In V4, Reading 23, Page 29, there is " In general, for an upward-sloping yield curve, the immunization target rate of return will be less than the yield to maturity because of the lower reinvestment return. Vice Versa"
Any idea why they have such conclusion? thanks
When the yield curve is upward sloping reinvestment income will be greater due to rising yields however the price risk is negative since rising yields lowers bond prices. I’m guessing that the Imm. Target return is now lower due to lower bond prices and since yields are rising the target falls below the rising YTM.
I am very much confused by this issue too. In my opinion, the target return is the target yield (as the 7.5% in Example 5 on p.27) and it shall be remain unchanged over the entire investment horizon, irrespective of the yield curve (upward, flat or downward) at the inception or any change in yield curve during the investment horizon. The target yield (return) of 7.5% in Example 5 is calculated by (13,934,413/9,642,899)^[1/(5x2)]. That is, the immunization target rate of return shall have nothing to do with the shape of the yield curve. Further comment is appreciated !
to Aloha, I agree with you that, for classical single-period immunization, the target rate of return is “locked” with a guaranteed rate of return. But the real return is not. Since there are price risk and re-investment risk, the shape of yield curve will decide if you could meet the target return.
what they say is " the imm target rate of return will be less than the YTM bcs of the lower reinvestment return" - it means for a upward-sloping yield curve, the reinvestment yield is assumed to be less than the YTM. I do not understand here.
the imm target rate of return will be less than the YTM with a upward-sloping yield curve bcs of the lower reinvestment return. Since it the yield curve is upward sloping. the short-term interest rate will be always less than the long term interest rate. after investor got the coupon and need to reinvest them, they have to reinvest them with a shorter term than the maturity horizon, so the reinvestment yield is assumed to be less than the YTM
oh, i see. thanks a lot. Given a upward-sloping yield curve, the YTM is interpolated with the maturity horizon. However the reinvestment rate must be less than the YTM since shorter period. Does make sense.
My views are as follows. 1. The immunization target rate of return shall be the “target yield” and it shall be fixed. YTM is the yield and IRR if the bond is held until maturity and all the coupons are reinvested at the IRR (=YTM), therefore YTM will be constant only if the bond is held until maturity and the yield curve is flat over the entire the investment horizon. 2. It is the “realized return (at the end of the investment horizon)” that will be dependent on the shapes of the yield curve (at the inception and over the investment horizon). However, the yield curve changes over the investment horizon. Actually, the “realized return (at the end of the investment horizon)” is dependent on the actual spot rates and/or forward rates at the time points of the coupon payments. 3. For above reasons, it seems to me that it is inconclusive regarding the relationship between the immunization target rate of return and YTM under the scenario on the textbook. Any comment is appreciated !
to Aloha, The immunization target rate of return shall be the “target yield” and it shall be fixed. - right. Given the yield curve is flat, the YTM is achievable, so you can set the imm target ROR be same with YTM. However once the yield curve is upward-sloping, as previous said, the YTM is not achivable since lower reinvestment rate, so you need set a smaller imm target rate of return, since it’s realizable. Vice verse.
redondo : In my opnions, 1. The immunization target rate of return shall not be RESET according to the shape of the yield curve since it is FIXED so that the target value ($13,934,413.- in Example 5 on p.27) will be achieved at the rate. 2. If the yield curve is upward-sloping at the inception and REMAIN UNCHANGED over the investment horizon, then the REALIZED return (yield) will be lower than the immunization target rate of return. If the yield curve is downward-sloping at the inception and REMAIN UNCHANGED over the investment horizon, then the REALIZED return (yield) will be higher than the immunization target rate of return. 3. As said above, the yield curve changes over the investment horizon. So it is difficult to have a conclusion at the inception of the investment horizon. Any further comment is appreciated !
so what exactly are you trying to say. you are reevaluating what will be achievable a year later. at that time - with a upward sloping yield curve you have higher reinvestment income, but lower price income (because at a higher yield - price falls). So now your YTM is not achievable. What you can achieve is a lower number since what you decided to immunize with was set a year earlier (and not changeable). So with an upward sloping yield curve your target rate of return will be lower then the YTM. key thing to remember - Price change trumps the reinvestment of coupon. So with an upward sloping -> you would have lower.
Aloha, 1. we never say 'RESET", the imm target ROR is defined at the beginning. Assume at the inception, the yield curve is upward-sloping, the liablity is due 5 years later. The YTM of 5year is 7.5%, interpolated from yield curve. However, the imm target ROR should be 7% (less than 7.5%). that’s the conclusion. make sense?
