Fixed income formula - Predicted Market Value Change

Curriculum states the formula as : PF Par Amount x Partial PVBP x (-curve shift)

Curriculum states the formul in EOC Q20 as : PF Par Amount x Partial PVBP x _ curve shift _

CFAI Practice Problem part 2 Q10 solution gives us the formula as : (PF Par Amount x ( -Partial PVBP ) x curve shift)_ /100 _

Which one is correct?

If the interest rates move up, the price of a bond will…

fall. I get that but just to memorize and to mechanically calculate… which formula is correct?

Obviously Curriculum mainbody and EOC formula is different meaning. right?

EOC formula for Q20 of what reading? I checked all the FI readings and see no such question.

Hi 125mph, EOC formula is referring to Reading 20 (Yield Curve Strategies) Q20 solution.


  1. C is correct. Given Edgarton’s expectation for a steepening yield curve, the best strategy is to shorten the portfolio duration by more heavily weighting shorter maturities. Pro Forma Portfolio 2 shows greater partial duration in the 1- and 3-year maturities relative to the current portfolio and the least combined exposure in the 10- and 30-year maturities of the three portfolios. The predicted change is calculated as follows:

Predicted change = Portfolio par amount × partial PVBP × (curve shift in bps)/100

(Institute 226-227) Institute, CFA. 2019 CFA Program Curriculum Level III Volume 4. CFA Institute, 5/2018. VitalBook file.


Any thoughts, anyone??

Not sure why you’re still asking… You already answered for youreslf:

If the curve rises, obviously you it falls… If the curve decreases, obviously it rises. The negative is the correct formula because your answer said its an inverse relationship between price and yield.

The context to the 2nd version likely is stating the “change” in market value as an absolute term (neutral on direction)

OP - I think you are asking why the formula is different.

  1. The formula in the EOC uses curve shift in bps, which is the shift in % times 10,000. If you divide by 100, the end result will be in %.

  2. Secondly the -ve sign can be applied either to shift or to PVBP to bear the same result

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.

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