What is the empirical evidence on the relationship between volatility and the level of interest rates?

What will be an ideal response?

Empirical evidence reviewed regarding the relationship between interest-rate volatility and the level of rates suggests that the relationship is weak at interest rate levels below 10%. However, for rates exceeding 10%, there tends to be a positive relationship. More details are given below.

To answer this question, we need to examine from an historical perspective the issue as to whether interest rate volatility is affected by the level of interest rates or independent of the level of interest rates. If it is affected, one might suspect a higher the level of interest rates will lead to greater volatility in the interest rates. That is, there will be a positive correlation between the level of interest rates and interest-rate volatility. If the two are independent, a low correlation would exist.

The dependence of volatility on the level of interest rates has been examined by several researchers. The earlier research focused on short-term rates and employed a statistical time series model called generalized autoregressive conditional heteroscedasticity (GARCH). With respect to short-term rates, the findings were inconclusive.

Rather than focusing on the short-term rate, Cheyette examined all the spot rates for the Treasury yield curve for the period 1977 to early 1996, a period covering a wide range of interest rates and different Federal Reserve policies. He found that for different periods there are different degrees of dependence of volatility on the level of interest rates. (Interest-rate changes are measured as absolute rate changes in Cheyette's study). Specifically, in the high interest-rate environment of the late 1970s and early 1980s where interest rates exceeded 10%, there was a positive correlation between interest-rate volatility and the level of interest rates. However, when interest rates were below 10%, the relationship was weak. Hence, the findings suggest that since the 1980s, interest-rate volatility has been independent of the level of interest rates. These conclusions were supported in a study by Levin of the Treasury 10-year rate from 1980 to 2003 and the 10-year swap rate from 1989 to 2003.

The implication is that in modeling interest rates, one can assume that interest-rate volatility is independent of the level of interest rates in an environment where rates are less than double digit. That is, in modeling the dynamics of the volatility term the normal model can be used.