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Unformatted text preview: 0 percent is certain to occur. Outcomes with a probability of zero will never occur. Example­Norman 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. 21 Probability Distributions Probability Distributions 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 are shown in the following Figure . 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. 22 Bar Chart for Asset A and B’s Return Bar Chart for Asset A and B’s Return 23 Probability Distributions Probability Distributions 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. The following figure presents continuous probability distributions for assets A and B. 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. 24 Continuous Probability Distributions Continuous Probability Distributions 25 Risk measurement Risk measurement In addition to considering its range, the risk of an asset can be measured quantitatively by using statistics. Here we consider two statistics—the standard deviation 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 the standard deviation, which measures the dispersi...
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