Sunday, January 11, 2009

The Real Yield Curve

Taking a break from exhorting/complaining about economic policy, I would like to discuss money. Specifically, the shape of the "yield curve".

It is the contention here that the yield curve is systematically misrepresented throughout the media. Consider the conparisons between the 3 month bill and 5 and 10 year Treasury notes. Assume that the 3-moth bill yields nothing, the 5-year note yields 1.5% per annum and the 10 year note yields 2.5% per annum. The yield curve would show those different rates in one graph. But the investor considering going to a yet longer maturity should want to know what the implied yield is on the "out" years.

The correct calculation requires calculus. The underlying principle here is that the short term is more knowable than the long term. Thus we can say that the first five years from now are more predictable than the second five years. If we therefore assume that the first five years have a "correct" interest rate of 1.5%, then what are we assuming if we instead choose to be paid 2.5% yearly via a 10-year instrument, including 2.5% (above market!) for the first five years. Clearly by having the opportunity to get an "above market" yield for the first five years, we are foregoing some market yield for the second five years. What is that foregone, "correct" interest rate?

Absent calculus, some basic arithmetic provides the answer: additional yield obtained in the first 5 years by purchasing a 10-year bond: 5 years X 1% additional yearly yield = 5% over five years. Thus the acceptance of only 2.5% in the second five years means that the "correct" implied interest rate in those years should be 1% greater yearly, or 3.5% per year. Of course, the "correct" or implied yield in year 10 will be greater than 3.5% and the "correct" or implied yield in year 6 will be less than 3.5%.

Applying this math to the current levels for the 10 and 30 year Treasuries suggests that the market is pricing in very low interest rates for the "out" years, years 11-30. This suggests to me that anyone holding Treasuries with over about a 10 year maturity is taking on a great deal of risk for little return.

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