janakisri, Are you saying that for a upward-sloping yield curve, a lower ITRR ( ITRR < YTM But this is contrary to what are said in the text. I am really confused. Anyone else can help ? Or shall we stop our discussion to avoid wasting more time ?
janakisri, CORRECTION to my previous message. Are you saying that for a upward-sloping yield curve, a lower ITRR ( ITRR < YTM But this is contrary to what are said in the text. I am really confused. Anyone else can help ? Or shall we stop our discussion to avoid wasting more time ?
Memorized the silly text and moved on. The objective is to pass the exam.
Ok, here is what I know from my research on this topic: The YTM and the ITRR mean the same thing (= total return). The only difference is how you calculate between the two: *With YTM, you assume coupons are reinvested at the YTM. *With immunization, you assume coupons are reinvested either at the implied forward rates or the treasury spot rates. So, it is a more realistic measure of the total return you might be able to achieve. They will both be equal if the yield curve is flat. In most cases, we can only reinvest the coupon at the short end of the yield curve, given an upward sloping yield curve, short end pays less than long end. That is why immunization target rate is lower than YTM.
Guys , you should see the table in Pg 28 ( Exhibit 8 ) and read between the lnes. If rates are moving down , the accumulated value is less than target value. This is because the bond used for immunization returns less interest on interest, at successive coupon payment dates. For such a downward sloping yield curve , obviously the manager cannot plan on reinvestments happening at the initial YTM ( when she is deciding which bond to select, all she knows for sure is the shape of the yield curve , the initial YTM for the liability at the horizon and different selectable bonds with different YTM’s , which we call ITRR). If she planned that reinvestments would happen at the initial YTM , the accumulated value will be less than target or required value . So she has to plan on HIGHER reinvestment return to offset the decline in acccumulated value dues to FALLING rates. ITRR > initial YTM when rates are falling. Now flip all the signs for a rising interest rate curve. ITRR < initial YTM when rates are rising
i have memorized this but am yet to see a clear and concise explanation…well at least thanks to AMA for bringing this up…i thought i was the only one to find this counter-intuitive upward sloping yield curve =========> LOWER Reinvestment rates ===========> ITRR< YTM The reinvestment rates being lower is the one that trips me up…what about an upward sloping yield curve means that reinvestment rates will be lower ??? a thought is this related to the fact that a upward sloping yield curve is related to a downward sloping interest curve? in other words if my yields are now higher it simply means i am in a lower interest rate environment??
No , in a higher yield environment , interest rates are higher. So you need LESS reinvestment return to reach a target value at the end of your horizon
janakisri Wrote: ------------------------------------------------------- > No , in a higher yield environment , interest > rates are higher. > > So you need LESS reinvestment return to reach a > target value at the end of your horizon Janakisri Thanks that makes sense but thats not what the book text says…it says the reinvestment rates are lower so how does higher interest rates mean your reinvestment rates are lower?
An upward slopping yield curve implies a higher forward rate (according to expectation theory). Reinvestment rate should be higher but … *faint*
reinvestment rates are not the same as “yield” at any point of time other than initially . Reinvestment rate ,not plural rates, is a planned number . Yield changes daily, reinvestment rate is set int the beginning when you’re planning to purchase a bond to make sure you reach your target
I’d like to clarify that reinvestment rate is an ex-ante value that is planned. Actual yield obtained drives realized reinvestment values. We plan for a reinvestment rate and either rates are higher or lower
janakisri Wrote: ------------------------------------------------------- > reinvestment rates are not the same as “yield” at > any point of time other than initially . > Reinvestment rate ,not plural rates, is a planned > number . Yield changes daily, reinvestment rate is > set int the beginning when you’re planning to > purchase a bond to make sure you reach your target no …the reinvestment rate is the investment rate that you are exposed to as u receive coupon payments from the bond …it is not known in advance ( well apart from forecast)
that is the realized rate. The ex-ante rate is the “planned” or targeted rate , which is the only one the pm has discretion on . After she purchases the bond , the realized returns may go up or down . The planned number may get her to the target in the face of a yield curve that is not flat as the TVM calculation suggests , but changes witgh time. If it behaves as anticipated ( ie rising yield curve or falling yield curve) she can plan on doing the opposite i.e. seek lower planned rate or higher planned rate to balance returns and get to the objective of the target value
I feel that it has a logical answer. If yield curve is upward sloping and let’s say our YTM for a ten year investment is 10%, we can immunize at a lower target rate of return only. lets say below mentioned is the yield curve structure: Y-2 5% Y-5 7% Y-7 8% Y-10 10% Now, all intermediate cash flows will be reinvested at forward rates prevalent at the time of reinvestment. A cash flow received at end of year 3 can only be reinvested at an interest rate applicable to 7 year investment which is only 8%. Similarly, a cash received at end the end of 9 years can only be reinvested for one year at 3%. Therefore, cash flows will be reinvested at lower rate compare to 10%. This will result in a lower than 10% realized yield. This explanation assumes the upward sloping yield curve remains same throughout the 10 year period. However, if yield curve represents expectation then cash flows will be reinvested at forward rates. These forward rates will be higher than current rates but not likely higher than 10%. For example the cash flow to be received at end of year 8 will be reinvested at a 2 year rate which may be higher then current two year rate of 5% but most likely will be lower than 10%. I hope it clarifies the issue.
