PrimeRateProjection
L. David Roper [email protected]
Introduction
A good definition of the Prime Rate is at http://en.wikipedia.org/wiki/Prime_rate (“Prime rate or prime
lending rate is a term applied in many countries to a reference interest rate used by banks. The term
originally indicated the rate of interest at which banks lent to favored customers, i.e., those with high
credibility, though this is no longer always the case. Some variable interest rates may be expressed as a
percentage above or below prime rate.”)
So, it is of interest to try to project the prime rate into the future. That is the purpose of this article.
Prime-Rate Data
The prime-rate data (% interest rate) can be obtained from
http://www.federalreserve.gov/releases/h15/data.htm
year
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
Rate
3.77
4.2
3.83
4.48
4.82
4.5
4.5
4.5
4.5
4.54
5.63
5.63
6.31
7.96
7.91
5.73
5.25
8.03
10.81
7.86
6.84
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
6.83
9.06
12.67
15.26
18.87
14.85
10.79
12.04
9.93
8.33
8.21
9.32
10.87
10.01
8.46
6.25
6
7.15
8.83
8.27
8.44
8.35
8
9.23
6.91
4.67
4.12
4.34
6.19
7.96
8.05
5.09
3.25
3.25
3.25
Plotted, the data look like this:
Prime Interest Rate (%)
20
18
16
14
12
10
8
6
4
2
0
There appears to be an approximate five-year period to the oscillations and, perhaps, a longer ~70 year
oscillation. There is an anomalous peak at ~1981.
Fit to the Data
Given the hints provided by the plot features described above, an attempt was made to fit the data with
the equation
 t − t0 i
P = c + ∑ ai sin  2π
λi
i =1

2
 ( t − t )2 

b
g
.
exp 
+
2


2
s
 s 2π


The fit is the red curve in the plot below:
Prime Interest Rate (%)
20
18
16
14
12
10
8
6
4
2
0
Rate
Fit
The parameters of the fit are:
Chi
Square
64.94
Constant
c
6.067039
Gaussian
b
29.73439
tg
1981.058
s
1.225523
a1
1.042141
λ1
5.308818
t01
88.062
a2
3.053355
λ2
72.8591
t02
0
sine
sine2
Conclusions
•
•
•
The 5.3-years oscillations are often about twice the values of the fit’s (1.04%)
Another anomaly similar to the 1981 one could occur in the future.
If the past ~73-years oscillation holds, the prime rate will not rise rapidly in the future.
References
•
•
•
http://primerate.wsjprimerate.us/
http://www.wsjprimerate.us/wsjprimerate/labels/prime_rate_forecast.html
http://www.forecasts.org/interest-rate/prime-interest-rate.htm