2005・40

Proposal for a New Solvency Index for Life Insurance Companies−Detection of Insolvent Companies at an Early Stage

by means of Adjusted Basic Profit and Solvency CI

Hideya Kubo

Proposal for a New Solvency Index for Life Insurance Companies― Detection of Insolvent Companies at an Early Stage by means of Adjusted Basic Profit andSolvency CI

HIDEYA KUBO
Graduate School of Business Administration, Kobe University, Japan

Mailing address: 2-1, Rokkodai,Nada-ku,Kobe,657-8501,Japan
Telephone number +81-78-803-6979
Fax number+81-78-803-6979

E-mail address: hkubo@kobe-u.ac.jp1Abstract
In light of the experience gained from seven insolvencies out of 40 life insurance companies
in Japan, this research paper proposes a new approach to the prior detection of insolvent
life insurance companies since such detection is considered difficult only with the risk-based
capital method (hereinafter referred to as the "RBC method"), the world’s mainstreamsoundness criteria.
The Solvency II, new framework to supervise the soundness being studied by the EU,
takes the Basel II Capital Accord as the basic concept and emphasizes the following three
1 quantitative capital requirements consisting of the minimum capital and target
points: ○2 identification of insurance companies that take high risks in terms of financial
capital; ○3 marketand organizational situation and monitoring them by supervisory authorities; and ○discipline by promotion of disclosure. However, merely an extension of the RBC method
2 and ○
3 fully functional because of the difficulties indoes not make the points ○continuous monitoring, in judgment by market participants, and others.
The soundness index developed this time puts importance on the life insurancecompany’s primary profit, that is, the transition of the income statements, while the RBC
method is based on the balance sheet and risk factors. This index is designed to identify, inadvance and from various angles, the phase where the soundness risk of life insurancecompanies is likely to come to the surface and to detect an individual company with a highprobability of insolvency, using the "Adjusted Basic Profit," "Solvency CI," etc. described
afterwards.
KEY WORDS:
Solvency margin criteria, adjusted basic profit, composite index, solvency CI, continuous
monitoring2

1. Introduction
It was believed in Japan that life insurance companies would never become insolvent
because the entry into the market was limited to a small number of large-sized companies(about 40 companies) by regulations and they were under severe supervision by thegovernment. Seven of them, however, have become insolvent one after another in merely
four years since Nissan Mutual Life Insurance Co. declared insolvent in fiscal year 1997.
The news caused a major disruption since the total net asset deficiency of those sevencompanies was 2,623.5 billion yen (23.8 billion U.S. dollars), and the number of their total
insurance contracts (20 million) accounted for 17.1 % of the entire market at the end of fiscal
year 1996. The Insurance Business Law, amended in 1996, introduced the solvency margin
control in fiscal year 1996, which is the RBC control in Japanese version, and started theearly corrective measures in 1999, in order to assure the soundness of life insurancecompanies. The reliability of the solvency margin criteria, however, was questioned for a
1 it was not disclosed in the beginning (though the ratio and breakdown
while, because ○were to be disclosed in the financial statements starting from fiscal year 2001 after a revision
2 the solvency margin ratio of five out of those seven insolventof the criteria); and ○companies exceeded 200% in the fiscal year immediately prior to the insolvency.
Mr. Mitsuhiro Fukao and others previously researched the problems concerning the
1 toJapanese solvency margin criteria. The improvements can be summarized as follows: ○2 to raise the risk weight (from 10% topromote the evaluation of assets at market values; ○3 to30% for the domestic and foreign securities, from 5% to 10% for the real estate, etc.); ○switch from the book basis to recovery basis, for example, the reduction of accrued profits
4 to revise the assumed interest rate risk. The solvency
and deferred tax assets; and ○margin criteria improved by this revision, however, still leaves the following essential issues.
1 Adequacy of risk factors. The risk factors, based on the standard deviation of assets,○vary depending on the period of estimate and indices in use. In addition, it is doubtful
whether or not the definition of assumed interest rate risk and the method of risk
calculation are reasonable.
2 The asset degradation of potentially insolvent companies may be faster than the○calculation of their solvency margins that requires the closing of financial accounts.
3 Confusion caused by the fact that the supervisory authorities have adopted another○method, "actual net assets criteria" (see Note 1), for the determination of insolvency
4 It is impossible to grasp soundness from various aspects only with the solvency○

