Sell convexity strategy

CFA Level III Fixed Income
#1

How does selling puts amount to selling convexity?

#2

Puts have positive convexity.

So do calls.

Selling puts _ calls _ also shortens duration, while selling calls _ puts _ lengthens duration.

#3

Thanks. Could it be said that puts have lower convexity as compared to calls and straight bonds though?

#4

You’re welcome.

I don’t know how the magnitudes of the convexity of call options, put options, and straight bonds compare.

It is, however, a bit of an odd question.

Bear in mind that we’re not talking about embedded options here. The calls and puts are _ stand-alone _ options, typically on Treasury notes and Treasury bonds. You go to the CBOE and buy put options on 20-year Treasuries, or sell call options on 10-year Treasuries, or whatever.

#5

Its much easier to think of… when the yield curve is stable, that means it isn’t suppose to move much (at least in your viewpoint). Then you should be writing puts and calls to collect a premium, which enhances yield.

#6

You’re right, I may have mixed the two. However, in case of stand alone options, when rates fall call options will be in the money and their prices may rise at a delta of 1, which won’t happen with puts. As puts will be out of the money. How do they then exhibit positive convexity?

#7

Not necessarily. It depends on the strike price on the option. If the market price is below the strike price, then the call option is out of the money.

Think about the shape of the option price vs. underlying price curve: it has positive convexity. (Mathematicians would describe the curve as being concave upward, which you may remember from a calculus class long, long ago.)

#8

Are you sure about that? Reading 24 (yield curve strategies) supports that:

Buy Call or Sell Put: increase duration

Sell Call or Buy Put: decrease duration.

#9

I presume that you were asking about the stupid comment I wrote above.

I was writing “selling” and thinking “buying”.

Thanks for catching that. I’ve corrected it.

#10

the interesting thing to think about and to connect some dots, is that you can create a long synthetic futures by buying calls and selling puts. Both can be used to extend duration, but both can have different sensitivities to interest rates and thus convexity effects. Convexity isn’t really explained well, but it is just Time2. The different products can allow you to trade convexity differences depending on your views/analysis/etc.

#11

I recently recorded a series of videos on the Level III fixed income readings and when I got to this section I pointed out that by using fixed income call and put options you can:

  • Increase duration and increase convexity – buy calls
  • Increase duration and keep convexity unchanged – buy calls and sell puts
  • Increase duration and decrease convexity – sell puts
  • Keep duration unchanged and increase convexity – buy calls and buy puts
  • Keep duration unchanged and keep convexity unchanged – this one’s almost too easy
  • Keep duration unchanged and decrease convexity – sell calls and sell puts
  • Decrease duration and increase convexity – buy puts
  • Decrease duration and keep convexity unchanged – buy puts and sell calls
  • Decrease duration and decrease convexity – sell calls
#12

Technically, the unit of measurement for convexity is time2 (usually years2), just as the unit of measurement of duration is time (usually years).