Earnings yield, rate correlation and regression for equity value

A three-step hygiene check

TradersWeek editorial: before treating a foreign equity market as an obvious calamity, run a three-step valuation hygiene check. Invert the headline multiple into a local earnings yield, watch rolling price-to-rate correlation for regime decay, then read a two-factor earnings-and-rates residual as a dated warning rather than as a crash headline.

In early 1987 Japanese price-to-earnings ratios were described as well above 60 while U.S. ratios were in the low 20s, and the October 1987 decline was larger in New York than in Tokyo.

Invert the headline multiple

The case study treats earnings divided by price, not price divided by earnings, as the first valuation measure because the latter inverts the earnings-to-cost relationship. That earnings yield is the arithmetic inverse of a price-to-earnings ratio.

A price-to-earnings ratio is treated as an inverted and incomplete screen unless it is turned back into a yield and compared with local rates.

Compare the yield with local rates

The second valuation step compares that earnings rate with short-term and long-term interest rates rather than judging the multiple in isolation.

Over a six-year window, Japanese price-to-earnings ratios sat near 50 or 60 for about half the observations, a visual that looks extreme until the inverse earnings yield is placed next to Japanese rates.

Watch the rolling price-to-rate link

Correlation analysis here is a rolling statistical measure of how tightly monthly average equity prices co-move with earnings or with interest rates, including how that tightness can fade before a later decline.

Correlations were computed on a rolling 50-month window. A value of +1 means two series move together, -1 means they move in opposite directions, and 0 means no measurable linear link.

For several years monthly average Japanese equity prices showed a correlation of about +0.8 with earnings and about -0.8 with interest rates. That tight negative price-to-rate correlation decayed about a year before the later market slip, and the plotted relationship stayed high until just before the 1990 decline.

Read the two-factor residual as a dated warning

Linear regression here is a fitted relationship that treats equity prices as the outcome and earnings plus interest rates as the explanatory inputs, producing a dated implied level against which the market can be compared.

A linear regression with equity prices as the effect and earnings plus interest rates as the causes produced a fitted value that moved below price from early 1989 as Japanese rates rose. That regression-implied value marks stretches when the market traded above the estimated relationship.

Except for a brief late-1987 stretch tied to high bond rates, the fitted series was not below price for most of the sample and in many months led price higher.

TradersWeek editorial: read the stretch when price stood above the fitted path as a dated warning, not as a crash headline.

A high multiple is not a self-explanatory break

Intermarket analysis here means reading one country's equity multiples against that country's interest-rate alternatives, and against a higher-rate market, instead of treating a foreign price-to-earnings number as self-explanatory.

The intermarket reading is that higher U.S. interest rates require higher equity earnings yields, so a low-rate Japanese market can carry high multiples without that contrast alone proving a valuation break.