i respectfully disagree with your calcs
Gah good point cpk, now I’m just confused. I should learn this material more thoroughly.
Janakisri - please show me the coupon addition in the problem in the text book with the 4.75% -> 3.75% case…
when it is not considered there, why should it be over here?
and what about the manager’s statement of looking at reinvestments at 7% throughout…
i agree with CPK
…
no where in Schweser or CFAI do they add back coupons like you are doing, that cannot be correct
For a 1 year total return on the bond at the 1 year horizon - yes the coupon reinvestment must be considered.
Schweser does a problem in the EOC weirdly as well - by saying an original bond was worth 817$ - manager invested to the tune of 100 Mill - so he had 122 K bonds.
Now if the rate immediately changed to make the bond a PAR - the 100 Mill originally invested will now become 122 Million. (122 K * 1000 = 122 Mill). Which is really weird. They then go on to calculate the Liability to have a value of 102 Mill - and say the contingent immunization (active mgmt) can continue.
But if the same were done as 100 Mill is all that is available - since the rate immediately changed to make them Par Bonds - you have a 2 Mill $ shortfall - and hence CI is not possible, the portfolio must be immunized immediately.
Given the text book does not solve any problem in this manner - I am really confused and lost as to what must be the right way to do it.
I have only Schweser 2011 , and there is a similar example in afternoon 3 of exam book 2 . They do it like tulkuu did , which is add up the present value of the coupons and the present value of the bond .
again it is schweser …
not sure about whether it is right, mainly because there is NO REFERENCE TO THIS METHOD IN THE BOOKS.
yea the book doesnt mention any of the coupon business. its just calculates PV of the bond based on the 3.75% and 5% rates, if i recall correctly
cpk , in your example from Scheweser , since I don’t have the problem with me , I am going to make these assumptions and do a calculation :
Say N=10 , PV=-817 , FV=1000 and PMT=80 , so I/Y = 11.123%
Now the rates suddenly change so this subpar bond ( considered risky until now and priced with YTM much above coupon ) becomes priced at par. The only way this can happen is if the YTM for the bond decreases dramatically to 8%. . If YTM decreases and the bond itself gets priced at 1000 , the new value of the 122,000 bonds is now 122 million ( price * number of bonds ) .
However the present value of the liability increases because rates have shrunk . The calculation showed by them is that CI is broken and they must immunize immediately
I don’t see what is wrong in their calculation . Please explain again.
if that is how they had done it in 2011 books it is fine.
they have done it as the new assets are 122 Mill … Liab required is 102 Mill. So CI is NOT BROKEN and can be continued.
I have trouble with using the # of bonds.
If instead you went with the FV=100 CPN=X, YTM=X, N=20 and calculate PV -> it is 100 …
since CPN = YTM
PV = 100 - is the amount of assets available for use.
your liabilities at X = 102 Mill.
Since Assets < Liabs -> you have to now stop CI and immunize immediately.
see the difference
igor and mcap11 and cpk , completely respectfully , the coupon addition business only figures in part B of the question , not in A or C . The text example on Pages 36 and 37 does not cover the case when 1 year has elapsed after the initial bond investment and the investment now consists of bond as well as re-invested coupon . Show me 1 example from the CFAI text that would cover this kind of example of 1 year elapsed please.
Schweser exam is the only place I found which has a practical example of a 1 year elpased case.
if for the first year the coupons were reinvested at the YTM (YTM being the 7%) - only then would the bonds have been worth 100 Mill at the end of one year. Otherwise - they would be worth more or worth less.
The fact that you took
FV = 100 CPN = 3.5 N=18 and calculated PV -> means that the Coupons have been reinvested at the 7%.
So your using it to calculate an additional amount is double counting it.
Does this make sense?
CPK, Now I am really confused, by your example.
A bunch of bonds worth $100 million yesterday is worth $122 million today because the YTM went from 11.23% to 8% . Yet you say the PV of the bonds is $100 million . Par value is not the PV of your investment . If you had invested the same 100 million today you would have only 100,000 bonds . Instead you smartly invested yesterday when you were getting 122,000 bonds . Since rates went in your favor big time you are richer by $22 million on the asset side.
But the PV the liability also ballooned dramatically because rates have shrunk from 11.23 % to 8% . The calculation showed that the A-L equation is now negative and we must switch to full immunization .
What’s wrong with that again, please ?
Not to interrupt the discussion between the OP and you, but could you please explain why that calculation means coupons have been reinvested at 7%? The calculation has N = 18 which means it’s only looking at the remaining 9 years worth of coupons from the 10-yr bond investment. The first year’s coupons have already been paid and aren’t part of that calculation, right? Where is the double counting?
Thanks~
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The YTM calculation is a IRR calculation of sorts. So its assumption is that coupons are being reinvested at the YTM. So when you did originally that the bond was worth 100 Mill in 10 years - and the YTM was 7% and CPN was 7% -> you ended with a PV of 100 Mill.
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Now one year later - you still have your FV=100 Mill --> so in the intervening period unless you have reinvested your coupons at the YTM - you could not have achieved this position. Otherwise with a different reinvestment assumption you would have a smaller amount - if reinvestment rate had been lower or a higher amount in the future if reinvestment rate had been higher.
Given that FV=100 Mill - you HAVE REINVESTED COUPONS for that 1 year period for the 3.5% per period.
Sorry, but I thought FV=100 Mill just refers to the $100 million payout that will occur at the end of the holding period? This value will not be affected by anything since no matter what, the borrower has to pay the $100 million in full at the end of the period. Right?
nash is correct . There is no double counting . 1 year later the bond is priced again in the market . The coupons are also priced seperately . The two are 2 completely different investments and three present values in all.
The TVM calculation in general gives you present value sum of all the re-investments that will happen in the future with that bond , plus the face value. The TVM calculation does not show you the value of the coupons that have already been paid out in the past .
I can’t remember if this is Level I or Level II fixed income basics