PVIF component - Solvency II basis in EEV

[Trevor]

Hi, I have a question about application of Solvency II Basis in Embedded Value calculation.

Referring to Section 3 of chapter 18, there are 4 points discussing why the PVIF shouldn't be ignored even if SII basis is used.

In the 2nd point, I understand that if SII uses Matching and Volatility Adjustment, which doesn't equal to the company's own illiquidity premium, then they should include the PVIF for extra profit if their illiquidity premium is higher than the Matching Adjustment.
But In the case of WITHOUT matching adjustment, shouldn't investment return = discount rate?

Because SII is in a market consistent basis, discount rate is definitely = risk free rate if no matching or volatility adjustment.
And investment return should be calibrated to risk free rate regardless of asset backing it.

So investment return = discount rate for all cases, therefore there should be NO DIFFERENCE at all. No additional future profit.

Can someone explain where I understood it wrongly?

At the same time I want to understand also what does "calibrated to risk free rate" means, I see this a couple of times in the examiner reports and course notes, but always assume it means set equals to risk free rate. Is this the correct understanding?

Regards,
Trevor

 

[Lindsay Smitherman]

Profit arises (in the PVIF) due to any difference between what the company expects to happen as per the EV projection basis (or experience basis) and what has been allowed for in the liability valuation basis (here = Solvency II). That's the basics of embedded value.

So maybe under Solvency II the company wasn't permitted to have an MA but its expectation of what it expects to earn on its investments going forwards is greater than the risk-free rate. The excess of the expected return over risk-free rate emerges as profit in the PVIF.

I think you are getting confused between the assumptions used for the liability valuation and the assumptions used for the EV projection.

 

[Lindsay Smitherman]

At the same time I want to understand also what does "calibrated to risk free rate" means, I see this a couple of times in the examiner reports and course notes, but always assume it means set equals to risk free rate. Is this the correct understanding?

It refers to the calibration of stochastic simulations and means ensuring that the average is the risk-free rate.

 

[Trevor]

Hi Lindsay,

I know that the PVIF has 2 components: PV(Future profit) + release of reserves
if the EV adopts a Solvency II basis, does that mean the:

Assume no matching or volatility adjustment, no illiquidity premium too:
1. Future Profit is projected using SII BEL assumptions (investment return calibrated to risk free rate), and then discounted using the risk free rate [therefore no profit from investment returns]
2. Reserves calculated (release of reserves) is based on SII, so BEL is SII BE assumptions (investment return = discount rate = risk free rate)

Or the BE assumption is applicable only on the release of reserves (2)?

The reason I'm thinking (1) and (2) are both applicable is because this is what is implied in the April 2015, question 2 (i) solution, where the examiner report mentions:
"Investment return and discount rate assumptions used for both MCEV and Solvency II are based on risk-free rates"

 

[Lindsay Smitherman]

1. Future Profit is projected using SII BEL assumptions (investment return calibrated to risk free rate), and then discounted using the risk free rate [therefore no profit from investment returns]

No: future profit is projected using the EV projection basis, NOT the liability valuation basis.

The reason I'm thinking (1) and (2) are both applicable is because this is what is implied in the April 2015, question 2 (i) solution, where the examiner report mentions:
"Investment return and discount rate assumptions used for both MCEV and Solvency II are based on risk-free rates"

The reason why that statement is made for that particular question is because it is talking specifically about an MCEV: a market-consistent EV.

In that case, the EV projection basis is market-consistent, so based on risk-free rates. But that won't always be the case.

 

[Trevor]

I see, does that mean the insurance risk assumptions (eg: mortality, expense, lapse assumptions) in the PV(Future Profit) do not need to take the SII BE assumption as well? So the insurance risk assumptions used in the Projection component is different to the reserving assumption?

Also:
1. the discount rate for PV(Future Profit) will be the risk discount rate, allowing for the inherent risk and shareholder required rate of return / illiquidity premium,
2. but the discount rate in the release of reserve will be risk free rate + matching adjustment.

Are the above 2 points true?

 

[Lindsay Smitherman]

The demographic etc assumptions in the EV projection basis can be whatever the company chooses them to be, but that will quite often be best estimate.

