Financial Markets and Institutions (2-downloads)

increase in wealth raises the quantity demanded of an asset.

Expected Returns

In Chapter 3 we saw that the return on an asset (such as a bond) measures how much

we gain from holding that asset. When we make a decision to buy an asset, we are influ-

enced by what we expect the return on that asset to be. If an Exxon-Mobil Corporation

bond, for example, has a return of 15% half of the time and 5% the other half of the

time, its expected return (which you can think of as the average return) is 10%.

More formally, the expected return on an asset is the weighted average of all possi-

ble returns, where the weights are the probabilities of occurrence of that return:

(1)

where

R

e

= expected return

n = number of possible outcomes (states of nature)

R

i

= return in the ith state of nature

p

i

= probability of occurrence of the return R

i

R

e

⫽ p

1

R

1

⫹ p

2

R

2

⫹ p ⫹ p

n

R

n

What is the expected return on the Exxon-Mobil bond if the return is 12% two-thirds of

the time and 8% one-third of the time?

Solution

The expected return is 10.68%.

where

p

1

=

probability of occurrence of return 1 

= = 

0.67

R

1

=

return in state 1 

= 12% = 0.12

p

2

=

probability of occurrence return 2 

=

= 0.33

R

2

=

return in state 2 

= 8% = 0.08

Thus,

R

e

⫽ 1.672 10.122 ⫹ 1.332 10.082 ⫽ 0.1068 ⫽ 10.68%

1

3

2

3

R

e

⫽ p

1

R

1

⫹ p

2

R

2

E X A M P L E   4 . 1 Expected Return

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66

Part 2 Fundamentals of Financial Markets

If the expected return on the Exxon-Mobil bond rises relative to expected returns

on alternative assets, holding everything else constant, then it becomes more desir-

able to purchase it, and the quantity demanded increases. This can occur in either

of two ways: (1) when the expected return on the Exxon-Mobil bond rises while

the return on an alternative asset—say, stock in IBM—remains unchanged or 

(2) when the return on the alternative asset, the IBM stock, falls while the return

on the Exxon-Mobil bond remains unchanged. To summarize, an increase in an