Hi folks, I would like to clarify whether my understanding of the Cost of holding capital from the EEV definition of EV is correct. This definition states EEV woulds consist of: 1) Free Surplus 2) Required Capital less cost of holding capital 3) Present Value of inforce business According to the paper ‘Current Developments in Embedded Value Reporting’, the cost of holding required capital is the difference between the amount of required capital and the present value of future releases, allowing for future investment return, of that capital. Please let me know if I have mapped the definitions EEV correctly from the simple example below. Suppose a life insurance company sells only without profits term products, then the definition of the general EV is: EV = VIF + Free Assets where VIF = Premium – Commission – Expenses – Benefit Outgo + I * (Premium – Commission – Expenses – Benefit Outgo) – (Increase in Reserve + Increase in Capital Held) + I * (Previous Reserve + Previous Capital Held) which is then discounted at RDR where I = investment return yield For simplicity I am ignoring taxes & the cost of options & guarantees. So, 1) Free Surplus = Free Assets 2) Required Capital = – Increase in Capital Held + I * (Previous Capital Held) , discounted at expected investment return Cost of required capital = Required Capital, discounted at RDR - Required Capital, discounted at expected investment return 3) Present Value of inforce business = Premium – Commission – Expenses – Benefit Outgo + I * (Premium – Commission – Expenses – Benefit Outgo) – (Increase in Reserve) + I * (Previous Reserve ) , discounted at RDR Is this correct? Thanks.
Yes, this is all correct except for the cost of required capital which I think you have the wrong way round. So: Cost of required capital = - Required Capital, discounted at RDR + Required Capital, discounted at expected investment return (I) RDR is bigger than I. So the required capital discounted at I will be bigger than the required capital discounted at the RDR. Hence the above equation gives us a positive cost of capital. So the EEV includes: 2) Required Capital less cost of holding capital = – Increase in Capital Held + I * (Previous Capital Held) , discounted at expected investment return - (- Required Capital, discounted at RDR + Required Capital, discounted at expected investment return) = Required Capital, discounted at RDR = – Increase in Capital Held + I * (Previous Capital Held) , discounted at RDR So, effectively we are accumulating the required capital with the expected return I and discounting it back at the RDR (ie the capital released each year is discounted back at the RDR). As the RDR is bigger than I this results in a value less than the initial required capital. Best wishes Mark
Thanks. I am wonder why then the core reading states that for EEV the way to calculate the cost of holding requires capital is not clear then.
The cost of the required capital will depend on the projected investment return and RDR. Both of these are subjective assumptions, so different companies will use different approaches. There are other frictional costs of holding capital eg tax, agency and financial distress - it is far from clear how these should be allowed for. MCEV needs to allow for these. I'm not sure of the extent that EEV allows for them too. You can find further details in the BAJ paper in Appendix B Section 2.5.8. Best wishes Mark
