Lesson 24 of 25 · 6 min
The asymmetry of attention between a rising month and a falling one
Checking a balance more often when it is up produces a record of a year that the year did not have.
Attention to a position is not constant, and it is not random either. It correlates with the direction of the position, which means the sample of moments a holder has actually observed is drawn with a bias built into the sampling.
Count it. Over twelve months a holding rises in 7 and falls in 5, so 7 ÷ 12 = 58.3 percent of the months were up. Suppose the account is opened 14 times during rising months and 3 times during falling ones. Of the 17 observations, 14 ÷ 17 = 82.4 percent occurred while the position was rising. The remembered year is 82.4 percent favourable and the actual year was 58.3 percent favourable, a gap of 24.1 points created by nothing but when the page was opened.
The magnitudes compound the effect rather than offsetting it. Suppose the 7 rising months averaged 3.4 percent and the 5 falling months averaged −5.1 percent. Compounding gives 1.034^7 = 1.264 and 0.949^5 = 0.770, and 1.264 × 0.770 = 0.973. The year ended down 2.7 percent.
So a year that finished 2.7 percent lower was observed in a state of increase on five sixths of the occasions it was observed at all. Both of those sentences describe the same twelve months. One of them is a measurement and the other is a sampling artefact, and the artefact is the one available to memory.
Under a pledge the same asymmetry applies to the figures that matter most. Headroom is checked when it is comfortable and checked again after a call, with the interval in between unobserved — which is exactly the interval during which the interval was closing.
Key terms
- Sampling bias
- A pattern in which observations are taken makes the sample unrepresentative of what it is drawn from, regardless of how many are taken.
- Attention asymmetry
- Looking more often when the news is good. It changes the record without changing a single underlying figure.
- Compounding
- Chaining percentage moves by multiplication. A run of gains and a run of losses do not cancel by addition.
Worked example
A year remembered and the same year measured
Twelve months: 7 up at an average 3.4%, 5 down at an average −5.1%. Seventeen account openings, 14 in up months.
- Share of months that rose
- 58.3%
- Share of observations in rising months
- 82.4%
- Gap created by the sampling
- 24.1 points
- Compounded effect of the up months
- ×1.264
- Compounded effect of the down months
- ×0.770
- Full-year result
- −2.7%
7 ÷ 12.
14 ÷ 17.
1.034^7.
0.949^5.
1.264 × 0.770 = 0.973.
Five sixths of the year was observed rising and the year fell. No figure was misreported and no statement was wrong.
Check yourself
A holding rose in 7 months averaging 3.4 percent and fell in 5 averaging −5.1 percent. What did the year return, and why might it be remembered as a good one?
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.