Tuesday, February 8, 2011

The Importance of Avoiding Large Stock Market Losses

During the recent crash, the stock market fell 54%; since then, it is up over 80% (as of February 1). Why am I still "underwater"? Seems like a reasonable question to ask.

In a recent post, I observed that since the market low of 6547 in March of 2009, the DJIA (Dow Jones Industrial Average) was up over 80%! Yet, it was still more than 15%, and more than 2000 points, below the all-time high of 14,164. How can an 80% gain be less than a 54% loss? Read on....

The Impact of Large Stock Market Losses

The above chart (click to expand) shows the gain required to offset losses from 0% to 90%. I wanted to go even beyond a 90% loss, but if you want to see what happens beyond that, to paraphrase Roy Scheider, "You're gonna need a bigger chart."

In the chart, losses are indicated on the horizontal axis -- from 0% to 90%. The green line shows the gain needed to offset each loss -- measured on the vertical axis. For example, it takes a 25% gain to recover from a 20% loss. For comparison, the red line just shows the size of the loss in order to emphasize the difference between the size of the loss and the gain required to offset it.

It Takes a 100% Gain to Offset a 50% Loss

The easiest way to think about this is to imagine that your holdings dropped 100%, i.e., to \$0. Would an 100% increase from there get you back to even? Not even close. A 100% increase from \$0 is still ... \$0. (That's why I stopped at a 90% loss.) Or, suppose your holdings dropped from \$10,000 to \$5,000 -- a 50% decrease. A 50% increase from \$5,000 would only get you back to \$7,500; you'd need a 100% increase to get you back to \$10,000.

In the latter case, the fact that you lost \$5,000 does mean that you need to gain \$5,000 to get even -- as you would expect. However, this \$5,000 required gain must be measured against the new starting portfolio of \$5,000 rather than the original \$10,000 portfolio. As a result, the required percentage gain is (\$5,000/\$5,000=) 100%. (For a more detailed explanation of how this works, see the note at end of the post.)

A 50% Loss Will Erase a 100% Gain

Another, and equally depressing, way to use the chart is to determine how large a loss would be needed to erase a given gain. For example, to reverse the earlier example, if you were ahead 100%, what percent would you have to lose to wipe out all of your gains? To find this answer, start at 100% on the vertical axis. Follow the 100% gridline until it intersects with the green line, and read below on the horizontal axis. As you already know, the answer is 50%.

MORAL

It pays to be careful. If you lose 1% of your investment, it only takes a 1.01% increase to recover. If you lose 10%, it only takes an 11.11% gain to recover. However, as you can see, this is not a linear relationship. The larger the loss, the larger the difference between the percentage loss and the percentage gain required to recover. And,the closer your loss gets to 100%, the closer the required offsetting gain gets to infinity! As a result, it is especially important to avoid large losses. Just so there is no confusion, this is not specific to the stock market; all investments behave the same way.

So, what percent increase will we ultimately need to recover from the crash? A little over 116%. And, a 45% loss would wipe out our 80% gain-to-date.

Note: In general, a decrease of 1/n requires an increase of 1/(n-1) to get you even. So, e.g., a decrease of 1/2 (50%) requires an increase of 1/(2-1) = 1/1 = 100%. A decrease of 1/4 (25%) requires an increase of 1/3 (33 1/3%). A decrease of 1/10 (10%) requires an increase of 1/9 (about 11%). Alternatively, a loss of x% requires a gain of 1/((1/x%)-1). So, a loss of 95% requires a gain of 1/((1/.95)-1)=19=1900%.
Note: The Observations Inflation Calculator/Spreadsheet will do these calculations for you. Just as it takes a 100% gain to recover from a 50% loss, 100% inflation translates into a 50% loss in purchasing power.

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