# Duration vs Convexity

Hi

Do they have opposite effects when assessing the values of assets and liabilities changes/surplus when interest rates changes?

Whichever has a higher convexity, lose less value when rate goes up and gain more value when rate goes down.

You’re assuming that their durations are equal.

Please be more careful in your answers, especially during this frenzied last week before the exam. You don’t want to do more harm than good.

Where’s the perfect question?

convexity is a good thing to have all else equal, the fixed income security with more convexity will loose less value when rate go up. S2K wisely pointed out that it has to be considered in the context of the other attributes of the security if there is a question on it

Ok!

The question is too ambiguous. Agree with Mr. Smart. Also agree w/ S2000. It depends on the context.

The Q is: assuming equal durations for assets & liabilities values, why convexity gives opposite results to duration when interest rates change?

It doesn’t.

%ΔP = −Deff(Δ_y_) + ½Ceff(Δ_y_)²

• If effective convexity (Ceff) is positive, the price effect is positive, no matter what the price effect of duration is
• If effective convexity (Ceff) is negative, the price effect is negative, no matter what the price effect of duration is
• If effective duration (Deff) is positive, the price effect is negative when Δ_y_ is positive and positive when Δ_y_ is negative, no matter what the price effect of convexity is
• If effective duration (Deff) is negative, the price effect is positive when Δ_y_ is positive and negative when Δ_y_ is negative, no matter what the price effect of convexity is

Now it’s clear. Thank you.

My pleasure.