Lesson 16 of 25 · 7 min
Overconfidence, and calibration on the position you know best
Familiarity narrows the range a person will state without narrowing the range prices actually travel.
Calibration is the match between stated confidence and observed accuracy. A well-calibrated 90 percent range contains the outcome nine times in ten. Overconfidence is the state in which the stated range is narrower than the accuracy justifies, and it is strongest for the subject a person knows most about.
The concentrated holding is that subject almost by construction. It has been followed for years, its results are read as they are published, and the detail accumulated is real detail. What familiarity supplies is the resolution of the picture. What it does not supply is any reduction in the volatility of the price.
Compare a stated range with an implied one. Suppose a holder puts a 90 percent range on a year-ahead price at $118 to $164. The midpoint is $141 and the half-width is ($164 − $118) ÷ 2 = $23, which is $23 ÷ $141 = 16.3 percent. Now take the same holding at an illustrative 34 percent annualised volatility. A 90 percent interval spans about 1.645 deviations either side, so the half-width is $141 × 1.645 × 0.34 = $78.86, giving a range of $62.14 to $219.86.
The stated range is $23 ÷ $78.86 = 29.2 percent as wide as the price history implies. Both cannot be right. A range that covers less than a third of the implied distribution is not a 90 percent range; it is closer to a 35 percent one, and it is the range against which a draw gets sized.
Knowledge of a company and knowledge of its price are different quantities. Only the second one has a width, and the width comes from the tape rather than from the research.
Key terms
- Calibration
- Whether stated confidence matches observed accuracy. A calibrated 90 percent range is wrong one time in ten, by design.
- Confidence interval
- A range stated with a probability attached. Its width is the claim; the midpoint is almost incidental.
- Implied range
- The interval a volatility figure produces for a given horizon and confidence level. Computed from price behaviour rather than from opinion.
Worked example
A stated range against the one the volatility implies
A 90 percent year-ahead range of $118 to $164, on a holding with an illustrative 34% annualised volatility.
- Midpoint of the stated range
- $141
- Stated half-width
- $23
- Deviations in a 90 percent interval
- 1.645 either side
- Implied half-width
- $78.86
- Implied range
- $62.14 to $219.86
- Stated width as a share of implied width
- 29.2%
($118 + $164) ÷ 2.
16.3 percent of the midpoint.
$141 × 1.645 × 0.34.
$23 ÷ $78.86.
The label on the range said 90 percent. The width said something closer to a third of that, and the width is the part that has consequences.
Check yourself
A holder states a 90 percent year-ahead range of $118 to $164 for a stock with 34 percent annualised volatility. How does that range compare with the one the volatility implies?
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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.