Risk of a Single Asset

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 Risk of a Single Asset:

The concept of risk can be developed by first considering a single asset held in isolation. We can look at expected-return behaviors to assess risk, and statistics can be used to measure it. 

Risk Assessment:

Sensitivity Analysis (Scenario Analysis) and Probability Distributions can be used to assess the general level of risk embodied in a given asset.

Sensitivity Analysis:

Sensitivity analysis uses several possible-return estimates to obtain a sense of the variability among outcomes. One common method involves making pessimistic (worst), most likely (expected), and optimistic (best) estimates of the returns associated with a given asset. In this case, the asset’s risk can be measured by the range of returns. The range is found by subtracting the pessimistic outcome from the optimistic outcome. The greater the range, the more variability, or risk, the asset is said to have.

Although the use of sensitivity analysis and the range is rather crude, it does give the decision maker a feel for the behavior of returns, which can be used to estimate the risk involved. 

Example:

Norman Company, a custom golf equipment manufacturer, 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 made pessimistic and optimistic estimates of the returns associated with each. The three estimates for each asset, along with its range, are given in Table 5.3. Asset A appears to be less risky than asset B; its range of 4% (17% - 13%) is less than the range of 16% (23% - 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). 


Probability Distributions:

Probability distributions provide a more quantitative insight into an asset’s risk. The probability of a given outcome is its chance of occurring. An outcome with an 80 percent probability of occurrence would be expected to occur 8 out of 10 times. An outcome with a probability of 100 percent is certain to occur. Outcomes with a probability of zero will never occur.

A probability distribution is a model that relates probabilities to the associated outcomes. The simplest type of probability distribution is the bar chart, which shows only a limited number of outcome–probability coordinates. The bar charts for Norman Company’s assets A and B.

Although both assets have the same most likely return, the range of return is much greater, or more dispersed, for asset B than for asset A—16 percent versus 4 percent. If we knew all the possible outcomes and associated probabilities, we could develop a continuous probability distribution. This type of distribution can be thought of as a bar chart for a very large number of outcomes.

Presents continuous probability distributions for assets A and B.7 Note that although assets A and B have the same most likely return (15 percent), the distribution of returns for asset B has much greater dispersion than the distribution for asset A. Clearly, asset B is more risky than asset A.

Example:

Norman Company’s past estimates indicate that the probabilities of the pessimistic, most likely, and optimistic outcomes are 25%, 50%, and 25%, respectively. Note that the sum of these probabilities must equal 100%; that is, they must be based on all the alternatives considered.



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