4207An Empirical Analysis of Investment Portfolio of China Insurance Company Hao Jia

8/14/2019 4207An Empirical Analysis of Investment Portfolio of China Insurance Company Hao Jia

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An Empirical Analysis of investment portfolio of China insurance company1

Hao Jia* Hao Yansu*

Abstract:As the crucial mainstay for insurance industry to survive and develop, the insurance

investment enables insurance companies to offset their possible underwriting lossesand make a considerable profit. Since a period ago, there have been many issues in

the investment of Chinese insurance companies, such as lack of investment vehicles,

low rate of return on investment, and irrational investment portfolio. These factors

restricted the development of China insurance industry. But this situation has greatly

changed since the year 2005 and 2006, when the channels of insurance investment

were expanded by China Insurance Regulatory Commission along with the prosperity

of the capital market. Therefore China insurance industry is embracing with greater

opportunities. Based on the analysis of insurance investment vehicles and the modern

portfolio theory, this paper proposes an optimal scheme of insurance investment

portfolio by formulating a series of models. Powered by those models, the optimalportfolios of China Life Insurance Company Limited, Ping An Insurance (Group)

Company of China and PICC Property and Casualty Company Limited are evaluated.

Furthermore, an explicit estimate on the portfolio can be made through comparative

analysis of theoretical results and real data. In the conclusion part of this paper, we

present recommendations to improve the investment portfolio management of China

insurance companies.

1 IntroductionBy an average of 38% high-speed growth per year, the total assets of China insurance

industry reached 1973.1 billion by the end of 2006. However, the rate of return on

investment of insurance companies maintained at a low level: 2.97%, 3.6% and 5.8%

in 2004, 2005 and 2006, respectively. Apparently, compared with the rapid growth of

China insurance industrys assets, improvement in the yield of insurance investment is

in high demand.

Fortunately China Insurance Regulatory Commission (CIRC) published a set of

regulations to expand the insurance investment tools in 2006. These give insurance

companies a great opportunity to get high returns on investment. The CIRC

promulgated and put into effect the "Indirect Investment of Insurance Capital

management on Infrastructure Projects" on March 23, 2006. On October 16, 2006, theCIRC approved that insurance companies could invest in shares of commercial banks.

Subsequently, the "Overseas Investment of Insurance Capital management (draft)"

was published on December 21, 2006 for public comment.

On one hand, the promulgation of these regulations and policies provides the insurers

with more investment tools and more opportunities to maximize the investment

1Thanks Professor Hao Yansu for his great support.*Postgraduate Student of Insurance School, Central University of Finance and Economics E-mail:

[email protected]*Professor of Insurance School, Central University of Finance and Economics, Director of ChinaInsurance Market Research Center


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returns. Meanwhile, it is a challenge for the young domestic insurers because it calls

for an adjustment of investment strategy under the new policiesthey must analyze

the returns and risks of both newly added investment vehicles and former vehicles

comprehensively, and then evaluate the optimal investment portfolios.

The purpose of this research is to provide theoretical and technical supports with

insurance investment in China, the largest emerging insurance market. Meanwhile,

other emerging insurance markets like India and Brazil also face the same situation

that they are all experiencing rapid development, which highly requires the

improvement of investment efficiency. This paper may also be used as a reference for

other emerging insurance markets.

2 Background of China insurance investment2.1 Investment vehicles

The economic system reform of China is still in its early stage, and this has limitedinvestment capability of the insurance industry -- investment vehicles are restricted by

the immature capital market and stringent insurance regulation, which have

significant impact on the insurance investment, to ensure the insurance companies

complying with the basic principles for insurance investment, such as diversification

and dispersion, maturity matching (including the liquidity principle) and currency

matching. Therefore it is necessary to make analysis to the insurance investment tools.

2.1.1 Deposit

When China domestic insurance industry resumed operation in 1980, little attention

was paid to investment management, so insurance funds could only be deposit in

banks. Since then, deposit has been the primary insurance investment tool, as at the

end of 2006, deposits of insurance funds reached 562.8 billion Yuan, accounting for

33.2% of the total funds. Deposit is highly security and liquid, but it is sensitive to

macroeconomic policies and its interest rate is lower than securities. Since 1996, there

has been a huge loss arising from difference of interest rate in Chinese life insurance

companies as China central bank has lowered the interest rate eight times. Till now

the interest loss is still a heavy burden for these companies.

