For AY 2014 on Dec 31, 2015, we are at age 24 with 3500 remaining to be paid. The payment pattern 10/60/100 indicates that everything will be paid by 36 months, which is the full 3500.
Or you can explicitly write out the formula for what will be paid in the 24-36 interval:
For the duration of claim liability, I am getting 0.9213 vs 0.8565.
This is how I did it -
Mac Duration - (0.5 x (0.555/1.02^0.5)) + (1.5 x (0.444/1.02^1.5)) / 0.9815 = 0.9395
Mod Duration = 0.9395 / 1.02 = 0.9211.
Is this method correct ?
No this method is not correct. The 0.555 and 0.444 is the weight that you would assign to the total unpaid. Your denominator should be the total discounted unpaid.
This would be the correct formula for MacD:
((0.5 x (3500+0.555x20000)/1.02^0.5) + (1.5 x (0.444 x 20000/1.02^1.5))) /(((3500+0.555x 20000)/1.02^0.5) + (0.444 x 20000/1.02^1.5))
You factored out the 20000 without considering the 3500 in unpaid for AY 2014
Is [3500 + 0.55 x 20000/(1.02^0.5) ] the unpaid amount for AY 2014, discounted back to 2014?
Is [0.444 x 20000/(1.02^1.5)] the unpaid amount for AY 2015, discounted back to 2015?
[3500 + 0.55 x 20000/(1.02^0.5) ] <- Amount Paid in CY 2016 from AY 2014 and AY 2015, discounted back to Dec 31 2015
[0.444 x 20000/(1.02^1.5)] <- Amount Paid in CY 2017 from AY 2014 and AY 2015, discounted back to Dec 31 2015
Since we are assuming mid-year payments, 3500 is paid out on July 01 2016. Should 3500 also be discounted back to Dec 31 2015?
So would the amount paid in CY 2016 from AY 2014 and AY 2015, discounted back to Dec 31 2015 be [3500/(1.02^0.5) + 0.55 x 20000/(1.02^0.5)]?
Comments
For AY 2014 on Dec 31, 2015, we are at age 24 with 3500 remaining to be paid. The payment pattern 10/60/100 indicates that everything will be paid by 36 months, which is the full 3500.
Or you can explicitly write out the formula for what will be paid in the 24-36 interval:
For the duration of claim liability, I am getting 0.9213 vs 0.8565.
This is how I did it -
Mac Duration - (0.5 x (0.555/1.02^0.5)) + (1.5 x (0.444/1.02^1.5)) / 0.9815 = 0.9395
Mod Duration = 0.9395 / 1.02 = 0.9211.
Is this method correct ?
No this method is not correct. The 0.555 and 0.444 is the weight that you would assign to the total unpaid. Your denominator should be the total discounted unpaid.
This would be the correct formula for MacD:
((0.5 x (3500+0.555x20000)/1.02^0.5) + (1.5 x (0.444 x 20000/1.02^1.5))) /(((3500+0.555x 20000)/1.02^0.5) + (0.444 x 20000/1.02^1.5))
You factored out the 20000 without considering the 3500 in unpaid for AY 2014
Is [3500 + 0.55 x 20000/(1.02^0.5) ] the unpaid amount for AY 2014, discounted back to 2014?
Is [0.444 x 20000/(1.02^1.5)] the unpaid amount for AY 2015, discounted back to 2015?
[3500 + 0.55 x 20000/(1.02^0.5) ] <- Amount Paid in CY 2016 from AY 2014 and AY 2015, discounted back to Dec 31 2015
[0.444 x 20000/(1.02^1.5)] <- Amount Paid in CY 2017 from AY 2014 and AY 2015, discounted back to Dec 31 2015
Since we are assuming mid-year payments, 3500 is paid out on July 01 2016. Should 3500 also be discounted back to Dec 31 2015?
So would the amount paid in CY 2016 from AY 2014 and AY 2015, discounted back to Dec 31 2015 be [3500/(1.02^0.5) + 0.55 x 20000/(1.02^0.5)]?
Yeah whoops you are right. 3500 needs to be discounted also - It's hard to see so many brackets