## Forward Rates Part 1: GAP Analysis

Gap Analysis, sometimes referred to as breakeven analysis, will get us 3/4 of the way to understanding forward rates. There are three different interest rates involved with gap analysis:

1. Term Rate: Security with the longest term to maturity.
2. Head Rate: A shorter maturity alternative to the Term Rate.
3. Tail Rate: A rate that starts at the end of the maturity of the Head Rate and matures at the end of the Term Rate.
4. See image below:

When we talk about interest rates, we are not talking about the yields available on the 5-year or 2-year Treasury notes. Two different quoted yields on securities that pays interest semiannually (as do Treasury notes) assume that each interest payment will be reinvested at the quoted yield (most likely two different yields).  In order to complete the gap calculations  we would have to know what rate each interest payment will be reinvested at, which we don’t know, plus the fact that there will only be one rate at any given reinvestment date, not two.

Spot Rates:  We get around this problem by using spot rates. Spot rates have no interest payments until they mature. The quoted yield may imply semiannual interest, but it is all calculated into the interest paid at maturity and the implied reinvestment rate is the initial quoted yield.  I will include one way to calculate spot rates for the yield curve in a different post. An example of available spot rates are Treasury STRIP (the acronym for Separate Trading of Registered Interest and Principal of Securities or zero coupon securities). When you buy a STRIP, you are purchasing a single interest payment (or a principal payment) that was literally stripped away from a semiannual  interest paying Treasury security, by a brokerage firm. Another type of investment that is closely related to a spot rate is a retail bank or credit union certificate of deposit (CD). If the interest is left in the account, the bank reinvests the interest at the same initial rate the certificate was issued at.

Continuous Compounding:  Just a quick note on compounding. The purist might insist on using continuous compounding in this type of analysis due to it’s convenient mathematical properties. Since I assume my audience is made up of fixed income investors, I will use semiannual compounding.

Gap analysis will tell us, given two of the interest rates, what the third rate must be. Consider the input cells below (yellow cells):

Forward Rate: Notice that we left the Tail rate zero and entered the Term rate of 1.0528% and Head rate of .6931%. The dates used were for a 7-year Term investment and a 5-year Head investment, leaving the Tail, a 2-year investment. What the GAP analysis has done is calculate the forward rate of 1.9549% on the 2-year investment , 5 years from now.

In other words, if an investor was willing to hold an investment for 7 years and his/her choice was 1.0528% for 7 Years or .6931% for 5 years, and the investor chooses the 5-year, the investor is implicitly saying that he/she will be able to receive a rate of at least 1.9549% or high in 5 years for the remaining two years.

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Don Pistulka

Retired Credit Union CFO - Finance
Background: over 40 years in investments, asset/Liability management, banking, securities trader.
Worked for: California Credit Union, WesCorp, CalFed S&L, Crocker Bank, Carroll McEntee, Federal Home Loan Bank Board (D.C.), Western Asset Management, Security Pacific National Bank.