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International Association for the Study of Insurance Economics études et Dossiers

études et Dossiers No. 369 World Risk and Insurance Economics Congress

25-29 July 2010

Singapore

Working Paper Series ofThe Geneva Association

The Geneva Association - General Secretariat - 53, route de Malagnou - CH-1208 GenevaTel.: +41-22-707 66 00 - Fax: +41-22-736 75 36 - [email protected] - www.genevaassociation.org

International Association for the Study of Insurance Economics Études et Dossiers

Études et Dossiers No. 369

World Risk and Insurance Economics Congress

25-29 July 2010

Singapore

February 2011

Working Paper Series of The Geneva Association

© Association Internationale pour l'Etude de l'Economie de l'Assurance

The Geneva Association - General Secretariat - 53, route de Malagnou - CH-1208 Geneva Tel.: +41-22-707 66 00 - Fax: +41-22-736 75 36 - [email protected] - www.genevaassociation.org

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AnAnAnAnEmpiricalEmpiricalEmpiricalEmpirical AnalysisAnalysisAnalysisAnalysis ofofofof CapitalCapitalCapitalCapital RequirementsRequirementsRequirementsRequirements

FFFForororor Non-lifeNon-lifeNon-lifeNon-life InsurersInsurersInsurersInsurers ininininChinaChinaChinaChina

Haiyan WangProfessor of Finance

School of Economics and Management, Tongji UniversityShanghai, China

E-mail: [email protected]

Yuehao LinMaster Candidate

School of Economics and Management, Tongji UniversityShanghai, China

E-mail: [email protected]

AbstractAbstractAbstractAbstract

The aim of our research is to assess the risk-related capital requirements under thebackground of European Union’s Solvency II project. By referencing to severalquantitative methods and fitting data from major non-life insurers in mainland China,we hope to reach a pragmatic approach and possible results that can be applied byregulators for solvency supervision.

Risk-related capital in insurance sector mainly refers to two thresholds, i.e. minimumcapital requirement (MCR) and solvency capital requirement (SCR), between whichthe supervisory process is intervened. Current researches tend to define MCR as apercentage of SCR and put efforts on assessing SCR. We employ ratio model byfitting data on the non-life insurance industry level to calculate MCR.

To measure SCR, we first divide all risks into four major modules. Then differentmethodologies are developed for different risk modules. Specifically speaking, for themarket risk, we extend the Delta-Normal to measure risk-based capital requirementscovering six major investment assets in Chinese market; for the underwriting risk, aformula derived under a mixed-compound Poisson assumption. Note that parametersneeded to build a framework for this part are borrowed from previous studies. Thenfor the credit risk and operational risk, we refer to the standard approaches defined inBasel II for the banking industry.

Keywords:Keywords:Keywords:Keywords:MCR; SCR; Solvency II; Delta-Normal approach; Basel II

The Geneva Association________________________Etudes et Dossiers no. 369

Document free to download www.genevaassociation.org

1.1.1.1. IntroductionIntroductionIntroductionIntroduction

Solvency is the capital needed as a buffer for unexpected risks. The quantitativeassessment of capital requirements, as well as the proportional allocation of capitalhas been widely discussed among academia and the practice field. The EuropeanUnion has been engaged in Solveny II project for the insurance sector since 2004. On10 November 2009, final text of the Solvency II Directive was adopted by theEuropean Parliament and of the Council. In doing so, EU members are expected toamend their national laws to comply with the Directive in 2010.

However, in China, capital requirements for insurance companies are still orientedtoward the business volume, other than risk structures. For example, in case of a non-life insurer, the margin based on premiums are 18 percent on the first RMB100 millionand 16 percent above that amount. When based on claims, the margin required is 26percent on the first RMB70 million and 23 percent above the amount. Non-lifeinsurers need to take the highest amount of the above two as the minimum capitalrequirement. Apparently, this rule-based minimum capital measurement is adaptedfrom the EU Solvency I.

Empirical studies have proved the volume-based requirement improper. Table 1illustrates two typical results by Chinese scholars compared with China InsuranceRegulatory Committee (CIRC). From these figures, we can get a general idea abouthow much the MCR is under-required for non-life insurers.

TableTableTableTable 1:1:1:1: Comparison of MCR across the regulator and scholars in China

Nevertheless, the regulator is advancing its legislation during recent years. Of the mostsignificant was the implementation of a revised Insurance Law on Oct.1, 2009. In thislaw, Chapter Four saw the legal establishment of a need for required risk-basedsolvency for each insurance company. In context, our research is timely and practical.

Our research has two tasks. The first task is to assess the MCR using Ratio Modeltypically used by the two scholars previously mentioned. We make somemodifications to the model. The second task, taking the major part of this paper, is to

CIRC (2003-present) Su,Yu(2002) Zhan(2006)

The highest of1) 18% of grosspremiums(<RMB100mil.);else 16%2) 26% of three-year averageincurred claims(<RMB70mil.); else 23%

Either of1) 30% of grosspremiums

2) 40.3% of netclaims

The highest of1) 18% of grosspremiums(<RMB100 mil.);else 16%2) 30% of three-yearaverage incurredclaims(RMB60 mil.); else27%



find a method to calculate the SCR, largely by referring to quantitative measurementsin Solvency II and recommendations proposed by relevant institutions (e.g. IAA, 2004)and scholars (e.g. Sandström, 2006; Eling et al, 2009 ). For the SCR, we divide thecalculation into four sub-parts, where the market risk module, the underwriting riskmodule, the credit risk module and the operational risk module are separatelyanalyzed before they are aggregated together by a predefined formula.

