American stocks are at their most expensive in decades

livemint.com:

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.