Wieviel Taschengeld bekommt ihr von eurer Frau ?

Taschengeld???

What I thought would be an uncontentious statement proved quite the opposite. People have told me that there has to be a relationship between interest rates and earnings on equities. So how, they ask, can the yield/earnings ratio not be telling us something? The answer is that what the ratio says, if anything, depends on why it is changing.

Earnings on equity are a claim on a share of profits. Profits are derived from real activity, more precisely on a company's ability to use real things (its assets and its inputs) to make real things (its outputs). But the yield on a conventional government bond is a promise to pay a given stream of money until maturity. That yield will depend on the real interest rate and inflation. The real interest rate will depend, in turn, on time preference and the prospective rate of economic growth. The inflation component will depend on expected inflation and inflation risk. Inflation is a sustained rise in the general price level, not a change in relative prices.

To simplify, consider an irredeemable bond issued with a coupon of $7 and a face value of $100, when the expected real rate of interest is 3 per cent and expected inflation is 4 per cent. Suppose expected inflation falls to 2 per cent. If one ignores rounding errors, the price of the bond rises to $140 and the yield falls to 5 per cent. The owner of the bond has made a $40 capital gain - but the yield for any new purchaser gives the same real return as before.

Now what does the fall in inflation do to the earnings yield and price of an equity? To simplify, the answer is absolutely nothing. To see this, assume for simplicity that the real return demanded from equities is the same as the real interest rate - the "equity risk premium" is zero. Assume also that the pay-out ratio is 100 per cent. The price of an equity expected to give earnings this year of $3 is $100. If inflation were to be 4 per cent, next year's equity price would be $104. If inflation were 2 per cent, next year's price would be $102. If one purchased a share and sold it next year, the money return would be $7 and $5, respectively, with $3 from the earnings and $4 and $2, respectively, from the rise in the price. The nominal and real returns would be the same as on the bond, as required.

If inflation falls, the ratio of the bond yield to the earnings yield will fall but there will be no effect on the price of equities now. The change in the yield ratio will also say nothing about the advisability of buying shares. All it does is indicate an alteration in the expected path of future nominal earnings and equity prices.

That is the theory. What about reality? The era of disinflation, from the early 1980s to the late 1990s, was a period when bond yields and earnings yields both fell. In contrast, the era of rising inflation between 1948 and 1968, saw a rise in bond yields and a fall in earnings yields. In Japan, in the 1990s, there has been no relationship: bond yields have collapsed with no visible effect on the earnings yields on equities.

This is a broken indicator. So why is there ever a relationship? To answer this, one needs to consider the two elements: inflation and real interest rates.

In the 1950s and 1960s, a combination of buoyant profitability with the desire for hedges against inflation gave the inverse relationship between bond yields, which rose, and earnings yields, which fell.

In the 1970s inflation exploded, partly because of the adverse shift in the terms of trade, after the oil price shock, and partly because of struggles over the distribution of income between wages and profits. Profits were squeezed, even more so than published accounts suggested, because of the fiction of historic cost accounts. So bond yields soared, together with equity yields.

In the 1980s and 1990s inflation fell, as oil prices declined and labour markets were deregulated. Profits recovered and the quality of reported profits improved. As bond yields fell, so did the earning yield.

Thus the link between inflation, bond yields and the price of equities is complex. It is neither mechanical nor easily predicted.

Sometimes there are changes not in inflation but in real interest rates. If expected future growth rates rise, so should real rates of interest. But if the equity risk premium were unchanged, rising real rates of interest would lower the price of equities. The familiar argument that superior growth prospects necessitate higher prices for existing equity is wrong. The opposite is more likely.

There are at least four conclusions.

First, a change in the expected rate of inflation will alter the yield on bonds but should have no effect on today's price of shares.

Second, if that is not true, it is because inflation is having real effects - on wealth or the level and distribution of income - or is altering the accuracy of reported earnings.

Third, where changes in the yield on bonds reflect changes in real rates of interest, the price of equities should change. In general, higher prospective rates of growth are as likely to lower the equilibrium price of equities as to raise them.

Last but not least, there is no consistent exploitable relationship between the yield on bonds and the price of equities.

Interest rate movements are telling us something: but what they are saying is complex. People who market shares on nothing more than the ratio of bond yields to earnings are quacks.

Contact Martin Wolf