Immunization target rate of return VS YTM

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. Conversely, a negative or downward-sloping yield curve will result in an immunization target rate of return greater than the yield to maturity because of the higher reinvestment return.
this is mentioned definitely in the book….
How else does a lower reinvestment return occur?
coupons are getting reinvested at a higher rate. So the Price at that end must fall.
The Bond price is remaining fixed in Example 5 - the 964989 number you mention so often because that is what the policy holder paid there. Here it is a GIC - which is why it remains fixed, the policy holder is guaranteed that.
Under normal circumstances - that would never happen for a regular bond. When yield increases - the Bond Price will fall - and then the price effect would be greater than the coupon effect. At least that helps me remember this picture. When the yield curve is upward sloping - you have a lower return ….
 
Aloha668,
In the glossary, the immunization target rate of return is defined as “the assured rate of return of an immunized portfolio, equal to the total return of the portfolio assuming no change in the term structure.” To my understanding, it is the return that the manager expects to actually realize. In your 7.5% example, if the manager needs to realize a 7.5% return to satify future liabilities, then he needs to invest in a bond (as in the example) with YTM greater than 7.5% if the current yield curve is upwardsloping. As yield curve changes with time, the manager will need to rebalance, or buy another bond in this example, to get the target return of 7.5%.
 
Here the maturity of bond is equal to investment horizon in this case.
so when they say “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.” this is simply because of the lower reinvestment income meaning the coupons are getting reinvested at higher rate (comparing at the begining while determining Immunized target return).
cpk123
So when u say that lower reinvestment return is due to higher coupon reinvestment income but lower price of the bond where decrease in price of bond is more than the increase in reinvestment income.
( but bond is held till maturity, its not sold then so how does the price decrease effect us & decreases return…) Infact it increases total return coz of higher coupon reinvestment return & hereon our target return to meet the liability is less.
Quite confusing..
This was debatable last year as well…
 
I have checked earlier posts (infact searched a lot by sorting topics alphabetically etc)
It has been confusing to all L-3 takers irrespective of year of exam. few post are:
http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91209541
http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91243622
http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/9978801
There are few views (copied from earlier posts) like:
1) YC is upward sloping so you are reinvesting at a lower rate therefore lower reinvestment return.
2) Immunization target rate is the total return on bond i.e., coupon + reinvestment return + capital gain/loss, arising from the horizon price rise/fall.
ITRR is less than portfolio’s YTM when the yield curve slopes upwards because you were originally assuming (when you calcualted your ITRR) that the reinvestment rate was fixed (say at 5%). But now the curve is sloped upwards, thus you are reinvesting at higher rates (above 5%), so your YTM will be greater than you originally calculated.
So,
Day one, your ITRR = YTM
Day 200, ITRR
the opposite is true when the curve inverts
If the yield curve is upward sloping, the reinvestment rate (return) will be higher, but the horizon price will be lower because of rising interest rates. Fall in Price would be more than the increase in return from higher reinvestment rate
But metega post make sense & you have to attribute lower investment return to price effect only to memorize it.
There is a statement in the curriculum that was stressed as the foundation of immunization… I will paraphrase.
When you immunize a portfolio, it is a kind of hedge such that when interest rates fall, the upward price movement of the bonds are counteracted by lower reinvestment rates and when interest rates rise, the downward price movement of the bonds are offset by the higher reinvestment rates. By doing this you are sure of getting your immunized rate, or very close to it.
True: if YC is upward sloping : yields are rising and so does your reinvestment income - coupon effect (because you are reinvesting your coupon at higher rates than to begin with) but your horizon price is falling-price effect (due to increase in interest rate) hence lower reinvestment income. Price effect is greater tha coupon effect.
Uuff…now I would stick to this logic & will move on :D
 
Rahuls
you mentioned in a couple of posts above:
quote:
cpk123
So when u say that lower reinvestment return is due to higher coupon reinvestment income but lower price of the bond where decrease in price of bond is more than the increase in reinvestment income.
( but bond is held till maturity, its not sold then so how does the price decrease effect us & decreases return…) Infact it increases total return coz of higher coupon reinvestment return & hereon our target return to meet the liability is less.
end quote
point is:
a) you are looking at total return on your bond.
b) total return comprises both total reinvestment as well as price return.
c) as you progress further along the life of the liability - you are reinvesting coupons at a higher rate (due to the upward sloping yield curve) for a shorter time.
d) but that does not make a difference to the quantum by which the price does fall due to the higher rate. At the end of the period - your price is going to be determined by the high rate present at the time. So your price drop will always trump the reinvestment income increase.
and total return WILL DROP.
this combined with the effect that earlier coupons were reinvested for lower rates for a longer period of time, while later coupons are reinvested for higher rates for shorter periods.
and total return is “over the complete life of the bond”.
 
cpk123
With regards to d) but that does not make a difference to the quantum by which the price does fall due to the higher rate. At the end of the period - your price is going to be determined by the high rate present at the time. So your price drop will always trump the reinvestment income increase.
Price of the bond is going to be determined by the higher rate….but my point is bond is also maturing at the end of the investment horizon So the bond will only provide maturity value….Would its price be determined by the market rate of interest then?
Thnx for sharing your views though! I read couple of your old view posted in 2011 as while scanning for this topic…Also re this Immunization Vs YTM….there you had a different view but i believe you have picked up a lot now in terms of deeper understanding of the topics…..Just curious to know Did you finish your study review? If yes then what different strategy you are pursing with comparison to your last year?
 
not sure about deeper understanding.
and am still working thro the topics….
and no review done yet. (lots of it needs a lot of review). so am scared !
and not sure how with work/life/ and various other things coming in the way, how I am going to be (most possibly a nut case) come Jun 2nd…
 
maturity of the bond is right. but here you are looking at the ability to be able to meet what you started out this entire process for - which is ability to meet the liability schedule. That is why you started out the ITRR/YTM entire thing, right.
Your liability had a particular required value. What is the impact of all of the change in the yield curve on your bond …. and that is what you are trying to see with the ITRR > YTM or ITRR
 
Actually, re-investment incomes (interests on interests) or re-investment return shall depend on the forward rates or the actual future spot rates, rather than the YTMs. That is, it is the term stucture of interest “spot” rates that shall be taken into account, not the yield curve.
Furthermore, re-investment incomes or re-investment return will “not” be lower if the the term stucture of interest “spot” rates (or yield curve, if we must say so) is upward-sloping as the forward rates will be higher than the spot rate at the inception. The opposite is also true for downward-sloping term stucture. I think this can be proved.
Anything wrong with my above views ?
 
reinvestment income will be higher on an upward sloping curve. that is based on the term structure - spot rates - as you have pointed out.
but the point I was making above - same spot rate would cause the price to drop…
and the price would trump the reinvestment income. esp. because the new reinvestment is for smaller periods as the liability that moves along on its life.
 
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