# Bond crash/course: Yield curve

More elementary school. But late elementary school, so there might be errors below. Let me know…

As mentioned in the previous post, Treasury yields provide the foundation from which all others are derived. (Well, for dollar-denominated bonds, anyway.) Consequently, these yields are very important, which is why they are the first thing that show up on Bloomberg’s Rates and Bonds summary page.

Treasuries with different maturities typically have different yields. A graph of Treasury yields versus maturities is called the yield curve, and it is the very next item on Bloomberg’s summary page.

A naïve person might say, “It is trivial that different maturities have different yields, because of course I would demand more interest for a two-year loan than for a one-year loan.” But this simple explanation is not correct, because yields are already annualized. For example, a zero-coupon 2-year bond with a 2% yield actually pays you 4.04% at the end of two years (because 1.02^2 = 1.0404). Similarly, a six-month bond with 2% yield pays you 0.995% interest after six months (because 1.02^0.5 = 1.00995). So it is perhaps not quite so obvious that the yield curve should even exist.

Suppose you were looking at a 1-year Treasury versus a 2-year Treasury. How much yield would you demand for each? Based on your expectations for possible investment opportunities over the next year, and based on your expectations for inflation, you might demand a particular yield on the 1-year Treasury. If you somehow knew today that, come a year from now, your expectations for the second year would be exactly the same, then you would demand that same yield on the 2-year Treasury too. That is, if you knew the likely prospects for investment in year 2 would be identical to those in year 1, and you knew that inflation would be the same in year 2 as in year 1, then your personal “yield curve” between these maturities would actually be constant.

The fundamental reason you generally demand a higher yield on the two-year Treasury is the higher uncertainty about the second year relative to the first. This is why the yield curve normally slopes upward. Now, if you happened to believe that (say) the rate of inflation will be higher in the second year than in the first, then you would demand an even higher yield. But if you believed that inflation will be significantly lower in the second year than the first, you might actually demand a lower yield on the longer-maturity Treasury.

Terminology: The difference between yields on otherwise identical bonds of different maturities is called a maturity spread. (This term is not used much.) When the spread between long-dated and short-dated Treasuries is large (or growing), the yield curve is said to be steep (or steepening). When it is zero (or shrinking), the yield curve is said to be flat (or flattening). And when it is negative, the yield curve is said to be inverted. (Aside: An inverted yield curve is pricing in lower inflation in the distant future than the near future. As such, it represents the bond market’s expectation of a slowing or contracting economy. The yield curve was inverted from roughly 2006 to 2007.)

More terminology: Treasuries maturing in 1 year or less are called Treasury bills (T-bills for short). Those maturing in more than 1 year but 10 years or less are called Treasury notes (or T-notes). Only those maturing in more than 10 years are called Treasury bonds. The longest-maturity Treasury — 30 years, at the moment — is called the long bond. Since only the longer-dated Treasuries are called “bonds”, we need a different term to refer to Treasuries of all durations, and that term is Treasury coupon security.

Just one technical detail… What I just described is a curve that shows the yield for zero-coupon Treasuries of every maturity. This is the zero-coupon yield curve. But strictly speaking, there is no such thing as a zero-coupon Treasury note or Treasury bond. For maturities longer than one year, the Treasury only issues securities with coupons, and they always pay semi-annually. Nevertheless, the zero-coupon yield curve can be derived from the market prices for coupon securities.

How? The basic idea is pretty simple. As we have seen before, you can think of a security with coupons as a bunch of little zero-coupon securities with different maturities. So start with the market-determined yield of six-month Treasuries; that is, Treasuries that have aged until they only have one payment left six months from now. That is effectively a zero-coupon six-month Treasury, so it tells us the yield for the six-month maturity. Next, look at one-year Treasuries; that is, Treasuries that have aged until they have two payments left (one coming in six months, and another coming in one year). Using the six-month yield we just found, calculate the Present Value of the payment coming in six months. Subtract that from the market price of the one-year Treasury to get the Present Value of the payment coming in one year. That tells us the yield for that single payment; i.e., the yield for the one-year maturity.

Proceeding in this fashion, use market prices of coupon securities to compute the zero-coupon yield every six months along the curve. This process is called bootstrapping the yield curve.

The actual process is more complicated, because there are “technical” factors involved, plus the yield curve is continuous… It can all be handled by doing the right corrections and interpolations and so forth, but I will not describe these because I do not understand them.

Even though the zero-coupon yield curve provides the “cleanest” information — and also the correct starting point for computing the present value of future cash — the usual yield curve shown on Bloomberg and provided by the Treasury itself are for coupon securities. As usual, the difference does not matter for approximate/qualitative discussion.

Enough details. Back to generalities.

The Federal Reserve normally implements monetary policy by holding its thumb on the far left end of the yield curve. That is, they intervene with their “infinite” balance sheet to fix the price (and thus the yield) for 1-day Treasuries at their desired rate of interest. The rest of the yield curve — and by extension, the entire bond market — flows out from that point. During normal times, this is sufficient to allow them to control the general availability of credit in the economy. Of course, since late 2007, we have been in decidedly abnormal times.

Since the Federal Reserve controls the short-term rates, you can make free money in the Treasury market if (a) you can borrow where the Fed plays and (b) you happen to know what they plan to do with interest rates for the next 6-24 months. You just borrow overnight, buy the slightly longer maturities, and roll your daily loan every day. Consequently, Treasury yields in the near term (a year, maybe two or three) have a lot to do with where the market expects Fed policy to go in the future.

And now we are ready to parse a typical Jansen closing comment.

I think that the three year auction tomorrow is a gift around current levels. As I compose this missive it is slightly behind 2 percent. I will reiterate what I said on Friday. To believe that that Federal Reserve will soon raise rates is to smoke some potent financial ganja weed and to engage in hallucinatory behavior from the effects of said narcotic.

He is saying that anybody who thinks the Fed is going to raise rates in the foreseeable future is smoking something, and therefore a 2% yield on a 3-year T-note is attractive.

The 2year/10 year spread has narrowed to 248 basis points. In advance of the labor data it traded 277 basis points.

The spread between 2-year and 10-year notes reached all-time highs last week, representing the market’s (apparent) expectation for inflation to be a lot higher 2-10 years from now than 0-2 years from now. Apparently, a lot of traders had/have placed bets that the curve would continue to steepen. In a bond market analogy of a “short squeeze”, that spread is now contracting violently.

The flattening of that spread as well as the even chunkier flattening in 2year/30 year makes, in my opinion the results of the 10 year note auction and the 30 year bond auction more problematical as the unwinds make those securities less attractive. We are busy sucking the premium from the market in advance of the auctions.

The Treasury is auctioning 3-year notes tomorrow, 10-year notes on Wednesday, and 30-year bonds on Thursday. Jansen is saying that this flattening curve is making the longer-dated Treasuries relatively less attractive.

The 2year/5year/30 year spread is now just 19 basis points.

This is one of Jansen’s pet favorites, the “butterfly spread”. He summarizes it here. You can read his explanation, or you can do this: Add the 2-year yield to the 30-year yield and subtract twice the 5-year yield. This gives you a sort of spread between the “belly” (the 5-year) and the “wings” (2-year and 30-year). Not sure why he loves it so much, but he always cites it, so there you go.