Interest Rate Indicators


The current yield curve represents a plot of the interest rates of various government securitites (vertical axis) against the lengths of maturity of the securities (horizontal axis). The government securuities are the 3 month and 6 month T-bills and the 1, 2, 3, 5, 7, 10, and 30 year Treasury notes. In constructing the yield curve we convert the 3 month and 6 month discount rates of the T-bills to bond equivalent interest rates vis-a-vis the formula

ib = 365*d/(360-d*t)

where
ib = bond yield equivalent interest rate (in decimal form)
d = T-bill discount rate (in decomal form)
t = number of days to maturity. For the 3 month T-bill, t=90. Fpr the 6 month T-bill, t=180.

(Reference: A COMPLETE GUIDE TO THE FUTURES MARKETS BY JACK D. SCHWAGER (NEW YORK: JOHN WILEY), 1984, P. 521.)
The interest rates used are:
fygn3 = 3 month T-bill discount rate
fygn6 = 6 month T-bill discount rate
fygt1 = 1 year Treasury note interest rate
fygt2 = 2 year Treasury note interest rate
fygt3 = 3 year Treasury note interest rate
fygt5 = 5 year Treasury note interest rate
fygt7 = 7 year Treasury note interest rate
fygt10 = 10 year Treasury note interest rate
fygt30 = 30 year Treasury note interest rate


Using the theory of effecient arbitrage, unbiased expectations, and risk neutrality, the term structure can be used to derive implicit forward interest rates. See, for example, THE TERM STRUCTURE OF INTEREST RATES BY CHARLES R. NELSON (NEW YORK: BASIC BOOKS), 1972, PP. 6-9.

The formula for the forward rates reported above are:

RE(3 mo, t+1) = {[(1 + R(6 mo, t))^2 / (1 + R(3 mo, t))]-1}*100

where
RE(3 mo, t+1) = the expected 3-month T-bill discount rate, three months from now (in annual percent)
R(6 mo, t) = add on current six-month T-bill discount rate (in decimal form)*
R(3 mo, t) = add on current three-month T-bill discount rate (in decimal form)*

*converted from discount rate to add on rate by formula

Of course one doesn't have to be content with using only the latest MONTHLY data available from the FAME data base to calculate the above forward rates. Instead the above forward rates can be calculated on a DAILY basis. For example, going to the Federal Reserve Board's web site for statistical releases on selected interest rates one can obtain the most recent data available on 3 and 6 month T-bills. For October 11, 1996 (the most recent data available for october 18, 1996) the following interest rates (at constant maturies) were obtained:

R(3 mo, t) = 5.13
R(6 mo, t) = 5.31

Using the formula for calculating forward rates we obtain
RE(3 mo, t+1) = 5.49%

Students: try to obtain the most current data available and recalculate these forward rates.

C. Futures Market Based Estimates of Future Interest Rates

The futures market for interest rates can be used to derive forecasts of interest rates at different points in the future. For example, in the Friday, October 18, 1996 WALL STREET JOURNAL, p. C16 under the heading ``Futures Prices'' the following data concerning futures for 3-month T-bills can be found:

Treasury Bills (CME) - $1 million
Discount Settle chg.
Dec 5.05 -0.04
Mar 97 5.15 -0.06
Jun 5.32 -0.05

From this report we can see that futures traders in $1-million T-bills believe that in December the 3-month T-bill discount rate will be approximately 5.05%,in March 1997, 5.15%, and in June 1997 5.32%. Using the formula 360*d/(360-90*d) where d = the discount rate in decimal form, the expected "add on" interests expected by futures traders of 3-month T-bills (in annual percent) are 5.11%, 5.22%, and 5.39% for the months of December 1996, March 1997, and June 1997, respectively.

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