can someone explain duration is related to extension risk? when interest rates go up, prepayments go down, and the investors loses out on the opportunity to reinvest at the now higher rates. the average maturity of the loans is extended. how does bond price sensitivity (duration) fit into all of this? and what exactly does an increase in duration mean?
Duration is a weighted average of payment on time. So with higher maturity means higher duration. higher duration, maturity, means higher price sensitivity.
so the duration here is a definition different from the price sensitivity to a 1% change in yield?
Duration can also be considered the amount of time it takes for an investor to receive his money back from an investment. the longer the duration, the longer the maturity (this is also why interest rates have an inverse relationship with duration. lower interest rate payments=longer amount of time for you to get your money back). I bet if you thought about it long enough (some longer than others) you could find some relationship between the price sensitivity to a 1% change in yield and my statement above.
SkipE99 Wrote: ------------------------------------------------------- > Duration can also be considered the amount of time > it takes for an investor to receive his money back > from an investment. the longer the duration, the > longer the maturity (this is also why interest > rates have an inverse relationship with duration. > lower interest rate payments=longer amount of time > for you to get your money back). > > I bet if you thought about it long enough (some > longer than others) you could find some > relationship between the price sensitivity to a 1% > change in yield and my statement above. if interest rates increase… duration on a bond/loan/ fixed rate cash flow INCREASES. This is not an inverse relationship.
pacmandefense Wrote: ------------------------------------------------------- > can someone explain duration is related to > extension risk? when interest rates go up, > prepayments go down, and the investors loses out > on the opportunity to reinvest at the now higher > rates. the average maturity of the loans is > extended. how does bond price sensitivity > (duration) fit into all of this? and what exactly > does an increase in duration mean? don’t confuse reinvestment risk and interest rate risk. Let’s say a 30 yr 6% coupon bond is issued at par with a 10 yr call, the bonds will have an effective maturity of 10yrs as long as rates are at or below 6% (implying a bond price of par or greater). Now assume rates increase then the bond is priced to a discount and the effective maturity is now 30ys. Hence the extension and now the bonds have a higher duration (in all forms of the definition, i.e. weighted cash flows, dollar value of the 0.01% etc)
Char-Lee Wrote: ------------------------------------------------------- > SkipE99 Wrote: > -------------------------------------------------- > ----- > > Duration can also be considered the amount of > time > > it takes for an investor to receive his money > back > > from an investment. the longer the duration, > the > > longer the maturity (this is also why interest > > rates have an inverse relationship with > duration. > > lower interest rate payments=longer amount of > time > > for you to get your money back). > > > > I bet if you thought about it long enough (some > > longer than others) you could find some > > relationship between the price sensitivity to a > 1% > > change in yield and my statement above. > > > if interest rates increase… duration on a > bond/loan/ fixed rate cash flow INCREASES. This is > not an inverse relationship. sorry about that. i need to keep my big mouth shut. its the coupon rates i was thinking of. the higher the coupon rate, the quicker you get your money back, the lower the duration.
SkipE99 Wrote: ------------------------------------------------------- > Duration can also be considered the amount of time > it takes for an investor to receive his money back > from an investment. the longer the duration, the > longer the maturity (this is also why interest > rates have an inverse relationship with duration. > lower interest rate payments=longer amount of time > for you to get your money back). > This can be best explained by taking the Zero coupon bond as an example. Since there are no coupon payements, the duration of a zero coupon bond is always the time till maturity.
Below is an excerpt from wikipepdia… This makes a lot of things clear… “The units of duration are years, and duration is always[note 1] between 0 years and the time to maturity of the bond, with duration equal to time to maturity if and only if the bond is a zero-coupon bond. The units may seem surprising; it can be understood via dimensional analysis as the ratio of “percentage change in price” over “change in interest rates”: the numerator has no dimensions (or units of %), while the denominator has dimensions of 1/Time (units of %/year, as interest rates are quoted is percentage per year). Thus the ratio has dimension of Time, units of Years. More concretely, this can be understood because more distant cash flows are more sensitive to interest rates, as measured via yield: when taking the present value via discounted cash flows of a bond, one discounts each future cash flow by (1 plus) the yield to the power of the number of years when that cash flow occurs: (1 + y) − n – thus the present value of more distant future cash flows are more sensitive to changes in yield. In particular, the duration of a zero-coupon bond (one with a single cash flow at maturity) is the time to maturity of the bond. How to define the duration of bonds with intermediate cash flows is subtler, as discussed below.”
eros79: I wouldn’t always trust wikipedia. For the record, Effective Duration has NO units.