2.1.2 Bonds

The CIRC promulgated and put into effect the Enterprise Bonds Investment

management of Insurance Capital on March 30, 2003. Then insurance companies

began to invest in enterprise bonds, but the bonds scope is strictly limited in central

enterprise bonds such as railway construction, construction of power et al, as well as

bonds whose credit rating are at least AA. The investment amount of enterprise bonds

is subject to not exceed 20% of the total assets of the company.

On August 21, 2005 CIRC launched Interim Measures for bond investment


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management of insurance capital. The official document approved that insurance

companies could determine the proportion of investment in Treasury bond

independently whilst the maximum proportion of investment in enterprise bonds

increases from 20% to 30%. Therefore insurance industry increased the bonds ceiling

substantially.

Due to its security and liquidity, which comply with the principles of insurance

companies investment strategies very well, bonds become the most important

investment tool for insurance industry. The bond accounts of China insurance industry

have grown rapidly. The amount of bond investment in 1999 was 80.5 billion Yuan;

however the amount rose to 944.6 billion by the end of 2006. And insurance

companies become the second largest institutional investor in bond market.

With the continuous growth of total proportion of bond investment, the investment in

Treasury bond has reduced in spite of its advantages in stability, liquidity and tax benefits. Compared with other high-yield bonds, Treasury bond becomes less

attractive so that insurance companies hold Treasury bond with purpose of security

rather than profits.

2.1.3 Security investment funds

In October 1999 CIRC and China Securities Regulatory Commission (CSRC) jointly

issued an announcement which officially approved insurance companies to invest in

security funds to indirectly enter the capital market.

By the end of 2001, attracted by the bull market, the security investment funds of

insurance industry increased from 1.5 billion Yuan to 200 billion Yuan, and the

average increasing rate reached 20%. But from the end of 2001, China's capital

market had started a long and painful period of adjustment.

In 2002, the rate of return on security investment funds invested by insurance

companies was -21.3%. Within following three years, the bear market made the low

return on insurance security funds get even lower. In 2005, the stock market met a

better situation: return on security investment funds gradually improved, and thesecurity funds amount increased to 8% of the total investment funds of insurance

companies. In the first eight months of 2006, 80.059 billion Yuan was invested in

securities investment funds by insurance industry. Compared with the growing

amount of the total investment funds, the amount of investment funds in the first eight

months was smaller than that of 2005, and the reduction was nearly 30 billion Yuan.

The reduction is mainly because of the increase of direct investment in stock. In the

first eight months, the amount of stock investment reached 49.903 billion. It seems

that insurance companies dont need security investment funds to help them invest in

stock any more.


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2.1.4 Stocks

On February 7, 2005, the CIRC approved that insurance companies could invest in

stock, and the amount that has deducted the premium income of variable life and

universal life products shouldnt exceed 5% of the total assets of last year.

The main characteristic of stock is its high risk: on one hand, the principal can not be

returned; on the other hand, the prices in secondary market fluctuate all the time, and

the influence factors of the prices are unpredictable and speculative.

In 2006, most companies in China have successfully completed the non-tradable

shares reform. And lots of blue chips issued in this year. So the market value of A-

Share2 was pushed to nine trillion Yuan. Shanghai Stock Exchange Index rose 130%

over the year, 300 stock index of Shanghai and Shenzhen Stock Exchange rose 121%.

So insurance companies received real benefit from the stock market and the yield ofstock investment reached 8.92 billion Yuan with a 27.1% rate of return. With the good

performance in stock market, the return of insurance funds ran up to 95.53 billion

Yuan at the end of 2006, with an average yield of 5.8%. Insurance investment has

created a new record.

2.1.5 Infrastructural Construction

On March 6, 2006, CIRC announced that insurance companies can invest in

infrastructure construction project indirectly. Compared with the original channels for

investing, infrastructure projects are low-risk and high-yield.

The infrastructure projects mainly cover transport, communications, energy,

municipal and other state infrastructure projects. These state-backed projects are

lower risk and relatively high yields. For example, the internal rate of return of Tian

jin railway project reaches 5.02% and the return of Shanghai underground railway

project is about 6.21%, whereas the total insurance investment return is only 3.12% in

the same period.

