Hi I'm trying to understand the formulaes in chapter 18. 1. On pg 10, the formula for contribution to surplus for investment return is I - iV - 0.5i(P-E-C) I get the idea of it being the actual investment minus interested earned on (P-E-C). My question is for the iV part, V is defined as "value of the liabilities under the contracts as at the beginning of the year". What do they actually mean by liabilities? Are the liabilities equals to the reserves + expected claims + expected expenses? So are we just minusing off half of this in the term (P-E-C) or does V simply refer to the reserves? 2. I notice use of (1+ 0.5i) in most of these formulas. Is this just a simplified method of saying the interest rate effectively from half way through the year? As opposed to (1+i)^0.5 3. In the mortality/CI formula, EDCS = k1.q (S-V) + k2.q (P-E') I don't undersand why k1 is 1 if the contracts were in force for a full year or exited because of death/CI, it would seem to me that there should be different values in these 2 scenarios? Similarly with k2, I don't understand. Please can someone explain this to me? Thanks
This formula looks at the difference between the actual return I and the expected return iV + 0.5i(P-E-C). At the start of the year we set aside assets equal to the liabilities which roll up with one year of interest. The liabilities (V) are the total reserves so will allow for expected claims and expenses less premiums over the remaining life of the contract. We will also have cashflows during the year (premiums less expenses less claims). Assuming that these happen on average half way through the year they will roll up with half a year of interest. Yes, we're assuming cashflows half way through the year. It would be more accurate to use (1+i)^0.5 as you suggest. The formulae approach has its origins in the days when these calcualtions were done by hand (rather than a computer) which explains the simplifying assumptions. Nowadays we'd do the analysis using the cashflow approach on a computer - we'd only use the formulae approach to do a quick check by hand. The k1 is used to get the exposed to risk right. If you were working out a mortality rate you would take the number of deaths divided by the total number of lives in force at the beginning of the year (so you wouldn't reduce the exposed to risk for the deaths). The idea is that the lives that died would have been in force throughout the year if they hadn't died (whereas contracts that entered or lapsed/surrendered will only have been in force for half a year on average and so have only half the probability of death). I hope these answers help. Best wishes Mark
This formula looks at the difference between the actual return I and the expected return iV + 0.5i(P-E-C). At the start of the year we set aside assets equal to the liabilities which roll up with one year of interest. The liabilities (V) are the total reserves so will allow for expected claims and expenses less premiums over the remaining life of the contract. We will also have cashflows during the year (premiums less expenses less claims). Assuming that these happen on average half way through the year they will roll up with half a year of interest. Yes, we're assuming cashflows half way through the year. It would be more accurate to use (1+i)^0.5 as you suggest. The formulae approach has its origins in the days when these calcualtions were done by hand (rather than a computer) which explains the simplifying assumptions. Nowadays we'd do the analysis using the cashflow approach on a computer - we'd only use the formulae approach to do a quick check by hand. The k1 is used to get the exposed to risk right. If you were working out a mortality rate you would take the number of deaths divided by the total number of lives in force at the beginning of the year (so you wouldn't reduce the exposed to risk for the deaths). The idea is that the lives that died would have been in force throughout the year if they hadn't died (whereas contracts that entered or lapsed/surrendered will only have been in force for half a year on average and so have only half the probability of death). I hope these answers help. Best wishes Mark
