Embedded Value - allowance of Risk Margin

[prachi]

Hi,

Could you please help me to understand the following - EV related questions:

Que 1: Could you please confirm to me the various ways in which RM can be allowed in EV ?
I understand that there are two ways:
a) Adding RM with "Required Capital" component and deducting the cost of holding it.
b) Include release of RM in PVIF .

Is it correct?
Is there any other method also?
In a) , the deduction is called as "cost of holding RM" or "Cost of residual non-hedgeable risk"?

Que 2: Could you please help me to understand below excerpt from chapter 18- Embededded value - page 10. In this piece I am not sure by using "risk margins" do they mean solvency II Risk Margin (as mentioned in Que1 above)
" There may be freedom about whether or not to adopt a market-consistent approach. A market-consistent valuation would typically use a risk-neutral approach, ie risk-free investment returns and discount rate, and allow for non-investment risk by using risk margins or deducting the cost of residual non-hedgeable risks from the embedded value."

Que 3: Again referring to excerpt from chapter 18- Embededded value - page 10.
Apart from in the choice of risk discount rate, allowances for risk may be made in:
 the prudence of the liability valuations
 the prudence of the cashflow projection assumptions, eg a reduction in the expected
long-term asset returns on corporate bonds to allow for credit risk
 deducting a risk margin from the value of future profits
 establishing the cost of required capital
 the valuation of options and guarantees.

a) How the prudence of liability valuation will impact EV?
I understand that it will decrease the Net Assets. But the release of margins would be more in PVIF. So PVIF will increase. But whether the increase in PVIF will fully offset the decrease in Net Assets will depend on the discount rate vs the investment return assumption in projection basis. If both the assumptions are market consistent risk free rates, then esentially increasing the prudency of liability valuation will have no impact on EV.
Is that correct?

b) Could you please what risk margins is being talked about in this line "deducting a risk margin from the value of future profits"
c) could you please explain how it decrease the EV-the valuation of options and guarantees.

Que 4: Exam April 2015, Q2, iv.
a) It is written in examiner report that "Expected return on free surplus would use the same basic approach as currently i.e. the risk-free investment return assumption earned on the free surplus. But the value of the free surplus will be different now."
Why would the free surplus value would be different?

b) " There will now be no expected return on the value of in-force since the embedded value does not allow for any VIF. Although there may be an “unwind of the discount rate” component in respect of the release of the RM and SCR (or equivalently on the “cost of capital” component in respect of the RM and SCR)."
The question mentions that company's approach is not holding PVIF. Therefore, impacts of RM and SCR should not be shown under "expected return on in-force business" . Am I correct? Rather, we can write using new header as
"Impact of Risk Margins"
- under solvency II, company will hold Risk margin. The approach of company is to combine it with Required capital. So, company also need to do analysis of change in "Risk margin - cost of holding RM"
- This will include "actual return earned on start of period RM
- Unwinding of discount rate on Cost of Capital by expected return
- etc...............


Thanks

 

[Lindsay Smitherman]

Hi - I'll take your points one by one

Que 1: Could you please confirm to me the various ways in which RM can be allowed in EV ?
I understand that there are two ways:
a) Adding RM with "Required Capital" component and deducting the cost of holding it.
b) Include release of RM in PVIF .
Is it correct?
Is there any other method also?

Yes, these two approaches are valid alternatives - assuming we are talking about an EEV style approach which is being used by a company that is subject to Solvency II.

There are only three components of EEV: free surplus, required capital and PVIF. The Solvency II risk margin is expected to fall into shareholder profit, rather than being needed to meet p/h obligations, therefore it should be in the EEV somewhere.

(a) is saying it could be in the required capital component. (b) is saying it could be in PVIF. It doesn't make sense for it to be in free surplus - because it isn't immediately available.

 

[Lindsay Smitherman]

In a) , the deduction is called as "cost of holding RM" or "Cost of residual non-hedgeable risk"?

These are different concepts.

The 'cost of holding required capital' is the frictional cost of having the required capital (RC) locked into the company and not immediately available for release to shareholders. So the value of that capital to the shareholders is a little less than its face value, due to this potentially erosive lock-in (eg because the capital would earn lower returns by being locked in than the shareholders would like to earn). The lock-in cost is deducted (from the value of the RC release) for any EEV calculation, whether market-consistent or not.

For a market-consistent EV, we need to have a market-consistent EV projection (or experience) basis. Market consistency of investment return assumptions is allowed for by using risk-free rates (the risk-neutral approach). Market consistency of other assumptions can be done either by including small margins within each of those assumptions, or by using best estimate assumptions and by deducting an overall 'cost' of those risks. This is described at the top of page 10 in the notes. [The latter approach is analogous to the risk margin concept within Solvency II.]

