  20.5   vividly  illustrates  this 

point. The slope of the all-option portfo-

lio is far steeper than that of the all-stock 

portfolio, reflecting its greater propor-

tional sensitivity to the value of the 

underlying security. The leverage factor 

is the reason investors (illegally) exploit-

ing inside information commonly choose 

options as their investment vehicle. 

 

The potential insurance value of 

options is the second interesting feature, 

as portfolio  

C 

 shows. The T-bill- 

plus-

option portfolio cannot be worth less 

than $9,270 after 6 months, as the option 

can always be left to expire worthless. 

The worst possible rate of return on port-

folio  C  is  2 7.3%, compared to a (theo-

retically) worst possible rate of return on 

the stock of  2 100% if the company were 

to go bankrupt. Of course, this insurance 

comes at a price: When the share price 

increases, portfolio  

C, 

 the option-plus-

bills portfolio, does not perform as well 

as portfolio  A,  the all-stock portfolio. 

Rate of Return (%)

100

S

T

−120

−100

−80

−60

−40

−20

0

20

40

60

80

86

88

90

92

94

96

98

100

102

104

106

108

110

112

114

116

118

120

A: All Stocks

C: Call Plus Bills

B: All Options

84