American stocks are at their most expensive in decades

downturn that may or may not materialise. Just buy and hold stocks, and wait for returns that will erase any number of brief dips. Unfortunately, there is a catch.

What matters today is not historical returns but prospective ones. And on that measure, shares now look more expensive—and thus lower-yielding—when compared with bonds than they have in decades. Start with why stocks tend to outperform bonds.

A share is a claim on a firm’s earnings stretching into the future, which makes returns inherently uncertain. A bond, meanwhile, is a vow to pay a fixed stream of interest payments and then return the principal. The borrower might go bust; changes to interest rates or inflation might alter the value of the cash flows.

But the share is the riskier prospect, meaning it needs to offer a higher return. The gap between the two is the “equity risk premium"—the 4.7 percentage points a year that stocks have historically earned over bonds. What of the next few years? Estimating the return on a bond is easy: it is just its yield to maturity.

Gauging stock returns is trickier, but a quick proxy is given by the “earnings yield" (or expected earnings for the coming year, divided by share price). Combine the two for ten-year Treasury bonds and the S&P 500, and you have a crude measure of the equity risk premium that looks forward rather than back. Over the past year, it has plummeted (see chart).

Now consider the equity risk premium’s moving parts: earnings, Treasury yields and share prices. Both expected earnings and Treasury yields are roughly where they were in October, when share prices hit a trough. But since then shares have risen a lot, shrinking their earnings yield and bringing it closer to the “safe" Treasury yield.