# How to interpret a Duration ??

Hi everybody, I have tormented my self since yesterday with this. I’m currently reading Fixed income part, LOS 63, and they talk about duration but according to the formula, it’s actually the formula of an effective duration. So it already made me confused. it’s still ok if this is only a wording problem, that they will mention the diffenrence between the 2 later But, when I check in the glossary, they also defined a duration as a weighted average maturity of all future CFs. So I saw that this interpretation doesn’t work for zero coupon bond (coz no CF untill maturity). But does it still work for classical bonds??? and how can I interpret the weighted average maturity??? is it over this average, my bonds are lossing values ??? I better hold them only untill this maturity and sell them to get the maximum benefits??? I really need your help to make it clear all for once… Thanksss

nhung.tran Wrote: ------------------------------------------------------- > Hi everybody, > > I have tormented my self since yesterday with > this. I’m currently reading Fixed income part, LOS > 63, and they talk about duration but according to > the formula, it’s actually the formula of an > effective duration. “Duration” is a pretty generic word that means something like “sensitivity to interest rates”. It might mean Macauley, effective, modified, etc. depending on context. > So it already made me > confused. it’s still ok if this is only a wording > problem, that they will mention the diffenrence > between the 2 later > But, when I check in the glossary, they also > defined a duration as a weighted average maturity > of all future CFs. That’s Macauley >So I saw that this > interpretation doesn’t work for zero coupon bond > (coz no CF untill maturity). Yes it does but the average is just one cash flow. > But does it still > work for classical bonds??? If “classical” bonds are coupon bonds. I don’t know what makes a coupon bond any more “classical” than a zero. > and how can I > interpret the weighted average maturity??? is it > over this average, my bonds are lossing values ??? I don’t understand this question. > I better hold them only untill this maturity and > sell them to get the maximum benefits??? > If you hold a bond to maturity, you don’t sell it. You get the principal paid back. Basically, on your next brokerage statement you will see that your cash balance has increased by the par amout of the bond times the number of bonds you owned. No muss, no fuss. > I really need your help to make it clear all for > once… > > Thanksss

ok I will try to make myself clearer… i’m ok with you to say that duration as a measure of time (weighted average maturity) could work for zero coupon bond but since there is only 1 cash flow, then D = number of years to maturity of the bond… For coupon bonds, it make more senses… but what i don’t get is the meaning of weighted average maturity for those bonds, will they “die” after this weighted average maturity???

nhung.tran Wrote: ------------------------------------------------------- > ok I will try to make myself clearer… > > i’m ok with you to say that duration as a measure > of time (weighted average maturity) could work for > zero coupon bond but since there is only 1 cash > flow, then D = number of years to maturity of the > bond… > YES! > > For coupon bonds, it make more senses… but what > i don’t get is the meaning of weighted average > maturity for those bonds, will they “die” after > this weighted average maturity??? No - the bond “lives” until final maturity. You can look at a coupon bond as a series of zero coupon bonds and those “die” as they get paid.

ok given a 5% bond with a par value \$100, and the market required rate of return (yield) is 5,25, I will have a duration of 6,775 and a modified duration of 6,437 Could you please help me to interpret the 6,775? and what kind of conclusion we can make by that interpretation (buy/sell or hold???) thxxx

I supposed it’s a 8-years bond

So an 8-year bond has duration <= 8 yrs. The higher the coupon, the lower the duration (all else equal). So your bond has a duration of 6.775 years and that probably means it is a standard issue semi-annual bond (and I am too lazy to check but there is enough info to figure it out). This bond will not be as interest rate sensitive as an 8-yr zero coupon bond but would be something like as interest rate sensitive as a 6.775-yr zero. The duration of a bond has nothing to do with buy/sell/hold unless you have some specific duration objectives in mind. It’s like saying should you buy or sell a 10-yr zero. I don’t know; it depends on what you are trying to accomplish. Edit: In the broader scheme of things, there is almost nothing in the CFA curriculum at any level about buy/sell/hold. The curriculum is about understanding the investments so you can evaluate them in the context of investor goals. So for example you might ask an investor with a bond portfolio with a duration of 7 yrs how they would feel about a 5% loss in portfolio value. If they say that would be terrible, horrible, jump-off-a-bridge you would calculate that it would take a 5/7% change in interest rates to do that which is too likely to risk losing such a good client to the waters below. So you would sell some long duration bonds in LI, sell some bond futures in LII, and write a very interesting investor policy statement in LIII.

is it ok if i just bypass the time measure concept of duration and consider it as a bonds’ sensitivity measure? (it would make it apparent to me to say that i should sell long duration coz it’s more sensitive toward the interest rate changes)

hmm…what does the LOS say?

i’m reading now debt features, and they only talk about duration as a sensitivity of bond’s price to change in interest rate, so i think that i will just forget the notion of time, weighted average maturity of duration for the moment…

That’s exactly correct. In fact, Frank Fabozzi dedicates a section as to why you should ignore interpreting duration from a mathematical standpoint (the first derivative of a bond function) and a temporal standpoint (average maturity). Duration is nothing more than a linear measure of a bond’s price sensitivity given a 100 basis point change in the interest rate. When you communicate that definition to a prospective client, that will make more sense than saying “the average maturity of these GNMA pass through instruments is 30 years.” Remember the formula: First you shock the price of the bond by a pre-determined move in the yield: say 10 or 25 basis points. You find the range, or the spread in price, between the high price (from a drop in yield) and low price (from an increase in yield). You then take the midpoint, or basically the average move by dividing this range by 2. Then you translate this average into a percentage change based on the initial price. Therefore, divide this average by the initial price. That percentage change is what occurs when you shocked the rate by the predetermined number of basis points–again, this could be 10 or 25 bps. To translate this into a 100bps change, you simply divide your percentage change in price by the basis points you used to shock the rate. These are essentially a proportional ratios. For instance, 2% to 25 bps is the same as 8% to 100 bps. This is why duration is considered a linear relationship. Hope that helps.