Term-structure: A More Detailed View

As a first step toward an understanding of the term structure of interest rates (the maturity effect), we should return to our discussion of real and nominal interest rates. In that section we defined nominal interest rates (r_n) to equal real interest rates (r_n) plus a premium to account for expected inflation (i) over the duration of the loan.  At this time we will simply expand that to include two time periods - short-term (ST) and the long-term (LT). When we lend out money for a short time, the nominal interest rate (r_n^LT) will reflect the real return (r_r^LT) we expect on our money as well as enough to cover for any inflation (i^LT) expected during this period. If inflation is expected to be 5 percent and the "real cost" of money is 4 percent, then the actual (nominal) rate will be 9 percent.  

Similarly, when we lend out money for a long period we will expect the nominal rate (r_n^ST) to reflect a certain real return on our money (r_r^ST) plus enough to cover for any inflation (i^ST) we expect during this longer time period. The relationships can be expressed in the following two equations. 

Long-term interest rates:    r_n^LT = r_r^LT + i^LT    r_n^LT = r_r^LT + i^LT

Short-term interest rates:    r_n^ST = r_r^ST + i^ST    r_n^ST = r_r^ST + i^ST

As a starting point in our explanation of the yield curve inversion you might return to the equations above which could, with a little bit of algebra, be transformed into the following equation for the maturity effect ( r_n^LT - r_n^ST ):

[r_n^LT - r_n^ST]   =  (r_r^LT - r_r^ST) - (i^LT - i^ST)

The difference between the actual long-term and the short-term rates [r_n^LT - r_n^ST] can be broken down into two separate components, the difference in the real rates (r_r^LT - r_r^ST) and the difference between expected inflation (i^LT - i^ST) over the two time horizons.

The difference between long-term and short-term real rates (r_r^LT - r_r^ST) is always positive [the maturity effect], but the inflation effect can be either positive or negative. In normal times, when the inflation rate tends to be stable, there is little difference between the short-term and long-term expected inflation rates (i^LT - i^ST) = 0 and the difference between the nominal rates will therefore be positive [r_n^LT - r_n^ST] > 0.

There are instances, however, when there are significant differences between short-term and long-term expected inflation. For example, if inflation is currently at historically high rates, then we would expect inflation in the future to fall so it is very possible that our expected long-term inflation rate is lower than our short-term rate (i^LT - i^ST ) < 0.  If the difference is large enough, then the inflation effect can reverse the normal maturity effect.

Real maturity effect:

(r_r^LT - r_r^ST) >0 always positive

Inflation maturity effect:

(i^LT - i^ST) >= 0 'normal' inflation

(i^LT - i^ST) < 0 above average current inflation rate