It may be useful for certain situations where the math works out, but in general it is incorrect. It is not a “second definition” when it is wrong. If you want to know that the duration of a bullet maturity instrument is equal to its maturity, just remember that fact. Also, duration is defined as (dp/dy)(-1/p). This is not the same as you have above.
So, you don’t like this definition? “Definition: The standard definition of duration is Macauly duration, the PV-weighted average number of years to receive each cash flow” http://en.wikipedia.org/wiki/Bond_duration
wyantjs Wrote: > Also, duration is defined as > (dp/dy)(-1/p). This is not the same as you have > above. I’m sorry for my idiosyncratic notation. I knew you would understand what I meant. The sign was the only important part of that equation.
maratikus Wrote: ------------------------------------------------------- > So, you don’t like this definition? > > “Definition: The standard definition of duration > is Macauly duration, the PV-weighted average > number of years to receive each cash flow” > > http://en.wikipedia.org/wiki/Bond_duration Sorry man…I don’t mean to split hairs. No. I don’t like that definition. Especially considering that nobody uses Macauly Duration. When quoting on vanilla bonds, we use modified, or use effective on bonds with options. It is not true in practice that the standard definition is Macauly.
I am not disagreeing with you either. Just playing devil’s advocate. Good luck on your studies!
did we forget to mention that duration implies a small, paralel shift in interest rates? or do I have it wrong?
Don’t think of duration as years. Think of it as how much value and hence price of income stream from fixed income instrument will change with change in interest rates. Longer the maturity, higher the change in price, or, equivalently, the stream of payments over time.
I had a fixed income teacher who used to explain in the following way. (maybe not exactly) If you think of a see-saw (for 3rd grade analogy), and you think of what you pay for the bond on the far left side, and then all the payments going across and the principal on the far right side. Duration would be the piece that makes it balance, the fulcrum. This piece won’t be right in the middle, since the buy price and principal aren’t the same. And as you go through time, you can think of the coupons over the life moving from the right to the left of the “duration fulcrum”, and the fulcrum/duration moving to the left (lowering) to compensate. The further along in the life of the bond, the fewer coupon payments you have left, and therefore lesser interest rate risk. I googled this and this link has what I am trying to explain: http://www.investopedia.com/university/advancedbond/advancedbond5.asp
Pylon, thanks for your explanation, very helpful.
i guess i understand mwvt9 somehow. duration seemed pretty clear to me as a first derivative of price in regard to interest rates. but after looking at the end of chapter problems in CFAI book, things became rather blurry. i got wacked on the item set involving a repo agreement and its effect on duration, or the other item set that asked for the spread duration of a portfolio…
CelticsFA11 Wrote: ------------------------------------------------------- > I had a fixed income teacher who used to explain > in the following way. (maybe not exactly) > > If you think of a see-saw (for 3rd grade analogy), > and you think of what you pay for the bond on the > far left side, and then all the payments going > across and the principal on the far right side. > > Duration would be the piece that makes it balance, > the fulcrum. This piece won’t be right in the > middle, since the buy price and principal aren’t > the same. And as you go through time, you can > think of the coupons over the life moving from the > right to the left of the “duration fulcrum”, and > the fulcrum/duration moving to the left (lowering) > to compensate. > > The further along in the life of the bond, the > fewer coupon payments you have left, and therefore > lesser interest rate risk. > > I googled this and this link has what I am trying > to explain: > http://www.investopedia.com/university/advancedbon > d/advancedbond5.asp This is a refreshing perspective over an impt but confusing terminology. Thanks
Another philosophical insight into Duration is that the cash flow that is disbursed/paid out, is that the weighting and timing of it affects duration, because before it is paid out, the time value of money changes the ‘value’ of the asset/cash due to changes in interest rates.
I prefer to think of duration as the time until I pass Level III so that I never have to read threads like this and then want to weep because I thought I understood something fully only to realize that I don’t really get it at all.
You are a lock Smarshy. Only a matter of time my friend.
Mandelbrot Wrote: ------------------------------------------------------- > Duation is to delta as convexity is to gamma. Duration/Delta is to Velocity as convexity/gamma is to acceleration.
good thread…was struggling with the concept a bit myself…this helps a lot…
ConvertArb Wrote: ------------------------------------------------------- > Mandelbrot Wrote: > -------------------------------------------------- > ----- > > Duation is to delta as convexity is to gamma. > > > Duration/Delta is to Velocity as convexity/gamma > is to acceleration. duration is to first partial derivative as convexity is to the second partial derivative 
maratikus Wrote: ------------------------------------------------------- > ConvertArb Wrote: > -------------------------------------------------- > ----- > > Mandelbrot Wrote: > > > -------------------------------------------------- > > > ----- > > > Duation is to delta as convexity is to gamma. > > > > > > Duration/Delta is to Velocity as > convexity/gamma > > is to acceleration. > > duration is to first partial derivative as > convexity is to the second partial derivative Don’t hijack this thread, nerds. It is meant for the dumb people. ; )
^^ agreed…
Just sharing as I just covered this topic: By definition, the duration of a bond is a linear approximation of the % change in its price given a 100 bp change in int rate. For eg, a bond with a duration of 7 will gain about 7% in value if i/r fall by 100 bp. Also a point to add is that for securities with random cash flows such as callable bonds, the definition using average maturity of the bond’s cash flows, weighted by PV may not be applicable. Any comment?