Hi All Hope you are well. Can I check with you on some queries from chapter end exercise from CH26, please. Q26.4 in the solution, page 34 of CH26. How are the ‘exposure units’ for each month derived? These are the boxes for year 1 and year 2. Q26.5 in the solution, page 37 of CH26. Money in on 15 June : (450 × 0.86) × (1.01^6.5 – 1) , is the -1 here required because we are dealing with monthly interest? If it was 1% per annual rate then it would be 1.01^6.5 ? Monthly expenses: (1.017 – 1) / (.01/1.01) – 7 , where is the formula from? why do we take away 7 which is the number of £1 expense. Monthly expenses : (1.0085–1)/(0.008/1.008) × 1.0087 – 5 , while this is very similar to the one above, but why × 1.0087? I feel these come from CM1, but just want to check. Many thanks! Jun
Dear All Please can I also check: For X assignment X6.4 Asset / liability ratio This is defined as the assets divided by liabilities, net of DAC. At the start of each year these figures are: Year X: 117.7% Year X+1: 122.8% Year X+2: 114.3% how are these ratios calculated? Thanks Jun
Each month there are 100 policies sold and in Jan, Feb, Nov and Dec the claims frequency is double. You could say normal frequency is x and double is 2x If the time unit for your exposure is a month, you can then define 100 policies per month at x frequency, 100x, as "1 unit of exposure". If a month with 100 policies with normal frequency is "1 unit of exposure" then months with double frequency have "2 units of exposure". Jan therefore has "2 units of exposure" ie (100 *2x)/100x. February with Jan and February policies, 200 policies at double the frequency has "4 units of exposure" ie (100 + 100)*2x/100x. March has policies for Jan, Feb and Mar, 300 policies at normal frequency has "3 units of exposure" ie (100 + 100 + 100)*x/100x and so forth. The policies are annual and sold only in the first year, so in year 2 the decline in policies follows the expiry of the terms. Jan 2nd year has 11 months policies after the policies sold previous Jan expire and double the frequency, therefore has "22 units of exposure" The basic formula per month is (Total policies in force during the month * claims frequency that month)/100x
Firstly, these are calculations of the investment income so the actual capital is removed, that's why the -1 and the subtraction of the 7. Secondly, for the monthly expenses, these are just being accumulated to the end of the year. The formula you see is just the formula for the future value of the annuity due at the end of the first year. Thirdly, the monthly expenses in the second year are being calculated at the end of the year so the first part of the formula calculates the interest to the end of May (annuity due) then the 1.008^7 accumulates to the end of the year.