Entering into long-term infrastructure construction has a long history for insurancefunds around the world. In Japan's post-war recovery period, the insurance companies

found by some large financial groups had more interests in infrastructure projects. By

the end of 1986, insurance funds that invested in real estate and city construction

reached 20.1845 trillion yen, so the insurance companies had made great

contributions to Japan in the post-war economic recovery.

China encourages foreign capital to participate into infrastructure projects especially

2A-Shares are common stock issued by mainland PRC companies, subscribed and traded in

RMB, listed on mainland stock exchanges, and reserved for trading by PRC citizens. The AShare market was launched in 1990.


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in various forms of municipal public facilities construction. Many foreign insurance

companies like New York Life, Yasuda Fire & Marine Insurance and Allianz Group

have invested in China public facilities construction already. And after the permission,

China domestic insurance companies are preparing to invest in infrastructure projects

the Beijing-Shanghai high-speed railway has attracted nearly 40 billion Yuaninsurance funds, which accounts for 30% of the total investment amount.

2.1.6 Overseas investment

On August 18, 2004, CIRC and Central Bank of China jointly issued the "Foreign

exchange insurance funds management(draft)", and allowed the foreign exchange

funds of domestic insurance companies to invest in overseas bond markets, with the

purpose of opening a new channel for the 10 billion U.S. dollars foreign exchange

funds of China insurance industry. International experience shows that the global asset

allocation capability is the core competencies of the insurance industry. Currently,there are no substantive overseas investments of China insurance industry, overseas

investment portfolio and risk control strategies have to be explored.

2.2 Analysis of China insurance investment portfolio

Capital utilization rate of insurance companies in developed markets usually can

reach 90%, and the investment involves stocks, bonds, funds, futures, foreign

exchange trading, real estate, and mortgage loan. Among these vehicles, some are

positively correlated to the market interest rates, like deposits, loans, treasury bonds,

and some are negatively correlated to the market interest such as real estate and

stocks. Transfer of insurance funds can help companies control the risk effectively. In

contrast, China insurance investment channels still need to be expanded, and the

financial environment needs to be improved.

Specifically, compared with developed countries, the securities investment proportion

of China insurance funds is smaller. The insurance funds are mainly used in low-

income bank deposits and treasury bonds. As of the end of 2005, China insurance

funds totaled 1.410011 trillion Yuan, with an annual increase rate of 30.82%. Within

this fund, bank deposits are 516.8 billion Yuan, accounting for 36.66% of the funds;treasury bonds are 359.176 billion Yuan, contributing 25.47%; enterprise bonds are

120.605 billion Yuan, accounting for 8.55%.


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36.66%

25.47%

12.81%

8.55%

5.82%1.12%

9.57%

Bank deposit Treasury bond Financial bond Enterprise bond

Subordinate bond Stock The others

Figure 1: Structure of China Insurance Funds in 2005

With the reform of economic system and development of capital market, the portfolio

of insurance investment is changing. Let us have a look at China Ping An Insurance

Company investment portfolio for the last three years. We can also find the same

trend of the whole insurance industry that bank deposits kept decreasing, while the

proportion of bonds, Security investment funds and stocks increased year by year.

0%

20%

40%

60%

80%

100%

2004 2005 2006

Fixed deposit enterprise bond and financial bondtreasury bond security investment fundstock

Figure 2: Investment Portfolio of China Ping An Insurance Group 2004 -2006


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Efficient and diversified insurance investments in developed countries have brought

their insurance companies huge profits. According to Swiss Re's statistics, during a

range of 20 years, the average rate of return on insurance funds in developed countries

is more than 8%. That high investment return helped the insurance companies to

consolidate their profit, although they may have an underwriting loss.

China insurance company's investment yield is below this level. From 2001 to 2004,

the insurance industry overall investment rate of return continues to decline and

reached the minimum rate 2.40% in 2004, far less than the Supervision Index 3%.In

2005 and 2006, the recovery of return is mainly dependent on the prosperity of capital

market.

