Pain Frequency By Kim Zussman

February 5, 2007 |

On 2/5/07, Andrea Ravano wrote:

Evidence from Capuchin Monkey Trading behavior: The study confirms for animals, what behavioral studies have shown for human beings; that to offset a loss of 1 you must have a profit 2.5 times as big. In other words the perception of your pain is greater than that of your pleasure.

That pain of loss is 2.5 greater than pleasure of gain, in absolute terms, has been bandied about in literature for a while. What is the nature of a trader's state of mind as a function of trading (or more specifically, position checking) frequency?

One check on this is to look at the effect of multiplying losses by 2, and comparing with gains scaled at 1. Using SPY returns since 1993, checked average returns for daily, weekly, and monthly intervals:

           Daily       Weekly    Monthly

Ave:   -0.003      -0.005     -0.002

Pos:    1855          411       411

Tot:    3529          730        169

%Pos:    52            56          65

When the "effect" of losses on your soul is double that of gains, you are suffering, on average, in all intervals. Therefore, it is no coincidence there are so many psychologists/psychiatrists involved in trading. Percentage of the positive, however, scales up with longer intervals, so you feel bad less often.

Philip McDonnell adds:

Consider what happens when you lose: How much is required to break even? 

Loss       Required Gain          Ratio
-20%           25%                    1.25
-25              33.3%                 1.33
-50              100                     2.00
-75              300                     4.00

Average Ratio                       2.15

The ratio of how much is required to break even rises rapidly as the losses increase. Although the above unscientific data points appear to be in the ball park of the putative 2.5 ratio, the underlying ratios are clearly non-linear and NOT well described by a simple number. In fact any simple ratio is far too simplistic to be a good measure.

I would argue that a log linear utility function is what an investor, and any rational individual, would want. In their famous paper on Prospect Theory, Kahnemann and Tversky identified what appeared to be irrational behavior on the part of university students and some faculty when presented with hypothetical bets. The Nobel Prize winning professors concluded that the students chose irrationally as compared to the Gold standard of statistical expectations based on an arithmetic utility of money.

But if money compounds, one would want a log utility of money. When the examples cited in the study were recalculated with a log utility based on the relative net worth of typical students the results showed that the student subjects were invariably quite consistent with a log utility function. This re-opens the question: Were the subjects or the professors the irrational ones?

If one expresses the gains and losses in the above table as the natural log of the price relative, then the negative logs of the losses exactly cancel the logs of the gains.

Charles Pennington adds:

These experiments that psychology professors run on students invariably involve the students' winning or losing maybe $100 or less. That's a small amount by any reasonable metric.
$100 is very small, for example, compared with their first year's salary out of school. So it's quite reasonable for the professors to assume that the amount is in the limit of a "small" amount, in the sense that it (1+x) is approximately x if x is "small."

Any reasonable person, offered the opportunity to bet with a 50% chance of winning $250 and a 50% chance of losing $100, should take the bet. That's true even if he only has $250 to his name, because he also has prospects for future earnings.

In this case, the professors are more rational than the monkeys.

J. T. Holley wrote: 

"Could it be that all the bruised and battered hold-outs from '00 - '03 will finally join in, and we resume the incessant trek toward the summit of market-based capitalism?" kz

How about this simple fact: For the first time in recent years that I can remember, the Dow and S&P indexes (headline purposes) outperformed the price appreciation, across America, of houses or real estate. This is roughly a two to one ratio. Now for the sake of simplicity, how many of the '00 - '03 bruised and battered people are going to scratch their heads and say, "twice as much, huh?"

I think the "Confidence Index" mentioned by Carret has a ways to go fellas; but this must obviously be tested.

 Philip McDonnell adds:

"Any reasonable person, offered the opportunity to bet with a 50% chance of winning $250 and a 50% chance of losing $100, should take the bet, and that's true even if he only has $250 to his name, because he also has prospects for FUTURE earnings." 

I would agree that future earnings can be and perhaps should be factored in. But to a freshman with $100 (not $250) the 50% chance of no beer, pizza, and dating for four years might seem an unacceptable risk. Losing it all results in a utility of Ln (zero), the way I look at things. Ln asymptotically approaches negative infinity.

A few points:

1. KT did include some bets in the thousands of dollars.

2. Most of the KT bets were fairly close calls even viewed from an expected arithmetic value as opposed to a log utility.

3. KT never concluded that the indifference ratio was 2.5 or any other number in their ground-breaking paper.


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