Chap 23, p. 13, formula

[echo20]

I know it's not terribly important to know the EV analysis of change formulae off by heart, but this one looks a bit iffy to me. It says the EV change from moving to a new EV projection basis will be:

Sum_over_t { [T_t(new EV basis) - T_t(old EV basis) ] / (1+r1)^t }

where r1 is the revised risk discount rate. However, the EV calculated on the old basis would have used the original risk discount rate, r, so I'd have thought the correct formula would be:

Sum_over_t { [T_t(new EV basis) / (1+r1)^t] - [T_t(old EV basis) / (1+r)^t] }

Can anyone tell me why I'm wrong and the core reading is right, or have I detected a chink in their actuarial armour?

 

[scarlets]

Can anyone tell me why I'm wrong and the core reading is right, or have I detected a chink in their actuarial armour?

Surely no actuary would admit to that, especially when there's get out of jail cards such as "it depends", "we can adjust for that", or "it is correct to assume it in this circumstance" can be used.

 

[Mark Willder]

I know it's not terribly important to know the EV analysis of change formulae off by heart, but this one looks a bit iffy to me. It says the EV change from moving to a new EV projection basis will be:

Sum_over_t { [T_t(new EV basis) - T_t(old EV basis) ] / (1+r1)^t }

where r1 is the revised risk discount rate. However, the EV calculated on the old basis would have used the original risk discount rate, r, so I'd have thought the correct formula would be:

Sum_over_t { [T_t(new EV basis) / (1+r1)^t] - [T_t(old EV basis) / (1+r)^t] }

Can anyone tell me why I'm wrong and the core reading is right, or have I detected a chink in their actuarial armour?

Your logic is quite right and we could do the analysis the way you suggest.

However, the Core Reading is right too. In practice we may want to separately consider the impact of changing the projection basis (as shown on page 13 of Chapter 23) and the imapct of changing the risk discount rate (which would involve the change you suggest while holding the projection basis constant).

The Core Reading approach is more suitable as we want to look separately at the impact on the operating return. Page 13 goes on to say:

"The impact of changes to the economic assumptions in the embedded value basis, including the related change in the risk discount rate, must be identified separately and excluded from the operating return in the analysis."

Best wishes

Mark

 

[echo20]

Thanks Mark, still not entirely convinced by the logic in the chronology of the steps but sure it's not worth arguing about!