Loss absorbing capacity of deferred taxes : a stochastic approach

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Loss Absorbing Capacity of Deferred Taxes

A Stochastic Approach

Thesis Actuarial Science & Mathematical Finance

August 15, 2018

Student:

J.W.C.A. van Strien AAG (11149701)

Supervisor (UvA): dr. L.J. van Gastel

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Abstract

This thesis is written in the context of my master’s degree of Actuarial Science & Mathematical Finance. The subject (the Loss Absorbing Capacity of Deferred Taxes) is very much under the attention of insurers and regulators at the moment, since it’s calculation can be very complex, it’s calculation depends on a lot of assumptions and it can have a huge impact on the Solvency Ratio.

First approaches of the Loss Absorbing Capacity of Deferred Taxes were done with deterministic calculations but it is known that the Loss Absorbing Capacity of Deferred Taxes does not have a linear behaviour. Therefor it makes sense to investigate other approaches of this calculation, for instance a stochastic approach.

In this thesis a setup for a stochastic approach of the Loss Absorbing Capacity of Deferred Taxes is discussed and created and the results of this approach are compared with a deterministic approach and discussed. Last but not least suggestions for further research to a stochastic approach are given and explained.

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Statement of Originality

This document is written by Student Jan-Willem van Strien who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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7.3.1 Scenarios 1 and 2 . . . 42 7.3.2 Scenarios 1, 3 and 4 . . . 44 7.3.3 Scenarios 4 and 5 . . . 45 7.3.4 Scenarios 1, 6 and 7 . . . 46 7.3.5 Scenarios 1 and 8 . . . 47 7.3.6 Scenarios 1, 2, 9, 11, 13, 15, 17 and 19 . . . 47 7.3.7 Scenarios 9-12, 13-16, 17-20 . . . 49 7.3.8 Scenarios 1, 21 and 22 . . . 51 7.3.9 Scenarios 1 and 23 . . . 52

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8 Conclusion and recommendations for further research 54 8.1 Conclusion . . . 54 8.2 Recommendations for further research . . . 55

Curriculum Vitae 58

References 60

Appendix A - Description of the used models 61

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Abbreviations

Adj . . . Adjustments

BSCR . . . Basic Solvency Capital Requirement CAT . . . Catastrophe Risk

CB . . . Carry Back

CDR . . . Counter party Default Risk CF . . . Carry Forward

CT . . . Corporation Tax

CVS . . . Centrum Voor Verzekeringsstatistiek DNB . . . De Nederlandse Bank/Dutch Central Bank DTA . . . Deferred Tax Asset

DTL . . . Deferred Tax Liability

IAS . . . International Accounting Standards

IFRS . . . International Financial Reporting Standards IM . . . Internal Model

LAC DT . . . Loss Absorbing Capacity of Deferred Taxes LAC TP . . . Loss Absorbing Capacity of Technical Provisions LLP . . . Last Liquid Point

MCR . . . Minimum Capital Requirement OF . . . Own Funds

OR . . . Operational Risk RM . . . Risk Margin

SCR . . . Solvency Capital Requirement SD . . . Standard Deviation

SF . . . Standard Formula SII . . . Solvency II

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tp . . . tax planning

UFR . . . Ultimate Forward Rate VaR . . . Value-at-Risk

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1 Introduction

Since January 1st _{2016 insurers are obliged to report according to Solvency II (}_SII₎

regulations. These regulations prescribe the calculation of a Solvency Capital Require-ment (SCR) and part of this SCR is the Loss Absorbing Capacity of Deferred Taxes (LAC DT).

Calculation of the LAC DT is the last step in the calculation of the SCR and in the beginning of the implementation of SII the impact of the LAC DT has been slightly underestimated/ignored. Later on it appeared that the impact of the LAC DT could be huge, as well as on the value of the SCR as on the calculation of the SCR (complexity, use of resources, it systems). This caused a lot of focus on the LAC DT, as well of the insurance companies as of the regulators.

It is possible to calculate the LAC DT with a deterministic approach and this is prob-ably the easiest way to calculate it, but since the LAC DT does not have a linear behaviour it is known that this leads to an over- or underestimation of the LAC DT. Due to the non-linear behaviour it makes sense to investigate alternative calculation methods, like for instance a stochastic approach.

For this thesis research is done to a stochastic approach of the LAC DT calculation. Research question herewith is:

What will be the impact on the estimate of the LAC DT by a stochastic approach compared to a deterministic approach? And additional: What will be the sensitivities of this stochastic approach?

In this thesis I will first describe what the LAC DT is, what its impact on the SCR can be and how the calculation of the LAC DT can be substantiated. Afterwards a stochastic approach will be described and results of such an approach will be dis-cussed, together with some sensitivity testing (by calculating the LAC DT for different scenarios).

At last an answer to the research questions will be given and suggestions for further research will be discussed.

Since there is a lot of focus on the LAC DT and the LAC DT calculation provides quite some strategic information as well, insurance companies are hesitant to provide information about these calculations. Therefor the analyses and calculations in this thesis will be done for a fictive insurance company.

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2 Solvency II

2.1 Recap

SII can be seen as a new method for setting up a balance sheet. Like is described in the technical specifications (Eiopa (2014)), SII describes:

• the valuation of assets and liablities

• the calculation of an SCR and a Minimum Capital Requirement (MCR)

• classification of the Own Funds (OF, the difference between assets and liabilities) 2.1.1 Valuation of assets and liabilities

For the valuation of assets and liabilities fixed descriptions are given (for instance for the valuation of tradable shares) or guidance is written (for less common financial instruments or for example the valuation of insurance liabilities).

2.1.2 Calculations of SCR and MCR

The SCR is defined as the Value-at-Risk (VaR) of the (basic) OF with a confidence level of 99.5% over a one-year period. In other words: the capital an insurance company has to hold in order to stay in business within a year with 99.5% certainty.

For the calculation of the SCR an insurer can choose to use the Standard Formula (SF) or develop and use an Internal Model (IM). An IM can only be used when it is approved by the local supervisor and given the complexity of it, only the bigger insurance companies will have the possibility to develop such an IM.

With an IM the calculation of the SCR will be more aligned with the risk profile of the insurance company but a disadvantage of internal models is the comparability with other insurers. Partly because of that insurance companies with an IM are also obliged to report figures according to SF.

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Figure 1: SCR structure for SF

As can be seen the calculation is divided in modules (Market, Health, etc) which are divided in sub-modules. On sub-module level the VaR (with confidence level of 99.5% over a one-year period) is calculated in order to get the SCR for each sub-module. The SCR of each module is calculated with the SCRs of the sub-modules and a (for SF) given correlation matrix. Thereafter the Basic Solvency Capital Requirement (BSCR) is calculated with the SCRs of the modules and again a given correlation matrix. Finally the SCR is calculated by adding the Operational Risk (OR) and some adjustments (Adj) to the BSCR.

The division into modules can also be made for an IM but is not obliged. So far however internal models more or less always follow this division into modules. Also since SII requires reporting per legal entity and the different lines of business usually are accommodated in separate legal entities.

The MCR is the absolute minimum capital an insurance company has to hold. It has a floor of 25% of the SCR and a cap on 45% of the SCR but further details about the calculation are out of scope for this thesis.

2.1.3 Classification of the OF

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The OF consist of capital of different qualities and these qualities are indicated with Tier 1,2 and 3, where Tier 1 capital has the highest quality. Furthermore Tier 1 capital can be restricted or unrestricted. The MCR and SCR have to meet some restrictions regarding these Tiers.

The solvency ratio is calculated by dividing a restricted part of the OF by the SCR. This restricted part of the OF is called the eligible OF.

