MCEV

[Viki2010]

Hi Lindsay,

Can I please confirm that the use of "Illiquidity Premium" was only applied to RFR (swap rate) for assets matching long term liabilities such as annuities. Essentially in this case the Illiquidity Premium in MCEV would operate in the same way as MA or VA in SII?

 

[Lindsay Smitherman]

Hi: yes, the illiquidity premium is added to the risk-free rate in the same way that it is under Solvency II. In particular, this means that projected profits will be higher due to higher expected future investment returns.

The MCEV Principles say something along the lines of being able to allow for the illiquidity premium for "non liquid liabilities", after taking into consideration "the ability of the company to access the liquidity premium". Which implies that it should only be used in situations where the bonds are intended to be held to maturity, ie where they match long term liabilities - such as for annuity business. [Bear in mind that the Core Reading states that you are not expected to know this extra level of detail of the MCEV Principles.]

In practice, i suspect that it might be harder for a company to meet the regulator's requirements for the use of a matching adjustment than to be comfortable about using the illiquidity premium in an MCEV calculation.

 

[Rajoshi Ray]

Hi: yes, the illiquidity premium is added to the risk-free rate in the same way that it is under Solvency II. In particular, this means that projected profits will be higher due to higher expected future investment returns.

Hi Lindsay
When the illiquidity premium is added to the risk-free rate for MCEV calculation, is the overall impact on PVIF positive? While projected profits will be higher due to higher expected future investment returns (RFR+LP) they will also now be discounted by the same higher rate. Do we expect that the former will outweigh the latter?

Thanks in advance.

 

[Em Francis]

Hi Lindsay
When the illiquidity premium is added to the risk-free rate for MCEV calculation, is the overall impact on PVIF positive? While projected profits will be higher due to higher expected future investment returns (RFR+LP) they will also now be discounted by the same higher rate. Do we expect that the former will outweigh the latter?

Thanks in advance.

In an MCEV calculation, the investment earnings that are being projected are the returns earned on the total assets held to back the policies (ie the reserves) and this would be a much higher amount than the profit. So an extra 1% earned on the reserves would be a higher amount than 1% of the profit that is being discounted. Hence yes, the former does outweigh the latter.

 

[lanceann]

Hi Lindsay
When the illiquidity premium is added to the risk-free rate for MCEV calculation, is the overall impact on PVIF positive? While projected profits will be higher due to higher expected future investment returns (RFR+LP) they will also now be discounted by the same higher rate. Do we expect that the former will outweigh the latter?

Thanks in advance.

Hi I have a follow-up question here. If it's MCEV and the liability is calculated on Solv II basis, then profit will emerge from investment variance, correct? Since the investment assumption is swap rate + illiquidity premium, while the discount rate is RF + MA or VA.

2. If it's EEV, then the investment assumption and discount rate assumption should be the same, i.e. no profit will come from investment variance?

 

[Lindsay Smitherman]

Hi - your thinking is along the right lines, although it's a little more involved than that.

As you indicate, profit will emerge in the EV projections to the extent that the investment return assumed in the projection (or 'experience') basis differs from the discount rate used for the liabilities. As you say, if the liabilities are determined under Solvency II then the latter will be a RF rate, possibly +MA or +VA (depending on meeting the various requirements, regulatory approval etc).

Under MCEV, if the assumed investment return is RF + illiquidity premium then there may be very little difference between this and the liability discount rate, since the MA and VA are intended to represent the illiquidity premium. However, the latter are effectively set by EIOPA: the MA through the fundamental spread, and the VA is based on a 'representative portfolio' rather than actual assets held (plus is calibrated to be less than the theoretical illiquidity premium). The company's own view of the illiquidity premium might well therefore differ from the MA/VA allowance, and thus there would be some profit arising due to the difference. Also, the company might believe that it could include an illiquidity premium in its projection basis, but might not have obtained approval for an MA/VA adjustment under Solvency II, in which case we again have a difference which would generate projected profit.

For EEV, bear in mind that the underlying basis was not prescribed in as much detail as it was under MCEV. EEV could be done on a market-consistent basis, in which case the argument would be as above - although fewer companies included an illiquidity premium than we see under MCEV (since the MCEV principles gave more detail and direction on this aspect). However, EEV could also be calculated using a 'traditional' basis, ie best estimate expected future investment returns. In which case, investment profits would be expected to arise in relation to the difference between this best estimate return and the risk-free rates used within the Solvency II liabilities.

Hope that makes sense.

 

[lanceann]

Hi - your thinking is along the right lines, although it's a little more involved than that.

As you indicate, profit will emerge in the EV projections to the extent that the investment return assumed in the projection (or 'experience') basis differs from the discount rate used for the liabilities. As you say, if the liabilities are determined under Solvency II then the latter will be a RF rate, possibly +MA or +VA (depending on meeting the various requirements, regulatory approval etc).

