11-18-06 - 2

The way everyone talks about stock and pricing past performance is completely wrong. The NYT says housing prices from 1950 to 2000 have gone up 3.5% per year in San Francisco (inflation adjusted). That sounds like you're getting a 50 year average and that should be a pretty stable number. In fact it's not at all. People do the same thing with stocks, they look at the average rate of return over an X year period. The problem with this is that it's incredible sensitive to exactly when you pick your start & ending point, which means you're incorporating a huge random factor.

Imagine your value(time) function was a sine function. The correct average rate of return is 0. However, depending on where you put your start and end, it could be largely positive or negative. In particular, with SF housing, if you looked at 1950 to 1998 you would see maybe a 2% annual gain. If you looked at 1950 to 2005 you would see a 5% annual gain. The problem is that the time span we're looking at is not very large compared to the magnitude of the noise. Take the ending price minus the starting price is super sensitive to the short term noise.

A much better way is to best-fit a line through the prices and take the slope of the line. This is way less sensitive to the edge effects. There are probably even better statistical ways, but it seems nobody does this even though it's totally obvious and everyone should do this.

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