August 17, 2006
Reading The Yield Curve
What are the implications of the current shape of the yield curve?
The yield curve is often used to summarize the interest rates on Treasury instruments of different maturities, with the yield plotted on the vertical axis against the time to maturity on the horizontal axis. In normal times, if you just know the average level and slope of this curve, you could predict the yield on a bond of any specified maturity pretty well.
The graph below, taken from Bloomberg, plots today’s yield curve. One glance at its odd shape lets us know that, whatever else is going on, these are not normal times. What should we make of the current serpentine pattern?
A starting point for any discussion about the yield curve is the expectations hypothesis of the term structure. This posits that, at any point in time, the differences in yields for different maturities are such that you can expect to earn the same total return regardless of which instrument you buy. For example, the current 3-month yield is 5.08%, while the 6-month yield is 5.23%. If the 3-month yield you could get in October turns out to be 5.38%, then you’d earn the same return from rolling over two 3-month bills as from buying the 6-month bill:
(1.0508)1/4 x (1.0538)(1/4) = (1.0523)1/2
Thus, according to the expectations hypothesis, the fact that the 6-month yield is currently 15 basis points above the 3-month yield means that investors expect the 3-month rate to rise another 30 basis points over the next 3 months
The top panel of the next graph plots the difference between the 6-month and 3-month tbill rates for every month since 1982; a positive value indicates that the 6-month rate was higher than the 3-month rate in that month. The bottom panel plots the difference between the return you’d actually have experienced six months later if you had (a) purchased the 6-month bill, rather than (b) purchased a 3-month bill and then bought a new 3-month bill three months later. Thus a negative value in the second panel indicates you would have ended up better if you had stayed with 3-month bills. The fact that this series is positive on average means that the yield curve usually slopes up and the longer-term security typically offers a little better yield.
An ordinary least squares (OLS) regression of the ex-post holding yield (the bottom panel) on the initial spread (the top panel) and a constant for the period 1982:01 to 2006:03 produces a coefficient on the spread of 0.96 with a t-statistic around 10. If the expectations hypothesis were true, this coefficient should have been zero. Instead, the coefficient near unity suggests that the differences between the 3-month and 6-month rates have almost nothing to do with expectations of the future 3-month yield.
Although the expectations hypothesis has also been decisively rejected with data prior to 1982, the inference in the post-1982 data set is heavily influenced by the fact that interest rates are much more volatile at some times than others, causing the OLS estimation method to be overwhelmingly dominated by observations such as those in 1982. If one re-estimates the regression allowing for time-variation in the variance as captured by the GARCH model, the estimated coefficient falls from 0.96 to 0.35. And if one simply restricts the sample to the tamer period since 1990, with OLS the coefficient actually becomes slightly negative and completely statistically insignificant. Indeed, one can see in the second panel above that since 2000, the 6-month yield has been doing an almost perfect job of predicting the 3-month yield, consistent with the observation that the fed funds futures prices have not had much trouble anticipating recent Fed moves.
Read more…
Bill Coppedge
The yield curve is often used to summarize the interest rates on Treasury instruments of different maturities, with the yield plotted on the vertical axis against the time to maturity on the horizontal axis. In normal times, if you just know the average level and slope of this curve, you could predict the yield on a bond of any specified maturity pretty well.
The graph below, taken from Bloomberg, plots today’s yield curve. One glance at its odd shape lets us know that, whatever else is going on, these are not normal times. What should we make of the current serpentine pattern?
A starting point for any discussion about the yield curve is the expectations hypothesis of the term structure. This posits that, at any point in time, the differences in yields for different maturities are such that you can expect to earn the same total return regardless of which instrument you buy. For example, the current 3-month yield is 5.08%, while the 6-month yield is 5.23%. If the 3-month yield you could get in October turns out to be 5.38%, then you’d earn the same return from rolling over two 3-month bills as from buying the 6-month bill:
(1.0508)1/4 x (1.0538)(1/4) = (1.0523)1/2
Thus, according to the expectations hypothesis, the fact that the 6-month yield is currently 15 basis points above the 3-month yield means that investors expect the 3-month rate to rise another 30 basis points over the next 3 months
The top panel of the next graph plots the difference between the 6-month and 3-month tbill rates for every month since 1982; a positive value indicates that the 6-month rate was higher than the 3-month rate in that month. The bottom panel plots the difference between the return you’d actually have experienced six months later if you had (a) purchased the 6-month bill, rather than (b) purchased a 3-month bill and then bought a new 3-month bill three months later. Thus a negative value in the second panel indicates you would have ended up better if you had stayed with 3-month bills. The fact that this series is positive on average means that the yield curve usually slopes up and the longer-term security typically offers a little better yield.
An ordinary least squares (OLS) regression of the ex-post holding yield (the bottom panel) on the initial spread (the top panel) and a constant for the period 1982:01 to 2006:03 produces a coefficient on the spread of 0.96 with a t-statistic around 10. If the expectations hypothesis were true, this coefficient should have been zero. Instead, the coefficient near unity suggests that the differences between the 3-month and 6-month rates have almost nothing to do with expectations of the future 3-month yield.
Although the expectations hypothesis has also been decisively rejected with data prior to 1982, the inference in the post-1982 data set is heavily influenced by the fact that interest rates are much more volatile at some times than others, causing the OLS estimation method to be overwhelmingly dominated by observations such as those in 1982. If one re-estimates the regression allowing for time-variation in the variance as captured by the GARCH model, the estimated coefficient falls from 0.96 to 0.35. And if one simply restricts the sample to the tamer period since 1990, with OLS the coefficient actually becomes slightly negative and completely statistically insignificant. Indeed, one can see in the second panel above that since 2000, the 6-month yield has been doing an almost perfect job of predicting the 3-month yield, consistent with the observation that the fed funds futures prices have not had much trouble anticipating recent Fed moves.
Read more…
Bill Coppedge
