Assuming a 3 year bond, 10% coupon with semi annual compounding, required yield 9%, calculate the convexity.
The answer provided is 8.2135
My calculation using the below convexity formula:
(Vminus + Vplus) minus 2Vzero (divided by) [Vzero multiplied by (delta Y)square]
gave me convexity as 32.87145538
Also, wanted to know whether 4.5 I/Y and 5 PMT are correct to be used for calculation. I considered +1% change ie. 5.5% and -1% change ie. 3.5%.
Could anybody help here.
Greetings friend! Here is how I would approach it, perhaps someone has a better explanation in which case I’ll defer to them:
to get current value of the bond:
FV=1000, PMT=50, I/Y=4.5, N=6 → computed PV= 1,025.79
to get bond value if yield increases 1% (annualized yield goes to 10% now, so 5% semi-annually):
FV=1000, PMT=50, I/Y= 5, N=6 → computed PV= 1,000
to get bond value if yield decreases 1% (annualized yield = 8% now, so 4% semi-annually)
FV=1000, PMT =50, I/Y=4, N=6 → computed PV= 1,052.42
So your convexity approximation formula is:
[(1,052.42 + 1,000) - (2 x 1,025.79)]/[1,025.79 x (0.01^2)] = 0.84/0.1026 = 8.19
Which is approximately their answer, probably you can get the same answer by different rounding of decimals.
Cheers - good luck - you got this
thanks a lot Greybeard_The_Elder. got it now.
my answer is 8.2145 now. I was wrong earlier when I calculated like this: 9÷2=4.5%, so +1% increase ie. 5.5% and -1% decrease ie. 3.5%.