2.2.2.2. ModelModelModelModel FrameworkFrameworkFrameworkFramework

2.1 MCR: Ratio Model

There are actually several kinds of models to assess the solvency requirements, ofwhich the ruin theory, tail value at risk, and expected policy-holder deficit arecommonly proposed or used by scholars (Eling et al, 2009). However, since thosemodels fund on the stochastic process, which is very complex, we refer to a muchmore predigested Ratio Model. Su and Yu (2002) is the first to extend Ratio Model onsolvency margin design to the case in China. By referring to it, we conclude a similarone, but make some improvements by adding weights to most variables when fittingdata to this model in part 3.

The probability of insolvency for an insurer at ε is given by

(1)1( )t t t p tP cP L P s P ε−+ > + =

Or

(2)1( )t t t l tP cP L P s L ε−+ > + =

Where, stands for net premium income in t year; denotes net claim amount;tP tL

is cost to net premium income ratio; and are minimum solvency margin ratiosc ps ls

(here, we consider them equal to MCR ratios)

,1

pt

MCRsP−

=1

lt

MCRsL −

=

.Assume that

, ,1

1

t tp

t

P PkP

−

−

−= 1

1

t tl

t

L LkL

−

−

−= t

tt

LlP

=

We get two transformations by putting the assumed ones into Eq.(1)(2) separately:

(3)( 1 )1

pt

p

sP l c

kε> + − =

+

And



(4)(1 )(1 )( )1

lt

l l

c kP lk s

ε− +

> =+ −

By fitting data of net claim ratio , we conduct interval estimation to get thetl

according to Eq.(3)(4). Then, we obtain the ratios as follows:*tl

(5)*( 1 ) (1 )p t ps l c k= − + × +

And

(6)*

*

(1 )( 1 )l tl

t

k l cs

l+ − +

=

Making a slight transform, we write

MCR based on net premium income: (7)*1( 1 ) (1 )total t p tMCR l c k P−= − + × +

MCR based on net claim amount: (8)*

1*

(1 )( 1 )l ttotal t

t

k l cMCR L

l −

+ − +=

2.2 SCR: Aggregation Formula

There has been a variety of discussion in academia and practice regarding approachestoward the aggregation of different risks. In quantity impact studies (QIS), CEIOPSadopts a bottom-up or “modular approach” for the SCR standard model. For practicalreasons, we also employ the modular approach. The total solvency capital requirement(SCR) can be expressed as (CEIOPS, 2008)

( , )total or i j i j ori j

SCR BSCR C C C C C Cρ= + = +∑∑

Where represent SCR in kinds of risk modules, excluding operational risk module;iC

is short for basic SCR, largely dominating the total SCR. is particularlyBSCR orC

referred to operational risk. denote the correlation factors between risk( , )i jC Cρ

modules, through which diversification effects are taken into account. If all risk

modules move in the worst direction simultaneously, i.e. , we obtain the( , ) 1i jC Cρ =

maximum ; if risk modules are all independent of eachmax i j ori j

SCR CC C= +∑∑

other, i.e. if i≠j, we arrive at the minimum .( , ) 0i jC Cρ = 2min i or

iSCR C C= +∑



Actually, assessing correlation factors is never an easy task. Sophisticated approachestowards correlation measurement include complex simulation model incorporating avariety of sources of variation (Panjer, 2001). Anyway, the correlations must be inbetween zero and one. According to QIS4 report (see CEIOPS, 2008, p173), in mostcountries the diversification effect on the BSCR level is between 15% and 35% fornon-life undertakings. To practice prudential supervision, in our paper we assume a15% diversification effect on the BSCR level. Dividing risks into four major kinds:market risk, underwriting risk, credit risk and operational risk, we then get ourbenchmark:

(9)85%( )total mr ur cr orSCR C C C C= + + +

2.2.1 Market Risk: Delta-Normal Approach

Market risk will be approximated by the investment risk. This risk is a result from thevolatility inherent in the market value of the insurer’s assets. We use Value at Risk(VaR) method to measure capital requirements for each asset category, and then sumthem up. There are three mainstream VaR methods, i.e. Delta-Normal, HistoricalSimulation and Monte Carlo simulation. We choose Delta-Normal method for itssimplicity, as well as its accuracy justified by a reality check to be carried out later on.

According to Jorion (2005), Delta-Normal method assumes that portfolio assets arelinear and risk factors are jointly normally distributed. The formula can be express as:

'covVaR_ratio= ( )p i ix xασ α= ∑

Where, is the covariance matrix of the risk exposures , denotes thecov∑ ix pσ

portfolio standard deviation, and is the quantile in normal standard distributions.α

Instead of calculating a portfolio, we employ Delta-Normal to compute the risk-basedcapital ratio for each single asset, and sum up individual VaRs as the total capitalrequirement covering the market risk. Another important calibration is that in case ofnonsymmetrical distributions, we provide an alternative approach to calculate thequantile. The percentile of loss distribution of each investment assets is set toε=0.5%.For normal distributions, the quantile atε-percentile is =α=2.575 while forκnonsymmetrical distributions, the normal power approximation (NP) is used (Ramsay

and Colin, 1991) to calculate the quantile: . Here is the2( 1) / 6X Y Yγ= + − X

standardized variable of random variable X. And Y ~ N (0, 1) is a standard normalvariable. Accordingly, for distributions X, theε-percentile is:

