Spring 2015, Q20b

jptardif2

Hi Graham,

When I first read that question, I felt like the actual problem was not the discount rate being used, but the amount of assets covering the liabilities. That seems to be part of the answer, but in the examiner's report they mention "need to consider other assets or sources of revenue to back up the liabilities, then a new discont rate would be calculated". Do we just add random assets until the undiscounted amount of assets and liabilities match and then calculate the discount rate?

Thanks,

graham

Hey @jptardif2,

Hope you're doing well today. The answer to your question is yes. You would add assets until they matched the liabilities then recalculate the discount rate. Here's a full explanation...

The concept they are testing in part (b) is "asset-liability matching". In part (a), both the assets and liabilities each total roughly 3m, so they are matched and you can base your discount rate on the 3 bonds given.

But in part (b), the liabilities total 5m. That means you have to find another 2m of assets to support that. Those extra assets might have a different yield so if you recalculate the discount rate using those assets, combined with the 3m of assets from part (a), you will probably get a different answer.

In real life, I'm not sure you would "randomly" add assets! It would be a more measured approach based on the available portfolio. But you're correct in general that you would need to add more assets to get them to match the 5m in liabilities, both in timing and amount. The examiner's report doesn't mention the timing aspect but that would be an important consideration. You would want your assets to mature at the same time the corresponding liabilities need to be paid.

Note that part (b) of the question is worth 0.75 pts so you know you have to give 3 separate bullet points for full credit.

jptardif2

Hi again Graham,

I have another question regarding that problem. The examiner's report used the MARKET value to weight the yield along with the duration, rather than the BOOK value. Is this an error?

Thanks,

graham

There seems to be an inconsistency between the section 4.2 of the CIA Discounting reading and the corresponding Excel Exhibits.

• Section 4.2 of the text says to use book value
• Appendix B, Sheet 1 of the Excel exhibit uses market value

In this exam problem, you didn't have choice because they only provided market value. If you get a problem where they give you both book and market value, I would probably use market value but include a short note that you're following the Excel exhibit versus the text, which is inconsistent. And then immediately after the exam is over, submit a notice of a defective question to the CAS.

See also 2016.Spring Q13a. (There was further material on how to deal with bond values that has been removed from the syllabus.)

chrisboersma

Market value is a type of book value

If the book value of the investment portfolio is insufficient to support the net policy liabilities, then the expected yield on other (non-investment) assets would be considered. A blended rate would be estimated assuming an appropriate yield on such non-investment assets, as discussed in section 4.2. The book value of an asset may be equal to the market value, the amortized value, or such other value consistent with Canadian generally accepted accounting principles.

emphasis added

book value = the value of a security or asset as entered in a company's books.
Which gives you the choice of MV or AV. However most of the IRR calculations in this exam use market value - so I suggest using MV unless otherwise told (book value = amortized value)