I have a question about Price value of basis point. It is written in two ways:
- PVBP = initial price - price if yield is changed by 1 bp
2)PVBP = [(V_ - V+) / 2] x par x 0.01
Which one is correct ? Thanks
They are both the same formula. Although the second is more of an approximation while the first will get you down to the penny. What you need to be doing is taking the average of the price changes for the bond if rates were to rise/fall by 1 bps. This is what the first part of the second formula is doing.
What the second formula does is that it scales the calculation to the par value that you have in the portfolio/in the bond, for exmple. Since prices are usually quoted in terms of $100 per par value the second formula will allow you to calculate the DV01 for say $20M of par value. See both formulas for a 10 year bond trading at par yielding 6% below:
- Current Price: 20,000,000
Price when rates rise by 1 bps = 19,985,287
Price when rates fall by 1 bps = 20,014,727
[(20,014,727 - 20,000,000) + (20,000,000 - 19,985,287)]/2 = 14,720.17 = DV01
2.) V_ = 100.07364 and V+ = 99.92643
[(100.07364 - 99.92643)/2] * 20,000,000 * .01 = 14,721 = DV01
Both yield almost identical results. The first one however is more exact.
That was very helpful. Thank you 
Hi!
Could you pls explain the usage of the first formula on a diferent example (QBank Schweser).
The price value of a basis point (PVBP) for a 18 year, 8% annual pay bond with a par value of $1,000 and yield of 9% is closest to:
A. $0.80.
B. $0.44.
C. $0.82.
The right answer is C:
PVBP = initial price – price if yield changed by 1 bps.
Initial price:
FV = 1000
PMT = 80
N = 18
I/Y = 9%
CPT PV = 912.44375
Price with change:
FV = 1000
PMT = 80
N = 18
I/Y = 9.01
CPT PV = 911.6271
PVBP = 912.44375 – 911.6271 = 0.82
PVBP is always the absolute value
Why is the initial price used in here, not the price when you use the one when rates fall by 1 bps and the price when the rates rise by 1 bps? Plus, without calculating the average of them?
Many thanks.