margin ratio.
2. Hypothesis for New Criteria of Soundness

3The change in risk preferences or management strategies of life insurance companies
brings about some changes in the transition of profits, as is the case for ordinary businesses.
However, it is difficult to get a clear grasp of life insurance companies' profits due to theuniqueness of their income statements.
Accordingly, the total amount of the following three gains is taken into account as a profit
index to measure the fundamental soundness of life insurance companies (hereinafter
1 the interest rate gain obtained from the difference
referred to as the "Triple Gains"): ○2 the death rate gain
between the assumed interest rate and the actual investment yield; ○3 the cost
obtained from the difference between the estimated and actual death rate; and ○gain obtained from the difference between the estimated and actual operating expenses.
The Life Insurance Association of Japan has disclosed the "Basic Profit", which is a concept
similar to the Triple Gains, since fiscal year 2000 in response to the criticism that the profit of
insurance companies was unclear.
The long-term index for life insurance companies’ profits, which is similar to the Basic
Profit (almost the same as the Triple Gains), is newly created here since it is not disclosed(hereinafter referred to as the "Adjusted Basic Profit"). The calculation is attempted for theperiod of 44 years starting from fiscal year 1960 to the latest fiscal year 2003 using the pastincome statements. Because the criteria for income statements were considerably amended
in fiscal year 1975, 1989 and 1991, adjustments are made when an account title itself does
not exist or is changed.
The Adjusted Basic Profit is obtained by deducting the "Basic Expenses" from the "Basic
Revenues." The Basic Revenues are obtained by deducting the gain on sale of marketablesecurities, gain on foreign exchange, revenues from derivatives, and reversal of contingency
reserve; from the ordinary revenues in the income statements. The Basic Expenses are
obtained by deducting the provision for contingency reserve, loss from sale of securities,
loss from appreciation of securities, bad debt expenses, provision for allowance foruncollectible accounts, loss from foreign exchange, cost of derivatives, and operating
expenses; from the ordinary expenses.
The entire industry’s Adjusted Basic Profit in fiscal year 2003 thus computed is 2,163.3
billion yen, 14 times as big as the Adjusted Basic Profit level in fiscal year 1960 (154.7 billion
yen) and approximately half of its peak in fiscal year 1991.
The Adjusted Basic Profit is based on the business performance and asset management
yield including the total amount of insurance in force and asset values, but does not include
the profit and loss on sales and appreciation of the asset management, which makes the
profit relatively stable. It represents very well the characteristics of the insurance businessmodel that aims the risk distribution and profit earning through long-term accumulation of4many contracts, but the Adjusted Basic Profit of a single year may increase by the bulk saleof single premium endowment policies under a single-year sales strategy or "booming"
profits due to reckless management by executives. The sharp rise in single premium
endowment policies includes the advancement of future revenues. Moreover, the short-term
income easily increases once the risk control is relaxed.
Therefore, a single-year's significant profit deviations from the average structure of
Adjusted Basic Profit in certain period suggest the abnormal managerial situation. The
average profit structure is derived from the long-term average structure of single year's
Adjusted Basic Profit, and it can also be expressed as the estimated value of the structure
model to explain the Adjusted Basic Profit (hereinafter referred to as the "Theoretical
Value").
In other words, the hypothesis is drawn that the problem in the soundness of a life
insurance company creates a significant divergence between the actual Adjusted Basic
Profit in a single year and the estimated value showing its average structure.
In the next chapter, the Adjusted Basic Profit model is formed from limited cases in Japanto verify this hypothesis through an empirical analysis.
3. Empirical Analysis
From a viewpoint of the Triple Gains, the Basic Expenses of the "Adjusted Basic Profit"
are classified into the "Operating Expenses" and others. The "Operating Expenses"
correspond to the cost gain, consisting of the pay to salespersons for solicitation and thecosts for offices and systems of insurance companies. Accordingly, the basic structure is
explained as this equation: "Adjusted Basic Profit" = "Basic Revenues" – ("Basic Expenses
other than the Operating Expenses" + "Operating Expenses").
Firstly, since the "Basic Revenues" consist of the insurance operation revenues and the
1 total amount of individual
asset management yields, three predictor variables are used: ○2 the converted premium which is obtained by converting the earned
insurance in force; ○3 difference inpremium of each product with margin percentage and aggregating it; and ○the interest of 10-year government bond between the current fiscal year and two years ago(duration of bond portfolio of a life insurance company).
Secondly, since the "Basic Expenses other than Operating Expenses" consist mainly ofthe death rate loss and the interest rate loss and they involve the provision of premium
reserve and the payment of claims and benefits, the following two predictor variables are
1 total amount of individual insurance in force and ○2 converted premium. Lastly,
used: ○

