Valuation & Risk Models- Tuckman-Chapter 4-Dollar Value of zero and Hedging

[gargi.adhikari]

Hi,
This in reference to the Topic Valuation & Risk Models- Tuckman-Chapter 4-Dollar Value of zero and Hedging:-
Learning Spreadsheet: 4c.3 DV01_hedge
The Actual Value of the Zero Coupon Bond was Computed to be 30.12. I'm having trouble with the formula that has been used which is face*EXP(-(C5+1)*T)-face*EXP(-C5*T) , where C5= Yield which seems off to me.

With a Yield = 4%, Isnt the actual value derived simply as Face * Exp( - YT)=100* exp( -.04*30) = 30.12 ...?

Want to make sure am not missing a key concept here...

 

[ShaktiRathore]

Hi,
face*EXP(-(C5+1)*T)-face*EXP(-C5*T) , where C5= Yield is nothing but the Duration only.
Actual=slope of the price yield curve=Duration = 100*EXP(-(4%+1)*30)-100*EXP(-4%*30)/(change in yield)
change in yield=100%=1 => Duration=100*EXP(-(4%+1)*30)-100*EXP(-4%*30)/1=-30.12
thanks

 

[gargi.adhikari]

@ShaktiRathore Thanks so much for the above explanation. I have a follow up question though-
Please pardon my ignorance on this ..

@David Harper CFA FRM
In reference to Learning Spreadsheet: 4c.3 DV01_hedge
When we calculated Duration= -28.85 = -T/ ( 1+ Y/k) , where did we get this formula of duration from in terms of the YTM, T= 30 years ? This formula looks similar to Mod Duration = Mac Duration/ ( 1+ Y/k) . So is should it be 28.85= 30.12 ( instead of T=30?) / ( 1+ Y/k)

But then, 30.12 is the Dollar Duration and not the Mac-Duration...

Duration value of 28.85 ( and not 30.12) has been used in the subsequent Duration Plot calculations....please advise...

 

[David Harper CFA FRM]

Hi @gargi.adhikari

Apologies but this spreadsheet tab is not well-labelled (it has the intent really of the DV01 hedge), and further, these cells which you indicate are not well-designed (highly confusing!). The only purpose of the -28.5 is to inform the plotted green tangent line. It is poorly designed because -T/(1+4%) is meant to be a modified duration for a 30-year bond where the yield is 4.0% per annual with annual compounding; as you say: Mod duration = Mac duration/(1+ yield/k). But it's confusing because it doesn't explain that, and then the subsequent pricing is with continuous compounding. If the 30-year bond is priced with continuous compounding, the Mac/Mod duration is 30 years. As Shakti noted, the "actual" = 30.12 is meant to be a price change given a shock to the yield, but it's not used, and i think it's incorrect because it adds 1.0, so its essentially subtracting the bond price (at 4%) from a bond price which is zero. Then intention here was to shock the yield at a full (unrealistic) 100% because that is the units of dollar duration, but it's very confusing, sorry. Thanks.

 

[gargi.adhikari]

@David Harper CFA FRM Thanks much David for the insight. However, think there are multiple/ too many glitches in this workbook sheet/tab. As this is the formative phase of these concepts for me, it would be highly beneficial if we could have a revised/corrected version of this sheet or at least all the glitches worked out in this thread at least.....? Hope it's not asking for too much.....

 

[David Harper CFA FRM]

@gargi.adhikari it's not asking too much (and thank you for being so polite about it), you are the customer. I added it to my list, will update this XLS as soon as possible. Thanks,

 

[gargi.adhikari]

@David Harper CFA FRM You guys are rockstars. The eLearning platform that you guys provide is nothing short of spectacular given the complexity of the topic and subject and we all are very thankful for the time and effort you put into this. Thank you for being so meticulous and helping us learn !

 

[bpdulog]

Related to this spreadsheet example, we are given the 1bps price movement of a call option. Had we not been provided with the prices, are we expected to calculate the DV01 of the call option using the implied vol and strike price info provided?