Looking for percent error for the duration and duration w/convexity rule. A 30 y
ID: 2787901 • Letter: L
Question
Looking for percent error for the duration and duration w/convexity rule. A 30 year bond making annual coupon payments w/coupon rate of 9.50 has a duration of 13.53 years and a convexity of 258.03. The bond currently sells at a yield to maturity of 6%(which is 1428.05) If the bond fell to 5% witch calculates to 1691.72 with a value of 1671.22 w/duration and 1689.92 duration w/convexity. I can not calculate the percentage error for duration rule (duration w/convexity is -.13) No matter what I come up with, it’s wrong. Same for the rise to 7% - price has been calculated to1310.54, duration is 1292.88 and duration w/convexity 1312.00. (Duration w/convexity is .13) all numbers have been verified - don’t need those , just the two percent errors for the duration. Thanks
Explanation / Answer
Duration = DURATION(settlement,maturity,coupon,yield,frequency,basis)
Modified Duration = MDURATION(settlement,maturity,coupon,yield,frequency,basis)
BondPrice = 1428.05, Copupon rate : 9.5%, Yeild= 6% for a convexity of 258.03 (base = 258.03/365 = 0.707)
DURATION ("1/01/2007","12/31/2037",0.095,0.06,1,0.707) = 13.71 = New bond price =
MDURATION("1/01/2007","12/31/2037",0.095,0.06,1,0.707) = 12.94=
New bond price = $1627.5
When Yeild change to 7%
BondPrice = 1428.05, Copupon rate : 9.5%, Yeild= 7% for a convexity of 258.03 (base = 258.03/365 = 0.707)
=DURATION("1/01/2007","12/31/2037",0.095,0.07,1,0.707) = 12.81
=MDURATION("1/01/2007","12/31/2021",0.095,0.07,1,0.707)=8.587
Duration :New bond price 1428.05-1%*12.81895*1428.05 = 1245
Mduration :New Bond Price : 1428.05-1%*8.5875*1428.05 = 1305
to find percent error for duration :
y = change in yield in decimal ( = "delta")
V1 = initial price
V2 = price if yields decline by y
V3 = price if yields increase by y
Duration = V2 - V3 / 2(V1)(? y)
= (1637.402-1245)/(2*1428.05*1%) = -13.73
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