Investment return assumption to calculate Best Estimate Liability (SII)

Yes: if a deterministic model, investment return = risk-free rate. If a stochastic model, expected investment return (ie probability-weighted average across simulations) = risk-free rate.

 

This question is largely academic, since you only need an investment return assumption to project future cashflows for BEL calculations for UL (unit fund projections for fund-based charges and benefits in excess of unit fund) and WP (asset shares for discretionary benefits in excess of guaranteed benefits) business.

A matching adjustment would not be given on these types of business, as the cashflows arising from them are not sufficiently predictable.

The permitted use of a volatility adjustment on such business is also questionable. See the following thread for further on this:
https://www.acted.co.uk/forums/inde...ility-adjustment-for-wp-or-ul-business.16614/

 

Sorry, I'm confused now about what you are asking - are you mixing up BEL and EV calculations? They are different things.

This thread started off (I thought, based on the title) being about the investment return assumptions used to calculate the BEL under Solvency II, which should be risk-free rates.

Have you switched to asking about the investment return assumptions in the projection (or experience) basis of an EV calculation? If so, it would be better to start those questions under a different thread heading, to help other students locate answers to their own queries more easily based on the titles.

If your question is now: what investment return assumptions do you use to project future profits in order to determine the PVIF under an EV calculation, the answer is: it depends on what experience/projection basis you are using. If you are doing a traditional EV using a best estimate basis, it will be best estimate total investment returns (income and capital gains). If you are doing a market-consistent EV, it will be risk-free rates.

 

No problem - an interesting digression! But back to Solvency II:

The EIOPA risk-free yield curves are used to discount liability cashflows and are also used to project forwards the unit fund (UL business) or asset share (WP business) where this is needed in order to determine what those liability cashflows are.

There is always a need for a discount rate (it's best not to call this a 'risk discount rate' as it is risk-free: there is no margin for risk; possibly again some confusion between EV and Solv II bases?). There may also be a need for future investment returns for projection purposes (UL & WP). But both, under Solvency II, are the risk-free rates. [Solvency II is performed under a risk-neutral market-consistent valuation basis: i.e. all assets are expected to earn risk-free rates (on average), so you both roll-up and discount-back at risk-free rates.]

For conventional without-profits business we don't need to project forward using an investment return assumption: the BEL is the PV of {benefits + expenses - premiums} and these cashflows don't depend on future investment returns for conventional without-profits business.

The non-unit reserve part of the BEL for UL business is the PV of {benefits in excess of unit fund + expenses - charges}. So we need to project forward the unit fund in order to determine charges that are a % of the unit fund, and any benefits in excess of the unit fund (I don't think you quoted my post quite correctly in what you have written here?). So, for example, the non-unit reserve would need to cover expected death benefit payments of 1% of unit fund if the death benefit under the policy is 101% of unit fund. And, for example, the non-unit reserve would need to cover the cost of any guaranteed benefits in excess of unit fund, for example if there is a guaranteed minimum return of premiums paid on a particular event and the projection has unit fund < premiums paid at that date.