Inverted Yield Curve

Inverted Yield Curve

December 28, 2005

I did a spot on CNBC Wake Up Call at 6:30 this morning; hope you were still sleeping. The topic was the inverted yield curve. Yesterday, the yield on the ten year Treasury dipped below the yield on the two year, reversing the “normal” relationship between short and long rates.

This happens about as frequently as a solar eclipse, so it gets everybody’s attention. And like the solar eclipse, it is viewed by some people as a sign of impending doom.

This is not the end of the world. It is, however, a time to be thoughtful about the economy and the markets.

First, the basics. The relationship between short and long rates is not a law of nature; it is an arbitrage condition. Let’s use r(1,t) to represent the current yield to maturity on a one-year bond measured at time t (t=today), and r(2,t) to represent the current yield on a 2 year bond measured today. And let (re(1,t+1)) represent the yield to maturity on a one-year bond that investors expect to be available in the market one year from today.

An investor who wants to invest $A in bonds for two years can do so in two different ways. He can buy a two year bond today and go to the beach until maturity, when he will collect:

$A (1+r(2,t)) (1+r(2,t)).

Or he can buy a one-year bond today, planning to re-invest his proceeds a year from now in a one-year bond at that time (t+1) and collect an amount at the end of 2 years equal to:

$A (1+r(1,t)) (1+re(1,t+1)).

If we assume (that means pretend in econo-speak) for the moment that people believe the two alternatives are equally risky, then the following condition must hold in order to prevent you and me from making a lot of easy money:

(1+r(2,t)) squared = (1+r(1,t)) (1+re(1,t+1)).

This expression, with long rates (i.e., multi-period yields) on the left hand side and short rates (i.e., single-period yields) on the right hand side, with obvious adjustments, is true for any maturity. It is the only relationship between long and short rates that must hold all the time. It simply says that long rates are the geometric average of expected short rates over their lifetimes.

Whether the resulting yield curve (a chart of long rates against years to maturity) slopes up or down is strictly determined by the pattern of expected short rates, which will be driven by investors’ expected inflation rates for future periods.

I wrote a book about this a long time ago (A Monetarist Model of Inflationary Expectations, 1973) in which I referred to expected future short rates as “marginal rates” and long rates as “average rates”, and introduced a concept I called the “marginal yield curve.”. I argued that this marginal yield curve can slope up or down, with resulting implications for the average yield curve (the one everybody writes about) depending on people’s views about how the Fed will behave in future years.

I’ll write more about this later, but will draw a few implications here:

1. An inverted yield curve is not the end of the world. The last 4 recessions have all been preceded by inverted yield curves, but that does not mean that an inverted yield curve always implies a recession.
2. The important thing is why the yield curve is inverted. If the yield curve is inverted because the Fed has just forced a sharp increase in short rates (like 1980-81) you may have a problem. If it inverted because long rates have been easing lower to reflect moderating inflation worries (like today) it might be fine.
3. The anchor on inflation today is Chinese and Indian wage and prices. It makes sense for investors to expect low inflation in future years.
4. Either way, the condition is likely to be temporary because inflation is not likely to fall forever. It could be resolved next year by the Fed backing away from tightening short rates to keep bank reserves growing. Or it could be resolved by a major bankruptcy (GM? Ford?) which would push the Fed away from tightening.
5. Implication: in a world where the Fed is targeting prices, it is not appropriate to view them as an exogenous driver of the economy. Their behavior will adapt to outside influences on prices, e.g., oil prices, price and wage differentials, and technology changes.
6. The economy is growing, inflation is low, and profits are increasing at double digit rates. This is a great time to buy stocks. If people get spooked by the inverted yield curve and prices fall, buy more equities.


John Rutledge

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