redondo: in any case, it’s helpful to me to discuss this issue here. In your example raised above, the imm target ROR became 7% while we agreed that the imm target ROR shall be fixed at 7.5%. This seems to be a discrepancy to me. In Example 5 on p.27, the YTM is 7.5% which is same as the the imm target ROR. My view is that the YTM was made to be the same as the imm target ROR by purcharsing a bond with YTM of 7.5% at the inception in the hope that the realized return (yield) in 5 years will be 7.5%. That is, the target value of $13,934,413 can be achieved in 5 years. Unfortunately, this does not ensure that the imm target ROR or the target value can be achieved 5 years later. Tthat is, the realized return (yield) 5 years later does not necessarily equals imm target ROR (or the YTM at the inception), this is because there are various scenarios regarding to the YC : 1. The YC (yield curve) at the inception is flat and stay at the level for the remainder of the 5 years, then the realized return (yield) will be 7.5% too. That is, the target value of $13,934,413 can be achieved 5 years later. This scenario is described in In Example 5 and Realized return (yield) = imm target ROR = YTM only under this scenario. 2. The YC (yield curve) at the inception is upward-sloping or downward-sloping at the inception and remain unchanged over the entire investment horizon (as descirbed in my prior messages). 3. The yield curve changes over the investment horizon (as descirbed in my prior messages). I will like to have any further comment !
Aloha, Ronando was not saying that the Immunization target rate “became” 7%, I believe he was saying the since the yield curve is upward sloping the immunization target rate started at 7% as opposed to the YTM of 7.5%. Example 5 doesn’t have anything to do with the immunized target ROR, rather it only shows how investing in a 7.5% YTM coupon bond may not return 7.5% if there is a change in the YC. The examples entire purpose is to show that investing in a coupon bond with a YTM = target yield and maturity = Inv horizon does not assure that the target value will be acheived. (The immunization target will be less than 7.5% for an upward sloping yield curve, hence the assumption that the Imm target ROR was 7% at the beginning as specified by Renondo)
FinNinja, I know that in Example 5, not the entire scenario that the the YC (yield curve) is flat at the beginning of the investing and it shifts parallelly immediately after the investing in the bond is different from the scenario that YC is upward or downward sloping. However, we can borrow the scenario (the figures at the inception) in this example. 1. The initial investment is $9,642,899 and the target value in 5 years is $13,934,413 so that we know that the immunized target ROR is 7.5% and this shall be fixed (redondo & I agreed, what is your opinion ?). 2. The YTM is also fixed at 7.5% at the beginning of the investing because the 7.5% of YTM is determined in the hope that the target value ($13,934,413) or the target yield (7.5%) can be achieved 5 years later, but this may not be achieved if the YC is not flat at the beginning of the investing and remain unchanged over the investment horizon. That is, the realized ROR (yield) may be lower than the initial immunized target ROR (or higher). This issue seems complicated to me and any further comment is appreciated.
did u read what I had posted above. when the yield curve is upward sloping - though the reinvestment return on the coupons is higher, but the price drop on the final value of the bond is much bigger. Hence the rate of return on the bond (total return) would be lower than the original YTM. Price drop trumps the reinvestment income. when the yield curve is downward sloping - the reinvestment return is lower, but the price rise on the bond is much higher. Again the Price rise trumps the drop in reinvestment income. Total return on the bond will now be > than the original YTM.
cpk123, Thank you for your messages. I think you mean that the YC is upward or downward sloping at the beginning and remain unchanged over the investment horizon. But very sorry, I have following questions: 1. Why price effect trumps reinvestment effect ? Is this always true ? 2. Do you think that both immunized target ROR and YTM are fixed (both are 7.5% in example) ? Your advices will be much appreciated !
No the YC was not upward or downward sloping at the beginning. It was flat, which is why the Target ROR = YTM = 7.5% at the beginning. Immunization Target ROR is fixed at the beginning. YTM is also fixed at the beginning of the period. and Immunization Target ROR was equal Subsequently there was a change in YC shape - and it sloped upward or downward (One year later, per the example). Change in Price will be greater than the Reinvestment return. This is because of the change in the YC shape. You have a small coupon - which accounts for the Reinvestment income. But a much bigger “Full Price” bond is available at the end of the Investment Horizon and that will need to be evaluated at the Spot rate at the horizon. In the case of an upward sloping yield curve - each coupon would be reinvested in a higher spot rate at the time the coupon is due. So Reinvestment Income increases. The Bond itself (full price) will be re-evaluated at a much higher rate - so its price when it is evaluated at a higher rate will fall much more.
pk123, 1.No any statement is found that the YC was flat at the beginning and it changed to be upward or downward sloping ONE YEAR later. 2.I still have no idea why price effect trumps reinvestment effect. The changes in price may be greater than or less than the change in reinvestment income (Quoted from the 6th line of the 1st paragraph under “4.1.1 Immunization Strategies” on P.26). 3.It is true that the “Full Price” will fluctuate “before the end of the investment horizon” due to changes in yields but the “Full Price” shall be fixed in this case (as the “Bond Price” of $9,642,899 on P.28) since the bond will be held until the end of the Investment Horizon and the value (price) of the bond will converge to its par value at the end of the investment horizon, irrespective of the changes in yields “before the end of the investment horizon”. 4.Since the bond will be held until the end of the Investment Horizon, the only difference will from the reinvestment incomes and they are dependent on the yield curves at the beginning and/or during the investment horizon. Any comment will be appreciated !