since the "Operating Expenses" consist of a medical examination fee and sales commission
for winning a new contract and the management cost of contracts in force, the following two

5

1 value of new contract (including net increase due topredictor variables are used: ○2 converted premium.
conversion of contract); and ○Since the period of estimate is as long as 44 years from fiscal year 1960 to fiscal year
2003, the estimate with the least square method probably results in a low Durbin-Watson's
ratio and in a serial correlation. For this reason, the following model is used with combinationof multiple regression model and autoregressive model. The formula for estimate is selectedon the basis of the Akaike's information criterion, t-values for each predictor variable, etc.
Log (R1) = α1 + α2 Log (Ht) + α3 Log (KPt) + α4 (It) + rt

rt = α5 rt-1 + ut

Log (Et) = β1+β2 Log (Ht) + β3 Log (KPt) + β4 (DMY) + rt

rt = β5 rt-1 + ut

Log (Ct) = γ1 + γ2 (Jt) + γ3 (%RCL (KPt)) + rt

rt = γ4 rt-1 + ut

Pt = EXP (Rt) – (EXP (Et) + EXP (Ct))

Rt, Et and Ct represent the adjusted revenues in the term t, the modified expenses in theterm t excluding the operating expenses, and the operating expenses, respectively. Pt, Ht,
and KPt represent the Adjusted Basic Profit in the term t, the total amount of individual
insurance in force in the term t, and the converted premium revenues in the term t,
respectively. DMY represents the dummy variable for significant change in the income
statements, with a value of 1 in and before the fiscal year 1974 and 0 in and after the fiscal
year 1975. %RCL(KPt), It, Jt, rt and ut represent the growth rate of the converted premium
revenues in the previous fiscal year, the difference in 10-year government bond yield fromthat of two years ago, the value of new contract + net increase due to conversion in the termt, the residual error, and the white noise, respectively. The Basic Revenues and the Basic
Expenses are as defined above. Data sources are the "INSURANCE, Life Insurance
Statistics Issue," "Nikkei NEEDS – Financial QUEST (Feb, 2005)."
The result of estimate is shown in Table 1. For the serial correlation of Rt, Et and Ct, every
formula shows that the P level under the Liung-BoxQ-Statistics is beyond the level ofsignificance of 5% (Table 1 shows the data for up to five terms while actual tests are
conducted for 16 terms.) and the hypothesis H0 (the residual error is the white noise) cannot
be rejected. The residual error, therefore, is the white noise. Although the interest rate is
weak as a predictor variable, it is left to clarify the interest rate gain in terms of the Triple
Gains. The estimate with two variables except the interest rate does not make a large
difference in the results.

6

Table 1: Estimate Result of Adjusted Basic Profit
Coefficient Std. Error t-statistic

Rt

Et(including
dummy
variable)

Ct(Reference)

Et

(not
includingdummyvariable)

