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Big Losses Followed by Big Gains: The Math of Loss and Recovery
By admin

According to a Bloomberg National Poll conducted March 19–22, 2010, only three of ten investors owning stocks, bonds, or mutual funds say the value of their portfolio had risen over the previous year.

Presumably then, 70% of investors might have been surprised to learn that the Standard & Poor’s 500 Index had gained more than 73% since its low on March 9, 2009.

Several experts were asked what could explain such a huge gap between perception and reality. The reasons given had primarily to do with people’s perceptions being colored by the weak economy and high unemployment. But, another reason may be that a significant percentage gain following a steep decline may not be enough to overcome the loss that people experience.

There is a tendency among investors to measure loss from peak portfolio value rather than from some other starting place, such as the date they opened an account, or from their portfolio’s value as of five years ago. This tendency naturally accentuates the perception of loss. 

Consider how much an asset must gain to recover after it loses 50% in value. If an asset valued at $100 falls to $50, in order for it to climb back to $100, the $50 must double in value—in other words, a 100% gain is required.

The S&P 500 was down 37% in 2008; it followed with a gain of 26.46% in 2009. The difference between the percentage of loss in 2008 and the percentage of gain in 2009 is a little over ten percentage points. But this does not translate into a ten percent loss over the two-year period.

To demonstrate the “math” of loss and recovery: For every $100 invested in the S&P 500 at the beginning of 2008, $63 remained at the end of 2008. Them in 2009, 26.46% of $63 was gained back (+$16.67), leaving $79.67 of the original $100 invested. The S&P 500 Index actually shows a loss of more than 20% for investments made on January 1, 2008 and held through December 31, 2009.

The mathematics of gains and losses may help explain why so many investors are still feeling beaten up by the stock market during the past couple of years, in spite of the tremendous market rally of the past twelve months. It also illustrates the importance of managing a portfolio’s down­side exposure.

R. Kevin O’Keefe, CIMA®, AIF ®
Chief Investment Officer

Posted: April 28, 2010