 

[Lindsay Smitherman]

Que 2: Could you please help me to understand below excerpt from chapter 18- Embededded value - page 10. In this piece I am not sure by using "risk margins" do they mean solvency II Risk Margin (as mentioned in Que1 above)
" There may be freedom about whether or not to adopt a market-consistent approach. A market-consistent valuation would typically use a risk-neutral approach, ie risk-free investment returns and discount rate, and allow for non-investment risk by using risk margins or deducting the cost of residual non-hedgeable risks from the embedded value."

No - the use of 'risk margins' here does not refer to the Risk Margin. It refers to adjustments that can be made to each of the best estimate non-investment assumptions such as mortality, expenses etc, in order to make them 'market-consistent' rather than best estimate. Bear in mind that the market is unlikely to trade in such risks at their best estimate - the market would need compensation for taking on the inherent risks, therefore would be likely to trade at slightly more prudent than best estimate.

 

[Lindsay Smitherman]

a) How the prudence of liability valuation will impact EV?
I understand that it will decrease the Net Assets. But the release of margins would be more in PVIF. So PVIF will increase. But whether the increase in PVIF will fully offset the decrease in Net Assets will depend on the discount rate vs the investment return assumption in projection basis. If both the assumptions are market consistent risk free rates, then esentially increasing the prudency of liability valuation will have no impact on EV.
Is that correct?

Yes, you're right - this will mainly impact if using a traditional EV basis.

Under a market-consistent basis there might be some impact, if there are additional 'frictional costs' arising on the prudential margins that are locked into the company.

 

[Lindsay Smitherman]

b) Could you please what risk margins is being talked about in this line "deducting a risk margin from the value of future profits"

This just means: risk could be allowed for in the EV calculation by reducing the calculated PVIF by a chosen amount. (This is relatively unlikely to be used in practice, as it is a rather ad hoc approach.)

 

[Lindsay Smitherman]

c) could you please explain how it decrease the EV-the valuation of options and guarantees.

If the company performs a deterministic EV calculation, it will only be capturing the intrinsic value of any options or embedded guarantees. It is ignoring the time value: the risk that the options/guarantees could come into the money (or 'bite') in future (or come further into the money if they are already in-the-money). So this could also be deducted from the PVIF. In fact, an EEV calculation requires that the time value is deducted from the PVIF . This would typically need to be determined using a stochastic modelling or option pricing approach, reflecting the underlying risks.

 

[Lindsay Smitherman]

Que 4: Exam April 2015, Q2, iv.
a) It is written in examiner report that "Expected return on free surplus would use the same basic approach as currently i.e. the risk-free investment return assumption earned on the free surplus. But the value of the free surplus will be different now."
Why would the free surplus value would be different?

Because the company was previously subject to Solvency I, with prudent reserves, and is now subject to Solvency II. So will have different liabilities, so different net assets or free surplus.

 

[Lindsay Smitherman]

b) " There will now be no expected return on the value of in-force since the embedded value does not allow for any VIF. Although there may be an “unwind of the discount rate” component in respect of the release of the RM and SCR (or equivalently on the “cost of capital” component in respect of the RM and SCR)."
The question mentions that company's approach is not holding PVIF. Therefore, impacts of RM and SCR should not be shown under "expected return on in-force business" . Am I correct? Rather, we can write using new header as
"Impact of Risk Margins"
- under solvency II, company will hold Risk margin. The approach of company is to combine it with Required capital. So, company also need to do analysis of change in "Risk margin - cost of holding RM"
- This will include "actual return earned on start of period RM
- Unwinding of discount rate on Cost of Capital by expected return
- etc...............

The company is unlikely to do a separate analysis of the change in 'Risk margin - cost of holding RM' , but it might do a separate analysis of the change in 'Required capital - cost of holding RC' over the period (assuming it is using the EEV style approach). In other words, as well as doing an analysis of the overall change in EV, it might want to split that down into the three underlying components, to understand how each of those has changed.

As you indicate, this would include the actual return earned, and the 'unwind' would reflect that the release of the RC to shareholders is now one period closer. There would also be any impacts that have changed the underlying split between free surplus and required capital, eg if the company has taken on more risk than it previously had (therefore more capital is locked in as RC to support that risk), etc etc.

 

[Lindsay Smitherman]

Overall, would add that it is important to remember that the Risk Margin as a defined concept is only relevant to Solvency II companies.

And bear in mind that the EV projection basis is separate from the liability valuation basis. A company will have to start its EV calculation with whatever balance sheet approach it has to use in its own jurisdiction (whether that be prudent liabilities, Solvency II or whatever). It can then choose what to use as the projection basis for the EV calculation (so that could be traditional or market-consistent).

 

[prachi]

his would include the actual return earned, and the 'unwind' would reflect that the release of the RC to shareholders is now one period closer.

Hi Lindsay, thank you so much for patiently replying in detail to such a long question.

