I hope none of you reading this has ever played Russian roulette. It might be a good bet when using arithmetic averages (on average, you win five out of six times), but according to geometric averages, you're a lot better off not playing Russian roulette. Sooner or later, you'll lose -- and you only need to lose once to lose everything.
Losing a chunk of your capital is not nearly as deadly, but I believe investors should approach portfolio losses with the same trepidation. That's why you need to calculate your investment returns using geometric averages and -- even more importantly -- why you need an investment strategy that minimizes downside risk and prevents total loss of capital.
Arithmetic vs. geometric averages
Most of the averages in life -- NBA scoring averages, student grade point averages, etc. -- are arithmetic. An arithmetic average is the sum of the outcomes divided by the number of outcomes. For example, the arithmetic average of 10%, 9%, and 11% is 10%. Here's the math:
(0.10 + 0.09 + 0.11) / 3 = 0.10, or 10%
Arithmetic averages measure independent events -- where one outcome is independent of the next. However, for dependent events such as Russian roulette, where if you lose one round, you don't survive to play the next, geometric averages should be used.
To calculate a geometric average, multiply "n" outcomes instead of adding them, and take the nth root of that product instead of dividing by "n." If that sounds confusing, let's go back to our simple example.
If your portfolio returns over the next three years are 10%, 9% and 11%, then the arithmetic average of this would be 10%. The geometric return, however, would be calculated differently. Here's that math:
(1.10 x 1.09 x 1.11)^(1/3) = 1.0999, or 9.99%
Remember that we're adding (and then subtracting) 1 here so we can work with negative percentages. And although this result is almost equivalent to the arithmetic average, there are key differences.
Let's go to the next level
With arithmetic averages, any single negative outcome is not as significant because it is "averaged out." If an NBA player, for example, averages 18 points per game but goes scoreless one game, he can make up for that bad game by scoring 36 points in the next game. With geometric averages, however, a single bad outcome has an exponentially larger effect.
For example, suppose you had the following portfolio returns for the next five years: 20%, 60%, 100%, 50%, and -90%. The arithmetic average of this is 28%. Here's the math:
(0.20 + 0.60 + 1.00 + 0.50 - 0.90) / 5 = 0.28, or 28%
Now, 28% average returns are incredible, and they'd have investors begging you to take their money. (For perspective, consider that Warren Buffett has averaged 21.5% average annual gains since 1965.)
The key difference is that the arithmetic average here is meaningless. Why? Because that last year, when you lost 90%, you lost almost all of your portfolio. Here's the true average annual return picture, calculated geometrically:
(1.20 x 1.60 x 2.00 x 1.50 x 0.10)^(1/5) = 0.896, or -10.4%
This makes sense, because as anybody who was invested during the dot-com bubble knows, a single really bad year can wipe out years of hard work and good returns. (Suddenly, Buffett's 21.5% annual average is looking a little more impressive.)
Maximize geometric returns
The math above should show you why you need to avoid bad years at all costs: They're incredibly difficult to recover from.
So what can Foolish investors do? Glad you asked:
- Avoid stocks with large downsides.
- Buy stocks with limited downsides.
After all, that modus operandi is precisely what made Buffett such a great investor. He's focused on finding cheap stocks with limited downside but decades' worth of adequate upside. And you can follow his lead. Just ask yourself when you make a purchase: If I'm right, how much will I make? And if I'm wrong, how much will I lose? To be a great value investor, you should only invest when what you could potentially make is at least 20%, and what you could potentially lose is no more than 10%.
Stocks to avoid
While growth investors might have more fun, they also stand to lose the most. High-P/E, high-growth stocks such as Crocs
Investing in "hot" stocks or industries like these can be like flipping a coin: You win some, you lose some. This isn't a great way to maximize geometric returns.
Stocks to consider
Instead, I believe investors should look for out-of favor companies that fulfill basic human needs. Three companies I've been studying recently that fit the bill are Mohawk
If you'd like some more stock ideas that fit the value investing profile, try our Motley Fool Inside Value service free for 30 days. You'll find a list of great companies in stable industries selling at cheap prices. In turn, that limits downside risk, provides ample upside, and maximizes geometric returns. Sound good? Just click here for more information.
This article was originally published on Nov. 7, 2006. It has been updated.
Fool contributor Emil Lee is an analyst and a disciple of value investing. He doesn't own shares in any of the companies mentioned above and appreciates your comments, concerns, and complaints. Overstock is a former Rule Breakers recommendation. The Motley Fool has adisclosure policy.