Probability Distributions
by MaestriAn event’s probability is defined as the chance that the event will occur. For example, a weather forecaster might state, “There is a 40 percent chance of rain today and a 60 percent chance that it will not rain.” If all possible events, or outcomes, are listed, and if a probability is assigned to each event, the listing is called a probability distribution.
The possible outcomes are listed in Column 1, while the probabilities of these outcomes, expressed both as decimals and as percentages, are given in Column 2. Notice that the probabilities must sum to 1.0, or 100 percent.
Probabilities can also be assigned to the possible outcomes (or returns) from an investment. If you buy a bond, you expect to receive interest on the bond plus a return of your original investment, and those payments will provide you with a rate of return on your investment. The possible outcomes from this investment are (1) that the issuer will make the required payments or (2) that the issuer will default on the payments. The higher the probability of default, the riskier the bond, and the higher the risk, the higher the required rate of return. If you invest in a stock instead of buying a bond, you will again expect to earn a return on your money. A stock’s return will come from dividends plus capital gains. Again, the riskier the stock—which means the higher the probability that the firm will fail to perform as you expected—the higher the expected return must be to induce you to invest in the stock.
With this in mind, consider the possible rates of return (dividend yield plus capital gain or loss) that you might earn next year on a $10,000 investment in the stock of either Martin Products Inc. or U.S. Water Company. Martin manufactures and distributes routers and equipment for the rapidly growing data transmission industry. Because it faces intense competition, its new products may or may not be competitive in the marketplace, so its future earnings cannot be predicted very well. Indeed, some new
company could develop better products and literally bankrupt Martin. U.S. Water, on the other hand, supplies an essential service, and because it has city franchises that protect it from competition, its sales and profits are relatively stable and predictable.
The rate-of-return probability distributions for the two companies are shown in Table 3-1. There is a 30 percent chance of strong demand, in which case both companies will have high earnings, pay high dividends, and enjoy capital gains. There is a 40 percent probability of normal demand and moderate returns, and there is a 30 percent probability of weak demand, which will mean low earnings and dividends as well as capital losses. Notice, however, that Martin Products’ rate of return could vary far more widely than that of U.S. Water. There is a fairly high probability that the value of Martin’s stock will drop substantially, resulting in a 70 percent loss, while there is no chance of a loss for U.S. Water.
Taken From : Five-Minute MBA – Corporate Finance
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