Pages 71-72 of Tuckman - PQ set #28.2

[Dr. Jayanthi Sankaran]

Hi David/Nicole,

The reason I am posting this question and answer here is that the link on page 72 is not working

Question
28.2 Assume a ZERO-COUPON bond with par value of $100 an yield (YTM) of 6%.

a) If the maturity is five years (5 years), use duration to find the DV01.
b) If the maturity is twenty years (20 years), find the DV01.
c) If the maturity is thirty years (30 years), find the DV01.
d) True or false: For a zero-coupon bond, duration is a monotonically increasing function of maturity.
e) True or false: For a zero-coupon bond, DV01 is a monotonically increasing function of maturity

Answer
28.2 @ 5 year maturity, DV01 =~ $78.12 * 4.88 /10000 = $0.038
@ 20 year maturity, DV01 =~ $37.24 * 19.51 /10000 = $0.073
@ 30 year maturity, DV01 =~ $22.73 * 29.27 /10000 = $0.067

My answer

DV01 @5 year maturity = Modified Duration*Price/10,000.
Modified Duration for zero-coupon = T/(1 + y/k) = 5/(1+ .06) = 4.716981
Price = $74.725817
Hence, DV01 @5 year maturity = 4.716981*74.725817/10,000 = 0.035248**

**Since we are assuming discrete compounding Macaulay Duration = T but not Modified Duration
In the case of continuous compounding Modified Duration = Macaulay Duration = T

DV01@20 year maturity = Modified Duration*Price/10,000
Modified Duration for zero-coupon = T/(1 + y/k) = 20/(1 + .06) = 18.867925
Price = $31.180473
DV01@20 year maturity = 18.867925*31.180473/10,000 = 0.058831

DV01@30 year maturity = Modified Duration*Price/10,000.
Modified Duration for zero-coupon = T/(1 + y/k) = 30/(1 + .06) = 28.301887
Price = $17.411013
DV01@30 year maturity = 28.301887*17.411013/10,000 = 0.049276

I don't know why the answers are so different. Would be grateful if you would elaborate

Thanks!
Jayanthi

 

[David Harper CFA FRM]

Hi @Jayanthi Sankaran

The source Q&A is here @ https://forum.bionicturtle.com/threads/l2-t5-28-dv01-duration-and-price-effects.3454
Apologies but that question has a mistake. My DV01s are based on a yield of 6%. Further, I imprecisely estimated DV01 by computing an effective duration; unnecessary for a zero-coupon bond when the precise modified duration is available. I'm really surprised I did that, even back in 2010

But using 5% yield and an annual compound frequency assumption, I get the same exact DV01s as you do!
https://www.dropbox.com/s/l26fjv08rwlhplv/T5.28_durationeffect-jayanthi.xls?dl=0

Sorry for the mistake ....