# Formula for money duration

What is the formula for money duration?

I’ve seen 2 different ways CFAI calculates it.

PVBP = $x .0001 x MD IT doesnt matter if you use .01 or .0001, as long as it is consistent in your calculations and consistent with the problem. I saw a variation where they said money duration = annualized modified duration * market value so the .01 or whatever doesn’t matter? no sir it matters very much. 1BP = 0.01% = 0.0001. when calculating money duration (PVBP of entire portfolio), it is essential that you multiply the .01% to assess the change in value of the portfolio in case of a 1BP shift in yields. I find this to be quite confusing. In the mock AM 2018 they have one problem where the guideline answer state: Money duration = modified duration × market value But shouldn’t dollar duration be (Modified duration x Market value) ÷ 100 ? The value displays how much the value change per 1 percentage change. Then to calculate BPV, you take dollar duration / 100 as there are 100 BPV for each percentage. I have this question too. Which one is the official definition of money duration? Money duration = in terms of the portfolio changing when rates change 1% PVBP = in terms of 1 basis point PVBP = Money duration * 0.01 you’re all confusing this GREATLY because you’re forgetting that money duration is already in terms of 1%. Stop getting concerned over “which do I use .0001 or .01” - this question will melt away when you understand what you’re actually working with. Take a step back for a second, it’ll make sense. Unfortunately, it’s not. If the (modified) duration is, say, 6 years and the portfolio value is, say,$1,000,000, then the money duration is 6 × 1,000,000 = 6,000,000 ($-years), not 6% × 1,000,000. The PVBP is 6,000,000 × 0.0001 =$600, not 6,000,000 × 0.01 (= $60,000). Okay my bad. It’s been a while. But the PVBP is Money duration * 0.01 I know that much is right - which still answers his question. That’s my point; it isn’t. PVBP = Duration \times Portfolio\ value \times 1bp = Duration \times Portfolio\ value \times 0.0001 In my earlier example, PVBP = 6 \times 1,000,000 \times 0.0001 = \$600 ; i.e., a 1bp decrease in the YTM results in a $600 increase in the value of the portfolio. I will fight you on this until the cows come home… There’s no difference between saying that… PVBP = Duration * portfolio value * 0.0001 PVBP = Dollar duration * 0.01 Go ahead, try it on your calculator - using your example you’ll get$600 both times.

Your calculation of dollar duration is wrong.

Dollar duration is 6,000,000 (\$-years), not 60,000.

I came across this link that does a pretty good job of explaining it:

Verbatim, from the link you provided:

“The money duration is equal to the annual modified duration times the full price per 100 of par value:”

Look at how they’re explaining the calculation:

"The money duration (MoneyDur) is calculated as the annual modified duration times the full price (PVFull) of the bond, including accrued interest.

MoneyDur=Annual ModDur×PV^{Full}"

I agree that their use of “per 100 of par value” is misleading. That wasn’t a good choice for an explanation. Sorry.

We’re still a great team and a force to be reckoned with. All CFA exams beware.

Here’s an example of money duration from the Level I curriculum. They start with the same formula as that weird link I sent you:

MoneyDur=AnnualModDur×PV^{Full}

For an example of money duration, consider the 6% semiannual coupon payment bond that matures on 14 February 2022 and is priced to yield 6.00% for settlement on 11 April 2014. The full price of the bond is 100.940423 per 100 of par value, and the annual modified duration is 6.1268. Suppose that a Hong Kong–based life insurance company has a position in the bond for a par value of HKD100,000,000. The market value of the investment is HKD100,940,423. The money duration of this bond is HKD618,441,784 (= 6.1268 × HKD100,940,423).

The money duration is the modified duration times the value of the portfolio.