While I was re-reading que 2 of April 2015 and cross checking chapter 18, I got confused that why the actual investment return on start of the period RC will be considered, especially if we follow below sequence (assuming no PVIF).

Is anything incorrect in below steps for analysis of EV on EEV approach.
1. Actual Return on opening Free surplus
2. Economic variance:
- Actual vs expected movement in interest rates for Assets backing the BEL
- Actual vs expected movement in interest rates for Assets backing the RC (SCR+RM)
*ignoring other economic variance such as adjustment in discount rate for simplicity here
3. Non economic Variance
- Results from difference between actual and expected non economic factors on BEL
- differences between the actual pattern of release of required capital over the period and that expected in the start of period calculation
- differences between the actual frictional ‘lock-in’ costs over the period and those allowed for in the cost of holding required capital as determined at the start of the period
4. Change in Operating assumptions
- Operating assumption changes will emerge into profit/loss if the BEL assumptions have changed.
- changes in the amount of capital requirements, eg due to changes in methodology, calibration or underlying risk profile.
- The assumed “cost of capital” factor might also change (i.e. parameters used to determine the cost of holding the RM and SCR), the impact of which would also need to be analysed.
4. New business
5. Other changes like

 

[Lindsay Smitherman]

Hi - no problem!

In terms of what you have set out above, you are treating the RC as if it has the same characteristics as the BEL. However, for the purposes of EV it should be considered as being more consistent with the 'Free surplus'.

This is because the RC (minus the cost of holding - which I will stop mentioning to save effort) is expected to belong 100% to the shareholders, and therefore will fall fully into the EV. Whereas the BEL is expected to be used up meeting obligations to the policyholders.

In terms of what will contribute to a change in EV over the period:
All of the actual investment return earned on free surplus belongs to the shareholders, so is part of the change in EV.
All of the actual investment return earned on the assets backing the RC is also expected to belong to the shareholders, so is also part of the change in EV.
However, in terms of the assets backing the BEL: only the excess of the actual investment return earned over the expected return (where expected return here = the risk-free rate used to discount the BEL) will fall to shareholders. The expected return is needed in order to have enough to meet the obligations to policyholders (since the BEL is the discounted value of those future cashflow obligations). Therefore we only see the investment return variance (ie excess of actual over expected) coming into the change in EV in relation to the assets backing the BEL.

Does that help to make a little more sense?

 

[prachi]

Hi - no problem!

In terms of what you have set out above, you are treating the RC as if it has the same characteristics as the BEL. However, for the purposes of EV it should be considered as being more consistent with the 'Free surplus'.

This is because the RC (minus the cost of holding - which I will stop mentioning to save effort) is expected to belong 100% to the shareholders, and therefore will fall fully into the EV. Whereas the BEL is expected to be used up meeting obligations to the policyholders.

In terms of what will contribute to a change in EV over the period:
All of the actual investment return earned on free surplus belongs to the shareholders, so is part of the change in EV.
All of the actual investment return earned on the assets backing the RC is also expected to belong to the shareholders, so is also part of the change in EV.
However, in terms of the assets backing the BEL: only the excess of the actual investment return earned over the expected return (where expected return here = the risk-free rate used to discount the BEL) will fall to shareholders. The expected return is needed in order to have enough to meet the obligations to policyholders (since the BEL is the discounted value of those future cashflow obligations). Therefore we only see the investment return variance (ie excess of actual over expected) coming into the change in EV in relation to the assets backing the BEL.

Does that help to make a little more sense?

yes this is surely making a lot of sense. But going my same logic, why in case of non-economic experience, we do actual vs expected release of RC?

The procedure to analysis on BEL movement is as follows. I am trying to work out the method for analysis of RC...do we start with same method...and how actual vs expected change the assets and RC?
Assets are allocated to the contracts equal to the value of the BEL at the beginning of the year;
 The assets and BEL are projected forward to the end of the year…
 … using the beginning of the year BEL assumptions as the expected experience over the year;
 The profit emerging during the year is then determined as the difference between year end assets and BEL;
 For the first step (i.e. all experience items taken their expected value) the profit emerging will be zero;
 Repeat the above projection of assets, liabilities and profit, changing one of the items of experience from the expected value to its actual value;
 The difference in the profit (or surplus) arising under the runs gives the contribution from that item of experience;
 Repeat for each item of experience.

 

[Lindsay Smitherman]

First, I should probably clarify that my post above was ignoring PVIF, ie I was assuming there are no expected future profits in order to keep things simple. This means that the expected future investment return in the projection basis must be the risk-free rate, as would be the case if we were doing the EV on a market-consistent basis. If the expected investment return in the projection basis exceeds the risk-free rate used to discount the BEL, there would be some PVIF - and it all gets more complicated! So if it's OK with you, let's continue to work on that basis for now.

