Principles of Managerial Finance

CHAPTER 5 Risk and Return 221

standard deviation (k)
The most common statistical
indicator of an asset’s risk; it
measures the dispersion around
the expected value.

05 7 9 1113151719212325

Probability Density

Return (%)

Asset B

Asset A

FIGURE 5.3

Continuous Probability
Distributions
Continuous probability
distributions for asset A’s
and asset B’s returns

expected value of a return (k)
The most likely return on a given
asset.

8. Although risk is typically viewed as determined by the dispersion of outcomes around an expected value, many
   people believe that risk exists only when outcomes are below the expected value, because only returns below the
   expected value are considered bad. Nevertheless, the common approach is to view risk as determined by the vari-
   ability on either side of the expected value, because the greater this variability, the less confident one can be of the
   outcomes associated with an investment.


9. The formula for finding the expected value of return, k,when all of the outcomes, kj,are known andtheir related
   probabilities are assumed to be equal, is a simple arithmetic average:





n

j 1

kj (5.2a)

n

where nis the number of observations. Equation 5.2 is emphasized in this chapter because returns and related prob-

abilities are often available.

returns for asset B has much greater dispersionthan the distribution for asset A.

Clearly, asset B is more risky than asset A.

Risk Measurement

In addition to considering its range,the risk of an asset can be measured quanti-

tatively by using statistics. Here we consider two statistics—the standard devia-

tion and the coefficient of variation—that can be used to measure the variability

of asset returns.

Standard Deviation

The most common statistical indicator of an asset’s risk is thestandard deviation,

k,which measures the dispersion around theexpected value.^8 Theexpected value

of a return,k,is the most likely return on an asset. It is calculated as follows:^9

k

n

j 1

kjPrj (5.2)

where

kjreturn for the jth outcome

Prjprobability of occurrence of the jth outcome

nnumber of outcomes considered

k