Hi all, apologies in advance for my longest post so far:
We are still trying to wrap our heads around the concept of bond duration. I'm much more au fait with the concept: i.e. yield sensitivity to price change, and a measure of how long it will take for the cash flows (present values of) to return one's investment.
However being slightly mathematical and wanting to know how a potential investment of ours works, I've soldiered on with the example that I posted on friday i.e.
https://www.thestreet.com/topic/46361/duration.htmlDuration measures the time it takes to recover half the present value of all future cash flows from the bond. The discount rate for calculating the present value of the cash flows is the bond's yield. So as a bond's price and yield change, so does its duration.
For example, a bond with 10 years till maturity and a 7% coupon trading at par to yield 7% has a duration of 7.355 years. At a yield of 6% (price 107 14/32), its duration is 7.461 years. At a yield of 8% (price 93 7/32), its duration is 7.246 years.So based on the replies I received on friday, in particular:
Alaric wrote:It says present value in the definition. So you have to discount.
and
Alaric wrote:If you just add up the payments, you are using an interest rate of zero.
I revisited my earlier thoughts: and my initial point of confusion is that Alaric mentioned the term
interest rate but the sited
thestreet article has no explicit mention of interest rate; but instead it mentions "yield" (presumably the bond's YTM or running yield?). Am I to understand that I should equate the term "yield" in the web article's for Alarics "interest rate"?
Anyway I proceeded with my thoughts, assuming that we are to take the term yield==interest-rate, and went ahead with
thestreet's example. After quickly getting irritated with carrying the figures around on paper and being a programmer by profession, I wrote a configurable program, in which I can feed in the numbers of interest (maturity, coupon, rate/yield/? etc.). So below is a screen dump of the program assuming the above bond bought at issue for 100 units maturity=10 years, coupon=7%, discount rate=7%.
The leftmost figure is the number of years since purchase, the next figure is the present value of that year's cash flow (interest payment discounted at rate compounded (1 + r)^n), and the last figure is the accumulated total of the cash flows:
Years:1 PV of cash_flow 6.542056 running total of cash flows PVs 6.542056
Years:2 PV of cash_flow 6.114071 running total of cash flows PVs 12.656127
Years:3 PV of cash_flow 5.714085 running total of cash flows PVs 18.370212
Years:4 PV of cash_flow 5.340266 running total of cash flows PVs 23.710479
Years:5 PV of cash_flow 4.990903 running total of cash flows PVs 28.701382
Years:6 PV of cash_flow 4.664396 running total of cash flows PVs 33.365778
Years:7 PV of cash_flow 4.359248 running total of cash flows PVs 37.725026
Years:8 PV of cash_flow 4.074064 running total of cash flows PVs 41.799090
Years:9 PV of cash_flow 3.807536 running total of cash flows PVs 45.606626
Years:10 PV of cash_flow 54.393374 running total of cash flows PVs 100.000000
So what I still don't get, is what
thestreet's article means when it associates
half the present value of all future cash flows from the bond and the time value of
7.355 years, since in my above calculations between years 7 and 8, I've accumulated approximately 39 units. What's that half of?
Apologies for my obsessiveness in all this, just eager to make our investments with more confidence, without reliance on a "bond fund" manager. (Love it if there was a decent book for all this....Mark Glowreys book useful though it is, doesn't spend much time on this stuff)
thank Matt