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Formula for computation of duration when redemption is at par vs at premium/discount
AFM
Got a slightly different answer when computing duration using the formula vs using the cash flows method. When analyzed deeper, it seems that the formula will return the exact same duration (as compared to duration calculated using the cash flows method) when the redemption is at par. But, when the redemption value is different from par, there is a deviation w.r.t the premium amount which in turn deviates the duration by a small figure. Is there any alteration to the formula when the redemption is not at par or is the computation using the cash flows method the only way to compute in this situation? I know this is a very advanced analysis & this much interpretation is not required from the examination point of view, yet asking this out of curiosity😁 Video Details ------------- Advanced Financial Management - AFM Security Valuation - Bonds #93. Illustration # 55
Answers (10)
Sriram Somayajula Admin
Same with duration or convexity impact on bond pricing. Best way to price a bond is with cash flows convexity and duration based pricing are only approximate
Ok sir Also I have a doubt regarding the difference between the terms “convexity” & “convexity adjustment” Formula as per Study material is C* x (Δy)2 x 100 whereas C* = V+ + V- - 2V0 divided by 2V0 x (Δy)2 Whereas in Illustration 1, we have used the “C* x (Δy)2 x 100” formula to compute the convexity of the bond (i.e., as per SM) Illustration 49, the “V+ + V- - 2V0 divided by 2V0 x (Δy)2” formula (i.e., where "(Δy)2 x 100" is ignored) Illustrations 50 & 51, the “Convexity x (Δy)2” formula whereas convexity is “V+ + V- - 2V0 divided by 2V0 x (Δy)2” (i.e., where " x 100" is ignored) To arrive at a single understanding & studying a sole formula for remembering, it’s little confusing when above illustrations are looked at the same time. Kindly advise on which formula to take when question is asked in the exam to compute "convexity" of the bond. Or is there any technical difference between the terms "convexity" & "convexity adjustment"?
Thread Starter
Vigneshwar MOk sir Also I have a doubt regarding the difference between the terms “convexity” & “convexity adjustment” Formula as per Study material is C* x (Δy)2 x 100 whereas C* = V+ + V- - 2V0 divided by 2V0 x (Δy)2 Whereas in Illustration 1, we have used the “C* x (Δy)2 x 100” formula to compute the convexity of the bond (i.e., as per SM) Illustration 49, the “V+ + V- - 2V0 divided by 2V0 x (Δy)2” formula (i.e., where "(Δy)2 x 100" is ignored) Illustrations 50 & 51, the “Convexity x (Δy)2” formula whereas convexity is “V+ + V- - 2V0 divided by 2V0 x (Δy)2” (i.e., where " x 100" is ignored) To arrive at a single understanding & studying a sole formula for remembering, it’s little confusing when above illustrations are looked at the same time. Kindly advise on which formula to take when question is asked in the exam to compute "convexity" of the bond. Or is there any technical difference between the terms "convexity" & "convexity adjustment"?
We should follow ICAI SM In Q1 we Found out convexity & the change in price | (Δy)2 x 100 is used to arrive at change in price ( will make change in notes & video if I mentioned otherwise by mistake ) in 49 we found out only convexity - we were not asked to find out change in price in 50 & 51 we found out change in price without multiplying with 100, however we converted the answer into % by multiplying with 100
Sriram Somayajula Admin
We should follow ICAI SM In Q1 we Found out convexity & the change in price | (Δy)2 x 100 is used to arrive at change in price ( will make change in notes & video if I mentioned otherwise by mistake ) in 49 we found out only convexity - we were not asked to find out change in price in 50 & 51 we found out change in price without multiplying with 100, however we converted the answer into % by multiplying with 100
So "C*" is used to denote convexity of the bond & "Convexity Adjustment" (i.e., convexity multiplied by square of change in yield & 100) is used to denote change in price as a result of change in yield. Am I right sir? Will interpret that "x 100" portion accordingly as per each question's requirement & I think that will not pose a great challenge while arriving at the answer.
Sriram Somayajula Admin
We should follow ICAI SM In Q1 we Found out convexity & the change in price | (Δy)2 x 100 is used to arrive at change in price ( will make change in notes & video if I mentioned otherwise by mistake ) in 49 we found out only convexity - we were not asked to find out change in price in 50 & 51 we found out change in price without multiplying with 100, however we converted the answer into % by multiplying with 100
I have not mentioned anything incorrect anyway cross checked all videos
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