| Fun with Compounding continued... |
| Time is compounding's magic wand. Over short periods of time, compounding produces a little extra return, but nothing to write home about. Over long periods of time, however, compounding produces incredible results. A commonly used example is the case of the doubling penny: Assume you invest a penny at the start of a month and earn a 100% return on your investment each day. If you didn't reinvest your earnings each day, you'd finish the month with 31 cents--almost enough to buy a stamp. If you reinvested all your earnings, however, and let compounding work its magic, you'd wind up with $10.7 million [$0.01 x (2.00)30]--enough to build an entire post office. |
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| Of course, daily 100% returns exist only in the realm of swindles and hypothetical examples. Returning to reality, let's consider the difference between the returns of stocks and bonds. Although it's tempting to use recent stock market performance for our comparisons, we'll probably be disappointed if we do--the past five years represent a significant aberration from the historical averages. Instead, we'll use the annualized returns of U.S. stocks and bonds from 1926 through 1996, as reported by Ibbotson and Associates. Over this time period, stocks have returned a little more than double what bonds have returned: 10.7% annualized for the stocks versus 5.1% annualized for the bonds. |
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| In an average year the average stock investor earned approximately twice as much as the average bond investor. Over time, however, compounding magnifies that difference greatly. After 30 years, the difference in the final value of a $10,000 portfolio invested in stocks, versus a $10,000 portfolio invested in bonds is no longer twofold, it's closer to fivefold: |
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| $10,000 x (1.051)30 = $44,500 (a 345% increase) |
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| Big deal, you might say, everyone knows intuitively that there's a huge difference between a 5% return and a 10% return. But even relatively small differences in rates of return translate into large differences in the end values of portfolios when compounded for many years. Suppose two investors each have $10,000 to invest, and a 30-year time horizon. Investor A opts to invest all of her money in stock mutual funds of her choosing. Investor B chooses to invest his $10,000 via a "wrap" account where a broker selects the mutual funds and charges 1% a year for his services. The investor initially balks at this fee, but he is told not to worry about it. After all, it's only one measly percentage point a year--it won't make that much of a difference. The broker proceeds to select the same funds that the first investor did. |
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| Let's assume that these funds return 10% each year for 30 years. The second investor's yearly return, however, is reduced to 9% by the wrap fee. |
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| Investor A's portfolio: |
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| $10,000 x (1.10)30 = $10,000 x 17.45 = $174,500 |
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| Investor B's portfolio: |
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| $10,000 x (1.09)30 = $10,000 x 13.27 = $132,700 |
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| Difference in portfolio values = $41,800! |
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| We're not trying to pick on brokers, active managers, or anyone else. However, even a seemingly small fee can be a huge drag on your portfolio. To be fair, let's calculate another example in which we assume that the broker is absolutely brilliant, and his picks outperform Investor A's portfolio by 2% each year. After accounting for the wrap fee, Investor B's return is 11%, and his final portfolio value is $54,400 larger than Investor A's. |
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| $10,000 x (1.11)30 = $10,000 x 22.89 = $228,900 |
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| Obviously, one percent in either direction results in big differences. The question is, which direction is more likely? | |
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