Tuesday, February 3, 2009

Number Games

When is ten percent not ten percent?

There is a game that gets played when people start talking about peak-to-trough declines. It goes like this: Let's say that the nearest historical parallel to the performance of an asset class is a 50 percent decline, peak to trough, and that the asset class in question has declined 40 percent to date. To reach the 50% mark, what further decline is required?

If you said, 10%, you are right, but only if you are measuring off the peak price. The percentage decline from the current price required to get from 60% to 50% is closer to 16.7%. That's because to drop from 60 to 50 requires a drop of 10/60, or 1/6. A 10% decline from 60% would be a reduction of 6% to 54%. A 16.7% decline from 60% gets you to 50%.

So, it's a common mistake. But not one you'd expect the former chief economist of the IMF to make writing in The Wall Street Journal.

Another common mistake is to take a factoid and mangle it. Assume that it is true that 10% of the residential real estate mortgages in the United States is in default, delinquent or otherwise troubled. That does not mean that 10% of American households are in default, or even that 10% of American homeowners are in default (the home ownership statistic in America is around 2/3rds, and about a third of the homes that are owned are not mortgaged.

Enough of this.

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