Summarized the restrictions are:

• At least 80% of the MCR must be Tier 1 capital • At least 50% of the SCR must be Tier 1 capital

• At least 80% of the Tier 1 capital must be unrestricted Tier 1 capital • The eligible OF can contain at most 15% Tier 3 capital

2.2 Position of LAC DT in the SII Framework

As can be seen in figure1, first a BSCR is calculated. To this BSCR the OR is added and adjustments can be subtracted. These adjustments consist of:

• Loss Absorbing Capacity of technical provisions (LAC TP) • Loss Absorbing Capacity of deferred taxes (LAC DT)

When an IM is used the calculation of the BSCR will differ but the position of the Adj and thus the LAC DT will be the same.

As mentioned in the introduction the LAC DT is calculated after all other items of the SCR are determined and the reason is that it depends (amongst others) on the size of the SCR before impact of the LAC DT. The base for the LAC DT calculation therefore is the BSCR + OR + LAC TP. This part of the SCR is also called the ’LAC DT shock’.

2.3 Definition of the LAC DT and impact on the SII ratio

The LAC DT is the tax that can be retrieved due to the loss caused by a ’LAC DT’ shock.

Tax has to be paid on profits and under particular circumstances these profits can be reduced with realised losses. The LAC DT shock is a loss, and when (part of) this loss can be deducted from realised or future profits the tax on this deductible part is what can be retrieved (and is called the LAC DT). This LAC DT can be subtracted from the BSCR in order to get the SCR.

The LAC DT is bounded by a maximum value and this value is reached when the complete loss of the LAC DT shock can be deducted from future profits (’recovered’). In that case the value of the LAC DT is given by:

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LACDTmax = tax rate ∗ (BSCR + OR − LACT P ) (1)

The minumum value of the LAC DT (of course) is zero. The SII ratio is calculated as follows:

SIIratio = EligibleOF

SCR (2)

From this equation can easily be seen that the lower the SCR (for constant eligible OF), the higher the ratio will be and therefor the higher the LAC DT (which lowers the SCR), the higher the SII ratio will be. The impact on the SII ratio with maximum LAC DT (SIIratiomax) compared to the SII ratio without LAC DT (SIIratiomin) is

given by:

SIIratiomax =

1

1 − tax rate ∗ SIIratiomin (3) As can be seen this impact completely depends on the tax rate and with the current tax rate of 25% the difference between SIIratiomin and SIIratiomax is one third of

SIIratiomin. When the tax rate gets lower (there are plans to lower the rate to 21%)

the impact will be smaller but still significant.

The following table shows the impact (for current and new tax rate) for several ratios:

SCR with tax rate 25% 21%

eligible OF LAC DT = 0 SIIratiomin SIIratiomax SIIratiomax

1,000 500 200,0% 266.7% 253.2% 1,000 600 166.7% 222.3% 211,0% 1,000 700 142.9% 190.5% 180.9% 1,000 750 133.3% 177.7% 168.7% 1,000 800 125,0% 166.7% 158.2% 1,000 900 111.1% 148.1% 140.6% 1,000 1000 100,0% 133.3% 126.6%

Table 1: Impact LAC DT on SII ratio

As can be seen (bold lines) the difference between the maximum and minimum SII ratios is huge and can be the difference between a weak ratio/a ratio in or near the danger zone and a good ratio.

Complete recovery of the LAC DT shock will be hard to realise for most companies but a substantial recovery must be possible for most companies. And given the impact, all companies will try to substantiate such a recovery and try to make the deductible part as high as possible. How this deductible part can be calculated and substantiated is explained in the continuation of this thesis.

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3 Tax Regulations

Under SII the treatment of income taxes follows the International Accounting Standards (IAS) of the International Financial Reporting Standards (IFRS), in particular IAS12 (2012). IAS12 deals with income taxes and defines the following:

• Accounting profit is profit or loss for a period before deducting tax expense. • Taxable profit (tax loss) is the profit (loss) for a period, determined in accordance

with the rules established by the taxation authorities, upon which income taxes are payable (recoverable).

• Tax expense (tax income) is the aggregate amount included in the determination of profit or loss for the period in respect of current tax and deferred tax.

• Current tax is the amount of income taxes payable (recoverable) in respect of the taxable profit (tax loss) for a period.

• Deferred tax liabilities are the amounts of income taxes payable in future periods in respect of taxable temporary differences.

This means that taxes have to be paid on taxable profit. Due to valuation differences between SII and fiscal valuation the taxable profit differs from the economic (SII) profit. This leads to taxable temporary differences which lead to deferred taxes on the SII balance sheet. This also counts for IFRS by the way but that is out-of-scope for this thesis (the theory is the same as discussed here).

3.1 Deferred taxes

As mentioned deferred taxes arise due to accounting differences with the fiscal valuation. Examples of these differences (the most common ones) are:

• Valuation of equity: the fiscal value is the purchase value or lower current value where the SII value is always the market value.

• Valuation of bonds: the fiscal value is the purchase value where the SII value is always the market value.

• Valuation of insurance liabilities: fiscal a fixed discount rate (usually 4%) and a prescribed morality table is used where SII prescribes the use of a market interest rate and a ’market consistent’ mortality table.

• Balance sheet items that don’t exist on the fiscal balance sheet. For instance the risk margin (RM) and in some cases the activation of future premiums.

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There are two types of deferred taxes: deferred tax assets (DTA) and deferred tax liabilities (DTL). The table below shows when a DTA and when a DTL will occur:

Fiscal value < SII value Fiscal value > SII value

Liability DTA DTL

Asset DTL DTA

Table 2: When DTA and when DTL

On the basis of two examples the DTA and DTL will be further explained. These examples concern a simple insurance company for which the following assumptions are made:

• The assets contain one type of assets, bought at the same time somewhere in the past

• The provision concerns annuity payments only and these payments are done at the end of the year only

• Corporation tax (CT) is set at 25% (the current one in The Netherlands)

NB: Cash positions can never have a DTA or DTL (in other words cash is always valued in the same way).

3.1.1 First DTA/DTL example

Suppose the starting balance sheets (t=0) look like:

t = 0

fiscal SII fiscal SII

Assets 180.00 205.00 Provision 120.00 140.00 Cash 20.00 20.00 RM 15.00 DTA 8.75 DTL 6.25 Equity 80.00 72.50 200.00 233.75 200.00 233.75 Net DTA 2.50

Figure 2: Starting balance sheet for the first DTA/DTL example

The valuation differences we see on these balance sheets are the following: • Assets: fiscal value is lower than SII value which leads to a DTL

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• Provision: fiscal value is lower than SII value which leads to a DTA

• RM: not recognized on the fiscal balance sheet and given that it is a liability this also leads to a DTA

Together with the given tax rate of 25% this leads to: • a DTA of 25% * (140 - 120 + 15 - 0) = 8.75 • a DTL of 25% * (205 - 180) = 6.25

Which results in a net DTA position of 2.50 (8.75 - 6.25).

