Hello everyone,
There is a formula I do not understand and it is driving me crazy:
Predicted change = Portfolio par amount x Partial PVBP x (-Curve shift)
Why do we multiply Curve shift by BOTH portfolio par amount AND PVBP since both metrics already contain the portfolio value (PVBP = modified duration x Portfolio value x 0.0001). Doesn’t it result in squaring portfolio value ?
Thank you much guys!
And to add twist to it… It need not be even the par value. Because the filthy bonds are traded once in a while the par value is taken default. If CFAI wanted to screw us bad… It can give both the par value and the market value…what will you use ?
Secondly the defualt par value to 100 is what matters …by your logic, otherwise the PVBP would differ for every f***ing investor …?? Ha ha
Hope it is clear now
It is even less clear : my question is, since the portfolio is in USD and the PVBP too, multiplying them gives USD squared , just like multiplying meters by meters gives you square meters… can someone just explains this part to me?
Is the predicted change supposed to be in USD2 ??? (I don’t think so, that’s why I am asking)
And please let us not get dirty by talking about filthy bonds 
Thank you for your answers dear colleagues
Change of portfolio if 1% change in yield = total partial duration (per basis point) * 10000 * (-curve)
1% = 100 bps => 1bps = 1/10000
partial duration is stated on 1$ par and 1bp
I still don’t understand one thing :
what is the unit of portfolio par amount -----> USD?
what is the unit of partial PVBP ------> USD too, like PVBP and money durations which are both stated in USD?
If they are both expressed in USD, how does it make sense to multiply them?
Portfolio Amount is a figure. But PVBP (and Partial PVBP by extenxion) is not actually a “ figure.” It is a scaling number that you multiply by every $1 of par value to get the change in price. Expand the calculations for the “PVBP” part of “Partial PVBP” to understand why you’re not squaring $s. PVBP is Money Duration / 100. Money Duration is Modified (or Effective) Duration times the Portfolio Value per $1 of Par divided by 100. Which means that the actual notation is “Portfolio Value in $s divided by 1 unit of Par Value in $s.” So the s cancel each other out. Put another way, if you rearrange the above equation to _Partial PVBP = Predicted change / (Portfolio par amount × (–Curve shift)_ and substitute ”_0.0001 x (Effective duration x (Portfolio value / Portfolio par amount)”_ for _PVBP,_ the “Portfolio par amount” expressions cancel each other out and you are left with only 1 “ figure” in the equation. Hence you are not squaring $s.