Wednesday, March 28, 2012

A Theory of What Drives Typical Investors

While thinking about the curious tendency for investors to feel more comfortable owning stocks when they are expensive, an idea occurred to me. Perhaps our mental arithmetic is calculating the wrong things. To explain the idea, I need to make a brief detour into sports.

Sports fans are familiar with the idea of “stealing a game.” The home team jumps out to an early lead and holds that lead for almost the whole game. At the end, the visitors finally catch up and take a small lead just as the game ends. Most fans feel that the home team somehow deserved to win because they held the lead so long, and the visitors stole the game.

This feeling is completely irrational, but it is prevalent anyway. The visiting team scored more total points, so they deserved to win. Why should points scored late in a game be worth less than points scored early in the game?

One model of how fans feel about a game is to take a snapshot of the score difference (with a negative value if the visitors lead) every minute and average these differences over the whole game. Then the team that seems to deserve to win is determined by whether this average is positive or negative.

This model gives more value to points scored early in the game, which is ironic considering that players who score points late in a game are judged to be more heroic. No fan would agree to an explicit statement that early points are worth more, but their gut feel about who deserves to win a game seems to implicitly value early points more.

What if this type of gut feel carries over to investing? Suppose that for a given year, a stock index started at 10,000, took a bone-rattling drop to 6000 by mid-year, and then recovered to 11,000 by year-end. An investor who held an ETF based on this index from the beginning of the year to the end with no trading made a 10% return. Ordinarily, a 10% return with low inflation is a fairly good year, but it may not feel this way.

Investors would have been beside themselves with worry over the excruciating 40% drop. If their gut feel tends to be based on the average price over the year as an emotional measure of how the year went, it would feel like they suffered big losses. The end of year price recovery more than compensates for the loss in reality, but perhaps only partially compensates for the emotional loss because the average index level for the year was around 8000 or so.

Consider a market timer who sold on the way down at 8000, and bought back in as the index rose again to 9000. If he started with $90,000, then he owned ETFS worth 9 times the index level. After the index dropped to 8000, he cashed out $72,000. When the index bottomed and then recovered back to 9000, he bought back in with his $72,000 (and owned 8 times the index level). The index finished at 11,000 leaving the market timer with $88,000 for a $2000 loss (2.2%) on the year.

The market timer’s return is obviously a lot worse than the buy-and-hold investor’s return of 10%, but the emotional model makes a different calculation. The market timer was out of stocks while the market was at its worst going from 8000 down to 6000 and back up to 9000. He avoided the worst of the pain and sleepless nights. The market timer feels better than the buy-and -hold investor even though his results are significantly worse.

So, the conjecture is that investors’ feelings about investments are affected by the average value of their holdings over a period of time. I don’t know if this idea has any validity, but it does seem to explain some peculiar investor behaviour.

3 comments:

  1. This video from Greg Davies of Barclay's Wealth Management adds to your theory and explains it from a behavioural viewpoint.

    http://gbgorr.wordpress.com/2012/03/21/using-behaviourial-finance-in-managing-clients-portfolios/

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  2. @Gary: Thanks for the link to the very interesting video of Davies' talk. I really like the idea of a middle ground between rational investing and optimizing for behavioural biases. The message seems to be that we should optimize a rational function with the constraint that an investor may make some irrational choices. Rather than make people the most comfortable that we can make them, we make them the most money we can make them given that they make certain investing mistakes.

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  3. That makes a lot of sense. I like this psycho-philosophical stuff -- I've been known to engage in it myself.

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