|Outcome||Probability of Outcome||Assumptions|
The probabilities in Table 13-1 may be based on past experience, industry ratios and trends, interviews with company executives, and sophisticated simulation techniques. The probability values may be easy to determine for the introduction of a mechanical stamping process in which the manufacturer has 10 years of past data, but difficult to assess for a new product in a foreign market. In any event, we force ourselves into a valuable analytical process.
Based on the data in Table 13-1, we compute two important statistical measures—the expected value and the standard deviation. The expected value () is a weighted average of the outcomes (D) times their probabilities (P).
The expected value () is $600. We then compute the standard deviation—the measure of dispersion or variability around the expected value:
The following steps should be taken:
The standard deviation of $190 gives us a rough average measure of how far each of the three outcomes falls away from the expected value. Generally, the larger the standard deviation (or spread of outcomes), the greater is the risk, as indicated in Figure 13-3. You will note that in Figure 13-3 we compare the standard deviation of three investments with the same expected value of $600. If the expected values of the investments were different (such as $600 versus $6,000), a direct comparison of the standard deviations for each distribution would not be helpful in measuring risk. In Figure 13-4 we show such an occurrence.
The investment in panel A of Figure 13-4 appears to have a high standard deviation, but not when related to the expected value of the distribution. A standard deviation of $600 on an investment with an expected value of $6,000 may indicate less risk than a standard deviation of $190 on an investment with an expected value of only $600 (panel B).
Figure 13-3 Probability distribution with differing degrees of risk
We can eliminate the size difficulty by developing a third measure, the coefficient of variation (V). This term calls for nothing more difficult than dividing the standard deviation of an investment by the expected value. Generally, the larger the coefficient of variation, the greater is the risk. The formula for the coefficient of variation is numbered 13-3.
For the investments in panels A and B of Figure 13-4, we show:
We have correctly identified investment B as carrying the greater risk.
Another risk measure, beta (β), is widely used with portfolios of common stock. Beta measures the volatility of returns on an individual stock relative to the stock market index of returns, such as the Standard & Poor’s 500 Stock Index.3 A common stock with a beta of 1.0 is said to be of equal risk with the market. Stocks with betas greater than 1.0 are riskier than the market, while stocks with betas of less than 1.0 are less risky than the market. Table 13-2 presents a sample of betas for some well-known companies from 2008 to 2013. We note that betas are not stable over time.
Table 13-2 Average betas for a five-year period (ending February 2015)
|Walmart Stores Inc.||0.36|
|Philip Morris International||0.57|
|Exxon Mobil Corp.||0.79|
|Nike Inc. Cl B||0.89|
|The Walt Disney Co.||1.15|
|Ford Motor Co.||1.80|
|Bank of America Corp.||2.56|