Suppose the value of the assets increased in one year with 11 and the fiscal provision is raised with 4% interest (fixed rate) and the SII provision with 1% interest (market rate). That leads to the following balance sheet before pay-out of the annuities:

t = 1 before pay out

Assets 180.00 216.00 Provision 124.80 141.40 Cash 20.00 20.00 RM 15.15 DTA 7.94 DTL 9.00 Equity 75.20 78.39 200.00 243.94 200.00 243.94 Net DTL 1.06

Figure 3: Situation after one year before pay-out for the first DTA/DTL example

As can be seen the DTA decreased (fiscal provision increased more than the SII provision + RM) and the DTL increased (SII value of the assets increased). In fact the DTL increased so much that the net value becomes a DTL. Calculation of this DTL is done in the same way as for the starting balances:

• a DTA of 25% * (141.40 - 124.80 + 15.15 - 0) = 7.94 • a DTL of 25% * (216 - 180) = 9.00

Suppose, besides the increase of the assets, the following happened in the first year: • Annuity payments are 60, which is exactly what was expected under SII

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• The fiscal provision decreases with 52 after the annuities are paid • Release of the RM is 6.43

This leads to the following P&L:

t = 1 P&L

Payments 60.00 60.00 Released 52.00 60.00 RM 6.43 Investment return 10.00 11.00 Profit 2.00 17.43 Loss 62.00 77.43 62.00 77.43 CT 0.50 4.36 DTA/DTL 0.00 -3.86 CT 0.50 0.50

Figure 4: P&L over year one for the first DTA/DTL example

The fiscal value of the investment return is the profit made on the sold part of the assets. For the payment of the annuities 60 was needed and the fiscal value of this 60 is: 180/216 * 60 = 50 (purchase value which is the fiscal balance sheet value of 180, divided by the market value which is the SII balance sheet value of 205 + 11, multiplied by the needed value for payment of the annuities of 60).

The CT that has to be paid can be deducted from the fiscal balance sheet: 25% of the profit of 2, which results in 0.50. Calculating the CT from the SII P&L will lead to the same result: take also 25% of the profit (25% of 17.43) and subtract the release of the DTA (3.86) from these taxes and the net CT is also 0.50.

The release of the DTA can be deducted from the P&L by taking 25% of the difference between the SII values and the fiscal values of the provision, RM and Investment return (all P&L items). This is the same as taking 25% of the difference between the fiscal profit and the SII profit (25% * (2 - 17.43)).

The P&L over the first year leads to the following balance sheet after payments of the annuities:

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t = 1 after pay out

Assets 130.00 156.00 Provision 68.00 80.00 Cash 19.50 19.50 RM 8.57 DTA 5.14 DTL 6.50 Equity 81.50 85.57 149.50 180.64 149.50 180.64 Net DTL 1.36 DTA (t = 0) 2.50 Delta DTA -3.86

Figure 5: Situation after one year after pay-out for the first DTA/DTL example

From these balance sheets also the current DTA and DTL positions can be calculated and by comparing the net value with the net value of the starting balances sheets, the release of DTA and DTL can be calculated. As can be seen this leads to the same release as is calculated for the P&L (which should be the case of course).

3.1.2 Second DTA/DTL example

The starting balance sheets are the same for this second example and the only thing that changes is the asset value after the first year: it will decrease with 5 to a value of 200.

The mentioned decrease of the assets leads to the following balance sheets:

t = 1 before pay out

Assets 180.00 200.00 Provision 120.00 140.00 Cash 20.00 20.00 RM 15.00 DTA 8.75 DTL 5.00 Equity 80.00 68.75 200.00 228.75 200.00 228.75 Net DTA 3.75

Figure 6: Situation after one year before pay-out for the second DTA/DTL example

As can be seen the net DTA increases here instead of the decreasing in the first example. The reason is that the DTL decreases (where it increases in the first example) and it

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decreases more than the DTA decreases and therefore a net increase of the DTA can be seen.

The decrease of the assets and the assumed payments of example 1 lead to the following P&L:

t = 1 P&L

Payments 60.00 60.00 Released 52.00 60.00 RM 6.43 Investment return 6.00 -5.00 Profit 1.43 Loss 2.00 60.00 61.43 60.00 61.43 CT -0.50 0.36 DTA/DTL 0.00 -0.86 CT -0.50 -0.50

Figure 7: P&L over year one for the second DTA/DTL example

The release of DTA and DTL can be calculated in the same way as for the first example: 25% * ( 1.43 - (- 2.00) = - 0.86. This means a negative amount of CT should be paid but that is rounded to zero. However there might be a possibility to compensate this negative amount but that will be explained in paragraph 3.2.

The mentioned decrease of the assets leads to the following balance sheets:

t = 1 after pay out

Assets 1260 140.00 Provision 68.00 80.00 Cash 20.00 20.00 RM 8.57 DTA 5.14 DTL 3.50 Equity 78.00 73.07 146.00 165.14 146.00 165.14 Net DTA 1.64 DTA (t = 0) 2.50 Delta DTA -0.86

Figure 8: Situation after one year after pay-out for the second DTA/DTL example

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3.2 Carry back and carry forward

Like mentioned, taxes have to be paid over the profit a company makes but in some cases losses from other years can be subtracted from the profit over which tax has to be paid (loss compensation). There are two options for this loss compensation:

• Carry back (CB) means that a loss in a specific year can be recovered with profit of earlier years. At the moment (in The Netherlands) the term for carry back is only 1 year. In other words the loss in year t can be recovered with profit of year t-1. When there is no profit in t-1 or less profit than the loss in year t, this loss can not (fully) be recovered with carry back.

• Carry forward (CF) means that a loss can be carried forward in order to recover it in the coming years. The current term for carry forward in The Netherlands is 9 years. A loss in year t (which cannot be recovered with carry back) can be subtracted from the profit in year t+1. When there is not enough profit in year t+1 it can be carried forward to year t+2 and so on. When there is still some loss left after 9 years this loss is non recoverable.

With the following example will be explained how this exactly works.

3.2.1 Example of carry back and carry forward

Suppose a certain year (t) a company makes a huge loss, whereas it made profit in the years before and will also make profit in the years after t. For carry back a period of one year will be used and for carry forward a period of nine years (both the current terms in The Netherlands).

Period t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 tot Taxable 100 80 -2,000 100 200 300 280 80 200 240 120 100 100 -100 CT * 25 20 0 25 50 75 70 20 50 60 30 25 25 475 CB 0 0 20 0 0 0 0 0 0 0 0 0 0 20 CF 0 0 0 25 50 75 70 20 50 60 30 25 0 405 CT 25 20 -20 0 0 0 0 0 0 0 0 0 25 50 CB+CF 0 0 20 25 50 75 70 20 50 60 30 25 0 425 Non rec 0 0 0 0 0 0 0 0 0 0 0 0 75 75 Av CF 0 0 480 455 405 330 260 240 190 130 100 75 0

Taxable = Taxable Profit, CT* = Corporation Tax without CB or CF,

CT = Corporation Tax with CB and CF, Non rec = Non-recoverable, Av CF = Available for CF

Table 3: Example of Carry Back and Carry Forward

In the first two years (t-2 and t-1) there is (taxable) profit and no losses so nothing happens. In year t, the huge loss occurs and by this loss an amount of 500 (25% of 2,000) becomes available for recovery. Immediately a carry back can be realised: the

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grey cell in the figure above for year t with value 20. This 20 is the CT paid in year t-1 and can be fully recovered because the loss in year t is higher than the taxable profit in year t-1. The profit of year t-2 cannot be used because the carry back period is only 1 year.

After year t the remainder of CT of the loss can be ’carried forward’ (500 - 20 = 480) and since in all the years after t a taxable profit is made, each year part of the amount carried forward can be used to subtract from the calculated CT.

After nine years there still is a carry forward amount left, but the term for carry forward has expired so the realised carry forward in year t+10 (first grey cell in that column) is zero while the available value after year t+9 is 75 (grey cell in the column of t+9). This 75 becomes the non recoverable amount (other grey cell for year t+10).

The result is that due to carry back and carry forward, the total CT for the given period is 425 lower than it should be without carry back and carry forward (compare CT* and CT in the last column). This is exactly the total gain by CB and CF (grey cell in the last column).

