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STREETSMART GUIDE TO VALUING A STOCK
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Principle 5: When Analyzing Returns, Simple Averages Are Never Simple
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Simple Averages versus Compound Averages
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The fifth principle deals with the math underlying investment returns. We examine the somewhat perverse math that computes investment gains more favorably than comparable investment losses. For example, Martha the portfolio manager tells you that she has good historical investment performance. Two years ago, her portfolio skyrocketed 100 percent. This year things haven t gone as well her stocks lost 80 percent. She states that her average annual return over the past two years is 10 percent a good showing in a tough stock market. Is she correct, or is she a pathological liar Her average yearly return over the past two years is: (100 percent 80 percent)/2 10 percent, as she alleges. Let s check her boast by injecting some real numbers into the analysis. We ll keep the example simple. Let s assume her portfolio consists of one stock, Stock A, which she bought two years ago for $10. Her timing and analysis were impeccable, and Stock A went up to $20 at the end of the first year a return of 100 percent. The next year the stock market tanked, and Stock A dropped 80 percent to $4. When we look at real dollars as opposed to the annual averages, her actual two-year return is negative 60 percent a $10 portfolio shrinking to $4. This is a far worse outcome than one would suspect from the 10-percent average annual performance that Martha is touting. How can this be The problem is embedded in the calculation of simple averages. In fact, if there is a negative percentage in the group, the calculation of a simple average return is biased upward. For example, look again at Table 2-2, which shows the returns and risks for the five asset classes. In each case, the compound annual return, also known as a geometric rate of return, is lower than the simple average return. The compound average return is the correct measure of what you would have received from holding an investment over time. Sometimes, as in the case of Martha s investment performance, the differences between simple and compound averages are substantial. Table 2-4 shows how Martha s investments performed over the past two years. The simple average annual return, or arithmetic mean,
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The 10 Principles of Finance and How to Use Them
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TABLE 2-4 Martha s Investment Performance Simple & Compound Average Returns
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Beginning Value $10 20 Ending Value $20 4 Annual Return 100. % 80. % 20. % Simple Average Return Compound Average Return 10. % 36.75%
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Year 1 2
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is easy to calculate and is equal to the sum of the annual returns (20 percent) divided by the number of returns (2). The compound average return is calculated by (1) dividing the most recent value (A) ($4 at the end of Year 2) by the beginning value (B) ($10 at the beginning of Year 1); (2) taking the resulting ratio to the (1/T) power, where T is the number of years in the compounding period; and (3) subtracting 1.0 to bring it into percentage terms. In math terms, the previous sentence looks like this: [(A/B)^(1/T) 1.0]. The calculation of the compound annual return above is: [($4/$10)^(1/2) 1.0] [(.4)^(1/2) 1.0] [0.6325
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36.75%
Many Investment Professionals Use Simple Averages to Tout Performance
Many investment managers and advisors use simple averages to portray their historic performance. Simple averages are a misleading way to assess investment returns compound or geometric averages are far more representative of actual investment performance. Be careful when you read advertising material that bases performance records upon simple average returns. John Brennan, Chairman of the Vanguard Group, calls simple averages . . . the insidious math . . . of investing. Mr. Brennan says that, Once you lose big, it is very hard to catch up. 5 With simple averages, a larger percentage gain is required to offset a given percentage loss. For example, The Wall Street Journal reports
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