The bond with higher convexity will have higher price than the one with lower convexity. In a volatile market, this is beneficial and we want to add convexity.
An example, is adding convexity by Buying a call option on a bond.
If interest rates decrease --> we’re in better shape than the straight bond -->because we can call --> Higher price using the higher convexity option.
If interest rates increase --> How is that this same higher convexity bond has a higher price than the straight bond? I just see it as the options being worth nothing and approaches the same price as straight. More specifically what they get at is they say total performance of the portfolio with options is greater than portfolio without options. Why in rising environment would total performance be greater? I think it would just match the portfolio with options because the option is worthless.
Total performance with bond with higher convexity will be higher because the price of bond with convexity decline less (and increases faster) than the price of a straight bond when rates increases (rate decreases). This is how higher convexity bond adds value.
"Total performance with bond with higher convexity will be higher because the price of bond with convexity decline less (and increases faster) than the price of a straight bond when rates increases (rate decreases)"
I understand the wording but not the logic. If we add call options --> WHY does the higher convexity bond (due to adding this call option) lead to the price of the bond declining LESS? I understand that higher convexity leads higher prices in a volatile interest rate environement.
A call option comes into play if yields drop and we can call it so performance is better. But with a YIELD increase --> what does this call option have to do with? The higher convexity bond with this option will perform the same as a straight bond. So where does this better performance come from in a increasing yield environment for this higher convexity bond with an option?
Your response FrankLiving
_ It may be easier if you remember it as positive convexity as it was referred to in previous levels… _
_ positive convexity = when rates drop price goes up more, when rates go up price declines less _
Again, I’m confused. I don’t know how this relates to my inquiry with options increasing convexity and how this works?
when yield increase, the bond with call option will fare better than a vanilla straight bond, because you can call it and lend out your capital at higher rate.
when yield decrease, you do not want to call your bond with call option. the call option does not add value in this case.
Victoryoe1984 is on point. Practically, if the yield declines, call option on bond with convexity increases more in value than low convexity option free bond and the bond could be called at the lower strike price leading to an increase in portfolio BPV. On the other hand, increasing rate will lead to lower bond value for both higher and lower convexity bond, but the decline in value of higher convexity bond will be lower. However, due to the decline in bond value, call option will expire worthless, and the portfolio value will only decline by the premium paid for the call option (if straight bond were purchased instead of the call option, the portfolio will suffer the full price decline).
It was my understanding that the higher volatility of short-term maturities adds positive convexity to a barbell structure. Until I read Vol. 4, page 164:
“Because the convexity of shorter maturities is relatively small…”
Confused. So interest rates on the long-end are relatively stable, but they add convexity to a portfolio?
What I’d like to know (and maybe I’ll do some calculations on this myself) is whether you can change the convexity with options without changing the duration.
“However, due to the decline in bond value, call option will expire worthless, and the portfolio value will only decline by the premium paid for the call option (if straight bond were purchased instead of the call option, the portfolio will suffer the full price decline).”
I follow you when you say that if I am long a call option and the yield goes up, hence the price goes down the call option expires worthless.
what I don’t understand is WHY you say that the portfolio value only decline by the premium paid for the call option. for what I understood if I am long a call, I have already paid a premium for the call, so I have the right to buy at a predetermined price (strike). if the price of the bond is going down I would never exercise the call because I would be in a position whereby I would buy a bond with a market value lower than the strike price.
In conclusion I still dont understand why buying a call would add convexity also when the yield goes up. In my view I would be screwed twice. not only the price is going down but I also paid a premium for a worthless option.
it could be from CFA level 2 that call options generally increase in value when interest rates rise holding other variables constant
this is because call options can be thought of a mechanism to gain exposure with leverage to an asset. higher interest rates will make it cheaper to gain this levered exposure with options so people would buy call options and their price would go up
calls have positive rho
the other thing is maybe worth saying that convexity is an overall figure for a bond portfolio. whether you are told rates will rise or fall, convexity is unchanged. its just the fact that the portfolio holder will still earn a greater return in the event rates fall that makes it more convex. the cost of the call premium is a sunk cost that has already been incurred and should not be taken into account when estimating portfolio convexity
lastly i would add that by saying the bond price is definitely going to fall if the rates rise implicitly assumes there is very little or no credit spread that may negate the interest rate effect. if credit spreads narrow significantly, we may even see a rise in the bond price and the call option e.g. emerging market USD debt last year
Embedded call options are the advantage of issuer not a bond buyer.
The advantages for buyers of callable bonds are in fact such bonds offer greater yield enhancement in a bond portfolio and are less volatile in 2 of 3 IR scenarios than straight bond of same characteristics.
It’s a common hedging technique in MBS to duration hedge with TBAs and then hedge residual convexity with swaption straddles because they’re heavy convexity with very little duration. This is the best example I can think of around moving convexity without moving duration (well, it moves by a couple decimals if you’ll allow me that).
I think I got it. I was making the wrong assumption that we care only about the value at the point of expiration. If we are away from expiration the call option still has some value even when the strike price is above the spot price.
This is a key point. I always pay careful attention when doing fixed income problems with options.
An example of a fixed income security with an embedded call is a typical mortgage with prepayment rights. In that case, the issuer of the mortgage bond (the borrower) has the right to call (buy back) the bond if desired. This occurs if interest rates decline enough.
On the other hand, in this thread we’ve been discussing what occurs when we have a bond + a call on the bond. This means that the investor benefits from the features of a call, which is to increase convexity.
Hi guys, I am trying to fundamentally wrap my head around low duration and high convexity. For example I read somewhere that options on bond futures have lower duration than a regular bond future but has higher convexity. I understand why options have higher convexity due to benefits being conferred on investor due to optionality. Why does it have lower duration though?