Spring 2018 Q 14

danielle4nan

Hi,

I am wondering why, in this question, the interest rate margin is calculated as

MV (assets) x Duration (assets) - MV(premium liabilities) x Duration(premium liabilities) - MV(unpaid claim liabilities) x Duration (premium liabilities)

Instead of market value-weighing the duration of all liabilities and multiplying it by the sum of all liabilities?

Thanks!

graham

I don't quite understand what you're asking. The formula you stated isn't quite right. You should be using APV for liabilities rather than MV. Then you basically multiply the whole thing by the interest rate risk %.

Note that the question actually omitted the interest rate risk %. Sample answer 1 used a value of 1.25%, but they forgot to provide it. You had no choice but to assume the interest rate risk was the same as the interest rate MfAD, which was given as 0.5%. That's why there was such a big difference between sample answer 1 (1078.03) and sample answer 2 (415).

jptardif2

Hi Graham,
Where in the question does it say that the claims will be paid out evenly over 3 years? Do we have to assume that it is asset-liability matched with the bonds portfolio? Is it something we should always assume unless specified otherwise?

Also, what is the (-0.5 +1/3) adjustment to the duration of premium liabilities? I guess it's all covered in different papers?

Thanks!

graham

Ok, this is an extremely difficult problem because it is long and covers 5 different readings:

• OSFI.MCT
• CIA.MfAD
• CIA.PrLiabs
• CIA.Discnt
• CIA.Duration

My general advice is to familiarize yourself with the solution when you first study the MCT reading, but don't spend too much time on it on your first pass. But you will have to return to it several times over the course of your study as you learn the different pieces. (I've placed links to the appropriate supporting material within the MCT reading.)

Your first question is how we know claims will be paid out evenly over 3 years:

• This information is provided in the Cumulative Accident Year Payment Pattern. You can see that 25% is paid out each year over 4 years. But we are already at the end of the first year, so you have to "rebase" the remaining 75% over the next 3 years, so that's 1/3 each year. This is covered in CIA.MfAD.
• Regarding asset-liability matching, there isn't much information provided, but whether they are matched or not doesn't really affect the calculation. Part of the interest rate risk margin arises due to the assets and liabilities having different durations, but you don't have to do anything special in your solution.

Your second question concerns the (0.5 - 1/3) adjustment:

• This is covered in detail in CIA.PrLiabs, so just file it away in the back of your mind until you get to that reading.

Different pieces of this calculation are covered in the practice templates in the quizzes in wiki articles for the readings listed above. So don't worry - you will definitely learn how to do this problem well - it will just take several weeks to cover everything you need.