α1
α2
α3
α4
α5
β1
β2
β3
β4
β5
γ1
γ2
γ3
γ4
β1
β2
β3
β4

-1.013447
0.2104608

0.159
0.085

-6.3792.463

0.8303319

0.102

8.125

0.0029504

0.007

0.405

0.5771986

0.127-4.158749

0.287

0.2915585

0.094

3.103

0.9048751

0.111

8.145

Log
Likelihood

AIC

Lag

AREG

Liung-Box

P level of

Q-Statistics

the test

1
2

-0.16
0.2

1.206
3.136

0.272
0.208

3

-0.006

3.138

0.371

4

0.52

3.276

0.513

4.541

5

0.172

4.812

0.439

-14.4781-0.112

0.595

0.44

82.005-100.224-154.011-93.088

2

0.239

3.345

0.188

3

-0.026

3.379

0.337

-3.847594

0.046

-8.37

4

0.112

4.016

0.404

0.5583643

0.124

4.513

5

0.012

4.024

0.546

1.232316

0.847

1.455

1

0.009

0.003

0.953

0.725328

0.043

16.758

2

0.064

0.199

0.905

0.206099

0.131

1.577

3

-0.21

0.221

0.974

0.995170.007

133.566

4

-0.63

0.415

0.981

5

-0.08

0.418

0.995

-139.538-132.493-6.062924

0.303-20.003

1

-0.08

0.03

0.955

0.395565

0.159

2.49

2

0.07

0.238

0.888

0.889649

0.19

4.694

3

-0.095

0.682

0.877

0.590423

0.122

4.823

4

0.37

0.753

0.945

5

-0.38

0.83

0.975

-100.224-93.088

Figure 1, which shows the estimated value computed on the basis of this parameter(hereinafter referred to as the "Theoretical Value"), the actual Adjusted Basic Profit and thedivergence [(actual value – Theoretical Value) ÷ actual value], has three characteristics.
Firstly, the actual value and the Theoretical Value show a significant divergence in fiscal
year 1989 through 1991 although they progressed in parallel till fiscal year 1988. The
expansion of bubble economy increased the profit well over the average profit indicated by
the Theoretical Value which should have been earned. This is largely due to the bulk sale ofsingle premium endowment policies as aforesaid and also due to the excessive demand for
products with higher assumed interest rate. The divergence of more than 25% clearly
indicates that reckless management was conducted during the period.
Secondly, the Adjusted Basic Profit subsequently decreased by 61.1% in five years from
4,000 billion yen in fiscal year 1991 to 1,600 billion yen in fiscal year 1995, while theTheoretical Value significantly decreased by 48.9% from 3,100 billion yen in fiscal year 1992
to 1,600 billion yen in fiscal year 1996.
Thirdly, the trend of the positive-value divergence between the fiscal year 1989 and 1991
changed to the substantially negative value of 59.4% in fiscal year 1995. Similarly, thedivergence changed from the positive value of 32.8% in fiscal year 1996 to a substantiallynegative value of 33.2% again in fiscal year 1998. The negative divergence indicates that
insurance companies face a difficult situation where they cannot earn theoretically expected7profits. The fiscal year 1995 happens to be two years before the fiscal year 1997 when aJapan's life insurance company became financially impaired for the first time in the postwar
period; and likewise, the fiscal year 1998 is two years before the fiscal year 2000 when fivelife insurance companies declared insolvent. It means that insurance companies became
insolvent two years after a substantially positive value of the divergence had switched to thesubstantially negative value.
In conclusion, what Japan experienced so far supports the hypothesis stated in Chapter 2,that is, "the problem in the soundness of a life insurance company creates a significant
divergence between the actual Basic Profit in a single year and the estimated value showing
its average structure." However, since there may be other possibilities in the future, it isnecessary to understand various aspects of the situation where the insolvency riskincreases.
Figure 1: Es tim ate of Adjus ted Bas e Profit (Fis cal Year)
Million yen％

4,500,000

400

4,000,000

350

3,500,000

300
250

3,000,000

200
2,500,000
150
2,000,000
100
1,500,000

50

1,000,000

0
-50

0

-100

19
60
19
61
19
62
19
63
19
64
19
65
19
66
19
67
19
68
19
69
19
70
19
71
19
72
19
73
19
74
19
75
19
76
19
77
19
78
19
79
19
80
19
81
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03

500,000

Divergence (right-hand scale)

A djusted Base Prof it (lef t-hand scale)

Theoretical V alue (estimated value; lef t-hand scale)

4. Development of Solvency CI to Grasp the Soundness from Various Aspects
Since complexly interrelated multiple factors, rather than a single factor, impair thesoundness of insurance companies, the situation should be judged comprehensively fromvarious aspects.
This is, in a sense, similar to the macro economic view, by which the economy is judged to
be expanding, even if one index shows the recession, when many other indices show thebusiness uptrend. The "current diffusion index" announced by the Cabinet Office is used forsuch multifaceted judgment. The current diffusion index consists of DI (Diffusion Index) andCI (Composite Index); both of them are based on the monthly data to select and determine

