# Duration

Why did the Gods of Finance dictate that duration refer to both a measurement of time (such as “long duration”) as well of change in price for a change in interest rates. Could there be a more confusing aspect of finance?

wait, so you’re taking 3 this year? awesome. you/me have been in the CFA program for an extended DURATION. let’s finish this up and then you can get engaged and all of that good stuff. i’m on SS15 now and took a break to go see black swan. dude. that movie save the makeout was weird. black swan is weirder than duration. now back to poppin’ an interest rate cap in yo’, umm, just welcome back pink.

I wouldn’t miss this party! Lets get this thing done. Saw Black Swan a month ago (the movie, not the poster). Very weird movie.

thepinkman Wrote: ------------------------------------------------------- > Why did the Gods of Finance dictate that duration refer to both a measurement of time > (such as “long duration”) as well of change in price for a change in interest rates. > > Could there be a more confusing aspect of finance? Maybe only CFAI can explain officially. Many candidates are confused by this issue.

i actually find it rather intuitive. the longer the bond maturity, the bigger the duration. see? longer in time = more sensitive to a change in rates.

8yr no coupon bond price moves up/down by 8% facing 1% interest increase / decrease but 1yr no coupon bond price moves up/down by 1% facing 1% interest increase/decrease 8yr = 8% 1yr = 1% maturity = duration

soundboy Wrote: ------------------------------------------------------- > 8yr no coupon bond price moves up/down by 8% facing 1% interest increase / decrease > but 1yr no coupon bond price moves up/down by 1% facing 1% interest increase/decrease > > 8yr = 8% > 1yr = 1% > maturity = duration For zero-coupon bonds, it is true that duration = maturity, but not all bonds are zero-coupon.

thepinkman Wrote: ------------------------------------------------------- > I wouldn’t miss this party! Lets get this thing > done. Saw Black Swan a month ago (the movie, not > the poster). Very weird movie. I saw the AF member not long ago. I haven’t seen the movie. Kill it pinkman!

How the duration of a stream of liability is measured ?

Just to add more into confusion, don’t forget that there are bonds with durations LONGER than their maturities.

My boss ALWAYS talks about duration as a measure of time - he was telling me the other day that it measured how long until the bond was repurchased by the issuer. Every time I mention sensitivity to interest rate changes he just gives me a blank look.

revisor Wrote: ------------------------------------------------------- > Just to add more into confusion, don’t forget that > there are bonds with durations LONGER than their > maturities. Like mortgage securities…

newsuper Wrote: ------------------------------------------------------- > My boss ALWAYS talks about duration as a measure > of time - he was telling me the other day that it > measured how long until the bond was repurchased > by the issuer. Every time I mention sensitivity to > interest rate changes he just gives me a blank > look. It is a common mistake, albeit understandable one since it is easier to remember duration as maturity year instead of a more mathematically correct definition. The most common definition: Duration is a measure of sensitivity of a bond’s price (as a percentage of initial price= to a change in yield), thus it can be also interpreted as the slope of the price curve (as function of interest rate). It is used to estimate the bond’s price change if interest rate changes. To compound the confusion, there are (at least) THREE (slightly) different definitions of duration. 1. Macaulay duration: - This definition is closest to the year to maturity interpretation. - = Average length of the bond weighted by discounted individual cash flow. - In effect, Macaulay by itself is not useful for anything by itself since it does not measure the price sensitivity. However, it is used as a starting point to calculate Modified duration which is more useful. 2. Modified duration: - Closest to the price sensitivity definition --> useful to estimate price change. - Can be proved to be equal Macaulay duration/ ( 1+yield/number of coupon paid per year). - One can see that modified duration = years to maturity for a bullet bond. For any coupon paying bonds, its modified duration < maturity. - Is only useful if the yield changes do not change the expected cash flows (e.g., option free bonds). 3. Effective duration: - ( Est price when yield moved down - Est price when yield moved up)/( 2*price* yield change) - Most useful if the yield changes do change the expected cash flows (e.g., option embedded bonds, MBS,…) - derived e.g., using binomial tree taking the exercising of option. Seriously guys, this is basic level I stuff, may be level II, not for level III’ers. MBS bonds’s duration is shorter than its maturities. However, its derivatives can have duration longer than the bonds’ own maturities. A standard example is inverse floaters. See here if you want to understand why http://pages.stern.nyu.edu/~eelton/debt_inst_class/Floaters%20&%20Inverse%20Floater.pdf