I’ll throw two more cents in the pot… Many people think of duration as the way Pylon explained it, so it’s good to be familiar with the “3rd grader explanation”, but I also agree with whoever said that at this stage you should not be thinking of it in this way. Instead, think of it as the sensitivity of a bond’s value to a parallel shift in interest rates. A good example of why the weighted avg time to receive your money back isn’t the best way of thinking about duration: a floating rate bond with a 20 year maturity. The duration of this bond will likely be something slightly less than the time until the next interest rate reset. So it may have a duration of say .45 if the rate resets semiannually, but the weighted average life will be significantly longer. And for what it’s worth, here’s PIMCO’s lay-man’s definition. “A measure of average maturity that incorporates a bond’s yield, coupon, final maturity and call features into one measurement. Duration measures the sensitivity of a bond’s, or portfolio’s, price to changes in interest rates.”
Had some confusion on bond duration, so checked out this thread discussion of last year. Summarizing the above discussion: there are basically two definitions of durations Definition 1 (macaulay): This is the loose definition, which is the weighted average time to receive back the cash flows which is explained in this link. http://www.finpipe.com/duration.htm My Doubt: I know that they are multiplying PV of cash flow with time because it is weighted average, but i am unable to figure out why we take weighted average. I mean, since we are taking PV of cash flows, isnt time factor already considered. Definition 2: Duration is the price sensitivity of the bond to interest rates i.e %change in price for 1 percent change in interest. In this link http://www.finpipe.com/duration.htm, it explains that modified duration = Macaulay duration/ (1 + y) and %price change = -1 * modified duration * change in yield which essentially means both the definitions are related. My doubt: I am still unable to connect the two definitions. Whats the relationship between the two and can one be mathematically derived from the other? Can someone throw some light please?
Duration is like a see-saw. Interest rates are sitting on one side of the see-saw, bond prices on the other. Time to maturity will mostly determine how long the “price” end of the see-saw is. Long duration would be like if the price end of the see-saw is really long, then every time you move the interest rate side of the see-saw, the price side moves a great deal. A bond that is far from maturity will have the longer duration, so every time rates move, the price end of the see-saw moves dramatically. Hey, I tried to put it in a third-grader’s context…
Think of it this way - Maccauleys - explains the math. Its the weighted average of cash flows. Good for explaining duration but no practical use. Modified - duration of choice for option free bonds. This mothod captures the fact that duration is “modified” as the price and yield change. Modified duration does not capture interest rate optionality so it cannot be used with MBS, callables etc Effective - Duration of choice for bonds with optionality. Also can be called OAS duration. This method uses a binomial tree to find bond prices in various interest rate scenarios and works backwards to an OAS and duration