Module 59: Curve Based and Empirical Measured

Question 1

What is Effective Duration?

Answer 1

It is a measure of duration for bonds that have embedded option, where the YTM might be different as their future cash flows and timings may not be known

Question 2

What does effective duration measure

Answer 2

Measures sensitivity of bond price to changes in benchmark yield curve (e.g. gov par curve)

Question 3

How do you calculate effective duration

Answer 3

V(-) - V(+) / 2Vo * Change in benchmark yield curve

Question 4

How do you calculate effective convexity?

Answer 4

• Callable bonds have positive convexity at higher yields but negative convexity at lower yields
• Putable bonds always has positive convexity

V (-) + V(+) - 2Vo / (Chnge in bench mark yield)^2 * Vo

Question 5

How do we apply effective duration and effective convexity

Answer 5

We can compute them to find out the % change in the full price of a bond
Effective Duration x % change in curve + [1/2 x effective duration x (curve change)^2]

Question 6

What is key rate (partial) duration?

Answer 6

• Measure of bond price sensitivity for non parallel benchmark yield curve change, so for only specific maturities
• We only shift for key points, one at a time
• Calculation: - 1/PV * Change in PV / Scale of Shift itself
• Sums of all key rate durations = effective duration

Question 7

What is analytical Duration and what’s the issue with it?

Answer 7

Duration measures based on mathematical analysis, example include MacDur, ModDur, EffDur, Key Rate
Issue: It has an assumption that government bond yields and credit spreads are independent which is not the case.

Question 8

What is empirical duration

Answer 8

Uses historical data in statistical models which incorporates various factors not affecting bond prices
* It accounts for the correlelation between yield spreads and benchmarks