Convexity and volatility

  1. The higher convexity of the barbell portfolio enhances portfolio performance only in the presence of higher interest rate volatility. In a situation of low interest rate volatility the bullet portfolio will outperform the barbell. Can someone please explain the above sentences? What does convexity has to do with volatility? 2. The portfolio manager would want to overweight embedded option spread sectors as volatility is expected to be low. Why? Can someone explain? Thanks.
  1. doesnt high interest rate volatility make call and put option features more valuable???

level3aspirant Wrote: ------------------------------------------------------- > 2. doesnt high interest rate volatility make call > and put option features more valuable??? This is probably referring to the most common embedded option, which is the call in a callable bond. If you are long the bond, you’re short the call option. The bond value will increase as the call value decreases (remember the call reduces the bond price vs. non-callable equivalent). Lower interest rate volatility will reduce the value of a call option, which will increase the value of a callable bond.

  1. Convexity has everything to do with volatility. There is a price to convexity. If all else were equal, you would want as much positive convexity as possible. Positive convexity means that you will gain more when interest rates fall, and lose less when interest rates rise (look at the price / yield graph). The MORE positively convex a bond or portfolio is, the more you gain / less you lose when interest rates move down / up respectively. Now back to my first point, you pay for convexity because of it’s relationship with interest rate movements. If you expect interest rate volatility to be higher than market expectations, you would buy the convexity. If you expect volatility to be lower than the market expectations, it wouldn’t be worth it. You can see that a higher convexity portfolio will outperform in high interest rate volatility if interest rates rise OR fall (all else equal). If interest rates don’t move much or at all, the added convexity is useless.

thanks Mcleod …

And why does a Barbell have higher convexity than a Bullet portfolio?

“The convexity of a barbell portfolio is generally going to be greater than the bullet portfolio. That’s because convexity increases with the square of maturity.” - David Harper, CFA Hence 2 and 10 is 104 vs. a midterm bullet at 7 which is 49.

mark. thanks man. you explained a lot of questions i have. i am taking notes word by word. i owe you a beer for all the points i am going to make :smiley: McLeod81 Wrote: ------------------------------------------------------- > 1. Convexity has everything to do with > volatility. There is a price to convexity. If > all else were equal, you would want as much > positive convexity as possible. > > Positive convexity means that you will gain more > when interest rates fall, and lose less when > interest rates rise (look at the price / yield > graph). The MORE positively convex a bond or > portfolio is, the more you gain / less you lose > when interest rates move down / up respectively. > > > Now back to my first point, you pay for convexity > because of it’s relationship with interest rate > movements. If you expect interest rate volatility > to be higher than market expectations, you would > buy the convexity. If you expect volatility to be > lower than the market expectations, it wouldn’t be > worth it. > > You can see that a higher convexity portfolio will > outperform in high interest rate volatility if > interest rates rise OR fall (all else equal). If > interest rates don’t move much or at all, the > added convexity is useless.

McLeod81 wrote >This is probably referring to the most common embedded option, which is the call in a callable bond. No. It makes both call AND PUT more valuable. Remember option’s value increases with volatility (call and put). Look at Black –Scholes equation, you will vega (volatility) is positive both for call and put. Now, Vcall = Vnoncallable – Vcallable Vput = Vputable – Vnonputable So callable bond’s value decreases and putable bond’s value increases with increases volatility. However, the comment “overweight embedded option spread sectors as volatility is expected to be low” applies to callable bonds only. sebrock wrote > And why does a Barbell have higher convexity than a Bullet portfolio? For two bonds with the same duration, a barbell has higher convexity. Remember that more positive convexity means that duration DECREASES as yield increases and duration INCREASES as yield decreases. It is because barbell has higher spread in duration. When yield rises, the RELATIVE weight of the cash flows far away in time are reduced more than a bullet since they get discounted more -> The Macaulay duration (=weighted average of the time to each coupon and principal payment of a bond) decreases more than of a bullet. The Macalay duration of a bullet bond does not change. The opposite happens when yield decreases. Last note: Do not think it is within scope in CFA III any longer (it was, I think)

elcfa Wrote: ------------------------------------------------------- > McLeod81 wrote > > >This is probably referring to the most common > embedded option, which is the call in a callable > bond. > > No. It makes both call AND PUT more valuable. > Remember option’s value increases with volatility > (call and put). Look at Black –Scholes equation, > you will vega (volatility) is positive both for > call and put. Obviously, higher volatility will increase the value of any option… But since you are LONG a put option in the puttable bond (value of the put is added to straight bond), you do not want low volatility. I think you were acknowledging this in your second comment below. > > However, the comment “overweight embedded option > spread sectors as volatility is expected to be > low” applies to callable bonds only. > >

McLeod81 Wrote: ------------------------------------------------------- > elcfa Wrote: > -------------------------------------------------- > ----- > > McLeod81 wrote > > > > >This is probably referring to the most common > > embedded option, which is the call in a > callable > > bond. > > > > No. It makes both call AND PUT more valuable. > > Remember option’s value increases with > volatility > > (call and put). Look at Black –Scholes > equation, > > you will vega (volatility) is positive both for > > call and put. > > > Obviously, higher volatility will increase the > value of any option… But since you are LONG a > put option in the puttable bond (value of the put > is added to straight bond), you do not want low > volatility. I think you were acknowledging this > in your second comment below. > > Right. We are saying same thing. Just want to clarify that your original comment " This is probably referring to the most common embedded option" as answer to the comment "Doesnt high interest rate volatility make call and put option features more valuable??? "to make sure does not get to be interpreted to imply that it ONLY applies for call value and exclude put value.

Can someone explain this in one line please? A) In a situation of low interest rate volatility the bullet portfolio will outperform the barbell, because…? B) Higher convexity leads to [???] volatility because…?

bidder Wrote: ------------------------------------------------------- > Can someone explain this in one line please? > > A) In a situation of low interest rate volatility > the bullet portfolio will outperform the barbell, > because… investors pay higher price (get lower yield) for barbell bonds compared to bullet bonds with same duration because of their comparative higher convexity which is useless in low interest rate volatility. > B) Higher convexity leads to [???] volatility > because…? Higher convexity in bond is useful in high interest rate volatility environment because the duration becomes lower when interest rate increases (thus less price decrease) and duration becomes higher when rate decreases (thus more price increase) compared to similar bond with same duration but with lower convexity.