Hi there, Please could you explain why the formula doesn't allow for the cash bonus paid? Also, I can't tell from the question whether the cash bonus is paid at the start of the year or at the end? Thanks, Matt
Hi Matt The question says: "Each year, there is a one-off bonus paid at rate B(t). This does not form a guaranteed addition to the benefits payable, and is paid out in cash as part of the annuity benefit payment." So the formula in part (ii) allows for the cash bonus as it is part of the annuity benefits paid out. The question also says: "Annuities are payable annually in advance" So as the cash bonus is paid out as part of the annuity benefit it is also paid out at the start of the year. Best wishes Mark
Hi Mark, Ah yes, sorry. I should have got that myself. Please could I also check some other things in this question? The "Calculation of B(t)" -> AS(t-1) = sum {A(t) x annuity} This equality can only be satisfied if we allow A(t) to be less than the g'tee? That is, is we allow B(t) to be -ve. But, at the same time, the lines above says that A(t) = A(1)/1.03^(t-1) x (1+B(t)) and that B(t) >= 0. The second bullet seems to contradict the first. Also, I think I'm getting confused about the interaction between the g'tee and the AS. Am I right in thinking that there is no interaction (I think this is what part ii is getting at)? My overall impression of how the contract works is as follows (please could you confirm whether or not this is correct): The key thing that determines how the contract works is the need to satisfy the AS equality: AS(t-1) = sum {A(t) x annuity} A(t) is the only thing that can change to satisfy this relation. That is, the AS is factual, and (assuming we're not fudging the assumptions then) the assumptions are factual too. And so the A(t) is just a balancing item (and is what it needs to be) to satisfy this equality. BUT, there is a distinction between the A(t) that is used in order to satisfy this equality and the A(t) that gets paid out (ie the latter is subject to the g'tee whereas the former is not). Thanks, Matt
Hi Mark, The first bullet just came from my thinking (not the question). I was thinking that if the investment performance is terrible, then the AS would be very low and so it would't be possible to satisfy that AS equality if the annuity payment term, A(t), couldn't drop below the g'tee.
Hi Matt Thanks, I understand now. So yes, if the investment performance is terrible then we have the situation where the asset share cannot support the benefits at their current level. In that case the bonus is set to zero and the insurer makes a loss. Effectively we have the situation described in your final bullet, ie there is a distinction between the A(t) that is used in order to satisfy this equality and the A(t) that gets paid out (ie the latter is subject to the g'tee whereas the former is not). And yes to your other question, there is no interaction between the asset share and the guarantee in this question. Best wishes Mark
