The Ugly Math of One Bad Year

Here’s an easy riddle:

Up.
Down.
Down some more.
Up.
Down – in a hurry.
Up.
Up again.
Down, then up in the same day.

Who am I?

a. A schizophrenic
b. The stock market
c. A roller coaster
d. All of the above

Those answering “a” or “d” may want to consider professional help. Those answering “c” are having more fun than the rest of us. But for all those who quickly identified with “b,” keep reading. You may not be aware of the exact numbers, but you probably understand stock markets have been somewhat erratic in the past few months. They move up, they move down; there’s no significant trend. Combined with the fall-out from the sub-prime mortgage situation, some people warn that investors may be on the verge of sustaining some substantial losses. Historically, this would not be an unusual occurrence.  Recessions, depressions, and bear markets have been a regular part of the financial landscape just as much as upward trends, booms and bull markets.  History suggests that even with the ups and downs, the long-term returns are worth it so we have been conditioned to accept some losses along the way. But that doesn’t mean that financial losses – from any financial decision – are trivial things. Losing money is a concept that perhaps doesn’t get as much attention as it should in financial programs, but in many ways, the losses you incur may have a greater impact on your total wealth than the gains you make.  There are a number of mathematical examples to illustrate this idea.

Here’s a simple illustration.

Suppose you have $10,000 in some non-guaranteed financial vehicle (i.e., the account values may fluctuate). For three years in a row, the account delivers a 10% annual return. At the end of the third year, your account would have grown to $13,280. Here’s the progression:

Beginning balance: $10,000 Annual Return
End of Year 1: $11,000 + 10%
End of Year 2: $12,100 + 10%
End of Year 3: $13,310 + 10%

So far, so good. But let’s assume that in the fourth year you experience a loss, which while not desired, was not wholly unexpected.  The loss is 10%. Your account balance drops to $11,979.

Beginning balance: $10,000 Annual Return
End of Year 1: $11,000 + 10%
End of Year 2: $12,100 + 10%
End of Year 3: $13,310 + 10%
End of Year 4: $11,979 – 10%

Three out of four years you gained 10%, right? But consider the impact of the one bad year: The average annual return was more than halved. Through the first three years, the average annual return was 10%. But the one bad year reduces the average annual return for the four-year period to just 4.62%! In order to get back to averaging 10% a year, your investment must earn over 34% in the fifth year! Look at the math. Here’s what comes from five years of steady 10% annual returns:

Beginning balance: $10,000 Annual Return
End of Year 1: $11,000 + 10%
End of Year 2: $12,100 + 10%
End of Year 3: $13,310 + 10%
End of Year 4: $14,641 + 10%
End of Year 5: $16,105 + 10%

But if there’s a blip in the fourth year, making up for it in one year requires a steep increase.
Beginning balance: $10,000 Annual Return
End of Year 1: $11,000 + 10%
End of Year 2: $12,100 + 10%
End of Year 3: $13,310 + 10%
End of Year 4: $11,979 – 10%
End of Year 5: $16,111 + 34.5%

Even if you don’t try to recover the loss in one year, it would take six years of earning 13.5% each year to average 10% for 10 years – all because of one bad year.
Beginning balance: $10,000 Annual Return
End of Year 1: $11,000 + 10%
End of Year 2: $12,100 + 10%
End of Year 3: $13,310 + 10%
End of Year 4: $14,641 + 10%
End of Year 5: $16,105 + 10%
End of Year 6: $17,716 + 10%
End of Year 7: $19,487 + 10%
End of Year 8: $21,436 + 10%
End of Year 9: $23,579 + 10%
End of Year 10: $25,937 + 10%

Beginning balance: $10,000 Annual Return
End of Year 1: $11,000 + 10%
End of Year 2: $12,100 + 10%
End of Year 3: $13,310 + 10%
End of Year 4: $11,979 – 10%
End of Year 5: $13,626 + 13.5%
End of Year 6: $15,500 + 13.5%
End of Year 7: $17,631 + 13.5%
End of Year 8: $20,055 + 13.5%
End of Year 9: $22,813 + 13.5%
End of Year 10: $25,950 + 13.5%

In the conventional paradigm, the opportunity for increased return comes with increased risk. Thus, you could argue that increasing your annual return to 13.5% from 10% means increasing the risk by 35%. Remember, this is all the result of one bad year! Frankly, there’s very little market appeal to “loss prevention” – high rates of return grab headlines. (In today’s economic climate, how interested would you be in an accumulation vehicle that averaged only 4.62% over four years?) But if you really care about maximizing your wealth, you should expend some planning energy on avoiding
losses. The fewer setbacks, the less you have to “catch up.”