, if the variable is a nonsymmetrical distribution; (10)2( 1) / 6κ α γ α= + −

, if the variable is a normal distribution; (11)κ α=

So for each investment asset, (12)_ i i iRisk ratio κ σ=



As for standard deviations , we refer to an Exponentially WeightedMovingiσ

Average (EWMA) generated by RiskMetricsTM (1996). In EWMA, a decay factor, ,λ

exists to give a much higher weight on the newest data reflecting market volatility, .2tr

The decay factor can be estimated by solving the following formulae:λ

, (13)

2 2 2

1

( )T

t tt

rMin

T

σ=

−∑1,2,...,T n=

Subject to , (14)2 2 2 2 2 21 2(1 )[ ... ]N

t t t t t Nr r r rσ λ λ λ λ− − −= − + + + + 1,2,...N = →∞

By transforming Eq.(14), we can use the following iteration formula to get the standarddeviation of the volatility of the assets:

(15)2 21(1 )t t trσ λ λσ −= − +

Assuming that there are kinds of investment assets with corresponding standardm iA

deviations , we get the total VaR (equal to , the SCR covering market risk):iσ mrC

(16)1 1

_m m

mr i i i i ii i

C VaR Risk ratio A k Aσ= =

= = × = × ×∑ ∑

2.2.2 Underwriting Risk: Mixed-compound Poisson

To measure the underwriting risk, we firstly classified business into six lines ofbusiness (LOBs) of which the financial statuses are disclosed in asset liability balancesheets by most insurers. They are 1) Motor; 2) Property; 3) Marine, aviation, andtransport; 4) General liability; 5) Accident and health; 6) Other.

For each LOB, the risk model we employ has the features proposed by Sandström(2006) that 1) the random claim count follows a Poisson distribution; 2) the randomclaim sizes are independent of each other and follow the same distribution; 3) the totalloss is a mixed-compound Poisson distributed variable. Using classical actuarialformulas, a certain percentile of the loss ratio distribution for each line can be deduced.An alternative method is TVaR given the mean and the variance of the insurer’s totalloss following the lognormal distribution (IAA, 2004).

Using the Poisson distribution to model claim counts is fairly standard assumption inthe actuarial theory of risk. Here is the standard model to calculate the SCR forunderwriting risk following previous assumptions:



6 6 62 2

ur1

C [(1 ) ] ( ) cov( , ) ( ) ( )i sti i i i j i ji i j

b L L L L Lα β σ= ≠

= + + Ε + Ε Ε∑ ∑∑

Where: and are the structure coefficients ( ), depending onib stiβ 0,0 1i stib β≥ ≤ ≤

how the reinsurance cuts the gross claims; and are the variance and2iσ cov( , )i jL L

covariance of the loss ratios respectively. is for the net claim amount of each( )iLΕ

LOB.

In this paper, from the very beginning we had exclude reinsurance. All of our analysisis based on net premium income and net claim amount and cost with reinsurance stuffexcluded. So we make a slight change to the formula, and assume a comparativelysimple one:

(17)6 6 6

2 2ur

1

C ( ) cov( , ) ( ) ( )i i i j i ji i j

L L L L Lα σ= ≠

= Ε + Ε Ε∑ ∑∑

Usually, variances and covariances are all predefined by regulators. Considering this,we apply data for variances taken from Rantal(2004) and data for covariances takenfrom Bateup and Reed(2001) as standards to calculate that of net claim amounts ofeach LOB. The reason we use their data is that they prove to be reasonable in thesolvency analysis by Sandström (2006). Non-life insurers only need to have the netclaim amount of each LOB.

2.2.3 Credit Risk and Operational Risk: Basel II Alike

Similar to Basel II, Solvency II bears a three pillar structure: quantitative aspects,qualitative aspects and market discipline. Although Basel II is different from SolvencyII project for insurance, it provides some source of inspiration as regards design, aswell as incorporates the latest thoughts of banking supervisory into Solvency II.(MARKT, 2001). In this sense, we begin to wonder if it is applicable to use theapproaches defined in Basel II to measure the capital requirements for insurancecompanies. This applicability had already been justified by the idea of arbitrageavoidance between the banking and insurance sectors (Sandström, 2006). As well asdue to lack of enough data on credit and operational events, our analysis includes asignificant degree of reference to the standardized approaches defined in Basel II.

The standardized approach for quantifying credit risk can be expressed as:

(18)1

0.08cr i ii

C r A=

= ∑

In which, is the value of exposed asset; is corresponding predetermined riskiA ir



weight. We extract the corresponding assets and risk weights to be included in ourcalculation for a typical non-life insurer according to Basel II. They are shown in Table2.

