The path of interest rates through time has been a matter of intense public concern. For interest rates are viewed as central to everything in the economy – as something abstract and fundamental, the price of time itself. And yet they show fluctuations through time that reveal a speculative and human component, not entirely unlike that of the stock market.

There are both short-term interest rates (rates on loans or bills for a year or less) and long-term interest rates, rates on bonds, mortgages or loans extending over decades. Prices of long-term bonds, once issued in the marketplace, move opposite the general level of long-term interest rates: when long-term interest rates fall, prices of still-outstanding long-term bonds previously issued rise, since, unless their price increases, investors would prefer those older bonds bearing higher interest to the newer ones. Thus, changes in the outlook for future interest rates can cause booms or crashes in the long-term bond market.

For over a century, central banks (in the United States, the Federal Reserve) have exerted control over short-term rates. It is well known that these rates are easily set, at least approximately, by central banks. Long-term interest rates, however, are more speculative and more difficult to control because, just as with the stock market, the public's demand for them depends on comparisons with the outlook for the distant future, which is dependent on things central banks cannot control today. Since the 2007-9 financial crisis, central banks have adopted important new policies to influence long-term interest rates, with names like "quantitative easing," "operation twist" and "forward guidance," but they still today do not really control this market.

Discussions over the past century have sometimes used the phrase "bond bubble" to describe upswings in the bond market. Certainly, the bond market has something akin to bubbles in it from time to time, occurring when long rates are falling and so people are excited by the rise in bond prices, just as they are by stock prices in a stock market bubble. And bubbles in these two markets might sometimes be related to each other.

Interest Rates and Cape

Interest rates are one of the most discussed terms relating to the level of the stock market. During the stock market boom of the 1990s, it was widely noted that long-term interest rates were falling. And the idea that the decline in interest rates could explain the rise in the stock market was widely expressed during the 1990s.

The Monetary Policy Report submitted in conjunction with Fed Chairman Alan Greenspan's testimony before Congress in July 1997 showed evidence of a noticeable negative correlation between the 10-year bond yield and the stock market's price-earnings ratio since 1982. Indeed, there did appear to be a relationship between interest rates and the price-earnings ratio at that time. In fact, between the mid-1960s and the early 1980s, interest rates were rising and the price-earnings ratio was declining. Between the early 1980s and the late 1990s, when Greenspan spoke, interest rates were falling and stock prices were rising. And this relation between the stock market and the 10-year interest rate came to be known as the "Fed Model."

In the late 1990s and the early 2000s, it became fashionable to use the Fed Model to justify the level of the market. Indeed, with declining interest rates, one might well think that stock prices should be rising relative to earnings, since the prospective long-term return on a competing asset, bonds, was declining, making stocks look more attractive in comparison. In the late 1990s, it sometimes seemed that one heard reference to the Fed Model almost ad nauseam on the television business shows.

However, the evidence for the Fed Model is rather weak. Over the whole 1881-2014 period, no strong relation can be seen between interest rates and the price-earnings ratio. In the Great Depression, interest rates were unusually low, which, by the Fed Model, would imply that the stock market should have been very high relative to earnings; that was not the case.

Interest rates continued to decrease after their peak in the market after the year 2000, and then we saw the opposite of the predictions of the Fed Model: both the price-earnings ratio and interest rates were declining. Since this happened, one has heard a lot less about the Fed Model. Although interest rates must have some effect on the market, stock prices do not show any simple or consistent relation with interest rates. Still, investors looking at a very high cyclically adjusted price-earnings ratio (the CAPE) when long-term government bond yields are very low, as they have been especially since the financial crisis of 2008, will not be as discouraged from investing in stocks because of the poor alternative.

The CAPE has come under some criticism since the second edition of this book. Bill Gross, founder of PIMCO and now at Janus Capital, complained that discussions of the ratio often do not take into account the very low interest rates since the crisis. Indeed, the 10-year U.S. Treasury yield to maturity in July 2012 fell to a historical low of 1.43 percent, and while higher today, remains very low by historical standards.

In such circumstances, perhaps investors will not want to switch from stocks to bonds even if the CAPE is high. Moreover, the U.S. bond market, showing such low yields, looks as if it may have been going through something of a bubble, too, and may collapse further eventually, especially given the imminent withdrawal of the support of quantitative easing from the Federal Reserve and a likely increase in inflation.

Gross, with his "new normal" or "new neutral" pessimistic view of the economy, gives lower probability to such a collapse than I would, but he is right that the apparent overpricing of the stock market – whenever it occurs – has to be compared with the possible overpricing of other markets as well.

Inflation and Interest Rates

The figure on the opposite page shows plots of U.S. government long-term interest rates (the 10-year Treasury rate since 1953) and inflation rates since 1881. Two inflation rates are shown. One is the annual rate of increase of a price index (the Consumer Price Index since 1913) for the preceding ten years. The other is the annual rate of increase of the same price index for the succeeding ten years. The two inflation rate curves are the same, but one is shifted relative to the other by ten years. Both are included here to make a point.

It is easy to see a positive contemporaneous relation between interest rates and preceding long-term inflation rates for much of the time – especially the most recent half-century – but there appears to be practically no relation between long-term interest rates and future long-term inflation. It is the future inflation rate that ought to matter more if investors successfully priced long-term bonds to protect their real returns from inflation over the future life of the bond they are investing in, just the opposite of what we see. Jeremy Siegel and I documented this in 1977 and linked this observation to descriptions of earlier observers A.H. Gibson in 1923 and John Maynard Keynes in 1930.

