A EUR100 million bond portfolio contains the following bonds:
| Bond | Maturity (yrs.) | YTM (%) | Market Value | Annualized Modified Duration | Annualized Convexity |
|---|---|---|---|---|---|
| A | 3 | 2.80% | EUR40,000,000 | 2.858 | 9.752 |
| B | 10 | 3.50% | EUR60,000,000 | 8.376 | 81.701 |
The expected percentage price change of the bond portfolio given a 50 bp increase in yield-to-maturity is closest to:
You have that equatiion
% chn. Price = - Mod Dur x Ch. in yield + 0.5 x Convexity x (ch.Yield)^2
Either
Work out chnage you each mbond and the weight the chnages by the weights of the bonds
or
Work out weighted average (suing mkt value) of Duration and Convexity for each bond.
Can I suggest if you post question you also ask a question. What is it you don’t understand. Even better post the answer to and explain where you want help. Otherwise it seems like you are just giving us quiz
For bond A:
The expected percentage price change is -2.8580.005+0.59.752*(0.05)^2, the second part is too small because of the (0.05)^2, thus you could just calculate the first part which is -1.429%.
For bond B:
Similarly, the expected percentage price change is close to -8.376*0.005 which equals to -4.188%.
For this portfolio:
0.4*( -1.429%)+0.6*(-4.188%)=-3.0844%.
Then choose the closest option, if there’s more than one option left you should take convexity into account
Yeah sure, my bad. My doubt for this sum was that we are asked to find % change of bond portfolio. And in the solution given % change in bond price formula is being used