The Problem with Losses

The Problem with Losses

Big Losses

This investment has an expected return of 9.50%. Standard statistical thinking tells us if we invest in this stock and hold it, some years we will have high returns and some years low returns, but that, on average, the return will be 9.50%. This assumption is true, but it is also a potentially misleading result.

Suppose an investor buys this stock and holds it 10 years. In each of 9 of these years, the stock advances 20%; in the other year it falls 90%. The 10 year arithmetic average return is 9%
{=(9x20% - 90%)/10}, slightly below the return predicted by the distribution.

In reality, a $1000 investment, however, 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%.

Learning points:

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

Small Losses

Over time, even small losses can be a problem if too many of them occur.

An example will show why. Suppose the proverbial statistical marble jar contains two colors of marbles: red and green. The red marbles symbolize a 10% gain in the stock market, while the green marbles symbolize a 10% loss. If, in simulating an investment and taking a number of marbles from the jar, we draw exactly the same number of red and green marbles, how did the investment fare?

The return is negative, but there is no way to tell how badly things turned out, because what matters is not the proportion of winners to losers, but the number of losers.

As the number of draw increases, the terminal value of the investment declines.

After about 1,000 draws from the jar, the investment is nearly worthless. #

# In the stock market, such an investment could not survive. No security should have an expected return of zero. No one would buy it. Consequently, its price would fall until it offered a return consistent with its risk.

Learnng point:

Over time, even small losses can be a problem if too many of them occur.

Risk and the Time Horizon

There is an important distinction between:

• the probability of losing money and
• the amount of money that you might lose.

Suppose you model a $100 investment by flipping coins. Heads means you win $1, and tails means you lose 50 cents. After one flip, there is a 50% chance of a loss. This declines to 25% after two flips and is down to 12.5% after three flips. After 10 flips, the probability of a loss is only 0.10%.

The maximum loss, however, increases with each succeeding toss of the coin. The maximum loss after one flip is $0.50, after two flips is $1.00 and after three is $1.50.

If you define risk as the probability of losing money, then risk decreases as the time horizon increases.

However, if you define risk as the amount of money you might lose, it increases as the time horizon lengthens.

Learning points:

1. In general, the longer you hold a common stock investment, the lower the likelihood that you will lose money.
2. On the other hand, the longer you hold the investment, the greater the amount you might lose.
3. The extent of the risk depends on how you define it.