3.89%4.30%

3.14%

2.68%2.40%

3.60%

5.80%

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

2000 2001 2002 2003 2004 2005 2006

Figure 3Rate ofReturn of China Insurance Industry 2000-2006

3 Literature ReviewHarry Markowitz initiated the work on portfolio management problems. He

developed a portfolio theory according to which the mean and the variance of the

portfolio return are sufficient measures of the uncertainty for the portfolio selection

purposes.

Since its introduction in the 1950s the theory has been utilized in several applications.

Most of these applications are static allowing only one time period, and then dynamic

models are developed. However, dynamic models have faced resistance due to the

computational difficulties and vast data requirements as well as the sensitivity of the

errors in input parameters.

Many researchers have used the portfolio theory to analyze investments of insurance

funds. Lambert and Hofflander (1966) used Markowitz's portfolio theory in research

of the investments of the property insurers. Forst (1983) considered the structure of

the insurance funds, and analyzed the feasibility of using modern portfolio model in


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the research of life insurers. Dominique (1989) used diffusion analysis to look into

underwriting profit and investment income. Cario and T. Kent(1994) present an

asset/liability model for a Japanese Insurance Company. They use multistage

stochastic optimization to determine an optimal investment strategy that incorporates

the uncertainty in future assets and liabilities as well as complex regulations imposedby Japanese insurance laws and practices.

In China, the study of insurance investment remained at the very early stage where

model assessment is much more done than empirical studies. Shan Mingli (2000)

proposed the main problems of the application of Maikowitz Portfolio Theory in

China , as well as presented their ideas of improvements for the optimal investment

portfolio model. Yang Guiyuan and Tang Xiaowo (2001) studied how to choose the

securities investment portfolio and established a correlation model. Guo Cunzhi(2001)

discussed the application of modern portfolio in securities choosing and studied the

prospects of this theory in the present stage in China, and put forward relevantproposals. Rong (2001), analyzed the gross income and risks of insurance companies,

and improved the theory of the insurance investment model with an optimal

investment ratio formula. Cui (2004), according to CAPM theory, constructed a

minimum risk investment portfolio under a given profit.

Shen Shuguang (2002)studied insurance investment systematically, contained

research of insurance investment tools, and the current insurance investment

environment and gave some strategies to regulate such situation, that the investment

should according to permission of the market and environmental conditions.

4 Research Methodology and Data4.1 Model4.1.1 Assumption

Portfolio Theory (Markowitz, 1952) holds that all the investors are risk-averse. And

investors expect to gain the maximum return under certain risk or suffer minimum

risk under certain expected return. It means the investors portfolio must seek the

balance between targeted risks and expected return in order to minimize the risk while

pursuing the maximization of return.

Markowitzs mean-variance assumption is that the investors must be rational-- they

are pursuing the maximum return and are risk-averse. Pursuing the maximum return

means the rational investors tend to prefer maximum-return security under the same

risk. Risk-averse means the rational investors tend to prefer the minimum-risk

security under the same expected return. Portfolio theory assumes risk-return tradeoff,

so extra return must be paid if investors stand extra risk.

4.1.2 CML


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CML is a line used in the Capital Asset Pricing Model to illustrate the rates of return

for efficient portfolios depending on the risk-free rate of return and the level of risk

for a particular portfolio.

The CML is derived by drawing a tangent line on the intercept point on the efficientfrontier where the expected return equals the risk-free rate of return. And CML is

considered to be superior to the efficient frontier since it takes into account the

inclusion of a risk free asset in the portfolio. The capital asset pricing model (CAPM)

demonstrates that the market portfolio is essentially the efficient frontier. The formula

and figure of CML are as below.

0

Figure 4: Capital market line

R=R0+ [(Ri-R0)]

Ri denotes the expected return of risk assets, R0 denotes return of the risk-free asset, R

denotes expected return of portfolio and denotes the portfolios risk.

According to Markowitzs theory, the ultimate goal of investing is to minimize the

risk under certain profit or maximize the profit under certain risk. An effective

insurance investment portfolio can increase investment income of insurance funds and

improve the solvency of insurance companies. It can reduce the operation risks of

insurance companies and enhance the competence of enterprises too.

4.1.3 Portfolio models

Currently, China insurance funds are used in bank deposits, bonds, stocks, securities

investment funds, insurance policy loans, indirect investments in infrastructure

construction and overseas investments. We set bank deposits be the risk-free

investment for insurance company, and take treasury bonds, enterprise bonds, stocks

and securities investment funds as risk assets.