Yes re risk discount rate for 1.

The release of reserves is part of PV(Future profit), so the amount of reserve being released (ie reduction in reserve amount over the time period) will be discounted using the risk discount rate. The calculation of the reserves at each future point in time (which then determines the amount of the release of reserves) uses the reserving basis.

You might want to refresh your memory on these basics of EV per your SP2 course notes?

 

[Trevor]

The release of reserves is part of PV(Future profit), so the amount of reserve being released (ie reduction in reserve amount over the time period) will be discounted using the risk discount rate. The calculation of the reserves at each future point in time (which then determines the amount of the release of reserves) uses the reserving basis.

My apologies, I haven't really thought about this level of detail. I think I understand the situation now.

If they are together, so PVIF = PV( Future Profit + release of risk discount rate) at each time period, then the discount rate for both should naturally be the same.

Assume we have a 10 years policy, paying out 100 at the end of year 10.
Assume Matching adjustment (MA) is applicable, MA = 1%
Risk free rate, rf = 2%
Projection discount rate = 5% (allow for inherent risk and shareholder required rate of return and illiquidity premium)
ignore mortality for simplicity:

Applying the SII basis, at t=5, our, our SII BEL Reserves = 100/(1.03)^5 = 86.3 ;
and at t=6, Reserves = 100/(1.03)^4 = 88.8;
release of reserve at t=6 is then 86.3 - 88.8 = -2.5 (ignore the sign)

To calculate the PVIF at t=0, this release of reserve at t=6 is then discounted using the Projection discount rate.
So the PVIF in respect of the year 6 component will be (Profit at t=6 + -2.5)/(1.05)^6

In summary, the SII BEL reserves is calculated using SII rules, but the discounting of the release of reserves and future profit are using the company's own risk discount rate (Projection discount rate).

Is this correct?

 

[Lindsay Smitherman]

Yes I think this is about right - except you shouldn't be considering 'release of reserves' and 'profit' as distinct things. The release of reserves is part of profit.

 

[Trevor]

Thank you. That is very clear now.

I have another question in this topic after revisiting the course notes.
The 4th bullet point mentions to include the PVIF if there is "release of the risk margin, after allowing for the cost of holding it"

I understand that if EV is taking the SII basis, then the required capital is SCR + RM, and the cost of holding this is the RM
so Required Capital - Cost of holding required capital is: (SCR+RM)-RM = SCR
The insurer wants to allow for the release of RM somewhere else to take credit of profit from this.

But in SII, the BEL should not contain any prudence margin.
Does the 4th point mean, release of RM within the reserves?
so reserves = BEL + RM, release of reserve then refers to release of BEL + release of RM

I am a little confused with the little caveat after this pont, it reads
"The required capital is the SCR. It could also include the RM, unless the release of RM is allowed in the PVIF"

Is this saying that if SII basis is used,
there are 2 ways to calculate EV:
1. [Own fund - SCR] + [(SCR +RM) -RM} + PV(future profit without release of RM); or
2. [Own fund - SCR] + [(SCR ) -RM} + PV(future profit with release of RM)

Is the above 2 statements true?

Follow up question:
Why is PVIF = 0 if SII basis is used?
It just says reserving assumption (BEL) has no prudence margin to be released, but that doesn't mean there is no future profit right? The profits are still within the contract boundaries.

 

[Lindsay Smitherman]

The cost of holding required capital doesn't equal the RM. That's just one approximation that can be used to justify not bothering to calculate EV anymore under a Solvency II world, because it allows EV to simplify down to equate to 'own funds' (for a without-profits company).

So your expressions are OK but with - RM replaced by {- cost of holding required capital} in both cases.

The simplification mentioned above also requires PVIF=0. PVIF doesn't necessarily equal 0 under Solvency II, for all the reasons set out in Chapter 18 Section 3.

However, it might do because PVIF represents the value of the release of prudential margins in the reserves held. If there are no such prudential margins to release, as would be the case if the reserves were best estimate (and the EV projection basis were also best estimate) then PVIF = 0.