Which of the following is correct about the application of duration? a. Duration can be used...

Which of the following is correct about the application of duration?

a. Duration can be used to provide an exact price impact from changes in interest rates.

b. Yield curve risk does not impact duration.

c. Effective duration is another name for modified duration.

d. None of the above.

Solutions

Expert Solution

Background:
Duration is a quantitative measure of the sensitivity of bond prices to change in interest rates. There are different measures of duration - like Modified Duration, Effective Duration and Macaulay Duration. Each measure has a slightly different formula. Please see images attached.

a) Incorrect. Duration gives only an approximate estimate of the price impact from changes in interest rates. This approximation is reasonable when the change in interest rates is small, but not otherwise. One should add the convexity adjustment to improve the estimate of price impact.

b) Incorrect. Duration itself changes with a change in yield. Hence, any change in yield curve is likely to impact duration.

c) Incorrect. Effective Duration is different from Modified Duration.
Effective Duration = - (% change in bond price)/(change in yield in %).
Macaulay Duration = (present value of cash flows of a bond weighted by their respective time of receipt)/(bond price). (See the formula in image attached.)
Modified Duration = (Macaulay Duration) / (1+YTM/n); where YTM is the yield to maturity of a bond and n is the compounding frequency. (See the formula in image attached.)

Hence, correct response to this question is Alternative (d): None of the above.

jeff jeffy answered 11 months ago

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