As the insurance funds have not yet been used in the infrastructure investments and

M

R

R0

Capital Market Line

EfficientFrontier


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overseas investments, this study does not include these two investment channels.

Bonds investments include financial bonds, subordinated bonds, convertible bonds

etc. To simplify the study, we only study more representative treasury bonds and

enterprise bonds. Hence some errors may exist because of the ignorance of some bond

varieties.

We suppose there are N+1 investment assets, including N risk assets and one risk-free

asset. Then the return of the portfolio is

R=r+ g 0 r0+g=

N

1i

iir 0 +=

N

1i

iir =1

rdenotes underwriting profit margin;

r0 denotes rate of return of risk-free asset;

ridenotes the rate of return on the ithrisk assets;

g denotes the proportion of the investment asset to total asset;0 denotes the relative amount invested in risk-free asset;

i denotes the relative amount invested in risk asset i (0 i 1). i can be seen as

the measurement of insurance investment portfolios. And r, riare stochastic variable

denoting the yield of the ithrisk asset. Hence, the expected rate of return and total risk

of portfolio are as follows:

ER= E(r)+ g 0 r0+g=

N

1i

ii )E(r

Var(R) = Var(r)+2g=

N

1i

ii )rCov(r, +=

N

1ji,

jiji2

)r,Cov(rg

Insurers generally expect to get maximum total return and minimum total risk.

However, the amount of risk they will take on is positively correlated to expected

return. So Insurers will balance the total return and total risk by their risk preference

to choose a portfolio with risk assets and risk-free assets, in order to maximize the

satisfaction of the proceeds, and meet the demand for insurance payments, while

minimizing its total risk. Therefore we are going to establish an insurance portfolio

model with minimum risks under certain rate of return to calculate the optimalportfolio of China insurance companies. That is:

min[Var(r)+2g

=

N

1i

ii )rCov(r, +=

N

1ji,

jiji2

)r,Cov(rg ]
http://www.investorwords.com/4292/risk.htmlhttp://www.investorwords.com/1840/expected_return.htmlhttp://www.investorwords.com/1840/expected_return.htmlhttp://www.investorwords.com/1840/expected_return.htmlhttp://www.investorwords.com/1840/expected_return.htmlhttp://www.investorwords.com/4292/risk.html


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s.t. E(r)+ g 0 r0+g=

N

1i

ii )E(r =E(R)

0 +

=

N

1i

iir =1

0 , i 0,(i=1,2,,N)

To calculate the optimal portfolio, we need to solve the optimal values of 0 and i

(i=1,2,,N).The insurance portfolio model above is a kind of nonlinear programming

problem, so we can use Kuhn-Tucker conditions to solve it. We will take the nonlinear

programming problem below as an example.

Min f(x)

gi(x)0 (i=1,2,,m)

s.t.

hj(x)=0 (j=1,2,,l) Function f(x), g i(x) and hj(x) all have first continuous partial

derivatives.

According to Kuhn-Tucker conditions, ifx* is the minimal point, and the constrained

gradients hj(x*)(j=1,2,,l) and g i(x*)(i I(x*)) are linear independence, there are

vectors = ( 1 , 2 ,, m )T and 1(= , 2 ,, l )T making the following

conditions come into being.

f(x*)+=

m

1i

ii *)x(g +=

l

1j

jj *)x(h =0

*)x(g ii =0, i0 (i=1,2,,m)

1 , 2 ,, m and 1 , 2 ,, l are called Generalized Lagrange

multipliers.

4.2 Data

The data adopted in this paper are extracted from Annual Report of InsuranceCompanies, Yearbook of Chinas Insurance, China Securities and Futures Statistical

Yearbook, Almanac of Chinas Finance and Banking, website of Shanghai Stock

Exchange, website of Hong Kong Stock Exchange and Cleaning Limited, website of

the CIRC and website of the China Banking Regulatory Commission. Then we will

determine the value of the independent variables. Firstly we take Ping An insurance

Group as an example.

4.2.1 Underwriting profit margin

Because insurance company's profits are mainly derived from investment profit and

underwriting profit, so this study set underwriting profit be insurance company profits


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minus investment profits. So we set underwriting profit margin=underwriting profit/

(underwriting income-change in unearned premium reserves-change in long-term

unearned premium reserves).

