Modified Duration

[robustening]

I understand MacDur is the time at which reinvestment risk and price risk cancel each other out. I can’t understand the intuition behind ModDur. Dividing the MacDur by 1+Yield is like discounting the MacDur by one period, right? But it is defined as the approx % change in the bond’s price given a 1% change in YTM. Where in the formula are you given the 1% change?

Been struggling with this for a while, I hope someone can make me understand so I dont rely on merely memorizing formulas.

[S2000magician]

@robustening

I understand MacDur is the time at which reinvestment risk and price risk cancel each other out. I can’t understand the intuition behind ModDur. Dividing the MacDur by 1+Yield is like discounting the MacDur by one period, right?

It looks like that, but it’s really a calculus thing. You’re probably better off accepting it and moving on. If you really need to see the derivation, you can search threads from last Spring; I recall writing up the derivation in one of them.

@robustening

But it is defined as the approx % change in the bond’s price given a 1% change in YTM. Where in the formula are you given the 1% change?

You aren’t, per se. Think of it as you would the slope of a line: if the slope m = 3.2, then y changes by 3.2 when x changes by 1. You don’t have to specify that; it’s inherent in the definition of slope: Δ_y_ = m × Δ_x_. Similarly, a bond with a 4.2 year modified (or effective) duration will have a price change of (approximately) -4.2% when its YTM changes 1%; it’s inherent in the definition of duration: %Δ_price_ ≈ Dmod × Δ_YTM_

[robustening]

@S2000magician

You aren’t, per se. Think of it as you would the slope of a line: if the slope m = 3.2, then y changes by 3.2 when x changes by 1. You don’t have to specify that; it’s inherent in the definition of slope: Δ_y_ = m × Δ_x_. Similarly, a bond with a 4.2 year modified (or effective) duration will have a price change of (approximately) -4.2% when its YTM changes 1%; it’s inherent in the definition of duration: %Δ_price_ ≈ Dmod × Δ_YTM_

thanks so much… after several hours this finally clicked thanks to your explanation.

[S2000magician]

Cool!

You’re quite welcome.

[nk1018]

Fully understanding the subtle difference btw the two may provide you with intellectual satisfaction, but if your goal is to learn CFAI material and pass the CFA I exam, I think spending several hours on that is a poor study tactic. Level 1 covers a lot of material, if you’re taking the December exam, try not to get stuck on one specific topic. Move on and come back later.

If you’re studying from a test prep provider, they do a great job of pointing out these things (whether minute differences are worth noting). In fact, I believe S2000’s clarification that its a matter of calculus (not the focus of CFA program), is stated in Schweser notes.

[S2000magician]

@nk1018

. . . I believe S2000’s clarification that its a matter of calculus (not the focus of CFA program), is stated in Schweser notes.

I’ve taught Level I classes from Schweser’s material for many years; they’ve never (to the best of my knowledge) mentioned calculus in the discussion of modified duration.