Fixed Income - Buying and Selling Convexity


In one of the practice questions on CFAI website, they say that if you have a portfolio of bonds and you expect a parallel shift in the yield curve (+ or - 50 bps) you should buy convexity by purchasing call options on the bonds.

Can someone please explain how this strategy would benefit the investor if yields increase? For me if there is an upward shift the value of your bonds decreases and the call option is worthless (since bond price will be lower)

And also why buying mortgage backed securities is considered to be selling convexity?

Thanks in advance

The investor won’t benefit if the yield increase, but would benefit if the yield decresae. When the yield decrease, bond value would increase and the value of the call option would also increase.

Buying MBS is like buying a callable bond,since the mortgage borrower can prepay the mortgage when the interest rate falls, which would limit the investor’s upside gain if the interest rate falls.

If the yield curve is parallel and upward sloping, the value of bonds will reduce. However, the value of a bond with higher convexity will decline less than the value of bond with lower convexity. So, buying an option is a way to gain positive convexity which benefits the bondholder when rates are expected to rise.

Hope that helps.

I think the two answers above summarize the response pretty well. If yields sell off, bond prices indeed drop but that’s the duration component, not the convexity component. The more positively convex a bond is, the lower its loss of value when the yields sell off (and the higher its gain when yield curve rallies).

MBS are basically long a bond and short an American option, where said American option is the right for borrowers to prepay. So the question of MBS convexity really comes down to where that option has the most gamma, which will be when it’s close to being ATM. For MBS that are deep in the money (FN 7.0, for example) or deep out of the money (FN 2.0 for example), the convexity will probably be positive since in the first case borrowers who were going to exercise that option have probably already done so and in the second case exercising the option is economically a poor decision.