The relation between long-term interest rates and long-term inflation that can be seen for the last half century is not the kind that a simple assumption of human rationality would lead one to expect. If investors are rational (have rational expectations), they should be employing past data on inflation in such a way as to adjust nominal bond yields to successful predictions of the future. We see that they did seem to respond to past data, but in a way that was very unsuccessful in predicting the future.

The fluctuations in yields that we do see in the long-term bond market cannot be well described as resulting from information about future inflation, nor are they well described as resulting from information about future short-term interest rates. They have a speculative component that is hard to pin down in terms of objectively rational behavior.

Real Interest Rates

Over most of the period shown in the figure, many investors perhaps had no idea about what the relation between nominal interest rates and inflation rates should be. It was not until 1895 that Columbia University economics professor John Bates Clark introduced the concept of real interest rates to the world. He wrote about this then-new concept because he discerned widespread public confusion about interest rates at the time of the national debate on the proposed bimetallic standard [for the money supply].

The real interest rate on any debt instrument, he said, is the interest rate minus the inflation rate over the life of the instrument. If the inflation rate is greater than the interest rate, the bond would be producing less than nothing in real terms for the investor, since the buying power of money would be reduced by more than the increase in the money the instrument provides to its investor.

A search on Google Ngrams shows that the phrase "real interest rate" was never used before 1892, began to appear incrementally from that time, and did not really become common until after 1960 – after a very long gestation period for Clark's idea.

One might think, if investors have good information, are rational and are interested in the real interest that they will receive, that market-determined bond yields would stay just a steady amount above the subsequent inflation rate.

One can see from the figure, though, that this has never been true for the United States – although, since around 1960, it became somewhat true for backward-looking rather than forward-looking inflation.

The significance of movements in long-term interest rates over time, as seen in the figure for the United States since 1871, is not clear. Plainly, people were not pricing bonds as if they were just reacting to rational expectations about future inflation rates. Theorists often say that ratios like the price-earnings ratio in the stock market ought to be more closely related to expected real (inflation-corrected) long-term interest rates, which have been largely unknown, than to nominal rates. But that is based on the assumption that investors routinely see through nominal rates to real rates.

Inflation-indexed bond markets, which directly reveal real interest rates, did not exist in any major country in the early 1980s, but have since begun to appear. These bonds promise to pay a constant real return. The figure on the opposite page shows the behavior of inflation-indexed long-term government bond yields for four countries that have had these markets for a long time.

All these countries show a long-term downtrend in real interest rates – down to amazingly low levels by 2012. Recently, the real bond yields have sunk to negative values in both the United States and the United Kingdom. It is quite striking that in 2012 in the United States, people were willing to tie up their money for 30 years at an essentially guaranteed negative real return.

This fact would certainly seem to have implications for the stock market, impelling it toward higher valuation.

Financial theorists, including John Campbell and Luis Viceira, have spoken of the long-term indexed bond yield as the true riskless rate, against which all risky asset returns should be compared, and which should figure into every long-term investor's most fundamental calculations.

But most investors just do not seem to see the centrality of the indexed bond yield that theorists often seem to attribute to it. They often do not even seem to understand that inflation indexation protects them from price-level risks, and sometimes seem to think that indexation introduces a risk – the risk that their nominal values will be lower. The path downward does not reflect the ups and downs of the stock market any more than does the downward path of nominal interest rates over this interval.

Unfortunately, even with these data, especially in the earlier years of inflation-indexed bonds, it has not been completely clear what the broad investing public likely thought over these years about expected real returns on safe assets. When each of the countries shown in the figure introduced their inflation-indexed bond markets, they did so in the face of widespread public indifference. The market for inflation-indexed bonds has grown somewhat over the decades but is only gradually becoming important enough compared to the market for non-indexed conventional bonds to pervade public thinking as some theorists assume. And so a few government officials in charge of the auctions could in principle, influence the prices of inflation-indexed bonds by adjusting the amount offered.

It is one of the puzzles of behavioral economics that people mostly just ignore inflation-indexed markets – that they have so much trouble appreciating the importance of inflation indexation. Still, it is clear that prices in both the market for nominal bonds and the market for inflation-indexed bonds have reached very high levels, and that this fact ought to be part of our thinking about the stock market. It remains unclear what this situation implies for the future. At the time of this writing in 2014, some observers refer to a "bond market bubble" that might burst, though it seems that this is not a classic bubble as defined in this book, since expectations for long-term return are apparently very low – not high, as one would expect during a bubble. But these trends in the bond market might in some sense be bubble-like.

In 2014 Jeremy Stein of Harvard University, in one of the last speeches he gave as governor of the Federal Reserve System, discussed concerns about a bond market bubble, though he did not adopt that term. He spoke of "overheating" in the credit markets and warned of economic consequences if the bond yields were to suddenly correct upward (bond prices correct downward); he worried about the economic consequences of such a correction.

There must be some hard-to-pin-down cultural factors driving people to invest in bonds at a time when their yield is very low or negative and the stock market has been soaring. Some of the same precipitating factors for the stock market and housing market booms might apply somewhat to the bond market. Also, falling bond yields have produced capital gains for bond investors over the decades, making bonds look successful even if they are guaranteed not to do well in real terms over their time to maturity. The extreme low or negative yields after the financial crisis of 2007-9 might also have something to do with a kind of a flight response, at times of financial turmoil, that does not fit our usual theoretical paradigms.

Where that response goes in future years remains to be seen. There is, indeed, reason to be concerned about the possible widespread economic effects of an end to this decades-long downtrend in real long-term interest rates, and of a corresponding drop in long-term bond prices.