“When interest rates fall, contingent immunization switches to more active management because the dollar safety margin is higher.”
If interest rates fall, would dollar safety margin necessarily fall, as there are assets and liabilities simultaneously?
I think you mean 2nd statement should be when interest rates rise?
I mean value of both assets and liabilities would rise, would you get the conclusion of higher dollar safety margin in the condition of falling interest rates?
if you look at the example solved in the book - the required terminal value of the liability - that you have your assets matched up to meet - remains fixed in $ terms.
you have a fixed “horizon” date portfolio requirement that you are gearing up to meet. This rate is affecting your asset portfolio only.
IR will affect the (present) values of both asset & liability. Dollar safety margin = PV of asset - PV of liability.
Where did you see in the CFAI book.
“When interest rates fall, contingent immunization switches to more active management because the dollar safety margin is higher”
My question is , how can we figure out whether $safety margin is high/low as IR falling affects both PV of assets and liab.
On P.36~37 of CFAI Text Vol 4 (R23)
DSM : Dollar safety margin
PVA : PV of Asset
PVL : PV of Liab ility
I/R (YTM) = 4.75% ==> DSM = PVA - PVL = 500M - 474.9M = 25.1M
I/R (YTM) = 3.75% ==> DSM = PVA - PVL = 541.36M - 489.06M = 52.31M (High)
I/R (YTM) = 5.80% ==> DSM = PVA - PVL = 460.55M - 460.52 = 0.03M (Low) ( ((’ (( ((loiw
The increase in PV of Asset is greater than the increase in PV of of Liability (thus, DSM increases) when I/R (YTM) decreases because the duration of the Asset is greater than the duration of the Liab.
Conversely, the decrease in PV of Asset is greater than the decrease in PV of of Liability (thus, DSM decreases) when I/R (YTM) increases because the duration of the Asset is greater than the duration of the Liab.
When interest rates fall, contingent immunization switches to more active management because the dollar safety margin is higher” - This is true only if “the duration of the Asset is greater than the duration of the Liab”. Without comparing durations of Assets and liab, we cannot figure out PV of assets will be greater or less than teh PV of liab.
Thanks for clarification anyway.
are we going to have to be perform contingent liability calculations on the exam? I know it’s not complicated but the LOS only says “discuss”
just curious
Dear all
This trouble me as well.
when YTM drop to 3.75%, can anyone demonstrate how it is caculated of
value of portfolio will be 541.36 mm
the initial asset value required to satisfy the terminal value ot 546.72mm at 3.75%YTM is 489.06mm
I have been search for old post and it shows as below:
PMT=500mm*4.75%/2
N=5*2
FV=500 mm
IY=3.75%/2
PV=CPT=541,376,014
however, the number of year is clearly 3 years, thus N=3*2
Can anyone clarify this.
Thanks a lot
Jessie
you are calculating how much the Assets would become. The assets were a 5 year bond, so 5*2.
Liabilities are due in 3 years. For the liabilities you would use 3*2 = 6.
This also confused me at first, but the key to understanding this is what Aloha said above.
“The increase in PV of Asset is greater than the increase in PV of of Liability (thus, DSM increases) when I/R (YTM) decreases because the duration of the Asset is greater than the duration of the Liab.”
The perception is that when rates rise, the value of your bond you’re using to immunize will decrease in value faster than the amount you immunize.
When interest rates change you have to recalculate the price of your investment used to immunize by doing a present value calc using the new yield. The amount you need in the future is going to be constant but you have to discount that terminal value at the new yield. Remember you already determined the amount you need in the future before rates changed but the amount you need today to reach that amount in the future is going to change if rates change.
Subtract the two new PV amounts and you have your new larger cusion (if rates fall) or no cushion at all (if rates rise).
Add my 2 cents:
1, When the yield curve shifts in parallel, it’s straightforward(I hates this “straightforward”, though-:)). 2, When the yield curve twists and the re-investment rate changes, it depends.
Th , tt, The duration of the asset is greater than that of the liability in the examples. My question : Is it always so in immunization ? It is not clearly explained in the text !
Hi CPK123
"you are calculating how much the Assets would become. The assets were a 5 year bond, so 5*2.
Liabilities are due in 3 years. For the liabilities you would use 3*2 = 6. “”"’
where did you see the asset were a 5 year bond?
i only find there "three year investment horizon "in page 36
and “manager invest entire 500mm in 4.75%, 10 years note at par …”
jessie
did you do the calculation on your calculator?
the 5*2 = 10 is a typo since it gives only 522.6
Investor invests entire PV $ 500 million - 10 year note at par. YTM = Coupon=4.75 (Semi annual < i assumed), So future value also equals PV = 100 Mili
Now YTM change to 3.75%.
keep everything same & calculate by changing I/Y
I/Y - 3.75/2 (Since YTM changed)
FV - 500
PMT - 500 * 4.75% /2 = 11.88 mil
N = 10* 2 = 20
CPT -> PV = 541.38 million approx as given in book $541.36 million
Hello
this question has been puzzling me a lot as well. After reading the CFAI book, Schweser, this forum and other websites, I can only conclude that the EoC question 23 (#21, p97) of the CFAI book is wrong and I needed to register on this forum to develop my point.
In the example you discussed from reading #20, we see that indeed, when D(A) > D(L) and the rates fall, the surplus increases, which is logical.
However, looking at question 23 and most specifically the fact the CFAI says that this statement is correct:
“When interest rates fall, contingent immunization switches to more active management because the dollar safety margin is higher.”
is incorrect because the question does not mention explicitly D(A). They do mention that D(L) is 12y (The weighted-average duration of Hanover-Green’s liabilities is about 12 years) but nothing wrt to D(A). If we look at the proposed benchmarks they all have a duration below 9Y. So we could either conclude that it is not possible to answer the question, or assuming that one the benchmarks is appropriate, D(A)
The other messages in this topic saying that change in IR does not impact FV of a fixed liability are correct, but have nothing to do with the surplus or the question.
If you look at Schweser p236 of #20, you see that, wrt contingent immunization, “if asset duration and convexity match those of the liability the surplus will be relatively stable”, in other words, there is no “rule” or “principle” indicating that the surplus of a contingent immunized portfolio should move in a particular direction. The only thing true is that under contingent immunization, if the surplus is <=0, you need to immunize, i.e. D(A) = D(L), so you are insensitive to change in IR. If surplus is >0, you switch to active management mode, which allow you to deviate (upward or downward) your D(A) from D(L),
I hope this helps,
Cheers, Romain
I think of it this way, the asset is 500 million. The liability is 474.90 million. So when ytm drops, assets will increase more than labilities