It’s conventional opinion that the Fed will begin to raise its policy rate by the end of 2015, and continue raising rates for the next couple years. In the FT, Larry Summers argues that this will be a mistake. And he observes that bond markets don’t seem to share the conventional wisdom: “Long term bond markets are telling us that real interest rates are expected to be close to zero in the industrialised world over the next decade.”

The Summers column inspired me to take a look at bond prices and flesh out this observation. It is straightforward to calculate how much the value of a bond change in response to a change in interest rates. So by looking at the current yields on bonds of different maturities, we can see what expectations of future rate changes are consistent with profit-maximizing behavior in bond markets. [1]

The following changes shows the yields of Treasury bonds of various maturities, and the capital loss for each bond from a one-point rise in yield over the next year. (All values are in percentage points.)

Maturity | Yield as of July 2015 | Value Change from 1-Point Rise |

30 year | 3.07 | -17.1 |

20 year | 2.77 | -13.9 |

10 year | 2.32 | -8.4 |

5 year | 1.63 | -4.6 |

1 year | 0.30 | -0.0 |

So if the 30-year rate rises by one point over the next year, someone who just bought a 30-year bond will suffer a 17 percent capital loss.

It’s clear from these numbers that Summers is right. If, over the next couple of years, interest rates were to “normalize” to their mid-90s levels (about 3 points higher than today), long bonds would lose half their value. Obviously, no one would hold bonds at today’s yields if they thought there was an appreciable chance of that happening.

We can be more precise. For any pair of bonds, the ratio of the difference in yields to the difference in capital losses from a rate increase, is a measure of the probability assigned by market participants to that increase. For example, purchasing a 20-year bond rather than a 30-year bond means giving up 0.3 percentage points of yield over the next year, in return for losing only 14 percent rather than 17 percent if there’s a general 1-point increase in rates. Whether that looks like a good or bad tradeoff will depend on how you think rates are likely to change.

For any pair of bonds, we can calculate the change in interest rates (across the whole yield curve) that would keep the overall return just equal between them. Using the average yields for July, we get:

30-year vs 20-year: +0.094%

30-year vs. 10-year: +0.086%

30-year vs. 5-year: +0.115%

20-year vs. 10-year +0.082%

20-year vs. 5 year: + 0.082%

Treasury bonds seem to be priced consistent with an expected tenth of a percent or so increase in interest rates over the next year.

In other words: If you buy a 30 year bond rather than a 20-year one, or a 20-year rather than 10-year, you will get a higher interest rate. But if it turns out that market rates rise by about 0.1 percentage points (10 basis points) over the next year, the greater capital losses on longer bonds will just balance their higher yields. So if you believe that interest rates in general will be about 10 basis points higher a year from now than they are now, you should be just indifferent between purchasing Treasuries of different maturities. If you expect a larger increase in rates, long bonds will look overpriced and you’ll want to sell them; if you expect a smaller increase in rates than this, or a decrease, then long bonds will look cheap to you and you’ll want to buy them. [2]

A couple of things to take from this.

First, there is the familiar Keynesian point about the liquidity trap. When long rates are low, even a modest increase implies very large capital losses for holders of long bonds. Fear of these losses can set a floor on long rates well above prevailing short rates. This, and not the zero lower bound per se, is the “liquidity trap” described in *The General Theory*.

Second, compare the implied forecast of a tenth of a point increase in rates implied by today’s bond prices, to the forecasts in the FOMC dot plot. The median member of the FOMC expects an increase of more than half a point this year, 2 points by the end of 2016, and 3 points by the end of 2017. So policymakers at the Fed are predicting a pace of rate increases more than ten times faster than what seems to be incorporated into bond prices.

If the whole rate structure moves in line with the FOMC forecasts, the next few years will see the biggest losses in bond markets since the 1970s. Yet investors are still holding bonds at what are historically very low yields. Evidently either bond market participants do not believe that Fed will do what it says it will, or they don’t believe that changes in policy rate will have any noticeable effect on longer rates.

And note: The belief that long rates unlikely to change much, may itself prevent them from changing much. Remember, for a 30-year bond currently yielding 3 percent, a one point change in the prevailing interest rate leads to a 17 point capital loss (or gain, in the case of a fall in rates). So if you have even a moderately strong belief that 3 percent is the most likely or “normal” yield for this bond, you will sell or buy quickly when rates depart much from this. Which will prevent such departures from happening, and validate beliefs about the normal rate. So we shouldn’t necessarily expect to see the whole rate structure moving up and down together. Rather, long rates will stay near a conventional level (or at least above a conventional floor) regardless of what happens to short rates.

This suggests that we shouldn’t really be thinking about a uniform shift in the rate structure. (Though it’s still worth analyzing that case as a baseline.) Rather, an increase in rates, if it happens, will most likely be confined to the short end. The structure of bond yields seems to fit this prediction. As noted above, the yield curve at longer maturities implies an expected rate increase on the order of 10 basis points (a tenth of a percentage point), the 10-year vs 5 year, 10 year vs 1 year, and 5 year vs 1 year bonds imply epected increases of 18, 24 and 29 basis points respectively. This is still much less than dot plot, but it is consistent with idea that bond markets expect any rate increase to be limited to shorter maturities.

In short: Current prices of long bonds imply that market participants are confident that rates will not rise substantially over the next few years. Conventional wisdom, shared by policymakers at the Fed, says that they will. The Fed is looking at a two point increase over the next year and half, while bond rates imply that it will take twenty years. So either Fed won’t do what it says it will, or it won’t affect long rates, or bondholders will get a very unpleasant surprise. The only way everyone can be right is if trnasmission from policy rate to long rates is very slow — which would make the policy rate an unsuitable tool for countercyclical policy.

This last point is something that has always puzzled me about standard accounts of monetary policy. The central bank is supposed to be offsetting cyclical fluctuations by altering the terms of loan contracts whose maturities are much longer than typical business cycle frequencies. Corporate bonds average about 10 years, home mortgages, home mortgages of course close to 30. (And housing seems to be the sector most sensitive to policy changes.) So either policy depends on systematically misleading market participants, to convince them that cyclical rate changes are permanent; or else monetary policy must work in some completely different way than the familiar interest rate channel.

[1] In the real world things are more complicated, both because the structure of expectations is more complex than a scalar expected rate change over the next period, and because bonds are priced for their liquidity as well as for their return.

[2] I should insist in passing, for my brothers and sisters in heterodoxy, that this sort of analysis does not depend in any way on “consumers” or “households” optimizing anything, or on rational expectations. We are talking about real markets composed of profit-seeking investors, who certainly hold some expectations about the future even if they are mistaken.