3.3 Tax planning

As can be seen in the carry back and carry forward example in paragraph3.2.1, it can make a difference in which year a taxable profit is realised. When the taxable profit of year t+10 in the mentioned example for instance, could be moved to an earlier year, the company would have a benefit of 25 by this earlier realization (the CT of 25 would be recovered by carry forward because it would fall within the term for carry forward). In the situation above it is useful to expedite a gain but it can also be useful to expedite a loss. Of course not all profits and losses are planable but it can be very useful to monitor this. Examples of planable profits and losses and situations where it can be effective are discussed below.

3.3.1 Sale of assets with a DTL

As already mentioned in paragraph3.1, assets are valued at purchase price (or in some cases the lower market value) on the fiscal balance sheet. This means that as long as assets with a higher value than the purchase price are not sold, the profit on these assets is not realised. Selling such assets can be useful when the carry forward term of a specific loss is ending and not completely realised (like in the example in paragraph 3.2.1).

Insurance companies usually hold a specific portfolio with assets in order to hedge their liabilities. Selling assets can disturb this hedge because a sale will disturb the duration of the asset portfolio. A solution is immediately buying the same asset back: in that case the hedge is not affected and the unrealised profit on the asset is realised!

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3.3.2 Realisation of non-recurring gains

Suppose a company wants to sell part of its business with which it will make a non-recurring gain. When the company already had the strategy to do this, it could be more profitable to change the year in which they were planning to do this.

3.3.3 Fiscal recalculations of balance sheet items with a DTA

At the moment insurance provisions are valued fiscally with interest rates of 3% or 4%, while the market rates are much lower. This leads to a huge DTA on the provisions under SII. The fact that mortality tables used for the fiscal balance sheet are less severe than the ones used under SII makes this DTA even bigger.

Normally this DTA will be released over the duration of the portfolio and will have a gradual dampening effect on the taxable profit but it can be interesting to realise this DTA earlier, for instance when in the last year a huge profit is realised or when a huge profit is expected in some particular year in the future (for instance due to a non-recurring gain as discussed in paragraph3.3.2).

The realisation of such a DTA can be realised by a fiscal recalculation of the provision with another (lower) interest rate and/or a more severe mortality table. For such a recalculation the company needs permission of the tax authorities and in order to get that permission the company has to come up with good substantiation why this recalculation should be carried out. For instance when the whole market agrees that mortality rates will only decrease in the future that can be a good substantiation to change the mortality tables that are used for calculation of the fiscal provision.

3.4 Treatment of participations

Participations are held for strategic reasons and usually without intention to be sold. This implies that fluctuations in the value of these participations will never be realised and from that point of view it doesn’t make sense to calculate a DTA or DTL for these participations. Therefor calculating a DTA or DTL for participations is not allowed. The fiscal definition of participations differs from the SII definition: on the fiscal bal-ance sheet every interest of 5% or more in the shares of another company is classified as a participation. On the SII balance sheet other criteria are used for classifying participations.

For calculating the DTA and DTL the value of the assets that are fiscally classified as participations must be omitted and since these assets can have a different classification under SII, re-calssification of these assets can be necessary.

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3.5 Run off of DTA and DTL 3.5.1 Assets

The run off of a DTA/DTL on bonds can be calculated with the maturity date and a yield curve: the yearly SII values until maturity can be predicted and together with the yearly fiscal values the yearly DTA/DTL can be calculated.

The run off of a DTA/DTL on property and equity is harder to predict. Property and equity don’t have a maturity date (investment policies can help estimating one) and predicting the development of the value is also difficult. A common method is using a prescribed period (for instance 5 or 10 years) as holding period and writing off the DTA/DTL in equal parts over this chosen period.

3.5.2 Liabilities

The run off of the DTA/DTL on liabilities can be estimated by projecting the fiscal value and the SII value of the liabilities. For both cases the best estimate cash flows are known and for the fiscal value the interest rate is also known (a fixed value, usually between 3% and 4%).

Valuation of the liabilities under SII is done with an interest rate curve with an Ultimate Forward Rate (UFR). From this interest rate curve new interest rate curves for each valuation year can be deducted but it is also possible to create new interest rate curves without UFR (from the yield curve) and then apply the UFR technique for each year seperately. With the last method the UFR is applied correctly, with last liquid point (LLP) for every valuation year at the same point in time. The UFR in fact ’moves’ in time. In The Netherlands insurers are obliged to value the liabilities with the last method (by DNB, the Dutch Central Bank).

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4 How to calculate the LAC DT

As discussed in paragraph2.3, the LAC DT is the amount of taxes that can be recovered by the loss that is caused by the LAC DT shock (BSCR + OR + Adj). Calculation of this amount takes place in several steps that will be discussed in this chapter.

4.1 Starting point

Starting point is the (SII) balance sheet without LAC DT at the calculation moment (usually the end of a quarter). Calculation of the LAC DT is the last step in report-ing because this calculation depends on the (run off of the) DTA/DTL and the SCR (without LAC DT).

The reported value of the DTA needs to be substantiated: this means that the entity needs to proof that there will be enough profit in the future (and at the right moment in the future) with which this DTA can be settled. Normally this will already be done when the DTA is determined but for the LAC DT this needs to be done on entity level, which can differ from the level on which the DTA is determined (the fiscal unit). The reason is that a fiscal unit can consists of more than one entity and therefor can have more room for settlement of the DTA. This explains that it can occur (within a company with several entities) that a DTA cannot be fully substantiated on entity level.

This, of course, does not count for the DTL, since a DTL leads to payment of taxes.

4.2 Allocate the SCR to the underlying risks and the balance sheet items To allocate the SCR to the underlying risks, an allocation methods has to be used. There are quite a few different allocation methods and more information about these methods and the differences between them can be found in a.o. McNeil et al. (2005) and Kyse˘lov´a (2011). In this thesis the impact of allocation on the LAC DT will be discussed on the basis of the following two (most common) allocation methods:

• Proportional allocation

This method consists of two steps: allocation within each module and allocation between the modules.

– Within module: the risk per module after ’within module diversification’ is divided by the sum of the risks of the sub modules that fall within that module.

– Between modules: the BSCR is divided by the sum of the risks of the modules after ’within module diversification’.

This means that the relative diversification benefit between modules is equal for all modules and that the relative diversification benefit within a module is equal for all sub modules.

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In formulas:

Divwithin module(x) =

N etSCRmodule(x)

ΣSCRsubmodule(x)

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Divbetween modules =

BSCR ΣN etSCRmodule(x)

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Divmodule total(x) = Divwithin module(x) ∗ Divbetween modules (6)

SCRLAC DT(sub module) = Divmodule total(x) ∗ SCR(sub module) (7)

Where x stands for a module and N etSCRmodule(x) stands for the Risk of module

x after ’within module diversification’. LAC DTscr(sub module) is the net risk of

a module after all diversification (within module and between modules). • Marginal allocation

With this method the net risks per sub module are determined in a way that the highest diversification per risk is reached. In other words the optimal net risks are determined. This is done by calculating the decrease in SCR for each sub module when the risk for that sub module would be set to zero. Thereafter per sub module the diversification benefit is determined by determining the relative diversification benefit (compared to the sum of all diversification benefits) and multiplying this with the total diversification benefit.

In formulas:

DBFtot = (ΣSCRsubmodule− BSCR) (8)

SCRLAC DT(sub module) =

(BSCR − BSCRwithout(y))

Σ(BSCR − BSCRwithout(y))

∗ DBFtot (9)

Where DBFtot stands for total diversification benefit (in e) and y stands for the

sub risk.

