## Thursday, 16 November 2017

### MEASURING THE VOLATILITY OF INTEREST RATES

We will measure interest rate volatility using a statistic called the standard
deviation. The standard deviation. The standard deviation measure how
dispersed a variable is around its average valve, If the standard deviation is high,
observations on a variable tend to be for away from the variable tend to be
clustered around the average valve. Therefore, as the standard deviation
increases, there is a greater chance that will see large changes in the valve of
the variables.
The volatility of interest rates can be calculated over the entire term structure of
interest rate; we supply use of historical data to calculate the standard deviation
of interest rates for each maturity. In describing the cyclical volatility of interest
rate, we would like to know not just how much interest rates ray but also how
they vary with the state of the economy. During recessions, real output is
declining; during expansion, its rising. We can get an idea of the behavior of
interest rate over the business cycle by evaluating how interest rates aid the level
of real output-co-vary over the business cycle. The correlation coefficient is a
measure of the strength of the co-variation between two variables, and it can take on valves between minus one and one when the correlation coefficient
between two variables track each other closely and move in the same direction;
when one variable is high, the other variable is very likely to be high. If the
correlation coefficient is negative and close to one, the two variable track each
other close but move in opposite direction: when one variables is high, the other
is likely to be low. When the correlation coefficient is zero, the two variable do not
track each other closely in either duration. Maturity, the contemporaneous
correlation is negative, though quite small. This implies that there is little co-
variation between the cyclical movements in current real output and the cyclical
movements in current real output and the cyclical movements in current real
output and the cyclical movements in long-term interest rates. These facts can be
expressed by saying that short- term interest rates are procyclincal and long-term
interest rates are cyclical. The result in table 2 suggest significant business cycle
using the data in table 2. We have seen that short-term interest rates tend to
move up when output moves up but that the correlation tends to decline as the
maturity of the bond increases. Thus, when current output rises, the yield-curve
tends to flatten, since short term interest rates tend to rise and long term
Interests rare move relatively little. Similarly, when current output declines, the
yield curve tends to steepen, since short term interest rates tend to fall with
output and long term interest rates tend to remain about the same.
We have seen how the volatility of interest rates changes with maturity and how
interest rates move in relation to real rates on bonds of different maturity lets take the case of the interest rates on a secondary with one quarter maturity. We see
that the one quarter interest rate is most highly correlated with the interest rate
on a bond with two-quarter maturity, and that the correction declines, though
remains strong, as we compare bonds with increasingly different maturities.
These current to shift up and down, while allowing for the possibility that the
shape of the yield curve can change.
Finally, if we re-examine figure 3, we might suspect that the measured volatility of
interest rates depends on the period we're look t. Since the late 1970s, long-term
interest rate appear to have shown more short—run variability, and the
deviations of the interest rate on 10-year bonds from the trend live have been
large and persistent (Sill 1994).
In fact, the results in table 4 show that interest rates at all maturities may have
been more variable since that time. The table shows the standard deviation of
interest rates using the same data, but the sample is divided into two sub
samples: from first quarter 1959 to first quarter 1979 and from second quarter
1979 to first quarter 1990. We see that iterest rates at all maturities have been
more volatile since 1979. This result suggests the possibility that some structural
change in the economy has affected the variability of interest rates and bond
prices.