### Yield Curves and Interest Rate Spreads

There's been a lot of discussion about the yield curve lately. Some of you may be afraid to ask what a yield curve is and how it relates to interest rate spreads. For those who are, here's a simple illustration. Suppose there are three assets in the economy, a 3 month bond, a 5 year bond, and a 10 year bond. Let the interest rate be 3% on the 3 month asset, 5% on the 5 year asset, and 10% on the 10 year asset. To construct the yield curve, simply graph the time to maturity against the return [the points are (3 months, 3%), (60 months, 5%), and (120 months, 10%)]:

There is another way to present these data in terms of spreads. Here for example the spread between the 10 year (120 month) and 3 month rates is 10% - 3% = 7% indicating an upward sloping yield curve between these two points. Similarly, the spread between the 5 year (60 month) and 3 month rates is 5% - 3% = 2% again indicating an upward sloping yield curve between those two points. A third spread can also be calculated between the 10 year and 5 year rates and this is 5% (the line connecting the 3 and 120 month rates is not shown but is easy to visualize).

The following graph presents the spreads between the federal funds rate, an overnight borrowing rate between banks, and the 3 month, 6 month, 1 year, 3 year, 5 year, 7 year, and 10 year Treasury rates. Again, recall that if the particular spread is negative, the yield curve drawn through these two points would be negatively sloped:

Two popular spreads (see here) are the difference between the 10 year and 3 month rates, and between the 10 year and 2 year rates. Here's a graph showing each:

As the graphs show, the spreads move in concert for the most part with the largest movements, as expected, for the largest spreads. The particular choice of a spread determines the level of the difference, with positive spreads more likely when the time to maturity is further apart, but the particular choice is somewhat arbitrary.

This brings up one more point. As many, including Jim Hamilton and Arturo Estrella have emphasized the yield curve should not be used in a binary fashion. That is, it should not be used to say all is fine until it has a negative slope, and once it has a negative slope, to say a recession is coming. One reason is that whether the spread is positive or negative in a given time period can depend upon the particular spread examined. Another is that the change in the chance of a recession is gradual, not binary. Historically, the narrower the spread between long and short rates, the slower is output growth on average, see Hamilton for more on this. There is not a sudden jump in the probability of a recession when one particular spread turns negative despite what recent news reports may have led you to believe. And as all who discuss this topic emphasize, the connection between the yield curve, interest rate spreads, and the probability of a recession is far from certain. A flatter yield curve does not gurantee slower growth.

Posted by Mark Thoma on Saturday, December 31, 2005 at 01:31 AM in Economics, Monetary Policy |
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