How to Calculate Interest Rate Volatility?

  • 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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