Key Rate Duration

Key Rate Duration

The effective duration calculates expected changes in price for a bond or portfolio of bonds given a basis point change in yield. This, however, is only valid for parallel shifts in the yield curve. The key rate duration presents an improvement to the effective duration because it gives the expected changes in price when the yield curve shifts in a manner that is not perfectly parallel. In other words, it measures a security’s sensitivity to shifts at “key” points along the yield curve.

key-rate-duration

The key rate formula is similar to the effective duration formula, except that it uses 0.01 in the denominator to reflect a 1% (100 basis points) change in the yield at a specific point on the yield curve:

$$ \text{Key rate duration} =\frac { { PV }_{ – }-{ { PV }_{ + } } }{ 2\times 0.01 \times { PV }_{ 0 } } $$

Where:

\({ PV }_{ – }\) = the bond price after a 1% decrease in yield

\({ PV }_{ + }\) = the bond price after a 1% increase in yield

\({ PV }_{ 0 }\) = the original bond price

Example: Key Rate Duration

A bond is originally priced at $1,000. With a 1% increase in yield for a certain maturity on the yield curve, the bond’s price would decrease to $980. A 1% decrease in the same yield, would occasion a rise of the price to $1,030. Based on the formula above, the key rate duration of the bond would be:

$$ KRD =\frac { { 1,030 }-{ 980 }}{ 2\times 0.01 \times { 1,000 } } =2.5$$

Why Use Key Rate Duration?

A financial analyst may want to know how the price of the callable bond is expected to change if benchmark rates at short maturities shift by a specific number of basis points, but longer maturity benchmark rates remain constant. This case would represent a flattening of the yield curve, given that the yield curve is upward sloping. For parallel shifts in the benchmark yield curve, key rate durations could indicate the same interest rate sensitivity as effective duration. 

Interpretation of Key Rate Duration

Interpreting each key rate duration in isolation can be quite difficult. That is because, in practice, it’s highly unlikely that a single point on the yield curve will exhibit an upwards or downwards shift while all other points remain constant. For this reason, analysts tend to compare key rate durations across the curve.

Question

The key rate duration formula is similar to which of the following formulas?

  1. Effective duration.
  2. Modified duration.
  3. Macaulay duration.

Solution

The correct answer is A.

The key rate formula is similar to the effective duration formula, except that it uses 0.01 in the denominator to reflect a 1% change in the yield at a specific point on the yield curve:

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop Graduate Admission Exam Prep


    Sergio Torrico
    Sergio Torrico
    2021-07-23
    Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
    diana
    diana
    2021-07-17
    So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
    Kriti Dhawan
    Kriti Dhawan
    2021-07-16
    A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.
    nikhil kumar
    nikhil kumar
    2021-06-28
    Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
    Marwan
    Marwan
    2021-06-22
    Great support throughout the course by the team, did not feel neglected
    Benjamin anonymous
    Benjamin anonymous
    2021-05-10
    I loved using AnalystPrep for FRM. QBank is huge, videos are great. Would recommend to a friend
    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.