8the indices from a viewpoint of statistics availability, compatibility with economic cycle, etc.
DI, as an indicator of the economic turning point, is composed of the Leading Index,
Coincident Index and Lagging Index, each of them consisting of 12, 11 and 7 indices,
respectively. DI represents the proportion of number of indices showing economic
expansion to the entire indices. DI more than 50% indicates the economic expanding phaseas well as the expansion of "individual economies" represented by relevant indices. On thecontrary, DI less than 50% indicates the economic recession.
On the other hand, CI grasps the economic volume by combining the variations of
selected indices. Such variations are averaged with the weighted average method,
accumulated, and then indexed to obtain CI.
While the conditions, which lead to a higher financial risk, can be probably detected by
1 theanalyzing the transitions of Adjusted Basic Profit as shown in the preceding chapter, ○2 grasping the "level of financial seriousness" will
judgment in more various aspects and ○certainly contribute to change of the insurance supervising agency and policyholders'self-defense.
For this reason, the " Solvency CI" is introduced as an index to show a variation in termsof volume and speed of financial risks. The absolute value of the Solvency CI indicates thelevel of soundness, that is, the higher numeric values mean improvement of soundness andthe lower numeric values mean deterioration of soundness. The Solvency CI prepared thistime is basically structured as follows.

xi(t) represents the rate of change in an individual index at the point t. di(t) is the valueof the i-th index at the point t.
(d (t ) − d (t − 1))
x (t ) = 200 × (d (t ) + (t − 1))
d
i

i

i

i

i

If the individual index is 0 or negative value, or if the index represents a proportion, thedifference is computed as below.

xi(t) = di(t) – di(t-1)
Next, the average rate of change in the individual index for the past five years, its standard
deviation, and the rate of change in standard deviation are represented by μi(t), σi(t), andzi(t), respectively.

tμi(t) =∑ x ( n)n =t −19i20∑ ( x i (n) − μ i (t ))t, σi(t) =2

n = t −19

, zi(t) =20( xi (t ) − μ (t ))σ (t )ii

The average of μi(t), σi(t) and zi(t) for the k (quantity of) indices is obtained as follows.

∑ μ (t )kk

μ (t ) =

i

i =1

k

, σ (t ) =∑ σ (t )
i

i =1

k

9

k

, z (t ) =∑ z (t )
i

i =1

k

And the combined variation rate for the individual index V(t) is obtained by combining theabove values.
V(t) = μ(t) + σ(t) × z(t)This combined variation rate V(t) is accumulated to obtain the index I(t) when the baseyear is 100.

I(t) = I ( t − 1) ×

( 200 + V ( t )),( 200 − V ( t ))I(t) = I (t ) × 100
I
Note: I represents I(t) of the base quarter.
In this case, the Solvency CI adopted 8 individual indices (k = 8) which influence theprofitability and soundness of insurance companies known from the past analyses, that is, (i)Adjusted Basic Profit; (ii) actual net capital ratio {(Adjusted Basic Profit + Capital – Risk
amount) / Total assets}; (iii) converted premium; (iv) total amount of individual insurance inforce; (v) total amount of newly insured individual policies (including the net increase due tothe conversion of contract); (vi) cash surrender value; (vii) difference in interest (of 10-year
government bond from that of two years ago); and (viii) the Nikkei Stock Average. The items(i) and (ii) represent the comprehensive risk; whereas the items (iii), (iv) and (v), theprofitability; the items (vi) and (vii), the assumed interest rate risk; the item (viii), the risk ofasset management.
In the data processing, the multiplicative model (see Note 2) excludes seasonal factors
and irregular factors from the time series data. The remaining trends and circulating portion,of an index that includes a trend, is excluded by adjustment with the year-to-yearcomparison. The stock data indices of (iv), (v) and (vi) adopt the year-to-year comparison,
which converts all the time series data to the stationary time series data. The rate of change
ranges over five years (20 quarters) in average, and the base quarter is the fourth quarter offiscal year 1991 (Jan – March quarter in 1992 = 100).
The Solvency CI thus obtained is shown in Figure 2. The numbers in the figure show thetime when insurance companies became insolvent. The lower points in the graph represent
higher financial risks. The cases of insolvencies are concentrated on the CI level below 93
5 , ○6 and ○
7 are concentrated on the CI
except one case in fiscal year 1997. Particularly, ○level of 91s. At this level, many of insurance companies are confronted with managerial
problems and financially ailing companies become insolvent.
Accordingly, the supervisory authorities need to reinforce the supervision and guidance atthe level of early 90s of CI and to prepare the proactive measures on the assumption that10

some companies result in insolvency if the level is less than 93 of CI. Incidentally, theJapanese insurance industry's soundness shows more than 95 at present, which meansthat the soundness risk is moderate.