Under MCEV, if the assumed investment return is RF + illiquidity premium then there may be very little difference between this and the liability discount rate, since the MA and VA are intended to represent the illiquidity premium. However, the latter are effectively set by EIOPA: the MA through the fundamental spread, and the VA is based on a 'representative portfolio' rather than actual assets held (plus is calibrated to be less than the theoretical illiquidity premium). The company's own view of the illiquidity premium might well therefore differ from the MA/VA allowance, and thus there would be some profit arising due to the difference. Also, the company might believe that it could include an illiquidity premium in its projection basis, but might not have obtained approval for an MA/VA adjustment under Solvency II, in which case we again have a difference which would generate projected profit.

For EEV, bear in mind that the underlying basis was not prescribed in as much detail as it was under MCEV. EEV could be done on a market-consistent basis, in which case the argument would be as above - although fewer companies included an illiquidity premium than we see under MCEV (since the MCEV principles gave more detail and direction on this aspect). However, EEV could also be calculated using a 'traditional' basis, ie best estimate expected future investment returns. In which case, investment profits would be expected to arise in relation to the difference between this best estimate return and the risk-free rates used within the Solvency II liabilities.

Hope that makes sense.

Hi Lindsay,
Thanks for your reply! That makes perfect sense. Just want to clear 2 things:
1. when calculating MCEV with Solv II liabilities, does the illiquidity spread embedded in the investment assumption cover the spread for default risk? I'm asking because in Solv II discount rate fundamental spread is explicitly deducted from MA (I guess there's a same deduction of default spread in VA calculation?), so wondering if the illiquidity spread in investment assumption in MCEV also deducts default spread, such that no profit emerges from the difference in default spread as well.

If the answer is Yes, then are the methods of calculating default spread under MCEV investment assumption and Solv II discount rate the same? Or in companies' real practice, would they set these 2 the same value?

2. when calculating traditional basis EEV with Solv I liabilities, then would companies use the same discount rate as their BE investment assumption, i.e. risk free + their own view of a spread?
Basically I'm trying to come up with a table below (sorry about the format! hope it's comprehensible...). Could you help me if the understanding is correct or not? Thank you so much!!!
Assume rf is the same and spreads are different due to difference in various valuation methods. The first 3 columns are conditions and the last 2 are conclusions.
reason 1: differences in the methods adopted for calculating spreads.
reason 2: investment doesn't include spread while discount rate has spread.
………........Invmt assup………...Disc assup-Solv I...….Disc assup-Solv II.....Invmt variance-Solv I.....Invmt variance-Solv I
MCEV........rf+illiquid sprd……..rf+sprd…………………..rf+MA or VA...……....Yes, reason 1...…………....Yes, reason 1
EEV-MC.....rf(most likely)……...rf+sprd…………………..rf+MA or VA...….......Yes, reason 2..................Yes, reason 2
EEV-Trad...rf+sprd..................rf+sprd.....................rf+MA or VA............NO..................................Yes, reason 1

 

[Lindsay Smitherman]

Hi Lindsay,
1. when calculating MCEV with Solv II liabilities, does the illiquidity spread embedded in the investment assumption cover the spread for default risk? I'm asking because in Solv II discount rate fundamental spread is explicitly deducted from MA (I guess there's a same deduction of default spread in VA calculation?), so wondering if the illiquidity spread in investment assumption in MCEV also deducts default spread, such that no profit emerges from the difference in default spread as well.

Hi - need to be careful not to confuse the 'credit spread' of a bond with the illiquidity premium/spread. The total credit spread (= excess of yield over an equivalent risk-free bond) broadly includes two components: the illiquidity premium (compensation for the bond being less liquid that the comparative bond) and the default risk element (compensation for the higher risk of default). When we talk about the illiquidity premium, we are therefore only talking about part of the credit spread. So whether we are talking about the MA, VA or the company's own view of an illiquidity premium, in all cases we are only talking about the compensation for liquidity risk, not the compensation for default risk. [Hence, as you say, to determine the MA the 'fundamental spread' (= the default risk element) is deducted from the actual yield on the bond.]

 

[Lindsay Smitherman]

Hi Lindsay,
If the answer is Yes, then are the methods of calculating default spread under MCEV investment assumption and Solv II discount rate the same? Or in companies' real practice, would they set these 2 the same value?

Bearing in mind my previous response, I am going to adjust this question slightly to interpret it as asking whether companies would set the risk-free rate + illiquidity premium in their MCEV projections equal to the risk-free rate + MA in their Solvency II liabs (if they are permitted to use an MA).

The MCEV principles (in draft form - they were never finalised) were published several years before Solvency II was implemented, so companies would have developed their own approaches to determining the risk-free rates, including illiquidity premium if appropriate.

The MCEV principles gave more leeway to companies as to how the rates were set. Under Solvency II there is much less discretion: EIOPA set the risk-free rates and also the fundamental spreads, so the company doesn't necessarily end up with discount rates that would reflect its own view.

