Understanding The Math Behind
Investment Losses
Most investors spend
their lives focused on average annual returns. But average returns hide
the critical role of portfolio volatility. It's compound returns, determined
by the degree of market ups and downs, that ultimately matter. And that's
where big investment losses really hurt.
Consider two portfolios. One loses 25% the first year, then surges
back with a 75% gain the next. The other portfolio gains 20% the first
year, and 30% the second. Where would you rather put your money? In
terms of average annual returns over two years, both portfolios did
equally well. The average of -25 and 75 is 25; so is the average of
20 and 30. But that doesn't mean their performance was equal.
Suppose each portfolio starts with $100,000. After the first year,
having lost 25%, Portfolio 1 is worth $75,000. Then, after the 75% gain,
its value rises to $131,250. Meanwhile, Portfolio 2 returns 20% the
first year, boosting its value to $120,000. Moving ahead an additional
30% the second year, it's worth $156,000. Portfolio 1 has a compound
return of 31%-no match for the 56% of Portfolio 2.
Where did that extra $24,750 come from? It's the bonus you get for
avoiding investment losses. Though this example is an extreme case,
it illustrates a basic principle of investing: To progress steadily
toward your objectives, you need to minimize setbacks along the way.
That's why diversification is so important. By spreading your investment
bets among several kinds of assets, you potentially reduce your portfolio's
volatility.
 During
the technology stock boom of the late 1990s, many investors didn't care
about volatility. They couldn't resist concentrating their portfolios
in the high-risk sectors that had posted several years of phenomenal
returns. These investors probably figured that even if returns later
tailed off, surely it was better to go for the biggest gains rather
than settle for lower returns, even if they were more sustainable.
As it turned out, though, it wasn't better. Consider again two hypothetical
portfolios worth $100,000. Each one earned an average of 10% a year
during the past 10 years. But one was invested aggressively, earning
22% a year during the mid- to late-1990s and then losing 2% a year during
the past five years. That makes it worth $244,300 today.
The second portfolio didn't aim so high. It earned 12% a year for two
years, then gained 11% the next two, 10% the two after that, then 9%
for two years, and 8% in the final two years. Though averaging 10% gains
like the first portfolio, this one is now worth $259,160. That's a 159.2%
compounded return versus 144.3% for the more aggressive portfolio. As
so many investors learned during the bear market, slow and steady really
does win the race.
What makes losses so bad? A little investment math shows that you need
to earn more than you lose on a percentage basis to get back to even.
Suppose you have $10,000 and lose 10%, leaving you with $9,000. To get
back to where you started, you now need not a 10% gain on the $9,000-that
gives you only $900, for a total of $9,900. It takes an 11% return to
restore the original value of your holdings. And the bigger the loss,
the harder it is to get your money back. If you lose 40% of your $10,000,
taking you to $6,000, you need a return of almost 67% to catch up. If
you lose 50% of your investments, you have to double your money-a 100%
return-to get back to even.
What's unnerving about the math behind investment losses is that you
may not realize how much risk you're taking when putting your money
in volatile investments. "This is a case where the risk is worse than
people think," says Donald Gjerdingen, a professor at Indiana University-Bloomington.
"You don't want to take on risk based on false assumptions."
The bottom line is the deeper the holes your portfolio has to crawl
out of, the harder it is for you to achieve your financial goals. The
more you can smooth out the ups and downs of your portfolio returns,
the more money you'll end up with in the long run.
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