Hence, with PVIF = 0, what we are effectively doing is (broadly speaking) an analysis of surplus. Except that in this case, because we are doing an EEV, we have to split the 'net assets' component (= assets - BEL here) between free surplus (FS) and RC.

Your process as described above will give us just the experience variance items for the analysis of surplus, where (as noted above) here we have surplus = FS + RC.

For the full analysis of surplus, we need to include the actual return on the start year surplus (ie on the assets backing FS + RC) and any changes in assumptions or other miscellaneous items of change over the period, such as a change in model.

Now: in order to move from doing an analysis of surplus to doing an analysis of change in EEV (still assuming PVIF = 0) there is one further item that we need to take into consideration: the COHRC. A change in that amount over the period will contribute to the change in EEV, since COHRC is deducted from EEV. If PVIF = 0, then basically EEV = 'net assets (surplus)' (FC + RC) - COHRC. We've thought about analysing the change in surplus - now we have to think about analysing the change in COHRC.

Therefore, for example, if the company has to put aside more (or less) regulatory capital as a result of changes in its risk profile, or due to its actual experience over the period, or due to changes in assumptions underlying the regulatory capital calculations, then the proportion of 'net assets' that comprises RC will increase (or reduce), with FS reducing (or increasing) correspondingly. If the amount of 'net assets' that is locked-in as RC changes, so will COHRC, and thus so will EEV. Furthermore, if there are any changes to the pattern of release of RC, this will also impact the COHRC calculation - and hence will be part of the change in EEV.

Another way to think about this is: if something happens that means that the amount of capital that is locked into the company changes, or if the pace of release of that locked-in capital to shareholders changes, then this will impact shareholder value - and hence is part of understanding the change in EEV.

Has this helped?

I think you might be in danger of trying to over-analyse this concept. It might be worth making sure that you can stand back from it and understand the concepts of the components of EEV and also how an analysis of EV relates (closely) to an analysis of surplus, rather than getting too absorbed in details? The full analysis of change of an EEV (including of the COHRC and PVIF elements) is a complicated process, and doesn't lend itself particularly well to a short bullet pointed list of steps!

 

[prachi]

First, I should probably clarify that my post above was ignoring PVIF, ie I was assuming there are no expected future profits in order to keep things simple. This means that the expected future investment return in the projection basis must be the risk-free rate, as would be the case if we were doing the EV on a market-consistent basis. If the expected investment return in the projection basis exceeds the risk-free rate used to discount the BEL, there would be some PVIF - and it all gets more complicated! So if it's OK with you, let's continue to work on that basis for now.

Hence, with PVIF = 0, what we are effectively doing is (broadly speaking) an analysis of surplus. Except that in this case, because we are doing an EEV, we have to split the 'net assets' component (= assets - BEL here) between free surplus (FS) and RC.

Your process as described above will give us just the experience variance items for the analysis of surplus, where (as noted above) here we have surplus = FS + RC.

For the full analysis of surplus, we need to include the actual return on the start year surplus (ie on the assets backing FS + RC) and any changes in assumptions or other miscellaneous items of change over the period, such as a change in model.

Now: in order to move from doing an analysis of surplus to doing an analysis of change in EEV (still assuming PVIF = 0) there is one further item that we need to take into consideration: the COHRC. A change in that amount over the period will contribute to the change in EEV, since COHRC is deducted from EEV. If PVIF = 0, then basically EEV = 'net assets (surplus)' (FC + RC) - COHRC. We've thought about analysing the change in surplus - now we have to think about analysing the change in COHRC.

Therefore, for example, if the company has to put aside more (or less) regulatory capital as a result of changes in its risk profile, or due to its actual experience over the period, or due to changes in assumptions underlying the regulatory capital calculations, then the proportion of 'net assets' that comprises RC will increase (or reduce), with FS reducing (or increasing) correspondingly. If the amount of 'net assets' that is locked-in as RC changes, so will COHRC, and thus so will EEV. Furthermore, if there are any changes to the pattern of release of RC, this will also impact the COHRC calculation - and hence will be part of the change in EEV.

Another way to think about this is: if something happens that means that the amount of capital that is locked into the company changes, or if the pace of release of that locked-in capital to shareholders changes, then this will impact shareholder value - and hence is part of understanding the change in EEV.

Has this helped?

I think you might be in danger of trying to over-analyse this concept. It might be worth making sure that you can stand back from it and understand the concepts of the components of EEV and also how an analysis of EV relates (closely) to an analysis of surplus, rather than getting too absorbed in details? The full analysis of change of an EEV (including of the COHRC and PVIF elements) is a complicated process, and doesn't lend itself particularly well to a short bullet pointed list of steps!

Thanks Lindsay, it was helpful. Yes sometimes I try to get into too much details of the things. But the replies were useful in clearing the concepts.