To add more details: we expect a steepening yield curve with short-term yields rising by 1% and long-term yields rising by more than 1 % and need to select an appopriate portfolio. We have 3 choices:
Because 2 has the lowest exposure to the highest part of the curve shift (I believe), thus your portfolio value will decrease by less than 1 and 3 which have higher exposures to the steepest point.
Portfolio Amount is a figure. But PVBP (and Partial PVBP by extension) 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.
The issue is not with the Partial PVBP number. On an earlier post, S2000 Magician guessed that it might be that Partial PVBP was supposed to be stated in % terms, but he was waiting for clarification from CFAI. Let’s take Exhibit 33 for example. The 2Y Maturity bond experiences an 18.3 Key Rate Curve Shift ( bps ) on a Portfolio par amount of 60,000 ( thousands) and has a Partial PVBP of 0.0056. If you multiply those #s out as per the equation below the exhibit (Predicted change = Portfolio par amount × Partial PVBP × (–Curve shift)), you get a number that is supposed to be in “ thousands:” “-6,148.” However, Exhibit 33’s answer is “-61.5.” So why the difference of a factor of 100? Here’s the disgusting answer: You have to convert the “Key Rate Curve Shift” from bps to %. Look at the difference in wording of the formula in the Reading vs the formula in the End Of Chapter Solution to Q20. “Predicted change = Portfolio par amount × Partial PVBP × (–Curve shift)” VERSUS ”Predicted change = Portfolio par amount × partial PVBP × (curve shift in bps)/100” (Forget the fact that the EOC Solution formula forgot to include a “negative” symbol for the curve shift portion). Once you convert the Key Rate Curve Shift to % from bps- i.e. divide by 100- all of the calculations will work.