Btw: further research to the impact of allocation on the LAC DT can be an interesting subject for a next thesis.

4.3 Determine the balance sheet after shock

When the allocation of the SCR is done, the balance sheet (SII and fiscal) after shock can be determined. All shocks have impact on the SII balance sheet and some will have an impact on the fiscal balance sheet as well. The following different impacts can be distinguished:

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• Immediate loss

Shocks that have an impact on both the fiscal and SII balance sheet will cause an immediate loss. Examples are: catastrophe shock, counter-party default shock, operational shock and in some cases the equity shock.

The first three items do not belong to a specific balance sheet item and it is hard to assign them to specific items. Therefor the values of these shocks will just be lowered from ’other asset’ or added to ’other liabilities’.

The equity shock will lead to an immediate loss when the market value after shock is lower than the fiscal value (usually the purchase value). Fluctuations above the purchase value are not recognized fiscally, but as soon as the market value becomes lower than the purchase value the loss has to be taken. The DTL on equity will become zero in that case.

• Postponed loss

Shocks that only have an impact on the SII balance sheet will usually lead to a postponed loss. Examples are:

– property: value change not recognized fiscally until property is sold. DTL will decrease (or DTA will increase) due to decrease of SII value.

– best estimate liabilities: shock on liabilities is not recognized fiscally. DTA will increase (or DTL will decrease) due to increase of SII value.

• Improper postponed loss

An improper postponed loss occurs for the interest rate shock and spread shock on the bonds portfolio which are meant to be held to maturity. The easiest way to show this is with a zero coupon bond. Such a bond has one pay-out moment (at maturity) and this pay-out value never changes. In other words: the fiscal and SII values at maturity are always equal. This effect is called ’pull to par’. For coupon bonds this effect can also be seen but the calculation is a bit more difficult because of the coupon payments.

In case bonds are not held to maturity but are sold immediately after shock a loss will be realised.

When the after shock balance sheets are determined the run off of the after shock DTA and DTL can be determined and the after shock SCR can be calculated.

Determination of the run off of the DTA an DTL will be done in the same way as before shock, the rules for these run offs can be found in paragraph 3.5. SCR calculation is also the same as before shock, with the remark that the LAC DT after shock is set to zero unless the entity can prove that it isn’t zero.

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4.4 Determine the recovery measures that have to be taken in order to stay solvable in the future

After the SII balance sheet after shock is determined, the solvency ratio can be calcu-lated. When the SII ratio before shock is lower than 200% (which is not unusual), the ratio after shock will be lower than 100%.

When the SII ratio drops below 100% a recovery plan has to be implemented by which the ratio will return to at least 100% within half a year and has to stay above 100% in the future. Such a recovery plan will consist of several recovery measures with which the ratio will increase. Examples of such recovery measures are:

• Derisking of assets

• Improve positions with hedges

• Capital injection by other entities within a group • External financing (loans, additional share issue)

• Derisking of liabilities (reinsurance, hedging of underwriting risks, sale of part of the portfolio)

In order to fulfill the requirements for recovery, the entity has to show that the SII ratio will stay above 100% in the future after the necessary recovery measures have been taken. The impact of the recovery measures on profitability will be taken into account for the calculation of the future profits after shock.

4.5 Determine the impact of the shock on future profits and determine the part of the DTA that can be recovered in the future

When the necessary recovery measures and their impact are known, the future profit after shock can be calculated. Together with the run off of the DTA an DTL the part of the DTA that can be recovered can be calculated (in the same way as this is done in the situation before shock).

4.6 Calculate the LAC DT

When a company is not able to take enough recovery measures to get a SII ratio that stays above 100% in the future the LAC DT has to be set to zero. The reason is that when the SII ratio stays below 100% the entity will get bankrupt and there will be nothing to recover.

When the entity can recover, the LAC DT is calculated by subtracting the recoverable DTA before shock from the recoverable DTA after shock. This value is limited by zero (LAC DT cannot be negative).

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5 Stochastic approach of the LAC DT calculation

5.1 Introduction

Because the LAC DT calculation uses future results there is uncertainty in the calcula-tion and this uncertainty increases when more projeccalcula-tion years are taken into account. Especially for insurers with (lifelong) pensions in their portfolio the number of projec-tion years can be large.

A deterministic calculation only shows the expected value in case exactly the expected situation arises. When this expected value is the average of all possible values the deterministic calculation makes sense, but when this is not the case it is just the value of a specific situation. In that case the value says nothing about ’the real value’. The first situation is only applicable when the process is exactly linear and this is not the case for the LAC DT calculation since:

• The value of the LAC DT is bounded by a maximum (the tax percentage multi-plied by the LAC DT shock) and a minimum (zero) and when the deterministic value is not the average of those 2 there can never be symmetry in the calculation. • The projection is done over more than 1 period. This means that you get the ’interest over interest’ impact. This can be best shown with an example of a simple interest calculation over 2 periods:

– Suppose the starting value in year t is 10,000.

– Average return is 5% with standard deviation (SD) of 5%.

– 3 situations are calculated: 10th_{percentile, 50}th_{percentile and 90}th_percentile.

Probability for every percentile is equal (1 third).

After the year 1 the average value is the same as the deterministic value but after year 2 this is not the weighted average will be higher. See figure 9. For the years after year 2 the difference will become bigger with the years.

t t+1 t+2 12,412 11,141 11,698 10,000 10,500 11,025 9,859 10,352 9,720 weighted average 10,500 11,034 deterministic value 10,500 11,025

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5.2 How to apply stochastics to the LAC DT calculation

The LAC DT shock is a pre-described shock and the entity has to prove that it can recover after such a shock. Starting point is therefor the position after LAC DT shock, so the recovery part will be calculated stochastically, not the shock itself (that is pre-described).

For the recovery the future profit is the main driver so it makes sense to investigate how this future profit can be made stochastic. The run off of the DTA/DTL after shock is taken into account for the calculation but will be treated as given (fixed).

First step is to analyse which variables can be made stochastic and if it makes sense to take them all into account in a stochastic way. Examples of such variables are:

• Interest rates

• Return on property and equity • Mortality rates

• Lapse rates

• Loss assumptions (non-life)

The more variables will be made stochastic, the more complex the calculation will become. It can also be the case that the number of simulations has to increase, which means longer calculation times.

After the stochastic variables are selected, a distribution per variable will be designed or chosen (by professional judgment). From these distributions the mean and SD for each variable can be determined and with that information for each simulation values for the variable can be drawn from these distributions.

Example: Suppose the return on property (p) is distributed normally with mean x and SD y, the return per simulation will be determined with a random drawing for p from N(x,y).

In the end ”M” simulations will be calculated and all these simulations will have the same probability. Thereafter for each simulation the LAC DT can be calculated and so M values of the LAC DT are produced with all the same probability. Therefor it makes sense to take the average value of these M LAC DT values in order to get the stochastic value of the LAC DT.

Much more information about stochastic calculations can be found inEtheridge(2002), which may be an interestin subject for further research.

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6 Assumptions for the example LAC DT calculation and

de-scription of the example

In order to discuss the behaviour of the LAC DT a fictive insurance entity is designed. In this chapter all assumptions for this entity and the calculations are described.

6.1 General assumptions for the entity

The example is calculated for a fictive pension portfolio. This portfolio only consists of lifelong old age pensions and lifelong spouse pensions. Retirement age is set at 65 and the spouse pension becomes in payment as soon as the main insured dies.

Furthermore the entity will pay dividend to the group it belongs to/the mother when the ratio is higher than 150%. De-risking (no investement in property and equity) will take place when the ratio drops below 110%.

