So have I got this right - the UL asset share is the value of the unit fund (at the current unit prices which reflect any reversionary bonuses added to date) plus the value of any guarantees above the value of the unit fund? What happens about the non-unit fund if it is negative for instance on early death or surrender? Is the value of the unit fund reduced in some way to allow for this?
This doesn't sound right I'm afraid - I think you are muddling up unit-linked and unitised with-profits. The relationship between the unit fund and the asset share is complex in these two cases. It might help if I give a few examples.
We can calculate an asset share for any policy (including unit-linked, unitised with-profits, conventional non-linked contracts). In all cases a basic asset share is the actual premiums less expenses and cost of claims accumulated at the actual investment return.
The asset share can be negative as you suggest. In this case the surrender value may be very low (or zero). If the unit-linked fund is positive then we might deduct a surrender penalty. The unit-linked fund could be negative (for example late in the policy term if mortality charges have been high and investment return has been low). However, the surrender value cannot be negative, so the insurer would make a loss.
We wouldn't apply penalties on death. So the death benefit can be higher than the asset share. The excess of the death benefit over the asset share would represent the cost of the benefits that would be shared by the surviving policyholders' asset share.
Unit-linked asset shares might be similar to the unit fund. The unit fund is the accumulated premiums less charges. Compare this with the asset share, which is the accumulated premiums less expenses less cost of claims. So the two will be the same if the charges exactly match the expenses and cost of claims.
Unitised with-profits (UWP, also known as accumulating with-profits) asset shares are unlikely to be similar to the unit fund. The asset share is accumulated with the actual investment return (which could be positive or negative). The unit fund is accumulated with bonuses (which cannot be negative). Normally we'd expect the asset share to be bigger than the UWP unit fund, as regular bonuses will on average be smaller than the investment return, so that a terminal bonus can be built up. However, the asset share might be smaller than the unit fund (eg if the stock market crashes), and then we would impose a market value reduction on early surrender so that the policyholder did not receive more than their asset share.
I hope this helps, but do let me know if you have further questions.
Mark