2018 Fall Q16 - Yield Calculation for APV
Hi, I saw from the solution when calculating the yield to discount the Cash Flow from Unpaid, the solution say using the weight of (Book Value of Bonds * Duration) because they are Held to Maturity. May I know the reasons behind. And I also recall that there are questions trying to ask for using the weight of (Market Value * Duration) if I am correct? So how can we know when to use weight on BV or MV? And how did using these yield curve discounting APV make sense? Any reasons behind as well? cause I understand some regulator or some other countries just using Local Government Risk Free Bond to discount, so I am trying to persuade myself what are the logics behind. Many Thanks 
Comments
Some of the answers to your questions are from a reading that is no longer on the syllabus. If a similar problem came up on a future exam, they would likely give you the discount rate instead of asking you to calculate it.
Very briefly however, the reason they use Book Value (and not Market Value) is that for HTM Bonds (Held-to-Maturity), the redemption value at maturity equals the Face Value of the bond, and this is known when the bond is purchased. The market value is not relevant. But again, this part of the problem is from a reading that is no longer on the syllabus.
Market Value would be used for AFS instruments (Available-For-Sale). If a financial instrument is AFS, then the market value is a more accurate measure of it's value than book value.
About your comment regarding regulators using the risk-free rate: I can't speak to what regulators in other countries would do, but using a risk-free rate, which is generally lower, would result in an APV that is higher. That means the insurer would have to keep more reserves. This is good for guarding against insolvency which is what regulators are mainly concerned with.
Thank you Graham! I can see your point. Good to know its no longer on the syllabus. But your explanation perfectly make sense for the use of BV and MV as well. And yes, maybe the "regulators" just want Prudency when prescribing using Risk Free rate to discount.
By the way, I saw in a formula and I am wondering this is still under the current syllabus "Investment Yield = Net Investment Income * 2 / (Beginning Total Investment + Ending Total Investment - NII)". I saw this from the solution when they trying to calculating the investment income for excess margin.
As far as I can tell, the formula for Investment Yield is still on the current syllabus.
The formula that seems to have been removed from the syllabus is "Investment Income from Insurance Operations". (This may also be referred to as "Investment Income on Unpaid Claims of Prior Years".) I'm going to double-check with the CAS about that however. It seems odd that one formula is on the syllabus and the other is removed.
Thank You Graham for taking this action point. I will wait for your updates and as at now I will just memorize this formula then
By the way, before knowing this formula I was thinking to apply the 2.34% (the one calculated from BV) Weighted Yield of Bond, and to apply it on the Excess Margin Investment Income Calculation ... Wells it will be wrong if I do so if following the solution... To be honest, it is quite confused for this question, since there is no particular given rate for Unpaid Investment Discounting or given rate for Excess Calculating.
Yes, I can see how that could be confusing. The reason they use 6.77% for the excess/deficiency ratio is that the bond yield is different from the total investment yield. For discounting purposes, you should use the bond yield because it's lower and will result in a higher APV. This guards against insolvency.
By the way, the average candidate score on this question was only 35%. That was the second lowest average score for the 2018.Fall exam. In other words, most people scored poorly on this question. You can check average scores for each question for the last few exams on this wiki page:
Okay, Thanks Graham, so I will stick to use the less Bond Yield for discounting then