YouTube T4-34: Fixed Income: Effective duration

[Nicole Seaman]

Effective duration approximates modified duration. Both express interest rate sensitivity: an effective (or modified) duration of 6.2 years tells us to expect a 0.620% price change if the yield changes by 10 basis points; i.e., 0.10% ∆y * 6.2 years = 0.620% ∆P. Effective duration is given by -1/P * [P(+∆y) - P(-∆y)]/(2*∆y) where ∆y is our selected, small yield shock. This video explain the intuition which is that we use effective duration when it's more realistic to retrieve to slope of a secant line, as an approximation to the exact slope of the nearby tangent line. Effective duration is appropriate when the price/yield relationship is non-trivial (e.g., embedded options cause negative convexity) and therefore doesn't lend itself to an easier, analytical modified duration.

 

[Shah59611]

Thank you !

 

[David Harper CFA FRM]

Hi @Shah59611 Did you view the video? Effective duration is given by, D = -1/P * [P(+∆y) - P(-∆y)]/(2*∆y) and this formula does not itself require a duration assumption (it only requires that we can re-price the bond as a function of a different yield). Rather, we are simply re-pricing the bond after we shock the yield. So we just need to decide how much to shock the current yield, maybe Δy = 20 basis points, then we price the bond at the higher yield and the lower yield, and plug in those prices into the numerator. This part of the formula, [P(+∆y) - P(-∆y)]/(2*∆y), is just the slope of the line (which is dollar duration in this context); think slope = rise/run where the graph is price (y axes) versus yield (x axis). In geometry terms, it computes the slope of the secant line; we never need modified duration, which is close because it is a function of the slope of the tangent line. If our shock is low, the slopes must be similar. I hope that's helpful,

append: it looks like you edited to "Thank you," rather than replied. No worries. Here is the question to which I replied FWIW:

Hi !
I have a doubt
If effective duration is an estimate of the modified duration but in the formula :-
Price of the bond if yield increases/decreases is calculated by modified duration relationship which itself requires modified duration?
So how can it be an estimate is what i am confused about.
Thankyou !