TableTableTableTable 2:2:2:2: Risk weights extracted from Basel II for quantifying the credit risk

Note: Risk weight of the account receivable for an insurer is the same as the one of past-due loanson the balance sheet of a bank.Source: based on BIS (2004)

For operational risk, the standard approach calibrated from Basel II can be written as:

(19)3

1 1

1 [ ]3 j

n

or j Li j

C Pβ= =

= ∑ ∑

This means, the capital requirement is calculated as the average of total three years’ netpremium income across each LOB with an assigned factor. As Sandström put it, the

factor serves as a proxy for the industry-wide relationship between the operationaljβ

risk for a particular LOB and the aggregate level of net premium income, for thatjL

P

LOB. Usually, is a predetermined parameter.jβ

3.3.3.3. EmpiricalEmpiricalEmpiricalEmpirical AnalysisAnalysisAnalysisAnalysis

3.1 Calculating MCR

Following previous studies (Su and Yu, 2002; Zhan, 2006), three premier inputs are

used in this study: net premium income , net claim amount and cost . WetP tL C

Assets and Ratings Risk weights

Bank and cashTreasury bondsCorporate bondsFinancial bondsInvestment fundsEquitiesMonetary investments

Residential propertyCommercial real estateAccount receivable

Other assets

---AAA to AA-AAA to AA-AAA to AA-AAA to AA-A+ to A-AAA to AA-

---------

---

0020%20%20%50%0

35%100%100%

100%



assemble data on those three for all non-life insurers whose reports are published inYearbook of China’s Insurance and whose net premium income exceeds RMB150million on average. The sample period is from 2003 to 2008. Data are listed in Table

3. Constants in Eq.(7)(8), the growth rate of net premium income , the growth ratepk

of net claim amount and the cost ratio , are measured by taking the weightedlk c

average of companies’ market share. Summary statistics of , and are alsopk lk c

reported in Table 3.

TableTableTableTable 3:3:3:3: Summary data on net premium income, cost and net claim amountNet Premium Income

PICC Pacific PingAn United Huatai TaiPing TianAn Continent08 77372.33 21370 22107.18 17204.64 1865.19 3547.94 4142.52 5803.4507 74889 18377 18005.42 15051.55 2073.13 2909.09 3518.25 5225.9206 61037 13821 13288.02 13214.78 1028.01 1629.29 4385.96 3811.1805 53440.36 11379.5 9293.04 8983 771.37 1150.88 4532.75 2929.1404 56299.81 9724.14 7375.23 5798.71 677.79 733.91 4507.67 1368.1103 46969.56 7925.8 5639.13 1651.81 579.28 382.43 1707.04 ---

DaZhong YongAn Alltrust AnBang MingAn AIU TMN MS08 695.99 4948.21 1656.7 4711.04 805.6 474.49 411.09 293.7107 976.89 4385.71 1066.96 5562.96 333.88 430.85 372.03 207.2106 1191.12 2988.13 237.09 3427.1 123.65 315.46 310.43 187.6505 860.06 1611.15 124.68 961.36 124.69 127.68 258.87 180.7104 795.27 1680.2 --- --- --- 104.2 227 126.603 777.01 655.76 --- --- --- 78.31 141 71.31

08 07 06 05 04 03 is :0.23196pkE&C 2906.89 2861.8 2234.27 1803.05 1323.13 843.14

Sunshine 4025.83 3599.63 --- --- --- ---

CostPICC Pacific PingAn United Huatai TaiPing TianAn Continent

08 21782.7 7554 7904.76 7124.12 1015.22 1748.53 2164.27 2584.5707 22909 6777 6333.49 5459.01 1130.12 1335.92 1522.46 2392.5306 17846 4873 4137.05 4382.68 520.3 730.28 1833.69 1563.6105 14772.66 3700.01 2528.61 3010 338.83 481.77 1537.22 1070.2504 12999.67 2978.89 1885.58 1790.13 280.14 318.76 1430.54 495.3303 12343.73 2554.6 1458.19 508.54 359.81 216.74 562.6 ---

DaZhong YongAn Alltrust AnBang MingAn AIU TMN MS08 484.06 2206.14 671.26 2156.45 506.26 290.37 161.06 96.807 463.05 1714.43 430.15 2659.11 197.13 236.75 136.24 73.4806 497.04 1128.46 123.22 1496.51 63.46 141.23 100.77 56.8405 285 562.55 35.3 308.45 48.51 47.24 73.09 44.07



Note: all the absolute data in this paper are in millions of RMB; TMU is short for Tokio Marine &Nochido Fire; MS, Mitsui Sumitomo; E&C, Export & Credit.Source: based on Yearbook of China’s Insurance, 2004-2009.

As to net claim ratio , it depends. In an OECD report, Campagne (1961) introducedtl

Ratio Model for the first time to calculate the minimum solvency margin to netpremium income ratios for European Community members, and assumed the netclaim ratio to be normally distributed. In 1980, De Wit et al conducted similarresearch with Ratio Model but under a different assumption that net claim ratiofollowsβ-distribution. There were also other assumptions like net claim ratiolognormal distributed.