The projection period for future profit is set at 100 years and finally the profit of the former year is set ate 150 million.

The LAC DT value for the future is estimated at 50% of the maximum value (before shock). After shock it is assumed to be zero.

6.2 Balance sheets before LAC DT shock

With a constant tax rate of 25% the balance sheet (valuation date end of 2017) before shock looks as follows:

SII Fiscal Cash 750,000 750,000 Property 1,000,000 500,000 Strategic participations 1,000,000 800,000 Equity 1,000,000 600,000 Bonds 49,805,344 42,334,542

Other receivables en assets 3,500,000 3,200,000 Deferred tax assets 724,892

Total assets 57,780,236 48,184,542 Best Estimate 44,188,511 34,622,499

Best Estimate - guarantees 0 0

Risk Margin 2,118,904

Other liabilities 3,000,000 2,950,000 Deferred tax liabilities 0

Total liabilities 49,307,415 37,572,499

Own funds 8,472,821 10,612,044

Table 4: Inital balances in e1,000

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• Cash: money that is available right away (also bank accounts). No difference between SII value and fiscal value.

• Property: assumed that the fiscal value (purchase value) is half the SII value. Run off of the DTL in 10 years.

• Strategic Participations: there is a difference between the fiscal and SII values but this is not taken into account for the DTA or DTL calculation (not allowed). • Equity: difference as shown. Run off DTL in 5 years.

• Bonds: assumed that liability cash flows are hedged for 102% with zero coupon bonds. Highest duration of the zero coupon bonds is 30 years so liability cash flows after year 30 are hedged with zero coupon bonds with duration of 30 years. The hedge for the cash flows after year 30 is rolled forward every year (after each year the zero coupon bonds for year 30 and further are sold and zero coupon bonds with duration of 30 years are bought back). Valuation is done with the yield curve as per the end of 2017 according to information produced by Bloomberg. See Appendix B - Data for the curve.

Fiscal value is a fictive value to create a DTL and it runs off in 30 years.

• Other receivables and assets: difference between SII value and fiscal value as shown. Run off in 10 years.

• The DTA is the net DTA (DTL is subtracted from the total DTA). The DTA and DTL are calculated as the tax rate multiplied with the differences between the SII and fiscal values (except for the strategic participations!).

• Best estimate (fiscal and SII) principles:

– annuity cash flows are calculated with AG2016 mortality tables and experi-ence factors based on data of the Dutch insurance companies which is pro-vided by the ’Centrum voor VerzekeringsStatistiek’ (CVS).

– In these cash flows a small lapse is included (only for annuitants not in payment).

– In these cash flows also expense cash flows of euro 25 per policy and monthly disbursement expenses (only when annuity is in payment) of 1% of the an-nuities are incorporated.

Monthly payments are assumed but for simplicity these payments are converted to yearly payments, since taxes are paid yearly. Fiscal valuation is done with a (constant) interest rate of 3% and SII valuation with the prescribed (by Eiopa) SII curve with a UFR of 4.2% (also per the end of 2017).

See Appendix B - Data for the used data.

• Best estimate Guarantees: for simplicity reasons assumed that there are no guar-antees.

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• Risk Margin: does not exist on the fiscal balance sheet. Value runs off with the run off of the provision (and so does the DTA). The risk margin is calculated with the so called ”Swiss Method”, which means that the SCR is projected on the basis of the development of the provision and the present value of 6% (prescribed cost-of-capital) of these SCR’s is the risk margin.

• Other liabilities: difference between SII and fiscal as shown. Run off in 10 years, comparable with ’other assets’).

6.3 BSCR and OR calculation 6.3.1 Before shock

The BSCR and OR are calculated with SF which gives the following results:

SCR Life 2,005,638 Mortality risk 0 Longevity risk 1,837,331 Disability risk 0 Lapse risk 0 Expense risk 449,144 Revision risk 0 CAT 100,000 SCR Market 2,927,586 Interest Rate 1,021,857 Equity 465,000 Property 250,000 Spread 1,717,623 Currency 0 Concentration 100,000 SCR CDR 500,000 Market risk 2,927,586 Counterparty risk 500,000 Life Underwriting risks 2,005,638 Health Underwriting risks 0 Non-Life Underwriting risks 0

BSCR 4,124,620 LacTP 0 LacDT SCR OR 329,970 SCR 4,454,590 Table 5: BSCR and OR ine 1,000

For the calculation of the provision (best estimate), a small lapse risk (only for annuities not yet in payment) is taken into account. A lapse risk was also calculated (according to

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SF) but including lapse risk made the LAC DT calculations unnecessary more complex. Effects on LAC DT calculations can also be shown without lapse risk. If lapse risk would be omitted for the provision, the provision would be slightly higher and the longevity risk and expense risk would also be slightly higher. Recalculating everything is rather time-consuming and for the behaviour of the LAC DT this won’t have an impact. Therefor there is lapse in the portfolio but it is considered as fixed and unchangeable. The other items of the BSCR and OR are calculated according with the following assumptions:

• Longevity risk is calculated with a 20% instantaneous shock on mortality (accord-ing to SF).

• Expense risk is calculated with a increase in yearly expenses of e 5 per policy (from e 25 to e 30) and a increase in monthly disbursement expenses (only when annuity is in payment) of 1% of the annuities (from 1% to 2%).

• Catastrophe risk (CAT) is is estimated on the basis of professional judgment. • Interest rate risk is calculated with the prescribed (SF) up and down shocks. • All equity is assumed to be of Type I and therefor equity risk is calculated with

the type I equity shock (SF) of 46.5%.

• Property risk is calculated with the SF shock of 25%.

• Spread risk is calculated as if all zeroes were exposures in euros to central gov-ernments or central banks where the distribution over the credit qualities is as follows:

Credit quality 0 1 2 3

Fraction of zeroes 40% 35% 20% 5% Table 6: Distribution of zeroes over credit quality

• Concentration risk is is estimated on the basis of professional judgment.

• Counter party Default Risk (CDR) is estimated on the basis of professional judg-ment.

• Operational Risk is estimated as 8% of the BSCR. 6.3.2 After shock

For the calculation of the BSCR and OR after shock only the market risks will change. For simplicity the other risks will be kept equal. The real values will not differ that much that it would influence the outcomes of this research.

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• Interest rate risk: the new value will be the value of the bond portfolio after shock divided by the value of the bond portfolio before shock multiplied with the interest rate risk before shock.

• Equity risk: value after shock decreases quite large. New risk value is calculated over the value after shock.

• Property risk: this value after shock also decreases quite large. New risk value is also calculated over the value after shock.

• Spread risk: estimated in the same way as the interest rate risk. LAC DT after shock is set to zero (see also4.3).

6.3.3 Future values of BSCR and OR

Future values for the several risks are calculated as follows:

• Longevity and expense risk: run off (portfolio is seen as a closed book) is known because the yearly cash flows are known. Basis for the present value calculation is the SII curve including UFR. Every year a new curve is calculated with a new UFR (moving UFR so that the last liquid point lies always in year 20 after the valuation year). This method is prescribed by DNB.

• CAT risk is calculated on the basis of the sum of the other underwriting risks. • Interest rate risk is calculated on the basis of the value of the bonds.

• Equity risk is always calculated as 46.5% of the equity value. • Property risk is always calculated as 25% of the property value. • Spread risk is calculated on the basis of the value of the bonds.

• Concentration risk is calculated on the basis of the sum of the other market risks. • CDR is calculated on the basis of the size of the market risk.

