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.
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