In our study, we leave the distribution of net claim ratio to be decided by historicaldata, and find that it follows the normal distribution. See Figure 1. Skewness/Kurtosistests here accept normality. Net claim ratio appears significantly normal in skewness(Pr=0.128>0.00005), kurtosis (Pr=0.63>0.00005), and in both statistics consideredjointly(Pr=0.2693>0.00005). So for a normal distributed variable, net claim ratio isapproximated as (2.575σ+μ) at 99.5% percentile. Here we get the net claim ratio

=0.924145.*tl

04 233.61 569.93 --- --- --- 30.6 71 36.703 248.43 167.91 --- --- --- 25.16 47 23.71

08 07 06 05 04 03 is 0.310622cE&C 409.96 349.38 212.4 413.31 312.5 199.3

Sunshine 2017.01 1631.06 --- --- --- ---

Net ClaimAmountPICC Pacific PingAn United Huatai TaiPing TianAn Continent

08 54845.52 11854 12644.71 11099.25 799.18 1782.83 3618.56 3372.7507 40738 8404 8982.01 10843.69 492.16 1009.06 2857.11 2270.7506 37377 6894 6660.23 6231.14 414.39 692.67 2850.64 1472.7305 35055.83 5707.54 4246.96 3866 375.48 453.01 2330.35 1112.704 34828.02 4440.55 3423.17 1767.45 344.12 226.4 1265.11 161.0903 27668.39 4567.25 3219.62 466.1 370.44 139.48 426.36 ---

DaZhong YongAn Alltrust AnBang MingAn AIU TMN MS08 653.84 2862.17 628.65 3002.27 246.73 138.25 187.93 85.7707 698.87 2162.55 261.29 2224.67 69.4 87.33 129.71 72.0706 690.32 1247.95 32.76 773.7 34.29 63.82 128.17 114.6205 582.93 978.59 15.56 27.92 39.17 23.19 92.27 33.8804 511.26 464.24 --- --- --- 20.06 44 21.3503 329.79 193.86 --- --- --- 17.46 38 12.9

08 07 06 05 04 03is :0.395514lk

E&C 1593.21 92.81 605.22 771.42 780.84 840.44

Sunshine 2014.68 1075.67 --- --- --- ---



FigureFigureFigureFigure 1:1:1:1: Histogram, quantile-normal plot and normal test of the net claim ratio

0.5

11.

52

Den

sity

0 .2 .4 .6 .8 1Net_claim_ratio

.138

1754

.427

8417

.720

4368

0.2

.4.6

.81

Net

_cla

im_r

atio

.4302544 .7457411.1147677

0 .2 .4 .6 .8Inverse Normal

Grid lines are 5, 10, 25, 50, 75, 90, and 95 percentiles

Net_claim_~o 99997777 ....4444333300002222555544444444 ....1111999911118888000022223333 ....0000222299990000444422222222 ....9999999966667777999977777777 Variable Obs Mean Std. Dev. Min Max

Net_claim_~o 0000....111122228888 0000....666633330000 2222....66662222 0000....2222666699993333 Variable Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 joint Skewness/Kurtosis tests for Normality

Now we have net claim ratio =0.924145 at 99.5% percentile, cost ratio =*tl c

0.310622 and growth rate of net premium income =0.23196, growth rate of netpk

claim amount =0.395514.According to Eq(5)(6)(7)(8), we get the minimal capitallk

requirement ratios based on both net premium income and net claim amount, i.e.

=0.289224,*( 1 ) (1 )p t ps l c k= − + × + 128.92%total tMCR P−= ×

=0.354512,*

*

(1 )( 1 )l tl

t

k l cs

l+ − +

= 135.45%total tMCR L −= ×

Compared with the previous studies (see Table 1), the value of MCR ratios in ourresults are in the middle. One of the reason lies in that constants in the formulas arederived from the average weighted ones, which means big companies with better riskmanagement and financial statuses take larger parts in the overall calculation. Thenewest data also count.

3.2 Calculating SCR

3.2.1 Calculating SCR of Market Risk

From the balance sheets of typical non-life insurers in China, we can conclude thatinvestment risk lies mainly in six kinds of assets, i.e. treasury bonds, corporate bonds,financial bonds, investment funds, equities and monetary investments. The following



table shows asset categories and corresponding market indices that we include. Notethat the market indices may not necessarily correspond to the actual investment of thenon-life insurer under consideration, but they can act as general criteria.

TableTableTableTable 4:4:4:4: Selected market index for six kinds of assets on balance sheet

Notes: SSE is short for Shanghai Stock Exchange; CSI is short for China Securities Index

For each selected market index, we extract daily returns between January 1st 2009 andDecember 31, 2009. The daily returns are measured by logarithmic return rate, i.e.

, with representing the closing price of market index. In order to1ln lnt t tr p p −= − tp

find the decay factor and then standard deviation incorporated in Eq.(13)(14),λ σwe do programming in EXCEL packages. The results are shown in columns 2 and 3 ofTable 5. We also transform the standard deviations of daily returns into annualizedones so as to calculate SCR for a time horizon of one year.

TableTableTableTable 5:5:5:5: Parameters for calculating VaR at a 99.5%confidence level

In Table 5, the last two columns list out each asset’s risk ratio. To derive those ratios,we actually do normality check for each asset. We find that for corporate bonds,investment funds and equities, the return rate are normally distributed, which meansthe quantile at a 99.5% confidence level; for treasury bonds, financial bondsκ α=and monetary investments, the quantiles are calibrated by Normal Power formulapreviously introduced.(See Eq.(10)). Details of the normality check are shown inAppendix A.

