Duration vs Convexity

[cfapasss]

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

 

[hlmasterchief]

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

 

[S2000magician]

hlmasterchief wrote: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.

 

[cfapasss]

S2000magician wrote:

hlmasterchief wrote: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.

So what’s the perfect answer?

 

[MrSmart]

cfapasss wrote:

S2000magician wrote:

hlmasterchief wrote: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.

So what’s the perfect answer?

Where’s the perfect question?

 

[Grrreg]

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

 

[cfapasss]

Ok!

 

[cebrach]

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

 

[cfapasss]

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

 

[S2000magician]

cfapasss wrote: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(Δy) + ½Ceff(Δy)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 Δy is positive and positive when Δy is negative, no matter what the price effect of convexity is
• If effective duration (Deff) is negative, the price effect is positive when Δy is positive and negative when Δy is negative, no matter what the price effect of convexity is

 

[cfapasss]

S2000magician wrote:

cfapasss wrote: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(Δy) + ½Ceff(Δy)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 Δy is positive and positive when Δy is negative, no matter what the price effect of convexity is
• If effective duration (Deff) is negative, the price effect is positive when Δy is positive and negative when Δy is negative, no matter what the price effect of convexity is

Now it’s clear.
Thank you.

 

[S2000magician]

My pleasure.