convexity- understanding it

CFA Level III Fixed Income
#1

I want to make sure I understand convexity. If told we want to reduce risk of a fixed income portfolio, and given two portfolios with the same durations, same yields, but different convexities, would we always choose the one w/ lower convexity?

I get confused because convexity is both a measure of risk (bad) AND protection from large rate changes (good), is it not?

#2

Everything else equal, you want _ higher _ convexity. Positive convexity gives you a greater price increase when the yield falls, and a smaller price decrease when the yield rises.

#3

Thanks!

#4

You’re welcome.

#5

In reading 22 convexity is a good thing But in reading 23 page 60 it is said to immunize the single liability we have to minimize portfolio convexity why??

#6

you want to minimize convexity so that it is slightly larger than the convexity of the liability. this way you end up in a better position (than the liability) when rates move. if you go crazy and just go for all the convexity you can get, you end up having a portfolio of very long bonds and very short bonds and as a result a lot of structural risk from yield curve twists.

#7

Different objective.

By minimizing dispersion you’re minimizing price risk and reinvestment risk, which is the objective in immunization.

#8

thank you

#9

You’re welcome.

#10

mrb102189,

This is how I look at convexity so maybe it’ll help you. Rates are going move, period. Whether they move up or down, in a volatile manner or a stable manner, they’re going to move. How should we participate/protect ourselves when that happens? Answer: It’s all about how we’re allocated to the yield curve!

What do I mean? Well, let’s look at a bond portfolio and its Modified Duration of, say, 4 years. We can have three different types of portfolios to get that duration of 4:

  • Barbell: ex) Some bonds w/MD of 2 and some bonds w/MD of 6 --> MD = 4
  • Ladder: ex) Some bonds w/MD of 2, Some bonds w/MD of 4, and Some Bonds w/MD of 6 --> MD = 4
  • Bullet: ex) All bonds w/MD of 4 --> MD = 4

There’s more than one way to skin a cat and more than one way to get that MD of 4. But when interest rates move or become volatile, how, exactly, do we want to position our portfolio? Are there certain strategies that we should implement? What about certain types of bonds to buy or sell to take advantage or protect ourselves?

HIGH CONVEXITY BONDS…WHEN TO OWN THEM?

Interest Rates: Going up and/or Become Volatile

Outperforming Strategy: BARBELL

What’s the Trade Move? BUY: Option-Free, Investment Grade Bonds SELL: Callable/High Yield/MBS

What’s the Rationale? RISK OFF!!! Because rates are moving and getting crazy! We need to get to safety! Give up some yield with those callable/high yield/MBS bonds by selling those and buying nice, safe, option-free IG Bonds

LOW CONVEXTIY BONDS…WHEN TO OWN THEM?

Interest Rates: Low and/or Remaining Stable

Outperforming Strategy: BULLET

What’s the Trade Move? BUY: Callable/High Yield/MBS SELL: Option-Free, Investment Grade Bonds

What’s the Rationale? RISK ON!!! Not much price appreciation, so let’s pick up some yield with some juicy callable/high yield/MBS bonds!

Conclusion: I always ask myself, do I want to have a portfolio of bonds that’s ‘more curved’ like a barbell strategy with higher convexity bonds to protect the portfolio when interest rate moves/vol. gets high? Or do I want to roll the dice, get my risk on and BULLET it straight for a particular part of the curve by selling convexity, getting rid of those safe option-free IG bonds and buying sexier callable/high yield/MBS bonds? The choice is yours…

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#11

TL;DR moment, but I like your enthusiasm!

#12

Hi, I would like to confirm few things on convexity. Are my thoughts right about convexity on below explanation:

  1. Positive Convexity. Duration increase as yield falls and duration decrease as Yield rises (as per your explanation above)
  2. Negative Convexity. Duration increase as yield rises and duration decrease as yield falls (I just using the opposite of negative convexity).
  3. Callable bond is negative convexity.
  4. Putable bond is positive convexity.
1 Like
#13

Yes.

Yes.

Partly.

Callable bonds have negative convexity at low yields, but positive convexity at high yields. The transition point depends on specifics of the bond (e.g., coupon rate, call price, time to first call).

Yes.

Option-free bonds also have positive convexity at all yields.

#14

As for callable bonds, I just try to ensure that it has negative convexity partly at the transition point as yields fall. It is usually shown on graph where bond price moves below expected price when using duration (hence it’s called negative)

As for putable bonds, I assume at the transition point have highter positive convexity than option-free bond as yields rise because it is usually shown on graph where bond prices moves above expected price when using duration.

In real market, are there any bond products that have negative convexity when yields rise? It means the price will be move deeper than option-free bonds when yield rises.