Figure 2: Trans ition of Solvency CI
91:4=100
101
99
97

①

95

③

93
91

②
④

89

⑤,⑥

⑦

91
,4
92
,2
92
,4
93
,2
93
,4
94
,
94 2
,4
95
,2
95
,4
96
,2
96
,4
97
,2
97
,4
98
,
98 2
,4
99
,2
99
,4
00
,2
00
,4
01
,2
01
,
02 4
,2
02
,4
03
,2
03
,4
04
,2
04
,4

87

Solvency CI
Note: The number shows the time when each of seven insurance companies declared insolvency.

5. Characteristics of Insolvent Companies and Soundness Check of Individual Company
So far, the conditions to increase the soundness risk have been examined for the entire
insurance industry using the Adjusted Basic Profit. However, this profit concept can beapplied to screen an individual life insurance company that is likely to be financially
impaired.
Four out of seven insolvent companies in Japan had assets of more than 2,000 billion yen,which shows the magnitude of insolvency compared with the cases in the U.S. such as the
Mutual Benefit Life Insurance Co. Seven companies had as much as 2,600 billion yen in the
total net asset deficiency in total, while their transfer of businesses amounted to 1,100 billion
yen, which suggests that the insolvent companies had great values in sales channel, etc.
These companies would have a better chance of survival if their management had been
1 a substantial reduction of themore rationalized. The reorganization plan includes ○2 10% reduction of policy reserve,
assumed interest rate to 1 through 2.75% level and ○shifting a heavy burden onto the policyholders. The deterioration of financial status to such alevel clearly indicates the absence of ALM (Asset Liability Management ) and the existenceof long-term peculiar sales and financial strategies by those insolvent companies.

11To clarify the characteristics of insolvent companies, the profit value of each company isestimated by the panel analysis for each fiscal year from 1991 to 2003. The panel data forthese 13 years is combined for the cross-sectional analysis by pooling. The result of
estimate is shown in Figure 3. The sample size of Adjusted Basic Profit computed inaccordance with the aforesaid formula is 503 in total, of which 63 are for seven insolvent
companies and 440 for other companies. The model structure used for the pooling analysis
is as follows.
Rtk = α1 + α2(Htk) + α3(KPtk) + rtk + Dmy1 + Dmy2 + … + Dmyt-1
Etk = β1 + β2(Htk) + β3 (KPtk) + rtk + Dmy1 + Dmy2 + … + Dmyt-1
Ctk = γ1 + γ2 (HNtk) +γ3(KPtkt) + γ4(Jtk) + rtk + Dmy1 + Dmy2 + … + Dmyt-1
Ptk = Rtk – (Etk + Ctk)
Rtk, Etk, Ctk and Ptk represent the Basic Revenues of the k-th company during the term t,
the Basic Expenses excluding Operating Expenses of the k-th company during the term t,
the Operating Expenses of the k-th company during the term t, Adjusted Basic Profit of thek-th company during the term t, respectively. Htk, KPtk, HNtk, Jtk and rtk show the total amountof individual insurance in force of the k-th company during the term t, the converted premium
revenues of the k-th company during the term t, the number of individual insurances in forceof the k-th company during the term t, the new contract amount + net increase due toconversion of the k-th company during the term t and the residual error, respectively. Dmy
represents a dummy variable where Dmy1 takes 1 for the actual values in fiscal year 1991
and otherwise takes 0; and Dmyt-1 takes 1 for fiscal year t-1’s actual values and otherwise
takes 0. Since the period for estimate is 13 years this time, t equals 1 through 12.
The result of analysis by pooling is shown in Table 2. The estimate result is stable for all
the companies except for those seven insolvent companies, for which the result is lesspredictable. Accordingly, two patterns of the estimate are made for the adjusted revenues
Rtk and adjusted expenses Etk. One formula contains the less predictable contracts as apredictor variable, and the other does not include them. The estimate result by pooling isshown in Table 2.
See the parameters of insolvent companies in the column "Estimate 1" of Table 2 where
the structure is simplified. The coefficient of converted premiums from the Basic Revenues
is 1.97300, 0.2 percentage point higher than 1.76526, that of the companies except thoseseven companies. It shows the structure where the increase of converted premium is likely
to cause the increase of Basic Revenues, that is, the products whose future income isincorporated in advance, such as single premium endowment policies, have a high12

