# schweser book 3 pg 50 #17--contingent immunization problem

Problem 17: I dont understand how they go the par value to be over 100M?? It says in the problem that they purchased \$100M bonds with 8% coupon—so now if interest rates fall to 8%, wouldnt that mean the par value is 100M, not that 122.333M (dont understand how they even got to this number) b/c the coupon equals the yield?

I am confused by this too. Anyone can explain / clarify ?

Wow, I don’t even know how they come up with that solution…I chose C because I got PV of 102,923,061 after the interest rates fall to 8%, which you don’t have enough assets. I haven’t seen this sort of explanation anywhere. Is this even right?

When interest rates fall to 8% *each* bond will be worth par, but you have to factor in the # of bonds he bought initially when the market rate was 10%. So if you buy 8% bonds when mkt rates are 10% you will pay less than par, 817.44 per bond to be exact. The investor will buy \$100m worth of bonds at 817.44 each, this equates to 122,333 bonds. Ques 17 then asks what happens if rates decrease to 8% (from 10%). Now each bond will be worth par, so the value of your entire position is \$1000*122,333 = \$122,333,000 If you discount back the terminal value at 8% you get \$102,923,061. The portfolio value is greater than this #, so dollar safety margin is positive.

I “understand” the logic that Schweser provides, but is that how we need to solve problems like this? They have been pretty straightforward without any of the complicated BS from their answer. Is this out we need to solve these problems?

not sure what’s so different about this example…figure out how much your position is worth based on a chg in rates and compare that to the PV of your liability. this is exactly how you solve any contingent immunization problem.

Ok, let me try and rephrase my problem. Why would you be concerned about the number of bonds or the price of individual bonds? Shouldn’t the only thing that should matter is how much you go to cover your liabilities? Now, the required terminal value is 164,783,136 and the amounts necessary to achieve this is 91,757,416. This is with the current interest rate at 10%. I hope we are on the same boat here. So, dollar safety margin is 100M - 91,757,416 = 8,242,584. So, we agree on this too. Here also, we use 100M for calculations because thats what we have here. Maybe the PV of the bonds would be 81.77M. But it doesn’t look like it matters here. If we had used 81.77M, then we would be having a negative dollar margin right now. Interest rates fall to 8%. So, shouldn’t the amount we have be 100M because coupon = interest rates? Therefore, the initial amount has now increased to 102,923,061. Which would mean dollar safety margin is negative. This is what the text shows us also. It doesn’t show any calculations of bonds or number of bonds. So, to conclude, why do we use 100M in the first part to DSM and then calculate value of each bond and no. of bonds for the second? Sorry for the rant, but I just wanted to get this cleared up.

When the interest rates were at 10%, the value of the portfolio was \$100M… If we turned around and converted our position to cash at that time, we would have sold our full position of 122,333 bonds, we would have realized \$100M, before transaction costs. The PV is still \$100M at this point - not 81.7M… After the interest rates drop, the value of our bonds is now greater (\$1000 each vs. the \$817 we purchased them at) so, as stated above, we would realize a total of \$122M. The dollar safety margin is calculated against the current porfolio market value.

sparty419 Wrote: ------------------------------------------------------- > Ok, let me try and rephrase my problem. > > Why would you be concerned about the number of > bonds or the price of individual bonds? Shouldn’t > the only thing that should matter is how much you > go to cover your liabilities? > > Now, the required terminal value is 164,783,136 > and the amounts necessary to achieve this is > 91,757,416. This is with the current interest rate > at 10%. I hope we are on the same boat here. > > So, dollar safety margin is 100M - 91,757,416 = > 8,242,584. So, we agree on this too. Here also, we > use 100M for calculations because thats what we > have here. Maybe the PV of the bonds would be > 81.77M. But it doesn’t look like it matters here. > If we had used 81.77M, then we would be having a > negative dollar margin right now. > > Interest rates fall to 8%. So, shouldn’t the > amount we have be 100M because coupon = interest > rates? Therefore, the initial amount has now > increased to 102,923,061. Which would mean dollar > safety margin is negative. This is what the text > shows us also. It doesn’t show any calculations of > bonds or number of bonds. > > So, to conclude, why do we use 100M in the first > part to DSM and then calculate value of each bond > and no. of bonds for the second? > > Sorry for the rant, but I just wanted to get this > cleared up. Understandable that one might not think to incorporate the # of bonds right away. But if you look back at your work, you are calculating the initial dollar safety margin as (100M - 91.8) when rates are 10%, meaning at 10% you’ve calculated your position to be worth 100M. So when rates go to 8% you know that bond px go up, so why are you using the same value as when it was 10%? That should tell you right away that the 100M is not right and you should be looking for a number greater than 100M…and hopefully that would intuitively lead you to consider the # of bonds involved…

Good call Green!! Thanks guys. I’ll try doing this again and practice a few more.