Effective Duration

What is the general term for duration measures that are based on a benchmark instead of the bond's yield?

Incorrect. Yield duration refers to a measure that uses the yield on the bond.

Correct! Curve duration is a general term for duration measures that rely on benchmark yield curves.

Incorrect. Modified duration is a specific duration measure, not a general classification of duration measures.

What is the term for the market convention for quoting the yield on a callable bond?

Incorrect. By convention, a callable bond must be priced to the lower of the yield-to-call or yield-to-maturity.

Correct! By convention, a callable bond must be priced to the lower of the yield-to-call or yield-to-maturity. This is referred to as the yield-to-worst.

Incorrect. By convention, a callable bond must be priced to the lower of the yield-to-call or yield-to-maturity.

Notice that based on the yield change, the bond is priced at a premium _and_ a discount in the effective duration estimate. This would not be captured using modified duration. For which of the following investments would you also expect to use effective duration instead of conventional measures?

Incorrect. Effective duration measures are for fixed-income assets, not common stocks.

Incorrect. Standard measures of duration such as modified duration can be used for non-callable bonds.

Correct! Effective duration is most useful for fixed-income assets with uncertain cash flows such as callable bonds and mortgage-backed securities. Mortgage-backed securities are essentially callable bonds. You could also use a pricing model to find the "credit duration" statistic, which is the sensitivity of the bond price to a change in the credit spread.

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As an example, consider a 6.00%, 10-year bond with semiannual coupons that is callable at par in eight years. The bond is priced with a yield-to-maturity of 6.10 at 99.259. If the yield curve increases by 30 basis points, it is estimated that the bond will sell for 97.078. However, if the yield curve decreases by 30 basis points, the bond will be priced-to-call at an estimated price of 102.551. Using effective duration, the duration estimate is equal to: $$\displaystyle \text{EffDur} = \frac{(102.551 - 97.078)}{2(99.259)(0.0030)} \approx 9.1898$$

__Effective duration__ is similar to approximate modified duration. It is a way of estimating price changes without starting with a duration measure. Actual changes in the bond price are used to approximate duration. This is the proper measure to use for callable bonds. Unlike other duration methods, instead of using changes in bond yields, changes in a benchmark yield curve are used in this measure.

Effective duration is most useful for bonds that have uncertain future payoffs. A good example is a callable bond that is selling at a yield close to the coupon. Such a bond would, by convention, be priced to the call date if the yield is below the coupon and priced to maturity if the yield is above the coupon. In this situation, using modified duration might overestimate or underestimate duration. Effective duration is better because it captures the price switch between priced-to-call and price-to-maturity.

Effective duration is computed as follows: $$\displaystyle \text{EffDur} =\frac{(PV_-) - (PV_+)}{2 \times (\Delta \text{Curve}) \times (PV_0)} $$ where $$PV_0$$ is the current bond price, $$PV_-$$ is the bond price if yields decrease, $$PV_+$$ is the bond price if yields increase, and $$\Delta \text{Curve}$$ is the change in a benchmark yield curve.

Yield duration

Curve duration

Modified duration

Yield-to-call

Yield-to-worst

Yield-to-maturity

Common stock

Non-callable bond

Mortgage-backed security

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