R26.P1.T4.Allen_v5.1 pag 40 Question 1

[Tania Pereira]

Please, i didn't understand the number 9 (year) in the equation of V@R.
Please, could someone explain the answer V@R = ...*9

 

[Deepak Chitnis]

Hi @Tania Pereira, Put it simply, first you need to discount the $1000 with 5% for 9 year (find the PV for the $1000), then daily yield volatility is 70 basis point(0.70%=0.0070), 99% one tailed deviate is 2.33 and finally it is duration based VAR so 9 years, all these together you will find out PV of $1000=$1000*EXP(-5%*9years)=637.62815. Then simply $637.62815*0.0070*2.33*9=$93.597. Hope that helps.
Thank you

 

[Dr. Jayanthi Sankaran]

Hi @Deepak Chitnis,

Could you please tell me which Question @Tania Pereira is referring to? I looked up the Study Notes and PQ set but it is not there. Thanks a tonne

 

[Dr. Jayanthi Sankaran]

Got it....the question is on Page 37 of Allen's Study Notes. I get the same answer as David and Deepak. Just wanted to add that the 9 years is Modified Duration, which is a measure of the yield based interest rate sensitivity of the bond. In the case of a Zero coupon bond under continuous compounding, the Modified Duration = Macaulay Duration = 9 years. It is important that we use only Modified Duration which gives us a yield based sensitivity measure. For instance, if the YTM = 5% per annum was under semi-annual compounding, then we would use Modified Duration = Macaulay Duration/(1 + y/k).
For a zero coupon bond, Macaulay Duration = T = 9 years. Hence, under semiannual compounding Modified Duration = 9/(1 + .05/2) = 8.780

Thanks
Jayanthi

 

[Dr. Jayanthi Sankaran]

Thanks for the star, Nicole - appreciate it

Jayanthi