8.2 Risk of a Single Asset

LG 2 8.2 Risk of a Single Asset

In this section we refine our understanding of risk. Surprisingly, the concept of risk changes when the focus shifts from the risk of a single asset held in isolation to the risk of a portfolio of assets. Here, we examine different statistical methods to quantify risk, and next we apply those methods to portfolios.

RISK ASSESSMENT The notion that risk is somehow connected to uncertainty is intuitive. The more

uncertain you are about how an investment will perform, the riskier that invest- ment seems. Scenario analysis provides a simple way to quantify that intuition,

scenario analysis and probability distributions offer an even more sophisticated way to analyze the An approach for assessing risk risk of an investment.

that uses several possible alternative outcomes

Scenario Analysis

(scenarios) to obtain a sense of the variability among returns.

Scenario analysis uses several possible alternative outcomes (scenarios) to obtain

a sense of the variability of returns. 2 One common method involves considering range

pessimistic (worst), most likely (expected), and optimistic (best) outcomes and

A measure of an asset’s risk,

the returns associated with them for a given asset. In this one measure of an

which is found by subtracting the return associated with the

investment’s risk is the range of possible outcomes. The range is found by sub-

pessimistic (worst) outcome

tracting the return associated with the pessimistic outcome from the return asso- from the return associated with ciated with the optimistic outcome. The greater the range, the more variability, or the optimistic (best) outcome.

risk, the asset is said to have.

Example 8.2 3 Norman Company, a manufacturer of custom golf equipment, wants to choose the better of two investments, A and B. Each requires an initial outlay of $10,000, and

each has a most likely annual rate of return of 15%. Management has estimated

2. The term scenario analysis is intentionally used in a general rather than a technically correct fashion here to sim- plify this discussion. A more technical and precise definition and discussion of this technique and of sensitivity

PART 4

Risk and the Required Rate of Return

TA B L E 8 . 2 Assets A and B

Asset A

Asset B

Initial investment

Annual rate of return

Most likely

returns associated with each investment’s pessimistic and optimistic outcomes. The three estimates for each asset, along with its range, are given in Table 8.2. Asset A appears to be less risky than asset B; its range of 4% (17% minus 13%) is less than the range of 16% (23% minus 7%) for asset B. The risk-averse decision maker would prefer asset A over asset B, because A offers the same most likely return as B

(15%) with lower risk (smaller range).

It’s not unusual for financial managers to think about the best and worst pos- sible outcomes when they are in the early stages of analyzing a new investment project. No matter how great the intuitive appeal of this approach, looking at the range of outcomes that an investment might produce is a very unsophisticated way of measuring its risk. More sophisticated methods require some basic statis- tical tools.

Probability Distributions Probability distributions provide a more quantitative insight into an asset’s risk.

probability The probability of a given outcome is its chance of occurring. An outcome with

The chance that a given

an 80 percent probability of occurrence would be expected to occur 8 out of 10

outcome will occur.

times. An outcome with a probability of 100 percent is certain to occur. Outcomes with a probability of zero will never occur.