Asset category Market index(SSE Market Code or ID)

Treasury bondsCorporate bondsFinancial bondsInvestment fundsEquitiesMonetary investments

SSE T-Bond Index（000012）SSE Corporate Bond Index（000013）CSI Financial Bond Index (Bloomberg ID: CSICFBON)SSE Fund Index（000011）SSE Composite Index (000001)Interest Rate in Inter-Bank Repo Market (R007)

Asset class

Decayfactor( )λ

StandardDeviatio

n(σdaily)

AnnualSD

(σannual)

Risk ratio(normal,

)f ασ=

Risk ratio

(NP, )f kσ=

Bank and cash -- 0 0 0 0Treasury bonds 0.8445 0.000939 0.014669 --- 0.0255139Corporate bonds 0.8870 0.000926 0.014461 0.037236 ---Financial bonds 0.9051 0.000873 0.013633 --- 0.0166781Investment funds 0.9116 0.016994 0.265462 0.683565 ---Equities 0.9082 0.018816 0.293921 0.756846 ---Monetary investments 0.8780 0.047376 0.749080 --- 1.2553017



As previously mentioned in Part 2, one reason that we choose Delta-Normal approachto calculate capital requirements is due to its accuracy. Here we carry out a realitycheck to justify that. One pragmatic way is to employ the Kupeic LR test (See alsoWang, 2006). The Kupeic LR test examines the null hypothesis using a likelihood ratiotest. If the approach is correctly specified, the number of failures is allowed to bevaried within certain fields whose upper and lower limits are listed in Table 6.

TableTableTableTable 6:6:6:6: Confidence regions of non-rejection under Kupeic LR test

Notes: N represents the number of failures in sample TSource: Kupeic (1995)

To express reality check in formula, the number of failures can be defined as

, where if ; and if ; is total days1

N CT

tt=

=∑ C 1t = t tr VaR< C 0t = t tr VaR≥ T

accounted. Following this idea, we do programming in EXCEL packages to realize thecheck. Table 7 lists out the results. From the table, we see that Delta-Normal approachis statistically appropriate to be employed to calculate VaR of four of the six kinds ofassets. For the other two kinds, equities and monetary investments, the number offailures exceed the field <1,11>. Two return rates of equities and one of monetaryinvestments are lower than corresponding risk value at 99% confidence level.However, we consider one or two exceptionally low return rates acceptable in times ofthe disastrous financial crisis lasting from late 2007 to even now. In our view, Delta-Normal approach is appropriate for calculating risk based capital requirements (orcalled SCR herein). Table 7 shows the failed number. To see exactly how the fewreturn rates exceed corresponding risk value at 99% confidence level, please go toAppendix B.

TableTableTableTable 7:7:7:7: Reality check with 99% confidence level in Sample T≈510

Note: data are collected from January 1st 2008 to December 31 2009; 99% confidence level is setin order to do comparison with Kupeic LR test.

VaR Confidence Level T=255 T=510 T=100099%97.5%95%92.5%90%

N<72<N<126<N<2111<N<2816<N<36

1<N<116<N<2116<N<3627<N<5138<N<65

4<N<1715<N<3637<N<6559<N<9281<N<120

Treasurybonds

Corporatebonds

Financialbonds

Investment funds

Equities Monetaryinvestments

Number offailures (N)

8 8 6 10 12 11

Modelvalidation

Yes Yes Yes Yes No No



Not only for calculating SCR of market risk, but also for remainder of the paperanalyzing SCR of underwriting risk, credit risk and operational risk, we will use datafrom a Chinese non-life insurer—PICC Property and Casualty CompanyLimited(PICC).

TableTableTableTable 8:8:8:8:Assessment of SCR covering market risk for non-life insurer PICC

Source: based on Balance Sheet 2009 of PICC; risk ratios are in accordance with Table 5.

3.2.2 Calculating SCR of Underwriting Risk

Primarily due to constraints imposed by the data available for this analysis, we applya borrowed variance-covariance matrix to do the calculation. The net claim amounts byLOBs are directly fetched in non-life insurer PICC’s financial reports. FollowingEq.(18), we arrive at a result that SCR covering the underwriting risk is RMB31100.28million.

TableTableTableTable 9:9:9:9: Covariances, variances and net expected loss for LOBs

Asset categories Market value Risk ratio(VaR99.5%)

Bank and cash.Treasury bondsCorporate bondsFinancial bondsInvestment fundsEquitiesMonetary investments

Other assets

TOTAL

32,14321,71816,96519,7756,7827,90110,947

49,152

165,383

00.02551390.0372360.01667810.6835650.7568461.2553017

--

--

Eq(16): = RMB 25873.19 million1

_m

mr i ii

C Risk ratio A=

= ×∑

LOBs Motor ||Property||MAT|| GL || AH ||Other σ2 E(L)

MotorPropertyMATGeneral liabilityAccident and healthOther

0.01 00

0.020.02

0

000

0.02

0.050.060.080.090.05

0.050.060.10.130.050.9

49,1363,8691,0902,1012,0896,232

Eq.(17) = RMB 31100.28 million6 6 6

2 2ur

1

C ( ) cov( , ) ( ) ( )i i i j i ji i j

L L L L Lα σ= ≠

= Ε + Ε Ε∑ ∑∑



Source: based on Sandström (2006) [data for variances taken from Rantal(2004); data forcovariances taken from Bateup and Reed(2001)]; Financial Report 2009 of PICC

3.2.3 Calculating SCR of Credit Risk and of Operational Risk

Following the methods introduced in part two, we can easily get the results byextending the Eq.(18)(19) to the case of Chinese non-life insurer PICC. The SCR ofcredit risk and SCR of operational risk are separately listed below.

TableTableTableTable 10:10:10:10:Assessment of SCR covering credit risk for non-life insurer PICC

Source: Balance Sheet 2009 of PICC; risk weights are in accordance with Table 2.

