Lecture 5
Historical Interest Rate Movements
Term Structure Shapes
Normal upward sloping
Inverted
Common Term Structure Shapes
Level
Humped
12
Interest Rate (%)
•
•
•
•
10
8
Upward Sloping
6
Inverted
Level
4
Humped
2
0
1
3
5
Years
10
30
How Do Curves Shift?
• Litterman and Scheinkmann (1991)
investigated the factors that affect yield
movements
• Over 95% of yield changes are explained by a
combination of three different factors
– Level
– Steepness
– Curvature
• Rates of maturities shift
by approximately the
same amount
• Also called a parallel
shift
Yield
Level Shifts
Maturity
• Short rates move more
(or less) than longer
term interest rates
• Changes the slope of the
yield curve
Yield
Steepness Shifts
Maturity
• Shape of curve is
altered
• Short and long rates
move in one direction,
intermediate rates move
in the other
Yield
Curvature Shifts
Maturity
Characteristics of Historical
Interest Rate Movements
• Rule out negative interest rates
• Higher volatility in short-term rates, lower
volatility in long-term rates
• Mean reversion (weak)
• Correlation between rates closer together is
higher than between rates far apart
• Volatility of rates is related to level of the rate
Summary Statistics for Historical Rates (1953-2001)
http://www.federalreserve.gov/releases/H15/data.htm
Normal
66.9%
Shape
Inverted
Humped
10.7%
15.3%
Yield Statistics
1 yr.
3 yr.
5 yr.
Mean
6.04
6.42
6.58
S.D.
2.93
2.82
2.78
Skew ness
1.03
0.90
0.84
Exc. Kurtosis 1.35
0.90
0.67
Percentiles
1 yr.
3 yr.
5 yr.
1%
1.11
1.60
1.95
5%
2.26
2.58
2.75
95%
12.04
12.09
12.40
99%
15.00
14.66
14.56
Corr (1 yr,10 yr) = 0.943
Other
7.1%
10 yr.
6.74
2.75
0.76
0.34
10 yr.
2.38
2.92
12.43
14.28
Run Graph Show of Interest Rates
• Go to:
http://www.cba.uiuc.edu/~s-darcy/present/casdfa3/intmodels.html
•
•
•
•
Download Graph Show
Click on Historical (4/53-5/99)
Click on Start Graph Show
You may want to shorten the time interval to speed up
the process
• Note how interest rates have moved over the last 46
years
• Pay attention to the level of interest rates, the shape of
the yield curve and the volatility over time
Current Interest Rates
• Yields
• Spot rates
• Implied forward rates
Yield Curve
December 2001
7
6
Interest Rate
5
4
3
2
1
0
0
5
10
15
Years to Maturity
20
25
30
Distortions
• U. S. Government stopped issuing 30 year
bonds in October, 2001
• Reduced supply of long term bonds has
increased their price, and reduced their yields
• Effect has distorted the yield curve
Conclusion
• Interest rates fluctuate
• Interest rate models are used to predict future
interest rate movements
• Historical information useful to determine type
of fluctuations that occur
–
–
–
–
Shapes of term structure
Volatility
Mean reversion
Long run mean levels
• Don’t assume best model is the one that fits
past movements the best