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"average" Total Returns ?

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Despite a Math degree, it did not occur to me for years (decades really) that year to year returns can not be averaged using addition to get a cumulative total return. The most important factor in growth, few if any negative years. They cause too much of a hit to the growth.


Why, because year to year, it is a multiplication factor on the money.


Start with $100. Gain 20%, you have $120.

Lose 20%, you have .80 * $120 = $96.


Is average return 0% ? No. Its -2%. Average of down $2 each year.


Continue, gain 50%, you have $144. Next lose 16.6%, you have $120 again.


Four years. Moved from $100 to $120. Looks like 5% a year to me. But as a 4th root, its actually a little less, 4.7%


+20, -20, +50, -16. Adding, its looks like +70-36 = +34, averaging about 8.5%, not +20% total and 4.7%.


To check a real cumulative return over a multi-year period, you need to add or subtract the decimal to 1.00, and multiply them all. For average ? You need the nth root. Use Excel or some other calculator that lets you do any root you want.


Why ? That speculative fund with the occasional huge returns, but occasional losses, comes down to a very mundane average very quickly. Turns out a consistent real return of 10% or 12% is far more impressive than you think.


Work with the consistent funds. Don't even bother looking at the big returns. I've done some of both, got lucky for awhile, then got burned. Now I've picked a few funds with nice low to mid teen long term returns, and few negative years. Better late than never.

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LJ Wager,

Great post. Couple of questions from this non math expert.

Is this calculation related to what you are saying?

You have $100,000 and the market pulls back and you lost $50,000=50% loss.

However, to regain you money to the original $100,000 the market has to grow 100%. It seems like you need twice as much to get back to $100,000. The down years are worse than the good years by looking at percents only.

Why look at percents? Perhaps, another the way around looking at the averaging of percents is to calculate what you started with, for example, $100,000 and after ten years, you have $200,000. 100% gain/10 years = 10% gain per year. The market could have gone up and down, it doesn't matter. Or does it? Its what you started with and what you ended with and divide the gain per year. I am quite sure I missed something.




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I think what you are really looking for is an equivalent yield, which is an annualized interest rate. You would take the initial investment as the starting value, and the final value, including reinvestment of all dividends, and plug them into a yield function. You may be able to get one of the Excel YIELD functions to do it.

I've done it in the past just for fun on the Dow Jones average (getting something like a 5.###### return over long periods, not including reinvestment of dividends) using PV or FV functions and iteratively plugging in interest rates until I got close to the right values.

Obviously, this may not be extremely helpful for predicting future income (what is?), but it will let you compare results to other investments over the same time period, such as money market or bonds.

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100% gain over 10 years might be 10% a year if you don't compound, which you do.


To figure that , for simplicity just use the Rule of 72. If it takes 10 years to double, then 72/10 = 7.2, your return in that case is about 7.2 % a year. A 10% return will double in about 7.2 years. Use a calculator, or Excel, and calculate 1.072 to the 10th power. You'll get 2.004. 1.10 to the 7.2 and you get 1.986.


But yes, those negative years are extremely punishing. If you eliminate funds based on negative return years, it makes fund selection far more simple, and considering a spiking fund just provides profits to market timers who will sell when and extract profit way too often for the casual investor to be able to do very well.


The "boring" funds actually produce superior returns in the long haul. If you can be an active trader, you can do more risky things, but then it is a "Do un to others before they do un to you." Let those people take advantage of each other. Look for consistency, and primarily positive returns. But if they are too high, then they will be the new darling, and they'll more tha likely have returns diminish, in a few years, if not in just one. I played that game somewhat successfully, then got burned.


After some success with American Funds, I shifted to Robertson Stephens funds about 10 years ago, and I got about 20+% returns for about 4 years. I then shifted to Weitz, which had had 30+% for the same period, and a $25,000 minimum. Well, Weitz had 1 good years followed by a series of bad years. When it came back after 5 years to where it had been after the first year gain, I shifted to a more sedate but regular upward fund. At least now I have a higher limit on Roth contributions, and am within 6 years of being able to take funds out, if I wanted, tax-free. But If I work 11 more years, I'll try to max the Roth contributions.


Even then, I'll just withdraw funds occasionally, and continue to let it grow.


By the way. I had a triple bypass last year. Everyone exercise 5 times a week 30 minutes minimum, break a sweat, and eat your fruits, vegies, and a low fat diet.



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