TableTableTableTable 11:11:11:11:Assessment of SCR covering operational risk

Assets and Values iA Risk weights ir

Cash etcTreasury bondsCorporate bondsFinancial bondsInvestment fundsEquitiesMonetary investment

Residential propertyCommercial real estateAccount receivable

Other assets

TOTAL

32,14321,71816,96519,7756,7827,90110,947

12,282706

17,170

18,994

165,383

00

20%20%20%50%0

35%100%100%

100%

---

Eq.(18): = RMB 4305.888 million1

0.08cr i ii

C r A=

= ∑

Net premium income of each LOB 2009 2008 2007 Factor iβ

MotorPropertyMATGeneral liabilityAccident and healthOther LOB

70,7006,0052,0183,2232,6778,673

60,5535,8592,4552,9582,4316,866

53,2735,6892,2712,5341,8383,123

0.010.010.010.010.010.01



Source: the factors are based on Sandström (2006) [original from Rantal(2004)]; financial reports2009-2007 of PICC

4.4.4.4. OverallOverallOverallOverall ResultsResultsResultsResults andandandand CCCConclusiononclusiononclusiononclusion

As to approaches for calculating SCR, there are no concrete forms similar to thosedefined by NAIC for all non-life insurers. What we try to achieve is to design anindividually-oriented model, much like the internal model defined by Solvency II.However, the principles and methods employed are plausible to most insurers. Sincethere is hardly any research which has been conducted for calculating SCR in China,we compare the SCR with the MCR previously concluded.

Take the non-life insurer PICC in year 2009 for example:

128.92%total tMCR P−= ×

22376.27=

85%( )total mr ur cr orSCR C C C C= + + +

85%(25873.19 31100.28 4305.88) 810.48= + + +

51.18% tP= ×

52897.95=

From the two data, we see the amount of SCR is 2.36 times higher than the amount ofMCR according to our comprehensive approach. If expressed in concrete formulae, theMCR is 28.92% of the previous year’s net premium income; while the SCR is 51.18%of the year’s net premium income. In this sense, our result is in accordance with manypractices conducted by several regulatory authorities in EU countries, which state thatMCR is in proportion with SCR.

However, due to lack of data to estimate parameters in several sub-modules, ourapproach needs further analysis, especially on the following aspects: take reinsuranceinto consideration; quantify diversification effect for market risk; parameters, forexample the correlation factors and risk weights, to be predefined should be set oncountry level, not by referring to experiential data fitting for other countries.

Net fluctuation of unearnedpremium reserve

10,053 3,749 6,161 ---

Total 103,349 77,373 74,889 ---

Eq.(19): = RMB 810.4867 million3

1 1

1 [ ]3 j

n

or j Li j

C Pβ= =

= ∑ ∑



References:References:References:References:[1] Bateup, R. and I. Reed. Research and Data Analysis Relevant to the Development

of Standards and Guidelines on Liability Valuation for General Insurance. IAAReport, 2004

[2] BIS. A Revised Framework, Basel Committee on Banking Supervision, Bank forInternational Settlements. 2004

[3] Campagne. Standard minimum de solvability, applicable aux enterprisesd’assurances. OECD Report. 1961.

[4] CEIOPS-SEC-82/08. CEIOPS’ Report on its fourth Quantitative Impact Study forSolvency II, Public Report, 2008

[5] Commission of the European Communities. Amended Proposal for a Directive ofthe European Parliament and of the Council on the taking-up and pursuit of thebusiness of Insurance and Reinsurance (Solvency II). COM, 2008

[6] Eling, M. et al. Minimum standards for investment performance: A newperspective on non-life insurer solvency. Insurance: Mathematics and Economics,2009

[7] Hamilton, L C. Statistics with STATA (Version 9). Thomson, 2005[8] IAA. A Global Framework for Insurer Solvency Assessment. International

Actuarial Association, 2004[9] Jorion, P. Value at Risk (Chinese Edition). CITIC Publishing House. 2005[10]J. P. Morgan. RiskMetricsTM Technical Document. Fourth Edition, 1996[11]Kupeic, P. Techniques for verifying the accuracy of risk measurement models.

Journal of Derivatives, 1995[12]MARKT. Solvency II: Review of the Work, MARKT/2518/02. EC DG Internal

Market, 2002[13]NAIC Staff. The NAIC Insurance Regulatory Information System. NAIC

Research Quarterly, 1998[14]Panjer, H. Measurement of Risk, Solvency Requirements and Allocation of

Capital within Financial Conglomerates. SOA, Working Paper, 2001[15]Ramsay A, Colin. A Note on the Normal Power Approximation. ASTIN Bulletin,

1991[16]Rantala, J. Illustrations of Magnitude of Some Parameters in the Standard

Approach. Working Paper, 2004[17]Sandström, A. Solvency: Models, Assessment and Regulation. Chapman &

Hall/CRC, Taylor & Francis Group, 2006[18]Su Fang, Yu Ziyou. Empirical Analysis on Solvency for Non-life Insurance

Industry of China. The Journal of Quantitative and Technical Economic. 2002[19]Wang Tingting. Application of VaR to measure risk based capital of China P&L

insurance companies, Graduate Thesis, Hunan University, 2006[20]Wirch J, Hardy M, A synthesis of risk measures for capital adequacy. Insurance:

Mathematics and Economics, 1999[21]Zhan, Mengya. Empirical Analysis and Reasoning on Margin of Solvency of Non-

life-insurance Industry of China. The Journal of Theory and Practice of Financeand Economics. 2006



AppendixAppendixAppendixAppendixA:A:A:A:Normality check for assets bearing investment risk.

