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or eliminated through proper diversification. In the valuation approach that we use, the expected return on a stock depends only on its systematic risk. Beta ( i) is a measure of the systematic risk of an asset. The total stock market as measured by the S&P 500 Index has a beta of 1.0. The beta of a stock with the same price movement as the market also has a beta of 1.0. A stock that has a price movement that is generally greater than the price movement of the S&P 500, such as a technology or Internet stock, has a beta greater than 1.0. A stock with a below-average price movement, such as a public utility, has a beta less than 1.0. Market Risk Premium [E(Rm) Rf] is equal to the expected return on the stock market, the expected return on the S&P 500 Index, minus the rate of return on the risk-free asset, Rf. It is a measure of the increased return that you expect to receive when you buy a stock with average risk in excess of the return on a Treasury bond. Assume that McDonald s stock has a beta equal to the market beta of 1.0. If investors expect an 8 percent return on McDonald s stock, and 10-year Treasury yields are 5 percent, the market risk premium is 3 percent. Market risk premiums increase when investors become more risk averse, and decrease when investors become less risk averse. Standard Deviation of Return ( ): The overall risk of an asset is measured by the variability of its returns. The standard deviation is the statistic that is used to measure how wildly or tightly the actual observed stock returns cluster around the average. Higher standard deviation means wilder fluctuations, more volatility, and greater risk. Although the term sounds intimidating, standard deviation is not difficult to calculate. We measure the standard deviation of a group of returns by taking each observed return, subtracting the average return, squaring the resulting difference, and adding the squares. This gives us the sum of the squares. Next, we divide the sum of the squares by the number of observations minus 1 (one). The result is the variance. Finally, we take the square root of the variance to get the standard deviation of the returns. While this may seem complicated to explain, it is easy to compute using any standard spreadsheet program like Excel, or a handheld calculator with financial functions built in. Furthermore, the interpretation of the standard deviation is much simpler than the calculation. An example may be helpful. Assume that ABC stock has the four yearly returns shown in column 2 of Table 2-1.
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The 10 Principles of Finance and How to Use Them
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TABLE 2-1
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Standard Deviation of ABC s Stock Return
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Observed Return 9.00% 15.00% 3.00% 21.00% 42.00% Average Return 10.50% 10.50% 10.50% 10.50% Deviation of Return 1.50% 4.50% 13.50% 10.50% 0.00% Squared Deviation 0.000225 0.002025 0.018225 0.011025 0.0315
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Year 1 2 3 4 Totals
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The average annual return over the four years is 10.5 percent as shown in column 3. The sum of the deviations around an average is always equal to zero, as shown at the bottom of column 4. The sum of the squares of the deviations divided by (n 1) yields the variance of the returns in this case it is equal to [.0315/(4 1)] 0.0105. The square root of the variance is the standard deviation of the distribution, in this case (0.0105)^(1 2) 10.25 percent. The standard deviation measures the spread of the observations around the average of the returns. A high standard deviation means a big spread of returns and a high risk that the actual return will not equal the expected return. In finance and economics, risk has both positive and negative implications. Normal Distribution: You may remember the grading curve that turned your high school Ds into Bs. The curve is called a bell curve and is a classic example of a normal distribution. Most theories regarding the pricing of financial assets assume that the distribution of returns for an asset follows a normal distribution. The normal distribution is a bell-shaped symmetrical curve. The shape of the curve is determined by two key variables: the average of the observations, and the standard deviation of the observations. In a normal distribution, about two-thirds of the observations will be in a range of plus and minus one standard deviation around the average, and 95 percent of the observations will be in a range of plus or minus two standard deviations around the average. In the case of the stock of ABC, the average return is 10.5 percent and the standard deviation is 10.25 percent. We expect that two-thirds of the observations will be in the range between 10.5 percent plus or minus 10.25 per-
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