6.4 Balance sheets after LAC DT shock

In this thesis two allocation methods (proportional and marginal, see4.2) will be used and in the figure below the balance sheets after shock for both allocation methods are shown:

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Proportional Marginal

SII Fiscal SII Fiscal

Cash 750,000 750,000 750,000 750,000

Property 839,160 500,000 838,234 500,000

Strategic participations 1,000,000 800,000 1,000,000 800,000

Equity 700,838 600,000 744,167 600,000

Bonds 48,042,875 42,334,542 48,174,948 42,334,542

Other receivables en assets 2,790,457 2,490,457 2,797,433 2,497,433

Deferred tax assets 752,052 587,622

Total assets 54,875,382 47,474,999 54,892,405 47,481,976 Best Estimate 45,647,287 34,622,499 45,796,435 34,622,499

Best Estimate - guarantees 0 0 0 0

Risk Margin 2,118,904 2,118,904

Other liabilities 3,063,800 3,013,800 3,096,105 3,046,105

Deferred tax liabilities 0 0

Total liabilities 50,829,991 37,636,299 51,011,443 37,668,604

Own funds 4,045,391 9,838,700 3,880,961 9,813,372

Table 7: Balances after shock, in e1,000

As can be seen the property values drop under SII and there is no impact on the fiscal balance sheet. Since the equity values after shock are still higher than the fiscal values the same effect can be seen for equity. SII values for bonds drop due to the interest rate shock and the spread shock (no impact on the fiscal values) and the Best Estimate value (SII) increases due to the underwriting shocks. As discussed in paragraph 4.3, the CAT shock, CDR shock and OR shock are charged to the other assets and other liabilities.

Risk margin is unchanged, as is prescribed by DNB.

6.5 Assumptions for the recovery measures

For the entity the following recovery measures are defined:

• Capital injection: after shock capital is needed in order to recover the ratio to at least 100%. When this capital must be collected from investors a fee must be taken into account. In most cases this fee is set to 2% which is rather low but the assumption is made that the company has a good reputation which will still be in place after shock. To show the impact there are also calculations made with 5% as fee percentage.

There are also scenarios where the fee is set to 0%: in those cases it is assumed that the other entities of the group have enough excess capital to invest in our entity. When the company’s rating becomes high enough it will pay dividend to the mother/other group members. In this case the injection is an investment which results in more dividend for the investors.

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The capital injection will be paid back in parts as soon as the ratio is higher than 130%. Furthermore it is assumed that no pay back will take place in the first 3 years.

• Lowering expenses: 10/110 part of the liability cash flows is meant for expenses. After shock this will increase with the expense shock and the measure will both lower the expense cash flows before shock as well as the expense cash flows of the shock. Calculations are made with 25% reduction in expenses and for sensitivity analyses also some higher percentages.

• Longevity hedge: with a longevity hedge part of the profitability of the portfolio is sold but the uncertainty of the portfolio is also lowered, which means a much lower longevity risk and thus a much lower SCR. A measure for the price of such a transaction is the risk margin. At the moment the risk margin is slightly higher that prices that are offered in the market so the assumption is made that a transaction with a price of 80% of the risk margin is made. Furthermore it should be possible to transact 20% of the provision. See also the description (in Dutch) of an indemnity hedge in Strien (2012b) or in Strien (2012a)

• Complete de-risking: no investment in property and equity after shock. 6.6 Assumptions for the stochastic part of the calculations

The recoverability of the DTA depends mainly on the profit that can be generated in the future. In the before shock situation this usually won’t be a problem but after shock it strongly depends on how fast the entity can recover. The future profit depends (for the entity in the example) on the following uncertain variables:

• Property returns • Equity returns

• Development of interest rates • Development of mortality rates

All these items can be approached stochastically but for this thesis the liability cash flows are assumed to be fixed (no stochastic mortality).

For property returns and equity returns a mean and SD of 5% are chosen and the SD for the interest rate is set at 0.02%. All distributions are assumed to be normal. These assumptions are based on professional judgment but in the future further research can be done to these assumptions.

The stochastic calculations of the profits are done in R. The number of calculations per stochastic run is set at 10,000 and for every year:

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• a new interest rate curve is determined based on the forward rates with which the initial curve is determined. A random error term (with SD 0.02%) is added to these forward rates.

• the return on property is set at the chosen average value and here also a random error term is added.

• the return on equity is also set at the chosen average value and here also a random error term is added.

For the calculations before and after shock the seed (in R) is set at the same value in order to get the same random returns before and after shock. Thereafter the total profit for the 100 projection years before and after shock are summarized and the rank of each sum is determined. With this method 10,000 ranked ’total profits before and after shock’ are created and they represent 10,000 decreasing (from the lowest to the highest rank) LAC DT values. In general the LAC DT will decrease when the sum of the profits is lower but there is a time dependency (due to restricted recovery periods for losses, see 3.2).

This method is chosen because the LAC DT itself is not calculated in R but in the excel model (building this in R can be subject for further research). SeeAppendix A -Description of the used modelsfor a description of the models.

6.7 Tax planning

For tax planning the assumption is made that the complete DTL can be realised at any moment in time. The DTL runs off according to a certain pattern but it can occur that the loss of a certain year cannot be fully recovered, while in another year there will be profit which will not be used to compensate losses.

Selling bonds (with DTL) will have an impact on the hedge with the liabilities but it is also assumed that the same bonds that are sold can immediately be bought back for the same price. The DTL will be realised and the hedge will be unchanged (the only thing that changes is the fiscal value of the bonds).

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7 Results of the LAC DT calculations for the example

port-folio

In the figures and tables in this chapter tax planning is abbreviated totp. All graphs show the LAC DT values for the percentiles of the distribution ine 1,000,000.

7.1 Description of the scenarios

The LAC DT is calculated (for the fictive entity) for the following scenarios:

Scen Cap inj Exp rate inj Hedge % Price hedge Exp red Return SD ret Alloc

1 750,000 2% 20% 80% 25% 5% 5% prop 2 750,000 2% 20% 80% 25% 5% 5% marg 3 750,000 5% 40% 80% 25% 5% 5% prop 4 750,000 0% 20% 80% 25% 5% 5% prop 5 650,000 0% 20% 80% 25% 5% 5% prop 6 1,000,000 2% 20% 80% 25% 5% 5% prop 7 1,500,000 5% 20% 80% 25% 5% 5% prop 8 1,100,000 2% 20% 80% 25% 5% 5% prop 9 650,000 2% 20% 80% 30% 5% 5% prop 10 350,000 0% 40% 80% 30% 5% 5% prop 11 650,000 2% 20% 80% 30% 5% 5% marg 12 350,000 0% 40% 80% 30% 5% 5% marg 13 600,000 2% 20% 80% 35% 5% 5% prop 14 300,000 0% 40% 80% 35% 5% 5% prop 15 600,000 2% 20% 80% 35% 5% 5% marg 16 300,000 0% 40% 80% 35% 5% 5% marg 17 500,000 2% 20% 80% 50% 5% 5% prop 18 200,000 0% 40% 80% 50% 5% 5% prop 19 500,000 2% 20% 80% 50% 5% 5% marg 20 200,000 0% 40% 80% 50% 5% 5% marg 21 750,000 2% 20% 80% 25% 5% 7% prop 22 800,000 2% 20% 80% 25% 3% 5% prop 23 0 0% 60% 75% 35% 5% 5% prop

Table 8: Assumptions per scenario

Explanation of the variables of the scenarios:

• Scen = Scenario. Scenario 1 is the base case scenario and the other scenarios are variants on this base case.

• Cap inj = Capital injection, which is the size of the capital injection (in e1,000) after the LAC DT shock has taken place.

