Wednesday, 14 November 2007

Yield Curve for Bonds

For those students who graduated from WA07 class, if you still remember Conrad mentioned about the Inverted Yield Curves for year 2006 and 2007 and their implication to the economy, you may be wondering what Conrad is trying to get across to us. I'll try to explain what causes the shape of the yield curve in this post.

There are three theories to describe the term structure of interest rates that affect the shape of the yield curve. They are

  1. Pure Expectation Theory
  2. Liquidity Preference Theory
  3. Market Segmentation Theory

So what does each theory say? The pure expectations theory states that the yield for a particular maturity is an average (not a simple average) of the short term rates that are expected in the future. If short term rates are expected to rise in the future, interest rate yields on longer maturities will be higher than those on shorter maturities, and the yield curve will be upward sloping. If short term rates are expected to fall over time, longer maturity bonds will be offered at lower yields.

Proponents of the liquidity preference theory believe that, in addition to expectations about future short term rates, investors require a risk premium for holding longer term bonds. This is consistent with the fact that interest rate risk is greater for longer maturity bonds.

Under this theory, the size of the liquidity premium will depend on how much additional compensation investors require to induce them to take on the greater risk of longer maturity bonds or, alternatively, how strong their preference for the greater liquidity of shorter term debt is.

The market segmentation theory is based on the idea that investors and borrowers have preferences for different maturity ranges. Under this theory, the supply of bonds (desire to borrow) and the demand for bonds (desire to lend) determine equilibrium yields for the various maturity ranges. Institutional investors may have strong preferences for maturity ranges that closely match their liabilities. Life insurers and pension funds may prefer long maturities due to the long-term nature of the liabilities they must fund. A commercial bank that has liabilities of a relatively short maturity may prefer to invest in shorter-term debt securities. Another argument for the market segmentation theory is that there are legal or institutional policy restrictions that prevent investors from purchasing securities with maturities outside a particular maturity range.

A somewhat weaker version of the market segmentation theory is the preferred habitat theory. Under this theory, yields also depend on supply and demand for various maturity ranges, but investors can be induced to move from their preferred maturity ranges when yields are sufficiently higher in other (non-preferred) maturity ranges.

The pure expectations theory by itself has no implications for the shape of the yield curve. The various expectations and the shapes that are consistent with them are:

  1. Short-term rates expected to rise in the future -> upward sloping yield curve
  2. Short-term rates are expected fall in the future -> downward sloping yield curve
  3. Short-term rates expected to rise then fall -> humped yield curve
  4. Short-term rates expected to remain constant -> flat yield curve

The shape of the yield curve, under the pure expectations theory, provides us with information about investor expectations about future short-term rates.

Under the liquidity preference theory, the yield curve may take on any of the shapes we have identified. If rates are expected to fall a great deal in the future, even adding a liquidity premium to the resulting negatively sloped yield curve can result in a downward sloping yield curve. A humped yield curve could still be humped even with a liquidity premium added to all the yields. Also note that , under the liquidity preference theory, an upward sloping yield curve can be consistent with expectations of declining short term rates in the future.

The market segmentation theory of the term structure is consistent with any yield curve shape. Under this theory, it is supply and demand for debt securities at each maturity range that determines the yield for that maturity range. There is no specific linkage among the yields at different maturities, although, under the preferred habitat theory, higher rates at an adjacent maturity range can induce investors to purchase bonds with maturities outside their preferred range of maturities.

Conrad showed us to this site where you can learn more about bonds. You can click on the link here.

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