Chapter 17 Embedded Value questions

For the benefit of those without the tutorial handouts, this question is based on part of April 2006 Question 1, updated for a Solvency II environment.

Yes - the same thing: the shareholders will require a rate of return that provides risk-free rate plus an additional margin that compensates for the inherent risks.

 

Considering the risk margin to be a potential proxy for the 'cost of holding required capital' is only used to demonstrate that it might not be worth a company calculating an EV now that we have Solvency II balance sheets available, since EV would be close to 'own funds'.

The methods for actually calculating the COHRC (in order to comply with EEV / MCEV Principles) are described on pages 8 and 9 of Chapter 17.

If a traditional EV basis is being used (as is the case in this particular question), the cost reflects the excess of the shareholders' rate of return over the expected investment return earned on assets backing the locked-in capital. [So yes, the same discount rate is used.]

If using an MCEV approach, the cost has to reflect explicit assumptions of the 'frictional costs' to shareholders of locking in that required capital (since there is no difference between expected return and discount rate under a risk-neutral market-consistent basis).

 

As noted in the details of the solution, assets could be allocated to the WP business equal to just the asset shares or to technical provisions (which would indeed include those other aspects) in order to determine the PVIF component of the EEV. What is allocated as 'required capital' forms a separate component of the EEV, and then whatever hasn't been allocated would count as the third component (free surplus).

So yes, if CoG etc weren't included in the first component, they would have to be counted as part of required capital, since that amount is locked into the company through the Solvency II balance sheet requirements - and so meets the definition of 'required capital'.

But it actually matters very little to the EEV calculation which of these approaches is used, as the insurer will end up with the same basic result. If those assets are projected as being needed to pay p/h guaranteed liabilities, they won't be included in the EEV. If they are projected as falling into the estate ultimately, they will be valued as being locked into the company for that period and at the relevant point of release the shareholders' 10% share will assessed within the EEV. Will end up with pretty much the same value whichever approach is taken to their initial allocation.

 

No - can also be used if the fund is open. Remember that EV is the value of the shareholders' interest in the business ignoring future new business.

 

The 'haircut' that you refer to reflects the opportunity (or frictional) cost of capital being locked into the company. If this amount were locked in, for whatever reason, then it would be part of the 'required capital' component, not 'free surplus'.

 

Yes, just taking x% is the much simpler and more pragmatic approach. It will give roughly the same answer as the more accurate projection forwards within asset shares (which in itself is also an approximation), since the difference in value would be due to the distribution delay, and hence would reflect the difference between the discount rate and the expected investment return on the assets comprising the free surplus. Since a reasonably high proportion of the free surplus is likely to be invested in higher return assets such as equities, the difference between those rates may not be that wide (and even zero if the projection basis were market-consistent, of course).