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• Exp rate inj = Expense rate injection, which is the yearly percentage that has to be paid over the outstanding amount of the injection.

• Hedge % = Percentage of the hedge that will be put in an indemnity hedge. • Price hedge = the price of the indemnity hedge as percentage of the risk margin. • Exp red = Expense reduction, which is the percentage with which the expenses

will be reduced after LAC DT shock.

• Return = Average return on property and equity (equal before and after shock). • SD ret = SD of the return on property and equity (also equal before and after

shock).

• Alloc = Allocation which means the used capital allocation method for the LAC DT shock.

All settings per scenario are chosen in such a way that, for the deterministic calculation, the SII ratio in the future will stay above 100%. A further explanation of the scenarios (only the difference with the base scenario is mentioned) is given below:

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Scen Description 1 Base scenario

2 Base scenario with different allocation method (marginal instead of proportional) 3 Higher expenses for the capital injection and a higher longevity hedge

4 No expenses for the capital injection (suppose the injection is done by ’the mother’ who gets dividend as soon as the ratio allows it)

5 Also no expenses for the capital injection combined with a lower capital injection 6 Higher capital injection

7 Higher capital injection combined with higher expenses for the injection (a more realistic external expense rate)

8 No investment in property and equity after shock and therefor higher capital injection 9 Lower capital injection and higher expense reduction

10 Lower capital injection, no expenses for the injection, a higher longevity hedge and higher expense reduction

11 As scenario 9 but with marginal allocation 12 As scenario 10 but with marginal allocation

13 Lower injection and higher expense reduction than scenario 9 14 Lower injection and higher expense reduction than scenario 10 15 Lower injection and higher expense reduction than scenario 11 16 Lower injection and higher expense reduction than scenario 12 17 Lower injection and higher expense reduction than scenario 13 18 Lower injection and higher expense reduction than scenario 14 19 Lower injection and higher expense reduction than scenario 15 20 Lower injection and higher expense reduction than scenario 16 21 Higher SD for property and equity

22 Lower average return for property and equity

23 No capital injection, much higher longevity hedge and higher expense reduction Table 9: Description of the scenarios

The situation before LAC DT shock is the same for scenarios 1-20 and 23 (changes only concern recovery measures) but this is not the case for scenarios 21 and 22. For these two scenarios also the situation before LAC DT shock changes compared to scenario 1 (because the SD of property and equity changes).

7.2 Results of the calculations

7.2.1 Calculation of the deterministic and stochastic LAC DT for scenario 1 The results of the deterministic calculation of scenario 1 can be seen in the following table:

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Without tp Before shock After shock Difference

DTA 766 1,880 1,114

Non-recoverable DTA 41 1,128 1,087

Recoverable DTA 725 752 27

With tp Before shock After shock Difference

DTA 766 1,880 1,114

Non-recoverable DTA 41 1,038 997

Table 10: Deterministic calculation of LAC DT for scenario 1 (ine 1,000,000)

The deterministic LAC DT without tax planning of scenario 1 is onlye 27 million and tax planning increases this amount toe 117 million (the blue cells in table 10). The theoretical maximum of the LAC DT is the difference between the DTA before LAC DT shock and the DTA after LAC DT shock. which is e 1,114 million. This amount is equal to 25% of the BSCR + OR (see figure 5). Conclusion for scenario 1 is that the part of the shock that can be recovered according to the deterministic calculation is very limited.

For the stochastic calculation 10,000 simulations are calculated and for scenario 1 two graphs of the development of the LAC DT are drawn:

• one based on all 10,000 simulations

• one based on every 10th _{simulation of the ranked simulations (see paragraph} _6.6

for an explanation). This comes down to the use of 1,000 LAC DT values instead of 10,000 which saves a lot of time per calculation.

It appeared that both graphs gave the same result, which shows that the second method can be used. The result of this method is shown below:

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The following remarks can be made about this graph:

• There is no simulation where the maximum value is reached (there is always a non-recoverable part).

• The value of the LAC DT starts to decrease rapidly after the 40th _{percentile and}

reaches zero (without tax planning) around the 60th _percentile.

• The value of the 50th _{percentile lies around 200 (without tax planning). The}

deterministic value is 27 which is much lower. The reason that these values differ so much is that the projection is made for 100 years and in that case ’interest over interest’ has quite a large increasing effect on the value.

• The average value of the LAC DT is 362 without tax planning and 411 with tax planning.

To substantiate the calculation, the same calculation is done with the seed (in R) set at a different value. This calculation resulted in a comparable graph, which shows that the number of simulations (10,000) is big enough.

The difference between the deterministic and stochastic LAC DT is huge in this case and therefor the impact on the SCR and the SII ratio will also be huge as can be seen in the next table:

Stochastic Deterministic Without tp With tp Without tp With tp

LAC DT 362 411 27 117

SCR 4,093 4,044 4,428 4,338

Eligible OF 8,416 8,416 8,416 8,416

SII ratio 206% 208% 190% 194%

Table 11: Impact of LAC DT on SII ratio for scenario 1 (ine 1,000,000)

The values in this table are based on the values of the DTA and Own Funds shown in table 4 and the BSCR + OR (LAC TP is assumed to be zero) shown in table 5. The values of the SCR and Eligible OF are calculated as follows:

SCR = BSCR + OR − LACDT (10)

EligibleOF = OF − DT A + min(15% ∗ SCR, DT A) (11) See also paragraph 2.3 for more impact information.

7.2.2 Calculation of the stochastic and deterministic LAC DT for all scenarios The outcomes of the calculations of all the scenarios are shown in the following table:

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Stochastic Deterministic Scenario Without TP With TP Without TP With TP

1 362 411 27 117 2 324 359 0 0 3 410 487 600 689 4 633 698 737 779 5 454 521 375 489 6 706 744 779 779 7 702 723 779 779 8 0 0 0 0 9 335 407 0 100 10 399 469 307 412 11 304 396 0 21 12 371 445 207 327 13 429 513 247 359 14 465 553 417 532 15 398 491 158 287 16 448 530 340 472 17 744 841 715 832 18 687 775 633 757 19 738 832 719 821 20 691 780 635 746 21 372 415 27 117 22 81 138 0 0 23 342 402 178 277

Table 12: LAC DT for the different scenarios

In the next paragraph combinations of scenarios are compared and discussed.

7.3 Explanation and discussion of the results 7.3.1 Scenarios 1 and 2

The difference between scenario 1 and 2 is the allocation method. In table 12 can be seen that proportional allocation leads to a higher LAC DT (for all calculations). What strikes is that the deterministic value with and without tax planning for the marginal allocation is zero in both cases. It looks like tax planning has no impact.

However, there is an impact but since the LAC DT cannot be negative the value is zero in both cases. The following table shows what happens:

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Without tp Before shock After shock Difference

DTA 766 1,880 1,114

With tp Before shock After shock Difference

DTA 766 1,880 1,114

Table 13: Deterministic calculation of LAC DT for scenario 1 (ine 1,000,000)

The recoverable part after shock increases by tax planning but not enough to generate a (positive) LAC DT value.

For the same reason the line with the stochastic results with tax planning for scenario 2 in figure11also goes to zero (which is not the case for the comparable line of scenario 1).

Figure 11: Stochastic results for scenario 1 and 2

summarised the deterministic and stochastic values of the LAC DT for scenarios 1 and 2 are:

Stochastic Deterministic Differences

Without tp With tp Without tp With tp Without tp With tp

scen 1 362 411 27 117 335 294

scen 2 324 359 0 0 324 359

Table 14: LAC DT compared for scenarios 1 and 2

Loss absorbing capacity of deferred taxes : a stochastic approach