I know these are simple concepts but i would appreciate if someone gives more clarity over these points.
1.As maturity increases, duration increases and the bond becomes more volatile(Duration increases immediately on the day a coupon is paid, but throughout the life of the bond, the duration is continually decreasing as time to the bond’s maturity decreases) 2. Second, as a bond’s coupon increases, its duration decreases and the bond becomes less volatile
If yield increases/decreases, bond duration will reduce/increase respectively. So that means higher yield is favorable as duration is falling( as price sensitivity will fall) and vice versa or there are other pieces to the puzzle that we need to consider too when yield rise or fall ??
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Macaulay duration (this is pv of cashflows/overall PV weighted by time,this is time weighted by the PV cashflows/overall PV)*, in years. So like the time it takes you to get paid back. A zero coupon bond Macaulay duration = years to maturity (there is only 1 cash flow). Period until x (PV CF1/PV) + … Period N * (PVCF n/PV)
There is also modified/effective/other durations. Those are rate of change in price due to a change in yield/curve/etc. Modified is used for option-free bonds, for bonds with options you use effective. Modified assumes cash flows do not change, effecitve allows you price in cash flows changing.
Macaulay duration and modified durations are related by MacaulayD/(1+Yield/Compound periods)
as maturity increases, the time it takes you to get paid back increases, thus duration increases.
As the coupon is higher, you get paid back “faster”, thus duration should be lower for higher coupons vs smaller. There is also something about how as rates go down, the Macaulay duration falls, and thus the PV of cash flows at the front are weighted higher (they are are now larger due to a lower discount rate relative to the later ones).
Just like coupons, the higher the yield the lower the duration.
As far as favorable goes…I’m not sure what you wrote how it relates, but in theory, if you expected rates to fall, you would want a bond with higher duration due to the price change being larger (remember -(Duration * Mkt Value * Change in Yield) = approx. price change. Also remember, that duration is only good for small changes, since bonds are convex (and bonds with options such as calls have negative convexity), you will need to do a convexity adjustment for larger changes.
If you expect bond rates to rise, you would want a shorter duration. 1) It’s a smaller price decrease; 2) it would allow you to reinvest at a higher rate due to the cashflows coming in quicker.
I saw you say that in the other thread…that makes sense this morning thinking about it. Per usual thanks, you rock! If you happened to read the rest…did I get that correct?
“can you explain this a little, so your rates go higher, bond payment come in quicker and you can then invest it in other things…right?”
Yes. So lets say you are getting paid 2%, rates move to 3%. You can now buy a bond giving you 3%, hence reinvesting at a higher rate.
Remember there are two types of risk: Price/Market risk and Reinvestment risk. They move inversely to each other and depends on your time frame which one dominates for you. For example, lets take short term again. Your coupon is 3%, rates are now 2%. You get some price appreciation, but now you can only reinvest @ 2%.
The whole point of immunization is to eliminate that based on my rudimentary understanding.