Question
Please solve and show work! Use the quick formula to find the approximated duration from a...
Please solve and show work!
Use the quick formula to find the approximated duration from a 10 basis point change in yield, note you will need to find the change in the price up and down using the bond pricing formula. (4 digits after the decimal). Bond ABC Coupon 3.0096 Yield to maturity 2.5096 Maturity (years) Par $100.00 Price per par $101.8920 Face value 1000
Answers
Solution) Coupon = 3%
YTM = 2.5%
Maturity (years) = 4
Par value = $100
Bond quoted at Price per par (V0) = $101.8920
Face Value = $1000
Change in Yield,
= 10 basis point = 10/10000 = 0.001 = 0.1%
First, increase the yield on the bond (YTM) by 10 basis points from 2.5% to 2.6%. The new price (V+), quoted on par, is computed as:
Year Cash Flows t=1 $ 3 t=2 $ 3 t=3 $ 3 t=4 $ 103 YTM 2.60% Bond Current Price =NPV(YTM, Cash flows) $ 101.5012 Thus, V+ = $101.50
Second, decrease the yield on the bond (YTM) by 10 basis points, from 2.5% to 2.4%. The new price (V-), quoted on par, is computed as:
Year Cash Flows t=1 $ 3 t=2 $ 3 t=3 $ 3 t=4 $ 103 YTM 2.40% Bond Current Price =NPV(YTM, Cash flows) $ 102.2626 Thus, V- = $102.26
Approximate modified duration is calculated using the below formula:
where,
Thus, Approximate modified duration = (102.2626 - 101.5012)/2*101.8920*0.001 = 0.7614/0.203784 = 3.7363
We were unable to transcribe this imageModified Duration = (V_-V) 2(V)(Ay)We were unable to transcribe this image
= 10 basis point = 10/10000 = 0.001 = 0.1%
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