Table 1Underwriting Profit Margin of Ping An Insurance Group 2000-2006

Unit: RMB 1 million

4.2.2 Return of risk assets

Table2Rate ofReturn ofRiskAssets 2000-2006

2006 2005 2004 2003 2002 2001 2000 average

treasurybond%

3.51 2.41 4.4 3.21 2.66 3.03 3.40 3.231

Enterprisebond%

4.13 3.73 5.34 4.17 3.43 3.79 4.11 4.100

SecurityInvestmentFunds%

53.63 -3.08 -13.86 8.89 -19.38 4.42 31.9 9.36

stock%

129.88 -7.86 -15.15 11.02 -17.48 -21.67 52.34 18.73

4.2.3 Restriction of assets investment proportion by CIRC

Table3 Restriction ofAssets Investment Proportion

investment tools restrictions

2006 2005 2004 2003 2002 2001 2000 average

underwritingprofit

-4936 -4843 -2741 -3527 -1503 -1613 -1634

underwritingincome

81712 54780 55911 59334 62027 46527 27375

unearned

premium reserves

2600 1372 1191 152 881 496 0

long-termunearned

premium reserves

-5.75 519 0 301 390 780 0

Underwritingprofit margin

-0.2 -0.09 -0.05 -0.06 -0.03 -0.04 -0.06 -0.07


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Deposit no limit

Treasury bondFinancial bond no limit

Enterprise bond,Subordinated Bond, Convertible Bonds 30%

Security Investment Funds 15%

Stock 5%

4.2.4 Return of risk-free asset

Table 4: Interest Rate of Bank

4.2.5 Proportion of investment insurance assets

Table5: Proportion of Investment Asset to Total Asset of Ping An insurance Group

2000-2006

Unit: RMB 1 million

2006 2005 2004 2003 2002 2001 2000 average

investmentasset

269596 246748 201444 155920 126530 34241 23249 -

gross asset 441791 319706 264496 206044 162596 94831 64290 -

investmentproportion

0.752 0.772 0.762 0.757 0.778 0.361 0.362 0.65

4.3 Calculation stepsWe expect to calculate the optimal investment portfolios of China insurance

companies, and compare them with the actual portfolios of the three representative

China insurance companies, and then we can get conclusions and proposals on how to

improve the investment gains.

2006 2005 2004 2003 2002 2001 2000 average

fixeddeposit

2.329 2.25 2.115 1.98 1.98 2.25 2.25 2.165

agreementdeposit

3.787 3.89 4.00 3.75 3.75 4.2 4.2 3.939

average 3.058 3.07 3.06 2.865 2.865 3.225 3.225 3.052


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According to the value of the independent variables, we can educe:

r0=3.052% where r0denotes rate of return of risk-free asset;

g=65% where g denotes the proportion of the investment asset to total asset;

E(r)= -7.0% where r denotes underwriting profit margin;

E(r1)=3.23%where

r1denotes rate of return of treasury bond;E(r2)=4.1% where r2 denotes rate of return of enterprise bond;

E(r3)=9.36% where r3 denotes rate of return of investment funds bond;

E(r4)=18.73% where r4 denotes rate of return of stock;

Then we can calculate the variances and covariances of these rates of return.

Table 6: Variance-Covariance Matrix of Return of Risk Assets and Underwriting

Profit Margin

treasury bond enterprise

bond

investment

funds

stock underwriting

profit margintreasury bond 0.418980 0.240391 -0.068184 0.262049 0.380583

enterprisebond

0.240391 0.370900 0.933010 0.165752 0.222950

investmentfunds

-0.068184 0.933010 668.5224 -0.019922 0.038324

stock 0.262049 0.165752 -0.019922 3056.934 0.937298

underwritingprofit margin

0.380583 0.222950 0.038324 0.937298 0.003210

We bring the values of the independent variables to the insurance investment portfolio

we established:

Min [0.003210+20.65=

4

1i

ii )r,r(Cov +=

4

1j,i

jiji

2 )r,r(Cov65.0 ]

s.t.-7.0%+0.653.052% 0 +0.65=

4

1i

ii )r(E =E(R)

0+=

N

1i

i =1

Furthermore, the Interim Measures for bond investment management of insurance

capital issued by CIRC stated that the proportion of enterprise bonds to total

investment assets of insurance companies should not exceed 30% of the total assets of

the company. So the result of enterprise bond investment proportion multiplying


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proportion of investment asset should be less than 30%, that is 2 g30%.So 2

30%/ g=30%/g=30%/0.762=39.37%. In the same way, we can deduce 3g15% 4

g5%, and 315%/g=15%/0.762=19.69% 4 5%/g=5%/0.762=6.56%.