percentage. Also the parameters of Basic Expenses show a great difference between
1.73362 of seven insolvent companies and 1.45584 of the other companies, which shows astructure where the products of highly assumed interest rate and the single premium
insurances have a high percentage and the large-scale provision of premium reserve. The
parameter of the converted premium of the operating expenses shows 0.00449, which ishigher than 0.01035 of companies except those seven for the same reason.
The insolvent companies have higher parameters for the income and cost functions thansound insurance companies do, which means that the former companies have a highproportion of the products which are both costly and significantly contributing to the earnings.
Although such types of portfolio instruments themselves are not harmful, the companies withthis product strategy require far more conservative and careful ALM than those without it.
Table 2: Estimate Result of Adjusted Basic Profit by Pooling
Estimate 1

Estimate 2

All theSeven Insolvent
Companies
Companies
except the Left

NumberAdjusted-R²

63
0.792
-120796-1.09100
110,767440
0.983-26031-0.772
33,714Seven Insolvent
Companies

63
440
0.792
0.983
Coefficient
74480-34469α1 t-statistic
0.707-1.031
Std. Error
105,356
33,4180.004790.00138
Rtk α Coefficientt-statistic
Excluded from predictor variables
1.020
3.338
2
Std. Error
0.005
0.000
Coefficient
1.97300
1.76526
1.761171.67561
1.66264
α3 t-statistic
14.739157.226
147.900
5.223
50.872
Std. Error
0.134
0.011
0.012
0.321
0.033
Adjusted-R²
0.768
0.978
0.970
0.765
0.978
Coefficient-126,768-13,274
9,538
80,362-16,920
β1 t-statistic-1.195-0.4170.287
0.792-0.531
Std. Error
106,050
31,80333,215
101,491
31,846
Coefficient
0.00288
0.00060Etk
β2 t-statistic
Excluded from predictor variables
0.636
1.513
Std. Error
0.005
0.000
Coefficient
1.73362
1.45584
1.45137
1.55504
1.41151
β3 t-statistic
13.527137.462
127.166
5.032
45.319Std. Error
0.128
0.011
0.011
0.309
0.031
Adjusted-R²
0.960
0.992
0.991
0.960
0.992
Coefficient
4,811
4,880
6,035
4,811
4,880
γ1 t-statistic
1.211
2.108
2.708
1.211
2.108
Std. Error
3,973
2,315
2,229
3,973
2,315
Coefficient
0.00186
0.006200.005620.00186
0.00620
γ2 t-statistic
1.223
17.06216.0771.223
17.062
Ctk
Std. Error
0.002
0.000
0.000
0.002
0.000
Coefficient
0.12594
0.06955
0.07478
0.12594
0.06955
γ3 t-statistic
10.23121.38423.951
10.23121.384
Std. Error
0.012
0.003
0.003
0.012
0.003
Coefficient
0.00449
0.01035
0.009990.00449
0.01035
γ4 t-statistic
3.061
34.01133.711
3.061
34.011
Std. Error
0.001
0.000
0
0.001
0.000
Note: Estimate 1 shows the results estimated excluding less predictable contract amount in force from the predictor
variables. Estimate 2 shows the results estimated with all the predictor variables.

