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How to Calculate Interest Rate Volatility?

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Step 1: Calculate yield change ratios as follows: YCR t = r t / r t-1

The yield change ratios are typically daily ratios (i.e., today's yield or interest rate divided by yesterday's) that are annualized later at a later step in the process.
Step 2: Convert yield change ratios into a continuously compounded return (Xt) as follows:

X t = ln YCRt

Step 3: Calculate the average of continuously compounded returns (X t) for the time period.
Step 4: Sum the squared the differences between the individual continuously compounded rates of return and the average calculated in step 3.

= Σ(X t - X average)2

Step 5: Divide the sum of squared differences by the number of time periods minus 1.

= step 4 value / (n-1)

In the context of statistics, this value represents the yield variance

Step 6: Take the square root of step 5 to arrive at a periodic (commonly daily) standard deviation (σ daily) for the bond's yield.

This value represents the percentage of the yield's daily standard deviation and not the actual basis point standard deviation.
Step 7: Annualize daily percentage standard deviation.

σ annual = σ daily × √num. of trading days per year

The annual standard deviation of a bond's yield is equal to the daily standard deviation multiplied by the square root of the number of trading days in a year.
The convention is 250 trading days per year.
This value reflects the percentage standard deviation of the yield, not the basis points standard deviation.
Step 8: Compute the basis points the standard deviation of the bond's yield.

σ yield = Yield * σ annual

This value will reflect the standard deviation in terms of basis points around the current yield of the bond.

A bond's yield can be analyzed in conjunction with the standard deviation of the yield in basis point terms from step 8 and z-score distribution to create a confidence interval for the bond's yield.
Candidates are advised to apply this approach to practice questions in order to completely understand the analysis of yield volatility and be appropriately prepared for the exam.

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