The case promised in lesson 1-3, now with the math
From Track 1 lesson 8 (derivative): growth stocks live and die on second derivatives. From the thesis lesson (1-3): NVDA can drop on a great quarter. Now we have the equity valuation tools to actually see why.
The setup. NVIDIA's stock has, throughout 2023-2024, traded at extreme P/E multiples (sometimes 50, 80, even 100+) during the AI boom. From last lesson, that implies r − g in the range of 1-2%. Whatever r the market uses, the implied long-run g has to be staggering — much higher than the broader economy's growth rate.
For that high g assumption to hold, NVIDIA's earnings have to keep growing rapidly. Not just grow — that's necessary but not sufficient. The growth has to be compounding fast enough to maintain the high implied trajectory.
The 2nd derivative game
Track 1 lesson 8 walked through this: growth stocks aren't priced on growth. They're priced on growth of growth. The market builds in not just rapid current growth but accelerating rapid growth. Or at least non-decelerating.
Here's the math. Suppose the market is pricing NVIDIA assuming long-run growth g = 30%. Each quarterly earnings report, the market re-evaluates whether g = 30% still holds.
- Earnings beat by 50%, with management guidance for next quarter pointing to even faster growth →
gstays high or rises. Stock can rise even if the absolute beat is "only" 50%. - Earnings beat by 50%, but next quarter's guidance is "merely" the same 50% →
glooks stuck in the market's eyes. The 2nd derivative just turned to zero. Stock drops. - Earnings beat by 50%, next quarter guidance is for 30% growth →
gvisibly decelerating. Stock crashes.
So you can have an "amazing earnings beat" headline and a stock crash. The headline measures the 1st derivative; the market is reacting to the 2nd derivative.
Putting it in Gordon Growth math
Suppose pre-earnings, the market priced NVDA assuming r = 10% and g = 8% (implying r − g = 2%, P/E ≈ 50). Earnings come out, beat estimates. Numerator (this year's earnings) goes up. But guidance says next quarter's growth is going to be "only" 7%. That's still huge in absolute terms. But the market re-evaluates and shifts g down to 7%. Now r − g = 3%, implying P/E ≈ 33. Stock has to drop ~30% even though absolute earnings rose.
This is what people mean when they say "growth stocks are priced for perfection." Any deceleration, even from "amazing" to "merely great," breaks the math.
What this means for investors
If you're long a high-P/E growth stock, you're betting on continued acceleration (or non-deceleration). Any signal that growth is slowing — even if the company is still healthy — can crush the stock. The math doesn't care about absolute health; it cares about the trajectory.
This isn't a recommendation either way. It's about understanding what you're actually buying. A P/E of 50 is a bet on g staying very high for a very long time. If you don't believe that, the math says you're overpaying.
The opposite case (Adobe — next lesson) is when the market goes from believing g is high to believing g is gone. Even bigger crash. Same math, even more dramatic effect.
The takeaway
NVDA dropping on a beat is the math of high-P/E growth stocks. They embed an implicit g that's already high. Any deceleration in growth — even from "incredible" to "merely amazing" — turns the 2nd derivative against the trade and the stock drops. Headlines react to the 1st derivative; the math reacts to the 2nd. The thesis lesson promised this picture; here's the equity-valuation version.