13

503
0.978
-1777
-0.051
34,655All theCompanies
except the Left
503
0.978
-9565
-0.27834,4360.001393.134
0.000
1.6582647.529
0.035
0.970
6,303
0.189
33,2740.00058
1.347
0.000
1.40863
41.784
0.034
0.991
6,035
2.708
2,229
0.00562
16.0770.000
0.0747823.951
0.003
0.0099933.7110Figure 3 illustrates the Adjusted Basic Profit value and the Theoretical Value (estimatedvalue) for each of those seven insolvent companies for the period between fiscal year 1991
and the fiscal year immediately prior to the year of insolvency. These values are calculatedwith the parameters of all pooling companies shown in the Estimate 2 of Table 2. The
theoretical value of the Adjusted Basic Profit shows the level of basic profit according to thetotal amount of insurance in force and sales of each company on the basis of the industry’s
average structures of income and expenditures computed from 500 Adjusted Basic Profit
samples that have been calculated for 13 years.
The result shows two patterns that lead to insolvency of an individual company. One ofthem is the significant drop in the actual value of Adjusted Basic Profit below the Theoretical
Value. The other is the continuous negative Theoretical Value of Adjusted Basic Profit, whichsuggests a serious deterioration in management vitality.
The Adjusted Basic Profit above the industry’s average is obtained through active sales,
followed by the sharp drops due to insufficient ALM. Although this is the case for the entire
industry, the pattern is more striking for the insolvent companies.
Thus, careful and long-term observation of the actual value and Theoretical Value of the
Adjusted Basic Profit of an individual company allows early detection of symptoms of its
financial deterioration.
Figure 3: Actual and theoretical values of Adjus ted Bas ic Profit of s even Ins olvent com panies
Million y en

Million y en
200,000

200,000

150,000

150,000

100,000

100,000

50,00050,000

0

K
K 91
K 92
K 993
K4
K 95
K 96
K 997
K8
K 299
TA 0
T A91
T 9
T A932
T AA94
T A95
T 96
T AA97
T A98
99
D
D991
D2
D9 3
D9 4
D995
D6
D9 7
D998
9
C
C91
C992
C3
C94
C995
C6
C97
C98
C299
TO 0
T O91
T O92
T O93
T O94
T O95
T O96
T 97
T OO98
T O99
20
TH
T H91
T 92
T H9
T H93
T HH945
T H96
97
N
N991
N2
N9 3
N994
N9 5
6

0

-50,000-50,000-100,000-100,000

Theoretical value of A djusted Basic Prof it

A ctual value of A djusted Basic Prof it

Note: K, TA, D, C, TO, TH and N on the horizontal axis indicate the initials of insolvent companies and the following
number indicates the fiscal year.

146. Conclusion
It is difficult to grasp the soundness of life insurance companies because of its abundant
cash flows. In most cases, the conditions are already severe when they are detected likechronic disease. Therefore, the supervisory authorities need to grasp the symptoms
carefully at a very early stage. People as well as the supervisory authorities need tools tojudge the soundness of life insurance companies at an earlier stage and from more various
aspects.
The Adjusted Basic Profit and the Solvency CI supplemented by multifaceted judgment,
which are proposed here, enables us to detect the conditions where a life insurancecompany gets financially impaired and to screen potentially insolvent companies. They
contribute to the framework in Japan, as well as to frameworks such as "Solvency II" aimedby the EU. It is important to set the target of the total net worth with the Tail-Var, whichadequately indicates the distorted distribution, and others on the basis of the RBC method.
However, considering the fact that most of insolvencies of the life insurance companies werecaused by erroneous managerial judgment, such as in ALM, it is imperative to first grasp thesoundness risk carefully from the changes in income statements where the managerial
judgment is clearly reflected. The Adjusted Basic Profit and the Solvency CI, herein
proposed, can be provided on a quarterly or monthly basis, which allows the supervisory
authorities to monitor the conditions all the time.
I hope that the creation of a stable index by further adding practical factors based on thistheory model will contribute to early detection of insolvency and more effective supervisionof soundness by the supervisory authorities.
1) The actual net assets are obtained by deducting liabilities at the book value from the assets evaluated at the market
value. They show the amount at which the company’s assets are sold in the market for the payment to policyholders incase of dissolution.
2) Although multiplicative model is a time-series model expressed by X(t) = T(t) x C(t) x S(t) x I(t), S(t) and I(t) is excluded
after factors are broken down. T(t) means trend; C(t), cyclical fluctuation; S(t), seasonal fluctuation; and I(t), irregularfluctuation.

[2005.9.1 730]

15

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