Reading 55: Term Structure and Volatility of Interest Rates- center, between, interpret, class

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Session 14: Fixed Income: Valuation Concepts
Reading 55: Term Structure and Volatility of Interest Rates

LOS g: Compute and interpret yield volatility, Distinguish between historical yield volatility and implied yield volatility, and explain how yield volatility is forecasted.

 

 

Which of the following is closest to the annualized yield volatility (250 trading days per year) if the daily yield volatility is equal to 0.45%?

A) 9.73%.

B) 7.12%.

C) 112.50%.

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Annualized yield volatility = σ ×

where:
σ = the daily yield volatility

So, annualized yield volatility = (0.45%) = 7.12%.

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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%

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Which of the following is closest to the annualized yield volatility (250 trading days per year) if the daily yield volatility is equal to 0.6754%?

A) 9.73%.

B) 168.85%.

C) 10.68%.

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Annualized yield volatility = σ ×

where:
σ = the daily yield volatility

So, annualized yield volatility = (0.6754%) = 10.68%.

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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) 0.0577.

B) 0.0349.

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 time horizon.

B) The shape of the yield curve.

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

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

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Yield volatility has been observed to follow patterns over time. One class of statistical techniques used to forecast those patterns is called:

A) autoregressive capital hedging models.

B) autoregressive heteroskedasticity models.

C) absolute regression chart highlight models.

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Autoregressive heteroskedasticity (ARCH) models incorporate past patterns of yield volatilities to forecast future patterns.

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Which of the following is the most appropriate model when we assume that volatility today depends only upon recent prior volatility?

A) A time weighted historical volatility model.

B) An autoregressive conditional heteroskedasticity (ARCH) model.

C) An implied volatility model.

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ARCH is commonly used with econometric forecasting techniques.

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Suppose that market participants give the most importance to the most recent movements in yield. Which of the following best describes how the historical yield estimate should be adjusted?

A) Use only the most recent observations.

B) Give increased weight to the most recent observations.

C) Give increased weight to the implied volatility measure.

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In this way the forecasted volatility reacts faster to a recent major market movement.

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To estimate yield volatility, an analyst may use historical yields or an implied yield volatility calculated from current market conditions. Identify the pair of terms below that correctly matches a key ingredient in each estimation process with the process itself.

A) Historical yield volatility: Duration. Implied yield volatility: A series of log ratios of daily rates.

B) Historical yield volatility: The standard deviation formula. Implied yield volatility: Derivative prices.

C) Historical yield volatility: Derivative prices. Implied yield volatility: The standard deviation formula.

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The historical yield volatility method uses the standard deviation formula. The implied yield volatility method uses derivative prices. In the latter method, the current derivative prices are entered into a formula along with other observed variables. The series of log ratios of daily rates is associated with the historical yield volatility. Duration is not directly relevant.