3. Sizing by the gap and by your confidence
Level 6: From reading to decision
You now have a written thesis and a criterion that can kill it. What remains is the question that really decides how much you make or lose, and that hardly anyone splits into its two halves: how much you put in.
Two separate questions people roll into one
The first is about the world: how much distance there is between what the price assumes and what you believe. That is the gap, and it depends on the company.
The second is about you: how much confidence your reading really deserves. It depends on how solid your line 4 is, on how many things have to go right and on when you will know.
They are independent. You can have an enormous gap with a flimsy reading and a modest gap with an almost mechanical one. And the dominant mistake is to size on the first alone, with the sentence that has ruined more people than any other: "if I am right, this triples".
An enormous gap is above all a warning
When the reverse reading says that the price of a large, liquid company followed by dozens of analysts builds in a perpetual decline in sales, and you believe it will grow at 6%, your first hypothesis should not be that you have uncovered a collective oversight, but that you have got one input wrong: cost of capital, net debt, diluted shares, leases or pensions, a subsidiary that does not consolidate.
Mauboussin insists that the expectations implied in a price are, on average, a rather good forecast. Not infallible, but good. That is why an enormous gap is information about your model before it is information about the company, and why the size of the gap ought to reduce your confidence, not raise it. The two variables are not merely independent: at the extreme they move in opposite directions.
Add to that the fact that the gap has to be expressed in terms of the driver, not as a headline. "It is worth 180 and trades at 100" is a conclusion; "the price assumes a margin of 15% and I am arguing for 19%" is a gap that can be checked.
Confidence is not a feeling, it is a checklist
Before putting in a single euro, answer these:
- How many drivers does it depend on? One alone is far more reliable than three chained together: if each had a two-thirds probability, three in a row leave less than 30%.
- Can you state, in one sentence, the best argument of the person selling you the share? If you cannot, you do not know the bet; you know your half of it.
- What is the base rate? Of all the companies that have promised to expand their margin by four points in two years, what proportion managed it? If you have no idea, that ignorance is itself data about your confidence. Do not replace it with a made-up figure.
- When does it get settled? The further off the resolution, the less confidence it deserves, because more events capable of invalidating it fit between today and that date.
- Does it depend on arithmetic already in motion or on somebody deciding something? A sales mix that has been shifting for eight quarters is more reliable than a management team that has promised to change strategy.
- How many times have you got this particular kind of reading right, with a written record? If the answer is "I do not know", your confidence is an impression.
A large gap with low confidence does not justify a large position
This is the point the module is named after. A very favorable outcome multiplied by a probability you have invented is still an invented number. And when the resolution is four years away, the cost of being wrong is not just the loss: it is having tied up capital and attention for four years only to discover at the end that line 4 never existed.
The four cases, ordered from best to worst:
- A reasonable gap and high confidence. Where money gets made repeatably, even if it is not spectacular.
- A large gap and high confidence. It exists, it is rare, and it tends to coincide with moments when the price is set by fear rather than by analysis.
- A small gap and high confidence. A small position, or none at all: it may not cover costs, nor the margin of error in your own reading.
- An enormous gap and low confidence. The combination that destroys the most money, because it is the one that looks most like an opportunity.
This far in this course; from here on, the Risk course
This module tells you what size depends on. It does not tell you how to calculate it, what fraction of your capital belongs to each level of conviction, what cumulative drawdown you can tolerate before you are out of the game, or what happens when five positions with different theses actually depend on the same driver. All of that is the content of this academy's Risk and portfolio management course, whose second level is devoted precisely to position sizing. I am not repeating it here; what is worth taking away is that the variable that course handles with formal instruments comes in through this door: confidence.
Worked example (illustrative figures)
Two ideas on the table.
Idea A. A gap of 55%. It depends on three chained drivers, you cannot state the seller's argument, you have no base rate and the resolution arrives four years from now. Honest confidence: 25%. If you are wrong you lose around 35%.
Idea B. A gap of 18%. A single driver, arithmetic already visible in the information published over the last two quarters, resolution in twelve months, and you can explain the opposing argument in one sentence. Honest confidence: 70%. If you are wrong you lose around 10%.
The naive sum, gap times probability, gives 13.75 for A and 12.6 for B, and would pick A. The complete sum includes what happens when you are wrong: A gives 0.25 times 55 minus 0.75 times 35, that is, some twelve and a half points negative, and takes four years to tell you so on top of that. B gives 0.70 times 18 minus 0.30 times 10, some nine and a half points positive, settled within a year.
The triple-sized gap makes up for nothing. And there remains the uncomfortable detail: you put those probabilities in yourself, which is reason enough for the final size to be smaller than either sum suggests.