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The Arithmetic of Loss

When we experience declines like we did in 2008 and the beginning of 2009 it produces a phenomenon wherein our mind is tricked by our common sense orientation to how mathematical calculations should work.

From a high in October 2007 through a low in March 2009, the S&P 500, a broad measure of how large capitalization companies perform during a given period of time, dropped nearly 57%. Common sense would suggest that if we then had a recovery of 57% we would be back to even. In fact, through December 31, 2009, this same S&P index rose 65%, so we might conclude we are back in the black. Unfortunately, a more rigorous examination reveals that we are still significantly underwater.

When using a simple calculator we find a loss of 10% requires an 11.1% gain to return us to even. A 20% loss requires a 25% gain to regain our original starting sum. A 30% loss requires of 42.9% recovery, a 40% loss requires a 66.7% gain and a 50% loss requires a 100% gain to get back to even. Our common sense has us way off the mark unless we have actually worked with numbers like this in the past. This means the loss from October 2008 to the March low of 2009 of 57% requires a 133% rise to move the value of the account back up to its original starting value. This phenomenon is what prompts  some experts to advise an investor to focus more on minimizing losses, which makes recovery a less daunting task, rather than being possessed with having to achieve all of the gains available from a rising market.

Another interesting phenomenon that occurs when you have a significant down year or period of time, is that all of your trailing 1-, 3-, 5-, and even 10-year returns will look poor at best and terrible as the norm. This happened at the end of 2008, when the market had one of the worst one-year declines in our lifetime. Measuring after this decline the trailing 10-year returns for the S&P 500, NASDQ, which is mostly technology, and EAFE, an international index, all showed that you would have lost money over the previous 10 years of investing. Some might use this discovery as a reason to abandon investing all together.  Someone with a more optimistic outlook could have the interpretation that this negative return is historically unusual and therefore suggests that there is a high probability that returns over the coming decade could be quite reasonable. Your interpretation determines your course of action.

The last example we can reflect on, that also tests our common sense, is a period of positive returns followed by a downturn in the market. The technology bubble of 2000-2002 is a perfect example. From January 1997 to December 1999 the NASDQ index rose 215%, which was followed by the three-year cumulative decline of 67.2%. Common sense would still have us well ahead of the game. Unfortunately, the loss is on our original capital as well as all the profits leaving us with a paltry gain of 3.4%.

The learning from all of this is that our common sense may cause us to have expectations that are not connected to the reality of what arithmetically occurs when we experience a loss in the market. If our expectations were properly grounded, we might participate in the journey with a lot less stress and be less prone to taking an action that turns out to be detrimental to our financial well being. 

Jerry Mosher, CFP® is a 30 year veteran of the financial planning industry and is president of Mosher & Ellis Financial Planning in Lafayette, California. He has been selected three times as one of the 150 best financial advisers for doctors by Medical Economics.Jerry may be reached at (925) 284-9470.  Securities offered through AMERICAN INVESTORS COMPANY Member NASD/SIPC.