If you drew it correctly, your sketch should look something like this:
Now erase the curve, leaving only points A and B on the page.
Here is the question: Which point is which? Which one lies on the descending side, and which one lies on the ascending side?
You cannot tell. That is not a failure of attention; it is because the two points contain the same information. Their height—their level—does not tell you which side of the curve they occupy. The only thing that can tell you is the slope. And slope cannot be determined by looking at a single point in isolation.
This is a picture of one of investing’s most expensive illusions.
The Two Mistakes Do Not Cost the Same
Suppose you are on the descending side but believe you are on the ascending side. What do you do? You wait.
“There’s still time,” you tell yourself. You interpret the decline as a prelude to a recovery that has not yet arrived.
The reverse can happen, too: you are on the ascending side but believe the curve is falling. You panic, sell too early, and watch the rest of the climb from the sidelines.
Both are mistakes. But they are not equally costly.
Real-world curves are not symmetrical. Improvement often takes time: it is gradual, slow, and demands patience. Deterioration, by contrast, can be swift and steep. A sector may take years to build capacity, only for its market value to collapse in a matter of months. A reputation may take a decade to establish and a weekend to destroy. A health problem may accumulate silently before becoming visible all at once.
The shape is not a parabola. It is a shark fin: a slow ascent followed by a cliff-like descent.
That distinction matters. If you misread the ascending side, the cost of your mistake is time. If you misread the descending side, the cost is capital. Time can be recovered; capital does not come back so easily, because percentage arithmetic does not work in your favor. Lose half your capital, and you need a 100% gain just to get back to where you started.
“Too early” and “too late” may appear on the same sign, but they come with very different bills.
You May Not Know Your Position, but You Can Measure the Derivative
Here is the good news: you do not need to know the answer to the original question. There is a better question to ask.
“Where am I?” is a question you can answer only in hindsight. “Is the slope flattening?” is something you can measure as you go.
And flattening becomes visible before the peak, because the slope is zero at the peak itself.
In practice, this means you should not merely ask whether something is doing well. Look at how quickly it is improving, then compare that rate with the rate of improvement in the previous period.
Do not just ask whether profits are growing. Ask whether the increase in profits is larger than the increase recorded in the previous period.
Do not just ask whether your salary went up. Ask whether this year’s raise is larger than last year’s.
Do not just ask whether business is busy. Ask whether new work is arriving faster than existing work is being completed.
The level reassures you. The second derivative warns you. Often, while the numbers are still setting records, the rate of improvement has already begun to collapse. The peak is when everyone feels best—and that is precisely why it is so hard to recognize as a peak.
The Wrong Solution: Trying to Make Better Predictions
At this point, the natural impulse is to estimate your position more accurately: gather more data, add more indicators, monitor more closely.
That will not solve the underlying problem. Your position is structurally unknowable in real time; if it could be known with certainty, everyone would know it, and the information would already be reflected in the price. If you can see it, thousands of people willing to pay for that insight can see it, too.
The better solution lies elsewhere: build a plan that does not depend on knowing the answer.
Consider three approaches:
Approach | Do you need to know where you are? |
|---|---|
“I’ll sell at the peak.” | Yes—and the answer cannot be known with certainty. |
“I’ll sell when things start to deteriorate.” | Yes—and by then, the signal may arrive too late. |
“I’ll reduce my position by a set amount each year.” | No. |
Why is the third approach more robust? Because it behaves reasonably even when your judgment is wrong. A rule that gradually brings a position toward a fixed target weight sells more as the price rises and, if implemented as a target-weight rebalancing rule, may buy as the price falls. It moves in a disciplined direction without requiring you to identify which side of the curve you are on.
The other two approaches can fail completely if your assessment is wrong.
This principle extends well beyond investing. A good system is not one that works only because you predict the future correctly. It is one that can withstand the possibility that your prediction will be wrong.
“I Don’t Know” Is the Right Answer—but It Is Not Enough
Suppose someone tells me, “We may be approaching the peak, but we are not there yet. In fact, we may already have passed it.”
I would want them to notice the tension within that sentence, because the tension itself conveys information.
If you say both “we are close” and “we may already be past it,” what you are really saying is this: I do not know where we are, and I know that I do not know.
That is an honest and defensible position. The mistake is building a position-dependent plan on top of that uncertainty. Accepting uncertainty and then making a decision that requires the uncertainty to be resolved is a way of deceiving yourself twice.
In Short
The level does not tell you the direction of travel. Two different stories can occupy the same height.
Real-world curves are asymmetric: declines can be steeper than advances. That is why “early” and “late” do not carry the same cost.
Position is easiest to identify in hindsight; slope can be measured as events unfold. The better question is not “Where am I?” but “Is the rate of improvement slowing?”
Do not chase ever-better predictions. Build a rule that does not require you to know the answer.
A good rule is valuable not because it guarantees you will be right, but because it helps you behave sensibly when you are wrong.
Try This
Choose something you track—a business’s revenue, a personal habit, or your savings. Write down the figures for the last four periods, side by side. Then, instead of focusing on the figures themselves, calculate the differences between them.
You will have three changes instead of four raw numbers. If those changes are increasing, the slope is getting steeper. If they are shrinking, the peak may be approaching—even while the headline numbers are still rising.
The calculation takes five minutes. Most people never do it.
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