The Problem with Big Losses

Risky situation must involve a chance of loss.

Suppose the possible returns on an investment fall into a normal distribution curve. This distribution shows this investment has an expected return of 9.5%. Standard statistical thinking tells use if we invest in this stocka nd hold it, some years we will have high rturns and some years low returns, but that, on average, the return will be 9.5%. This assumption is true, but it is also a potentially misleading result.

To see why, suppose an investor buys this stock and holds it 10 years. In each of 9 of those years, the stock advances 20%; in the other year it falls 90%. The 10-year arithmetic average return is 9%, slightly below the return predicted by the distribution. A $1,000 invesment, howver, would be worth only $1,000(1.20)^9*(0.10) = $516, less than the starting value! The compound annual rate of return is a negative 6.40%.

The lesson is that a large one period loss can overwhelm a series of gains. If an initial investment falls by 50%, for instance, it must gain 100% to return to its original value. Big losses complicate actual returns, and investors learn to avoid situations where they may lurk.