I get your message , I believe you are correct. The short end is lower in a rising yield curve , while the short end is higher in a downward sloping yield curve. So you will get less income from reinvestment in a rising yield curve and more income from reinvestment in a falling yield curve. So ITRR < YTM when rates are rising , you successively get less and less interest income for the same horizon date. So ITRR > YTM when rates are falling , you successively get more and more interest income for the same horizon date
mitchells Wrote: ------------------------------------------------------- > I feel that it has a logical answer. > > If yield curve is upward sloping and let’s say our > YTM for a ten year investment is 10%, we can > immunize at a lower target rate of return only. > > lets say below mentioned is the yield curve > structure: > > Y-2 5% > Y-5 7% > Y-7 8% > Y-10 10% > > Now, all intermediate cash flows will be > reinvested at forward rates prevalent at the time > of reinvestment. A cash flow received at end of > year 3 can only be reinvested at an interest rate > applicable to 7 year investment which is only 8%. > Similarly, a cash received at end the end of 9 > years can only be reinvested for one year at 3%. > Therefore, cash flows will be reinvested at lower > rate compare to 10%. This will result in a lower > than 10% realized yield. > > This explanation assumes the upward sloping yield > curve remains same throughout the 10 year period. > However, if yield curve represents expectation > then cash flows will be reinvested at forward > rates. These forward rates will be higher than > current rates but not likely higher than 10%. For > example the cash flow to be received at end of > year 8 will be reinvested at a 2 year rate which > may be higher then current two year rate of 5% but > most likely will be lower than 10%. > > I hope it clarifies the issue. yes yes by georges i think you have it ole chap …thanks to all
janakisri Wrote: ------------------------------------------------------- > reinvestment rates are not the same as “yield” at any point of time other than initially . > Reinvestment rate ,not plural rates, is a planned number . Yield changes daily, > reinvestment rate is set int the beginning when you’re planning to purchase a bond to > make sure you reach your target I think the “reinvestment rates” mentioned here by you is the ITRR which shall be determined initially, but my understanding is that actually the “reinvestment rates” shall refer to the rates of return from the investings of the coupon payments and principal (if the bond is matured before the horizon date of the liability). Please correct me if I am wrong.
mitchells Wrote: ------------------------------------------------------- > This explanation assumes the upward sloping yield curve remains same throughout the > 10 year period. However, if yield curve represents expectation then cash flows will be > reinvested at forward rates. These forward rates will be higher than current rates but > not likely higher than 10%. For example the cash flow to be received at end of > year 8 will be reinvested at a 2 year rate which may be higher then current two year > rate of 5% but most likely will be lower than 10%. It seems to me that the story is differnt. For a upward sloping yield curve, the forward rates will be HIGHER (not LOWER) than the YTM which is “measured” at the inception of a bond investment for a bond matured at the horizon date. For example and for simplicity, assume the yield curve is : 6/8/10% at T=1/2/3. An annual bond with 3 years maturity is purchased at par of $100 when T=0, the the YTM= 10%. Also we assume that the yield curve will remain unchanged (as it was at T=0) in 3 years. The 1st coupon payment of $10 can be reinvested at the forward rate of 12.06% {=[(1.10^3/1.06)]^1/2]-1} for 2 years and the 2nd coupon payment can be reinvested at the forward rate of 14.11% {=[(1.10^3/1.08^2)]-1} for 1 year. We can see from this example, the coupon payments will be reinvested at the forward rates which are higher than the YTM of 10%, not lower than the YTM. In this case, it seems that the ITRR can be set to be LOWER than the YTM. That is, a ITRR lower than the YTM will be enough to meet the liability at the horizon date. This is due to the fact that reinvestment rates (i.e., the forward rates) HIGHER (not LOWER) than the YTM can be attained. If I am wrong, correct me ! Thanks !
It seems that whether the YC (yield curve) is upward or doward is irrevant in determining the ITRR and only the parallel shift IMMEDIATELY after the the investing in the bond is relevant (as in Example 5 / Exhibit 8 on P27~28). In the example raised in my previous meassage, suppose further that we have a liability of $133.96 in 3 years. We can meet the liability as long as we invest $100 to buy a bond with 3 years maturity at par of $100 when T=0, irrespective that the YC was upward/doward or flat. The reinvestment values of the C/P (coupon payment) will be : 1st C/P:10x[(1.1206)^2]=12.55, 2nd C/P:10x1.141=11.41, 3rd C/P:10x1.00=10.00 The total value at maturity=100(principal)+12.55+11.41+10.00=133.96 and the (realized) rate of return=(133.96/100)^1/3 -1=10.2% (=10.0%, if rounding error is negleted) In case of downward sloping, the (realized) rate of return shall be around 10% too. Of course, in case of flat, (realized) rate of return = YTM = ITRR (set at the beginning) The case shown in Example 5 / Exhibit 8 is that the parallel shift IMMEDIATELY after the the investing in the bond, which is a different story. In case that the maturity date of the bond does not match the horizon date of liability (or the the investment), then I don’t what the conclusion will be. Any challenge is welcome !
In calculation of forward rates, you are assuming no liquidity premium.