Effective Duration and Key Rate Duration | CFA Level I Fixed Income

In this lesson, we’ll learn about the last two duration measures for the exam: effective duration and key rate duration. We’ll dive into their importance, how to calculate them, and how they apply to bonds with embedded options. Let’s get started!

Understanding Effective Duration

So far, we’ve learned that modified or approximate modified duration measures the approximate percentage change in a bond’s price for a 1% change in the bond’s yield-to-maturity (YTM). YTM can be broken down into two components:

By removing the spread, we can find the bond’s sensitivity to changes in the benchmark yield curve, called effective duration.

Formula for Effective Duration

The formula for effective duration is similar to approximate modified duration but uses the change in the benchmark yield curve instead of the bond’s YTM:

Effective Duration = (V- – V+) / (2 * V0 * ΔCurve)

Effective Duration for Bonds with Embedded Options

Effective duration is crucial for measuring interest rate risk for bonds with embedded options, like callable bonds, which have uncertain future cash flows. Thus, yield duration statistics like modified and Macaulay durations don’t apply. This is also true for mortgage-backed securities with prepayment options.

Calculating Effective Duration: Callable Bond Example

EXAMPLE

Given:

Calculate the effective duration for the callable bond.

Solution:

V0 = 102.43, V- = 103.13, V+ = 99.83, ΔYield = 25 basis points

Effective Duration = (103.13 – 99.83) / (2 * 102.43 * 0.0025) ≈ 6.44

Key Rate Duration: Assessing Shaping Risk

Key rate duration helps estimate the change in a bond’s price under different yield curve scenarios, assessing the “shaping risk” of a bond. It is the sensitivity of a bond’s value to changes in the spot rate for a specific maturity, holding other spot rates constant.

Using Key Rate Duration

For each maturity, an analyst projects the scenario to study (e.g., the effect of a steepening yield curve) and multiplies the changes in spot rates with their respective key rate durations. Summing these individual effects gives the overall effect on the bond’s price.

Wrapping Up Effective Duration and Key Rate Duration

We’ve covered effective duration and key rate duration, both crucial measures for bonds with embedded options. In the next lesson, we’ll learn how to calculate duration for a portfolio of bonds.

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