Hence, many companies who continued to produce MCEVs after the implementation of Solvency II could well have stuck with their own existing approaches to setting the rates. Some, however, may have shifted to using the same for purely practical reasons. Also bear in mind that under Solvency II there is considerably less need to calculate a separate embedded value (as explained in the course notes), so to some extent this is becoming a theoretical rather than actual consideration!

 

[Lindsay Smitherman]

Hi Lindsay,
2. when calculating traditional basis EEV with Solv I liabilities, then would companies use the same discount rate as their BE investment assumption, i.e. risk free + their own view of a spread?

Hi - typically a traditional embedded value basis would mean best estimate assumptions about what is going to happen in the future (for the present value of future profits projection), including for investment returns. Some companies might load in a small risk margin (ie a small deduction for investment returns).

The discount rate would be a 'risk discount rate', ie with a risk margin added into it. So it might be based on the shareholders' required rate of return, allowing for the risks inherent in the business.

The risk discount rate would normally be higher than the investment return assumption. [Since if the shareholders were happy with just the basic investment return on the underlying assets, they might as well invest in those rather than in this riskier life insurance business!]

The above is true whatever the liability valuation basis being used.

 

[Lindsay Smitherman]

Basically I'm trying to come up with a table below (sorry about the format! hope it's comprehensible...). Could you help me if the understanding is correct or not? Thank you so much!!!
Assume rf is the same and spreads are different due to difference in various valuation methods. The first 3 columns are conditions and the last 2 are conclusions.
reason 1: differences in the methods adopted for calculating spreads.
reason 2: investment doesn't include spread while discount rate has spread.
………........Invmt assup………...Disc assup-Solv I...….Disc assup-Solv II.....Invmt variance-Solv I.....Invmt variance-Solv I
MCEV........rf+illiquid sprd……..rf+sprd…………………..rf+MA or VA...……....Yes, reason 1...…………....Yes, reason 1
EEV-MC.....rf(most likely)……...rf+sprd…………………..rf+MA or VA...….......Yes, reason 2..................Yes, reason 2
EEV-Trad...rf+sprd..................rf+sprd.....................rf+MA or VA............NO..................................Yes, reason 1

Ah, I see what you are trying to do! You might want to reassess some of these based on the answers above, and here are a few other thoughts which might help to tidy it up:

• Be a little careful about using the term 'investment variance' - this is normally used to refer to the difference between actual investment experience and expected investment experience (eg in an analysis of change in EV). What we are talking about here, I think, is whether we expect any investment profits to arise and therefore be included in the PVIF (present value of future profits on in-force business). Investment profits (losses) will arise and be included in the PVIF if the investment return in the EV experience/projection basis is greater (lower) than the liability discount rate.
• Bear in mind that you would only be able to have an MA or VA applying under Solvency II on certain portfolios / under certain circumstances, so the discount assumption could well be just the unadjusted risk-free rate
• Under Solvency I, liabilities were typically discounted at a prudent rate, ie less than the yield on the assets held (eg 97.5% of the risk-adjusted bond yield, if bonds were held; potentially even lower for equities as was based on 97.5% of just the dividend yield). Hence it was pretty much always the case that you would get an investment profit arising within the PVIF under the traditional EV method at least, since best estimate investment return > Solvency I (prudent) liability valuation rate of interest

Hope that helps a bit ...

 

[lanceann]

Ah, I see what you are trying to do! You might want to reassess some of these based on the answers above, and here are a few other thoughts which might help to tidy it up:

• Be a little careful about using the term 'investment variance' - this is normally used to refer to the difference between actual investment experience and expected investment experience (eg in an analysis of change in EV). What we are talking about here, I think, is whether we expect any investment profits to arise and therefore be included in the PVIF (present value of future profits on in-force business). Investment profits (losses) will arise and be included in the PVIF if the investment return in the EV experience/projection basis is greater (lower) than the liability discount rate.
• Bear in mind that you would only be able to have an MA or VA applying under Solvency II on certain portfolios / under certain circumstances, so the discount assumption could well be just the unadjusted risk-free rate
• Under Solvency I, liabilities were typically discounted at a prudent rate, ie less than the yield on the assets held (eg 97.5% of the risk-adjusted bond yield, if bonds were held; potentially even lower for equities as was based on 97.5% of just the dividend yield). Hence it was pretty much always the case that you would get an investment profit arising within the PVIF under the traditional EV method at least, since best estimate investment return > Solvency I (prudent) liability valuation rate of interest

Hope that helps a bit ...

Thanks for your detailed explanation Lindsay!
Based on your replies, what I understand is that in a broad sense we can say that for all the combinations of MCEV, EEV(MC or Traditional) with Solv I or Solv II liabilities, there may always be an element of investment profit coming from the difference between the investment assumption and the discount rate assumption used for liability valuation, as the logics/purposes for setting those assumptions are not necessarily the same.
Only for MCEV with Solv II liability, the investment profit (i.e. the difference between investment assumption and Solv II discount rate) could be very minimal or even zero in some cases.

 

[Lindsay Smitherman]

Yes