Reading 53: Term Structure and Volatility of Interest Rates- div, class, center, interpret

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Session 14: Fixed Income: Valuation Concepts
Reading 53: Term Structure and Volatility of Interest Rates

LOS g, (Part 1): Compute and interpret yield volatility.

 

 

 

What is the annualized yield volatility if the daily yield volatility is equal to 0.6754%?

A) 9.73%.

B) 10.68%.

C) 168.85%.

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Annualized yield volatility = σ × √(# of trading days in a year)

Where σ = the daily yield volatility.

So,

Annualized yield volatility = (0.6754%) √(250) = 10.68%

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Yield volatility is a measure of the:

A) relative daily yield changes over a period.

B) absolute daily yield changes over a period.

C) difference in the beginning interest rate and ending interest rate over a period.

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Yield volatility measures the relative daily yield changes over some period. To see why this might be important, note that an interest rate series could begin and end at the same point but have very large changes during the period. Such information would likely be of value to the bond analyst.

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For a given three-day period, the interest rates are 4.0%, 4.1%, and 4.0%. What is the yield volatility over this period?

A) 0.0349.

B) 0.0577.

C) 0.0000.

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The yield volatility is the standard deviation of the natural logarithms of the two ratios (4.1/4.0) and (4.0/4.1) which are 0.0247 and –0.0247 respectively. Since the mean of these two numbers is zero, the standard deviation is simply {[(0.0247)² +(-0.0247)²]/(2-1)}^0.5=0.0349.

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Which of the following is the most important consideration in determining the number of observations to use to estimate the yield volatility?

A) The appropriate time horizon.

B) The liquidity of the underlying instrument.

C) The shape of the yield curve.

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The appropriate number of days depends on the investment horizon of the user of the volatility measurement, e.g., day traders versus pension fund managers.

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Which of the following is a major consideration when the daily yield volatility is annualized?

A) The appropriate day multiple to use for a year.

B) The appropriate time horizon.

C) The shape of the yield curve.

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Typically, the number of trading days per year is used, i.e., 250 days.

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Suppose that the sample mean of 25 daily yield changes is 0.08%, and the sum of the squared deviations from the mean is 9.6464. Which of the following is the closest to the daily yield volatility?

A) 0.4019%.

B) 0.3859%.

C) 0.6340%.

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Daily yield volatility is the standard deviation of the daily yield changes. The variance is obtained by dividing the sum of the squared deviations by the number of observations minus one. Therefore, we have:

Variance = 9.6464/(25 – 1) = 0.4019

Standard deviation = yield volatility = (0.4019)^? = 0.6340%