Money Duration

CFA Level I Fixed Income
#1

What does ‘per $100 of face value’ mean while calculating money duration.

#2

I’ll have a go at this. Correct me if I’m wrong. Duration is a measure of interest rate risk. When interest rates rise, the current value of future (coupon) payments and face value declines. Duration is the time you need to hold the bond to achieve the stated yield at time of purchase. As bond payments are stated as a percentage of face value, you need the face value amount.

#3

I have a problem with the explanation of duration as well. So let’s say the duration of 10 year bond comes up to be 7.56. Does it mean that I get all the coupon payments and principal within 7.56 years.

So I study using kaplan and there is a statement saying "The money duration is $751.56 per $100 par face value. How is this a percentage of face value ? Confused.

#4

There are different sources of returns for bonds: - Coupon and face value payment - Price return - Coupon reinvestment return Duration of 7.56 years means that if you hold the bond for this period of time, your price risk (due to higher interest rates) will be offset by the coupon reinvestment return.

Therefore you achieve the stated yield at time of purchase. To get back to your FV question. Not too sure about that one but if you divide 751.56 by the FV of 100 you basically end up with the duration value 7.56 (mind rounding of values)

#5

Don’t entirely get this concept. But thanks AndrV.

#6

I would like to put into place the big picture which you may or may not be seeing.

First, each brand of duration has its own interpretation attached to it.

MacDur----- the years until it is equally as beneficial to sell the bond for profit or hold for coupons.

Effective Duration----- a measure of interest rate sensitivity

ModDur------ % change in price given a 1BP change in yield

Money duration------ the actual price change given a 1BP change in yield

…so… the “money duration per $100 of face value” means how much the price of the bond will change _ per 1BP. _ when you asked what the meaning of “751.56 per $100 face value”, it is not simply $751.56, it is _ actually _ $756.56/1BP. In order to get a strait usable number you have to multiply by 1BP (.0001). …you know, get rid of “per 1BP” part.

$756.56/1BP x 1BP = 7.5cents

Result: for every $100 of face value, if the yield changes BP, then the price will change by 7.5cents

#7

Both modified duration and effective duration are measures of interest rate sensitivity: the (approximate) percentage price change for a 1% (not 1bp) change in yield.

I wrote an article on various forms of duration that may be of some help here: http://financialexamhelp123.com/macaulay-duration-modified-duration-and-effective-duration/

Money duration – which is called dollar duration in the US – is simply the effective (or modified) duration multiplied by the price of the bond; it gives the price change for a 1% change in yield. It’s a dollar (or euro, or yen, or pound, or . . .) value rather than a percentage.

Instead of quoting the money duration based on the price of the bond, it can be quoted for $100 of par value. For example, if the market price of a $1,000-par bond is $985 and its effective duration is 6.6 years, then its money (dollar) duration can be quoted as:

$65.01 (= $985 × 6.6%)

or

$6.501 per $100 of par

#8

^sorry about the 1BP vs. 1% confusion. The example I was basing my understanding on must have been a special case tailored around the basis point. Thanks for clearing it up.