## Yield Curve – Theories

*by Eric Bank on May 11, 2011 · No Comments · in Documenting the Search for Alpha*

Recall that yield curves (also known as the ** term structure of interest rates**) plot

**(the independent variable) against**

*debt maturities***(the dependent variable). Debt maturities indicate the length of the borrowing period for a debt instrument. We spoke last time on how a yield curve is shaped; today we’ll look at a few theories that attempt to explain yield curve behavior.**

*interest rates***Pure Expectations Theory (PET)**

In this theory, it is assumed that any maturity of debt can substitute for any other through the miracle of compounding. For instance, if you have a view as to what the one-year interest rate will be one year from now (the ** forward rate**), then you can determine the current two-year interest rate as the compounded sum of the current one-year rate and the one-year forward.

This generalizes to the ** geometric mean **of short-term yields as the determinant of long-term yields. A geometric mean differs from an average in the it is calculated by taking the

*n*th root of the product of

*n*terms. For example, if you have two terms, say 4 and 16, the average is of course 10, but the geometric mean is the 2

^{nd}root – the square root – of their product (64), or 8.

The Pure Expectations Theory accounts for the fact that yields tend to change together over time, but doesn’t explain the fine details of the shape of the yield curve. It posits that forward rates are perfect predictors of future rates, which they are not. It thus ignores interest rate risk and also reinvestment risk. The latter is the risk that one cannot reinvest interest payments at an expected rate. The theory also assumes that the ability to arbitrage among different maturity bonds is minimal.

**Liquidity Preference Theory (LPT)**

This is a variant of the Pure Expectations Theory. It basically adds a premium to the PET-calculated yield for long-term debt to account for investor preference for short-term bonds over long-term ones. This premium is called the term premium or the liquidity premium. It acknowledges the risks involved in holding long-term debt, which is more likely to experience catastrophic events and price uncertainty than is short-term debt. A second premium is also included in LPT, for default risk, which is more likely when holding a bond for a long period of time, once again due to uncertainty.

**Market Segmentation Theory (MST)**

This theory acknowledges that different maturities of debt cannot be substituted for each other. This results in separate demand-supply relationships for short-term and long-term debt. Since investors (assumed to be risk-adverse) prefer the less risky short-term maturities, the demand for short-term debt is higher than that for long-term debt, and thus prices of the former are higher, driving down their yields. This helps to explain the normal shape of the yield curve, but not the fact that long and short term rates tend to change in unison, since they are supposed to be two separate and independent markets.

**Preferred Habitat Theory (PHT)**

Preferred Habitat Theory is an extension of MST which posits maturity preferences, or habitats, for debt investors: some investors like 3-year bonds, some prefer 6-year maturities, etc. If you want to sell an investor a bond outside the investor’s preferred investment horizon, you must offer the investor a premium. Since it is assumed that more investors have short-term habitats, it explains the higher yields on long-term debt, and is consistent with the tendency of short- and long-term debt yield curve segments to retain their shape when overall yields change.

Now that we have a good understanding of yields and the yield curve, we can resume our review of hedge fund strategies. Next time: * fixed-income arbitrage*.

## Eric Bank

Based in Chicago, Eric Bank has been writing business-related articles since 1985, and science articles since 2010. His articles appear on eHow and on numerous other websites. He holds a B.S. in biology and an M.B.A. from New York University. He also holds an M.S. in finance from DePaul University.

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