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  1. 100A central bank cuts rates by 50 basis points. For a stock valued as next year's earnings divided by (r minus g), with the required return r falling from 12% to 11.5% and growth g at 7%, what happens to the fair P/E? And why might the market fall anyway?Valuation riddlesCorePIMCOLos Angeles · 2024

    Try it first

    What happens to the fair P/E if growth stays at 7%?

    Show the worked solution

    The fair P/E rises from 20x to about 22.2x, about 11%, if growth holds. P/E equals 1 over (r minus g): 1/0.05 is 20x and 1/0.045 is 22.2x. But a cut often comes because the economy is weakening. If growth expectations fall to 6.5%, the gap is back to 5 points and the P/E is unchanged; at 6%, the P/E falls to 18.2x. The market may also have priced the cut in already.

    Why does a small rate cut move the P/E so much?

    Think of a ladder leaning against a wall: move its foot a few centimetres when it is nearly upright and the top barely moves; move it when the ladder is almost flat and the top drops a long way. The P/E depends on the gap between the required return and growth, and when that gap is small, a half-point change in it moves the P/E by a large fraction. Here the gap goes from 5 points to 4.5, a tenth smaller, and the fair P/E rises by about 11%.

    The relationship
    PE=1r−g10.12−0.07=20.0x  →  10.115−0.07=22.2x\frac{P}{E} = \frac{1}{r - g} \qquad \frac{1}{0.12 - 0.07} = 20.0\text{x} \;\rightarrow\; \frac{1}{0.115 - 0.07} = 22.2\text{x}
    P/Ethe price over next year's earnings
    rthe return investors require, falling from 12% to 11.5%
    gthe long-run growth rate of earnings, 7%
    What it says in wordsThe fair multiple is one over the gap between the required return and growth, so narrowing the gap lifts the multiple.
    A rate cut raises fair value only if growth holdsGrowth holds at 7%20.0xBeforer 12%22.2xAfter the cutr 11.5%+11.1%The cut signals weaker growth20.0xBeforeg 7%20.0xAfterg 6.5%18.2xAfterg 6%-9.1%
    With growth held at 7%, the cut lifts the fair P/E from 20.0x to 22.2x, but if the cut comes with growth expectations falling to 6.5% the P/E stays at 20.0x, and at 6% it drops to 18.2x, 9% below where it began.

    So why might the market fall on a rate cut?

    Three reasons, all visible in the formula. First, growth: central banks usually cut because they see the economy slowing, and if the market lowers its growth estimate by as much as the cut lowers r, the gap and the P/E do not change at all; lower it by more and the P/E falls, to 18.2x at 6% growth. Second, expectations: if a 50 basis point cut was fully expected, it was already in the price, and only the surprise moves the market; a cut smaller than hoped can disappoint. Third, earnings themselves: E in the ratio is next year's earnings, and a weakening economy can lower that number even as the multiple rises.

    Say the simplification. Writing P/E as 1 over (r minus g) assumes all earnings are paid out and growth is steady forever; with partial payout, the numerator is the payout ratio instead of one. The direction of every effect survives, but the sizes are illustrative. The general point holds firmly: a rate cut raises fair value only if what it says about growth does not undo it.

    Where candidates lose it

    The common slip is assuming the P/E rises by about the size of the cut, half a percent. The P/E moves on the gap between r and g, and a half-point change in a five-point gap shifts the P/E by about 11%.

    The other loss is answering only the first half. The question is designed to test whether you know why markets can fall on good-sounding news: say that a cut carries information about growth, and that expected cuts are already in the price.

    What the interviewer asks next

    • What growth rate would leave the fair P/E exactly unchanged after the cut?
    • Why does the same cut matter more for a high-growth stock than for a low-growth one?
    • How might a rate cut affect a bank's earnings differently from a consumer company's?

    Asked at PIMCO, Product & Strategy, Los Angeles, 2024 (Wall Street Oasis): had only one 'technical' question about the effect of a rate cut on equity prices