A $1000 par value 4 year bond pays 4% coupon annually. The bond yields an effective...

A $1000 par value 4 year bond pays 4% coupon annually. The bond yields an effective annual interest of i% and has a modified convexity equal to 17.47. Calculate i

Expert Solution

A $1000 par value 4 year bond pays 4% coupon annually. The bond yields an effective annual interest of i% and has a modified convexity equal to 17.47. Calculate i

We know the value of modified convexity and we have to calculate the value of i which is yield to maturity (YTM) of the bond.

To get the modified convexity = 17.47; we use different values of i in following calculation (trail and error method)

Time (t)	Cash Flow from Coupon Payment (4% of $1000)	Cash Flow from maturity amount	Total Cash Flow (CF)	Present Value (PV) of cash Flow = CF/(1+i)^t	Weight = PV of cash Flow/Price	Convexity = Sum of [t (1+t) weight * 1/(1+i)^2]
1	$40		$40	$38.83	3.74%	0.07
2	$40		$40	$37.70	3.64%	0.21
3	$40		$40	$36.61	3.53%	0.40
4	$40	$1,000	$1,040	$924.03	89.09%	16.80
Total				$1,037.17		17.47
				↑ Price		↑ Convexity

We got the value of i = 3.00%

Formulas used in excel calculation:

jeff jeffy answered 1 year ago

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