Convexity and impact on economic surplus

[sfad]

This is 2013 mock q8. The durations of the assets and liabilities remain matched but the convexity of the assets remains greater than the convexity of the liabilities. We are asked to explain the effect of an upward shift in yield curve on economic surplus. Answer says: Because duration of assets equals duration of liabilities, changes in value due to duration will be equal. As a result, there is no change in economic surplus due to duration effects. However, since convexity of liabilities is less than convexity of assets, the decline in value of assets as a result of yield curve shift will be greater than decline in value of assets, thus increasing economic surplus.

I thought convexity behaved the same as duration, so when convexity of liabilities is less than convexity of assets, an upward shift in yield would mean liabilities decrease in value less than assets decrease in value. Can someone please clarify?

[MissYiota]

I remember it that way. Positive Convexity is a good thing. So it always works better on the side it is positive

[MrSmart]

You wrote assets twice, but yes, the economic surplus will imporve.

You always want convexity, because it adds to the price whichever way interest rates go.

[sfad]

I’m still unsure on this. I understand that with duration: If duration of liabilities is less than duration of assets, upward shift in yield means liabilities decrease in value less than assets decrease in value. But with convexity is number 1. or number 2. correct? 1. If convexity of liabilities is less than convexity of assets, upward shift in yield means liabilities decrease in value less than assets decrease in value. 2. If convexity of liabilities is less than convexity of assets, upward shift in yield means liabilities decrease in value more than assets decrease in value.

[Grrreg]

answer #1 as assets are more sensible to extremities of the curve move and a parallel upward shift mean they will loose more value than less convex liabilities

[MrSmart]

@Grrreg

answer #1 as assets are more sensible to extremities of the curve move and a parallel upward shift mean they will loose more value than less convex liabilities

False.

@sfad

I’m still unsure on this. I understand that with duration: If duration of liabilities is less than duration of assets, upward shift in yield means liabilities decrease in value less than assets decrease in value. But with convexity is number 1. or number 2. correct? 1. If convexity of liabilities is less than convexity of assets, upward shift in yield means liabilities decrease in value less than assets decrease in value. 2. If convexity of liabilities is less than convexity of assets, upward shift in yield means liabilities decrease in value more than assets decrease in value.

Two, imagine the price-yield curve of liabilities to be linearly flat, or recall the convexity-duration forumula from level 1, convexity always add to price.

That should help you remember

[cpk123]

Price Change = -Duration * (Delta Rate) + Convexity * (Delta Rate)^2

Rate falls - Delta Rate is negative - the Price Change gets a double positive impact. (both due to Duration and due to Convexity)

When Rate increases - Price Falls due to Duration effect - but increases due to Convexity effect.

===

And this is Level I stuff.

This happens both for Asset and for Liability.

And Asset - Liability = Surplus

[Grrreg]

@MrSmart

@Grrreg

answer #1 as assets are more sensible to extremities of the curve move and a parallel upward shift mean they will loose more value than less convex liabilities

False.

@sfad

I’m still unsure on this. I understand that with duration: If duration of liabilities is less than duration of assets, upward shift in yield means liabilities decrease in value less than assets decrease in value. But with convexity is number 1. or number 2. correct? 1. If convexity of liabilities is less than convexity of assets, upward shift in yield means liabilities decrease in value less than assets decrease in value.

2. If convexity of liabilities is less than convexity of assets, upward shift in yield means liabilities decrease in value more than assets decrease in value.

Two, imagine the price-yield curve of liabilities to be linearly flat, or recall the convexity-duration forumula from level !, convexity always add to price.

That should help you remember

Seems I need to get back to my books on this one, happy to discover that before the exam. thx

[sfad]

@MrSmart

@Grrreg

answer #1 as assets are more sensible to extremities of the curve move and a parallel upward shift mean they will loose more value than less convex liabilities

False.

@sfad

I’m still unsure on this. I understand that with duration: If duration of liabilities is less than duration of assets, upward shift in yield means liabilities decrease in value less than assets decrease in value. But with convexity is number 1. or number 2. correct? 1. If convexity of liabilities is less than convexity of assets, upward shift in yield means liabilities decrease in value less than assets decrease in value. 2. If convexity of liabilities is less than convexity of assets, upward shift in yield means liabilities decrease in value more than assets decrease in value.

Two, imagine the price-yield curve of liabilities to be linearly flat, or recall the convexity-duration forumula from level 1, convexity always add to price.

That should help you remember

1. Sorry what is meant by convexity always adds to price? 2. So when convexity of liabilities is less than convexity of assets, we have: When interest rates increase then Decrease in liabilities > Decrease in assets When interest rates decrease then Increase in liabilities < Increase in assets Is that correct