Dollar Safety Margin

I don’t understand the solution for question #17 on schweser, ss9 page 50.

If the question says interest rates fall to 8%, to calculate the value of the bond, wouldn’t you do,

n=50

fv=100

pv=?

i/y=4%

pmt=4?

so this means the bond is priced at par, pv=100

wouldn’t you take the 100 and compare it to the required asset once rates fell to 8%, in this case, \$102? I just don’t get why they would use the current yield of 10%. I would think only the required rate and the rate the interest rate fell to were the only rates that mattered to answering question 17. On the blue box of page 34 on schweser, step 3, it looks like they used the immunized rate that it rised to (12%) and not the current immunized return (9%). Why is the solution solving this differently than page 32 or even the problems on the CFAI text?

after falling of interest YTM = coupon so bond is now worth par value only. So they have taken 100 not 102. 102 is PV of their req terminal value.

Intially they have calculated their req terminal value from acceptable rate of return. Then after decrease in int rate, PV of req terminal value has increased (which is \$ 102.92 mil)

they have not solved the problem the way the text solves it.

they have taken initially 122.513 bonds are purchased for 100 Million because price of bond was 817.47.

now bond is par.

so 122.53 * 1000 = 122.53 Mill. (amount of assets available).

Amount of assets required = 102 Mill, so we can continue to be in contingent immunization mode.

But the way CFAI solves it

Amount of assets required = 102 Mill.

Amount of Assets available = 100

So we have a shortfall and need to immunize immediately.

(Answer choice would be C per CFAI way, their answer is B, I think).

SCH ans is A

But even in CFAI way which u mentioned, Amt of assets req = 102 but asset available before the bonds were bought & he change in int rate = 100 which they invested. But after decrease asset r worth more no…so they won’t req immunization.

before when the rate was 10% - Assets Available = 100, Assets required = 91

so there was a positive cushion of close to 9 Mill \$. So contingent immunization was possible.

After decrease:

Assets available = 100, Assets Required = 102. Your cushion is negative.

So no longer possible to do active management - and you must immunize immediately.

Schweser’s answer : No immunization is not necessary because \$ safety margin is positive. But as you can see it is negative above.

No of bonds equivalent to assets available has already been bought as a part of active strategy. So MV = 100

These bonds increase in value after decrease in rate so MV of bonds has increased. Still + ve cushion.

Can you please understand what I am saying? In the text (CFAI) they never talk about # of bonds purchased. They only talk of the amount …

so this method that Schweser is doing stuff with is not consistent with the curriculum.

Ok. got it now!

In GIC ex 5: i think PV of liability is equal to assets availale (i.e. the premium receipt) but yes in exhibit 8, no change in bond price is shown due to int rate.

If inconsistent then we should follow CFAI only, rt

Schweser seems to be approaching it in a different way, but the result is the same as they CFAI way.

You started with 100mm and bought a bond below par (8% coupon trading at 10% yield - price 817.44).

Yields then dropped by 200 basis points, so the bonds are now priced at par, so your portfolio value went up from 100mm to 122mm.

At the new rate, you need \$102,923,060 to meet your terminal value, but you have 122mm in your portfolio, so your dollar safety margin is positive.

What seems weird with that solution is that in the initial instance itself - since the bonds are going to be worth 81.74 Mill - and they required 91.757 Mill - they could not have ever gone to contingent immunization to start with… do you agree?

No. You had \$100,000,000 in cash, and bought \$100,000,000 worth of bonds that were priced at 817.44.

The example in the Schweser text had you buying a bond at par but in this case you bought a bond that was trading below par.