Constructing a stock-versus-bond regime from earnings yields

Convert the equity into an earnings yield

An earnings yield is constructed by dividing earnings per share by price and expressing the result as a percentage, which inverts the price-to-earnings ratio so equity income can be compared with a Treasury yield. A $1 earnings-per-share figure on a $20 price produces a price-to-earnings ratio of 20 and an earnings yield of 5 percent.

As of mid-June 2004, the 10-year Treasury yield used as the bond-side comparison was about 4.75 percent.

Map the Treasury rate into fair-value and risk-adjusted P/E

Fair-value price-to-earnings is constructed by treating the interest rate as an earnings yield, so a 4 percent rate implies a 25.0 multiple and a 10 percent rate implies a 10.0 multiple. That fair-value P/E is the reciprocal of the Treasury rate.

A risk-adjusted price-to-earnings multiple is the reciprocal of the interest rate multiplied by 1.3, reflecting an average historical 30 percent discount from that fair-value multiple. The scaling keeps uncertain earnings from being treated as equivalent to guaranteed Treasury coupons. The extra expected return required for variable earnings versus a risk-free Treasury yield is the equity risk premium.

The gap between actual and fair-value price-to-earnings has varied widely, from a 95 percent discount in 1941 to a 160 percent premium in 2001.

Read the position inside the yield-gap regime

A yield-gap regime is a cross-market state defined by whether equities are cheap or expensive relative to the rate-implied P/E, and whether earnings growth or price adjustment is closing that gap.

The usual inverse stock-bond link follows from earnings yields needing to rise with interest rates, through lower prices, higher earnings, or both, with the dominant channel depending on the business cycle. Rising rates need not force lower equity prices at once, because stronger demand for money can lift earnings fast enough to offset a contracting multiple until higher rates later slow spending.

Apparent breaks in inverse correlation can occur when equities are still closing a large gap to fair value even as rates fall, as after the 2000 valuation extreme.

Keep the slower secular rate cycle in view

Secular interest-rate trends typically last for decades, with historical bottoms identified in 1898 and 1946. A secular rate cycle of that length can dominate shorter business-cycle swings in earnings and valuation.