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STREETSMART GUIDE TO VALUING A STOCK
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EXHIBIT 2-1
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cent or 20.75 percent to 0.25 percent. We also expect that 95 percent of the observations will be between 10.5 percent plus or minus (2 * 10.25 percent), or 31 percent to 10.0 percent. If the distribution of the returns of ABC stock over time is normal, it would appear as in Exhibit 2-1. Congratulations! If you made it through the preceding discussion of variance and standard deviation and you re still reading, you ve already survived the densest material you will encounter in this book. These concepts are to modern finance what Newton s laws of motion are to black holes both are theories that are crucial to understanding some very dense matter. Now, let s review a study that examines the relationship between the expected rate of return of an asset and the risk of receiving that return.
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The Ibbotson and Sinquefield Study
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Professors Roger Ibbotson and Rex Sinquefield1 calculated historical annual rates and distributions of returns from 1925 until 2001 on the following classes of investments: 1. U.S. Treasury bills with a three-month maturity 2. U.S. government bonds with an average 20-year maturity 3. High-quality corporate bonds with an average 20-year maturity
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The 10 Principles of Finance and How to Use Them
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TABLE 2-2
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Compound Annual Return 3.80% 5.30% 5.80% 10.70% 12.50% Simple Average Annual Return 3.10% 3.90% 5.70% 6.10% 12.70% 17.30% Std. Dev. of Return 3.20% 9.40% 8.60% 20.20% 33.20%
U.S. Treasury Bills U.S. Treasury Bonds Corporate Bonds Large Company Stocks Small Company Stocks
4. Large cap common stocks as represented by 500 of the largest companies in the United States 5. Small cap common stocks as represented by the smallest twenty percent of the companies listed on the NYSE The results of the study are important and show the direct relationship between the expected return of an asset and the risk associated with receiving that return. Table 2-2 presents the summary statistics for returns on the five asset classes. The average return is calculated on a compound average and simple average basis, the difference between which we describe in Principle 5. Risk is measured by the standard deviation of returns. The I&S Study demonstrates the direct trade-off between return and risk. An investment in a Treasury bill with no default risk and little price volatility has a lower expected average return (3.8 percent) than a large cap stock (10.7 percent). The Treasury bill also has a lower risk measure 3.2 percent relative to a portfolio of large company stocks with a standard deviation of 20.2 percent. Returns on individual stocks can swing more wildly than the portfolios shown in Table 2-2. For example, we showed how the price of Internet Capital Group fell from $200.94 per share to $0.36 per share in a brief period of time. As shown below in Exhibit 2-2, on average, investing in common stocks and accepting risk have increased returns significantly. When we think about risk, most of us focus only on negative outcomes losing a job, breaking a leg while skiing a double black dia-
STREETSMART GUIDE TO VALUING A STOCK
EXHIBIT 2-2
Risk versus Return Line
mond on Ajax Mountain, or being gored while running with the bulls in Pamplona. In economics and finance, risk is measured by assigning equal probability to both negative and positive outcomes. As we discussed, we typically calculate the risk of an investment by its standard deviation. The measure of risk is the same if the observed return exceeds the average return by 10 percent or if it is 10 percent below the average return.
Return versus Risk: Our Recommendation
When deciding whether to buy or sell a stock, we assess whether the probabilities of positive or negative surprises are equal, or whether the probabilities of reward or risk are skewed in a particular direction. Over time, there is a tendency for the return and risk of the markets to revert to their average levels, a concept known as reversion to the mean. For example, the returns on the S&P 500 over the 1995-1999 period were as follows: 37.4 percent, 23.1 percent, 33.3 percent, 28.6 percent and 21 percent. The average annual return over this five-year period was 28.7 percent the best five-year run in the history of the stock market! However, the average annual return for large company stocks over the long run, as we can see from Table 2-2, has been about 12 percent.
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