020

040

060

080

0D

ensi

ty

-.006 -.004 -.002 0 .002 .004T_bonds_return

-.001

3217.000

0817.0

0149

5

-.006

-.004

-.002

0.0

02.0

04T_

bond

s_re

turn

.0000382 .0016051-.0015288

-.002 0 .002 .004Inverse Normal


T_bonds_re~n 0000....000000000000 0000....000000000000 55553333....11115555 0000....0000000000000000 Variable Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 joint Skewness/Kurtosis tests for Normality

T_bonds_re~n ....0000000000000000333388882222 ....0000000000009999555522226666 9999....00008888eeee----00007777 22224444....99994444888866665555 ----....888899990000555511117777 11110000....11113333000099998888 variable mean sd variance cv skewness kurtosis

For treasury bonds, Skewness/Kurtosis tests reject normality. The return rate is not significantlynormal in skewness (Pr=0.128>0.00005), kurtosis (Pr=0.63>0.00005), and in both statisticsconsidered jointly(Pr=0.2693>0.00005).

020

040

060

0D

ensi

ty

-.004 -.002 0 .002 .004Corp_bonds_return

-.001

439.

0000

745.0

0164

81

-.004

-.002

0.0

02.0

04C

orp_

bond

s_re

turn

.0000219 .0015615-.0015177

-.002 0 .002Inverse Normal


Corp_bonds~n 0000....777766665555 0000....000000003333 8888....11115555 0000....0000111177770000 Variable Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 joint Skewness/Kurtosis tests for Normality

For return rate of corporate bonds, Skewness/Kurtosis tests accept normality.



020

040

060

080

0D

ensi

ty

-.004 -.002 0 .002 .004Fin_bonds_return

-.001

5464.0

0007

78.0

0116

5

-.004

-.002

0.0

02.0

04Fi

n_bo

nds_

retu

rn

-.0000222 .0014211-.0014656

-.002 -.001 0 .001 .002Inverse Normal


Fin_bonds_~n 0000....000000000000 0000....000000000000 77773333....44447777 0000....0000000000000000 Variable Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 joint Skewness/Kurtosis tests for Normality

Fin_bonds_~n ----....0000000000000000222222222222 ....0000000000008888777777775555 7777....77770000eeee----00007777 ----33339999....44447777777744447777 ----1111....444444440000333300007777 11110000....44442222888822229999 variable mean sd variance cv skewness kurtosis

For return rate of financial bonds, Skewness/Kurtosis tests reject normality.

010

2030

40D

ensi

ty

-.05 0 .05Inv_funds_return

-.027

3858

.002

8736

.028

5421

-.05

0.0

5In

v_fu

nds_

retu

rn

.0025396 .0307757-.0256964

-.04 -.02 0 .02 .04Inverse Normal


Inv_funds_~n 0000....000000009999 0000....000000005555 11112222....55556666 0000....0000000011119999 Variable Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 joint Skewness/Kurtosis tests for Normality

For return rate of investment funds, Skewness/Kurtosis tests accept normality.



05

1015

2025

Den

sity

-.1 -.05 0 .05Equities_return

-.032

409

.004

3221.0

2955

8

-.1-.0

50

.05

Equ

ities

_ret

urn

.0022853 .0335697-.0289992

-.05 0 .05Inverse Normal


Equities_r~n 0000....000000000000 0000....000000003333 11119999....66668888 0000....0000000000001111 Variable Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 joint Skewness/Kurtosis tests for Normality

For return rate of equities, Skewness/Kurtosis tests accept normality.

05

1015

Den

sity

-.4 -.2 0 .2Mon_inv_return

-.066

7175

-.000

7573.081

8648

-.4-.2

0.2

Mon

_inv

_ret

urn

.001826 .0820488-.0783967

-.2 -.1 0 .1 .2Inverse Normal


Mon_inv_re~n 0000....000000000000 0000....000000000000 77770000....77770000 0000....0000000000000000 Variable Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 joint Skewness/Kurtosis tests for Normality

Mon_inv_re~n ....000000001111888822226666 ....000044448888777777772222 ....0000000022223333777788887777 22226666....77770000999900007777 ----....9999555588881111999977778888 11116666....33334444666622227777 variable mean sd variance cv skewness kurtosis

For return rate of monetary investments, Skewness/Kurtosis tests reject normality.



AppendixAppendixAppendixAppendix B:B:B:B: Reality test of the Delta-Normal approach for each of the six assetcategories exposed to market risk

-.01

-.005

0.0

05.0

1

0 100 200 300 400 500Date

T_bonds_return VaR(99%)

-.02

-.01

0.0

1.0

2

0 100 200 300 400 500Date

Corp_bonds_return VaR(99%)

-.01

0.0

1.0

2

0 100 200 300 400 500Date

Fin_bonds_return VaR(99%)

-.1-.0

50

.05

.1

0 100 200 300 400 500Date

Inv_funds_return VaR(99%)

-.1-.0

50

.05

.1

0 100 200 300 400 500Date

Equities_return VaR(99%)

-.4-.2

0.2

.4

0 100 200 300 400 500Date

Mon_inv_return VaR(99%)



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