In Reading 23, pages 140,141 it is suggested that callable bonds can be used to increase the portfolio’s convexity… but that’s wrong! Isn’t it?! Callable bonds have negative convexity!
The author uses Exhibit 8 to show that the value a call with underlying a bond has basically a positive convexity… but, if we are talking about callable bonds , the argument is flawed… the bond holder is short on the embedded call option, not long! Above the strike, the bond value decreases.
I guess what they actually meant was to buy a call option tout court, with underlying the bond already in the portfolio. Would also make more sense since the author is talking about using derivatives… not purchasing more bonds with embedded securities.
Also MBS have negative convexity… this is quite confusing… Can someone please confirm the mistake? Or am I missing something?
I agree with you. Buying callable bonds (short call option) and MBS will reduce convexity, but buying a call option (long call option) on bonds will increase convexity.
Just to reiterate what Mr RS has stated, Callable Bonds and Calls on Bonds are two different things.
Callable bonds display negative convexity and when volatility is low you want to decrease convexity, you would pick up callable bonds as they are cheap during that time.
When volatility is high you would increase convexity by selling any callable bond holdings (- convexity) and picking up calls on bonds (+convexity)
I agree this is confusing, but I think Mr RS and AlexMo have it right.
MBS has negative convexity because the home-owner’s right to pre-pay their mortgage early is like an embedded call option. When interest rates fall, home owners are likely to pay down their mortgage faster, which is conceptually similar to a high yield bond with an embedded call option being called back by the issuer (home owner) when interest rates fall and the value of the bond rises. So if you expect interest rates to remain stable, you can sell convexity by buying MBS.
The MBS should have a higher yield than a comparable 30-year bond with no embedded option, to compensate the investor for the risk that the MBS could be repaid before the 30-year term of the mortgage, particularly if rates fall.
Forgot to put here the answer received by the CFA Institute… basically the curriculum is wrong, it’s mixing up the topics, but because each statement taken in isolation is right, they don’t admit this section of the curriculum is wrong: