I was checking if both the formulas of convexity that I know lead to the same solution. I had posted this in another topic but am still confused. Could you please help me.

There are 2 formulas for convexity that I used:

1. C = [ BV(2) + BV(1) - 2*BV(0) ] / BV(0) * (delta y)^2

2. C = Summation of ( t^2 + t) * Present Value of Cash Flow / [ Current Bond Value * (1 + y)^2 ]

The Question: What is the convexity of a bond which pays a coupon of 2.5 every 6 months for 2 years and a principal of 100 at the end of 2 years. The market rate is 4.5% compounded semi annually.

When using the 1st formula I got 4.53

Here is the calculation:

BV2 = 102.873 (when interest rate is 3.5%)

BV1 = 99.06514 (when interest rate is 5.5%)

BV0 = 100.9462 (when interest rate is 4.5%)

When using the 2nd formula I got 5.23

Here is the calculation for the 2nd formula:

t(t+1) * PVCF = 1.84, 4.78, 8.77, 562.62

Sum of the above: 578.01

denominator: B ( 1 + y )^2 .... Now B = 100.95 and taking y = 4.5% we get this = 110.24

So convexity = 5.24

(I am also confused about what value of y to take. The effective annual yield comes to 1.04551. Should I use this instead? This gives convexity = 5.23)

Please let me know if there is something wrong.

Thanks.