Duration Funda

[notjusttp]

Jorion FRM handbook question No 1.9 states the following

Higher Duration is associated with Physical characteristics that push payments into the future i.e

1) Longer Term
2) Lower Coupon
3) Less frequent coupon payments
4) Lower Yields which increase the relative weight of payments in future

Doubt

Though i am clear on first 3 points i am confused as to the 4th point. According to my understanding a lower yield will discount the future cashflows to a lesser extent thus decaying it to a lesser extent thus reducing duration as the payback would be faster.

I am sure i am missing some point but am not clear what. Kindly assist.

Thanks & Rgds
Amit :roll:

 

[rahul.goyl]

Hi..

I am not sure but let me try this one..

"According to my understanding a lower yield will discount the future cashflows to a lesser extent thus decaying it to a lesser extent thus reducing duration as the payback would be faster".


decaying it to a lesser extent thus (not reducing) increase duration .. & leave more cash flow for future thus higher duration if there is large chunk of cash flow is to be received in future....

Another way to look as a Lower Yield, itself justify to have higher durations, as cash flow will take much time to realize bcoz of lower yield.

Hope this will help
Rahul

 

[notjusttp]

Hi Rahul,

Thanks for your assistance however i tend to disagree with you as yield is a rate given externally by market while the coupons on your bonds are fixed. So for eg you wud receive 6$ every year..this would be fixed.

Now if you use a lower yield to discount your this fixed coupon cashflow it gets discounted to a lesser extent than using a higher yield interest rate. hence a lower yield should reduce my duration as i would receive my money faster and larger.

Trust you get my point.

Thanks & Warm rgds
Amit

 

[David Harper CFA FRM]

Amit,

You are correct (of course) that a lower yield increases the PV of future coupon/principal cash flow, but the *relative* impact on the bond is greatest for the large, most distant cash flow (the principal).
The 2nd sheet in this learning XLS may be helpful: http://www.bionicturtle.com/premium/spreadsheet/5.b.2.tuckman_ch6_durations/
(screenshot below)

This is tuckman's table 6.2
first, note Mac duration is a function of the PV cash flows. It helps to understand fully the duration calculation (see first sheet for a clean example)
then, as yield drops from 7% (left) to 3% (right), all PVs are increased, HOWEVER, as a % of price, the final PV is greater (up to 79.02%): it now contributes to a higher duration (just as the first coupon went down in %, to 2.47%)...hope this helps, David

http://learn.bionicturtle.com/images/forum/sep4_duration.png

 

[rahul.goyl]

Hi David,

This is simply outstanding Example... Always like your way of making things easier to understand...

You mean to say the bonds with low yield will be trading rich compare to bonds with higher yield & if we take return in terms of PV of cash flow by bond price. The return will be lesser than the bond with the higher yield but less PV of cash flow.
So bottom line higher yield Low Duration - rate of returns are high, less cash flow in future
Lower yield High Duration - rate of returns are less, large cash flow in future

Hope my comments make sense... please correct me if am wrong
Thanks
Rahul

 

[notjusttp]

David,

As always you fascinate me with your solutions. You are just too good. Now that concept is crystal clear as always it happens once u clarify. I missed on the point that duration is a wtd average of tTIMES the payments are made so the largest cashflow would be more distant in time taking the duration beyond what it is currently...

Splendid r u and u r ways of explaining stuff..

Thanks a ton and Warm Rgds
Amit