# Money Duration

I think I’ve studied too much as I’m starting to mix things.

In the CFAI book : Dollar duration is a measure of the change in portfolio value for a 100 bps change in market yields

Dollar duration = Duration × Portfolio value × 0.01

However in the following example, this is not how they compute it.

____________________________________________________________________________________________________

The current portfolio consists of three bonds, details of which are displayed below. Each holding is of size \$1 million par value. Based on the data above, the current money duration of the fixed-income portfolio is closest to which of the following?

A. \$2,950 B. \$295,000 C. \$29,500,000

Answer is C but I would have put B.

Thank you !

Where did you get this question?

It was from the Wiley mock exam took in class (simulation of the real exam) this weekend.

____________________________________________________________________________

The first thing to do is to calculate the market value of each holding. Given that there is a \$1m par value holding in each bond, and that the prices are expressed as a percentage of par the market value of each holding is given as:

Bond 1: (102.36/100) × \$1,000,000 = \$1,023,600 Bond 2: (97.61/100) × \$1,000,000 = \$976,100 Bond 3: (95.14/100) × \$1,000,000 = \$951,400

The money duration of the bonds is given by: market value x modified duration, hence:

Money Duration of Bond 1 = \$1,023,600 × 3.7 = \$3,787,320 Money Duration of Bond 2 = \$976,100 × 9.9 = \$9,663,390 Money Duration of Bond 3 = \$951,400 × 16.9 = \$16,078,660 Hence the Dollar Duration of the portfolio = \$3,787,320 + \$9,663,390 + \$16,078,660 = \$29,529,370

_______________________________________________________________________________________

However I’m a bit confused with what you already wrote here https://www.analystforum.com/forums/cfa-forums/cfa-level-i-forum/91334459

According to the current Level III curriculum, Wiley got it wrong.

Go ahead: convince me that you’re surprised.

In the Level I curriculum they do not multiply by 0.01, but in the Level III curriculum they do; the curricula are inconsistent.

Go ahead: convince me that you’re surprised.

As you stated the dollar duration = modified duration x portfolio value x 0,01 (or in the case of BPV x 0,0001).

But what is confusing me is, they give you the maculay duration, shouldn’t you first calculate the modified duration out of the maculay?

They won’t give you Macaulay duration and expect you to calculate modified duration, then money duration. The formula for converting Macaulay duration to modified duration isn’t included in the Level II III curriculum.

But in the image above, the Maculay duration is given not the modified, this is the reason why I am asking.

Modified duration = Macaulay Duration /(1+cashflow yield)

(we are in the L3 section) But the image above doesn’t come from CFA Institute. Third party prep providers sometimes get it wrong.

Go ahead: convince me that you’re surprised.

I know that; I learned it at Level I. But it’s not in the Level III curriculum. (Well, OK: it’s in a footnote. That hardly counts.)

Good catch! (Though it’s not in Level II at all, and only in Level III in a silly footnote.) I’ve made the correction, above.

Ok, I just wanted to be sure that what I was saying is correct. I agree that what we see in the image above is wrong. And yes, you’re totally right, I think that third party prep are just bullshit and incompetent.

Coming back to curriculum for L3, they explain the relation between MD and Maculay in a very extensive example (including calculating convexity and dispersion).

When I studied I got frustrated by the inconsistency of duration throughout the curriculum. I just try to be consistent with the text, which in Level III is to multiply by the 0.01.

The key idea is that money duration measures the sensitivity of a portfolio’s value relative to interest rate changes. So we need to multiply duration by the price of each security. There are different ways this can be expressed (per 100 of face), so the different formulas are just a matter of units, I think.

The important thing to show the graders, I think, is that we understand how money duration differs from duration, which just measures the sensitivity of a security’s price relative to interest rate. I would guess that showing that you we know money duration = sum(security price * duration) would get most of the points.

To clarify… we use .01 for (money) duration and .0001 if the question specifies BPV, correct? For example, from Exam 2 of the 2018 Schweser mock:

Lewis Atkins has been asked to construct and manage a portfolio of fixed-income bonds to fund multiple debt liabilities of a large corporation. The liabilities have a market value of \$24,465,120 and a modified duration of 6.12. Atkins buys a portfolio of U.S. Treasury notes with a market value of \$25,875,724 and a modified duration of 4.27.

Compute the surplus and (money) duration gap measured in BPV for this set of assets and liabilities.

Surplus: \$25,875,724 - \$24,465,120 = \$1,410,604

BPV assets = \$25,875,724 x 4.27 x .0001 = \$11,049

BPV liabilities = \$24,465,120 x 6.12 x .0001 = \$14,973

Duration gap (in BPV) = \$3,924

So, if the question had asked for the (money) duration gap (without specifying BPV) the calculation would be:

Money duration assets = \$25,875,724 x 4.27 x .01 = \$1,104,893

Money duration liabilities = \$24,465,120 x 6.12 x .01 = \$1,497,265

Duration gap = \$392,372

We should use modified duration to get money duration and we scale the money duration by 100, assume the right duration is used, the answer should be B.

welcome any discussion.

same here, the duration description makes me crazy… do you have any summary for the PVBP, partial PVBP, money duration etc expression?

Just think of money duration as duration expressed in dollars (or applicable currency) terms given your position size --(just as duration is expressed in percentage terms, so “10” means 10% or .10 – hence the .01 multiplier).

BPV is the equivalent of money duration but for a 1bp move.

The answer is B, and the curriculum is not inconsistent At level 1, the Formula was denoted as: DD = -ModDur * Portfolio Value(per dollar par)

In other words, the second term was denoted as: Portfolio Value / 100 (or * 0.01)

At level III, the second term was just broken down to 2 terms: DD = -ModDur * Portfolio Value * 0.01 If you think of it rationally, the Duration is the change in the portfolio given a 100 bps change. How can the answer be C?? What your saying is the portfolio will more than wholly disappear if yields go up by 100 bps!! xD

Magician S2000,

I think this was rather confusing even last year when they introduced it. Not sure if they’ve changed it this year but there were 2 problems like this in the 2018 curriculum and neither of them followed the same format/process of solving for it. But your explanation here is legit and accurate and i assume naturally would coincide with the curriculum.

Hello 2000 - never thought i will be back here but happy to see you are still around.

So i’m kind of confused with this and i was hoping you could help.

So you are saying that the formula is x0.01 for Level III

Nevertheless, in the CFAI books i can only find Mod Duration x Price x 0.0001 which contradicts 2017 exam Q9 A answer which solves using Duration x Value x 0.01

Am I doing something wrong here??

Bill, I’m surprised.

Money Duration and PVBP aren’t the same thing depending on the context.

And it doesnt matter if you use .01 or .0001 as long as you are consistent with the calcuation for whatever you’re trying to compute.