So we have a new model with the added constraint conditions, and the solution of this

model is the efficient portfolio of Ping An insurance Group.

Min [0.003210+20.65=

4

1i

ii )r,r(Cov +=

4

1j,i

jiji

2 )r,r(Cov65.0 ]

s.t.-7.0%+0.653.052% 0 +0.65=

4

1i

ii )r(E =E(R)

0 +=

N

1i

i =1

2 39.37%

3 19.69%

4 6.56%

0 , i 0(i=1,2,3,4)

This model is a kind of nonlinear programming problem with constraint conditions, so we can

use Kuhn-Tucker conditions to solve it. We input the data into Excels programming function,

and get the efficient portfolio as follow:

Table 7: Efficient Portfolio of Insurance Funds

rate ofreturn

1 2 2.5 3 3.5 4 4.5 5

variance 2.537 9.794 15.195 21.776 29.541 38.493 44.208 72.064

deposit 0.768 0.659 0.550 0.420 0.311 0.273 0.165 0.027

treasurybond

0 0.077 0.157 0.271 0.364 0.344 0.437 0.501

enterprise bond

0.198 0.198 0.210 0.210 0.210 0.230 0.230 0.220

funds 0.017 0.033 0.041 0.049 0.057 0.087 0.102 0.186

stock 0.017 0.033 0.042 0.050 0.058 0.066 0.066 0.066

Table 7 shows the total risk increased with the total return. Bank deposit proportion

reduced significantly when the total investment return increased, however Treasury


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bond proportion increased with the total return significantly. Enterprise Bond and

Security Investment Fund changed a little, for example the proportion of enterprise

bond is about 21% in various efficient portfolios. The restraint condition of stock is

less than 6.56%, whereas the proportion of stock has reached the ceiling when the rate

of return increases to 4, so the proportion of stock is unable to rise.

Optimal portfolio can peak the slope of CAL, which means the reward-to-variability

ratio reach the maximum too. And the function of CALs slope is:

Si=[E(ri)-r0]/ i

Si denotes slope of CAL

i denotes standard deviation of the portfolio

Figure 5: CAL and Effective Frontier

By calculating the slope of these CALs, we know that when rate of return is 4.5%,

variance is 44.408, and the slope of CAL reaches the maximum 0.23. So we can

conclude that when total return is 4.5%, the portfolio meet the two requirement of

high return and low risk. Lets compare this optimal portfolio to Ping An groups

actual portfolio.

Table 8: Actual Portfolio of Ping An Insurance Group 2004-2006

3.052%

E(r)

E(r)=4.5 =6.6

0


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Actual portfolio (%) Optimal portfolio(%)

2006 2005 2004

deposit 25.21 27.95 39.87 16.5

bondmeanwhile

treasury bond

enterprise bond

63.19

34.44

12.51

64.74

37.70

9.81

56.03

34.96

7.47

66.7

43.7

23

fund 4.4 4.08 2.85 10.2

stock 5.64 2.1 0 66

In the same way, we can deduce the optimal portfolios and actual portfolios of China

Life Insurance Company and PICC Property (Casualty) Company.

Table 9: Actual Portfolio of China Life Insurance Company 2004-2006


2006 2005 2004

deposit 33.35 37.93 46.81 15.3

bond

meanwhile

treasury bond

enterprise bond

58.05

26.41

5.14

29.59

18.2

0.66

21.23

14.01

0.72

63.6

42.6

21fund 4.46 5.00 3.53 13

stock 2.64 0.20 0 81

Table 10: Actual Portfolio of PICC Property (Casualty) Company 2004-2006


2006 2005 2004

deposit 17.78 32.22 33.50 15.1

bond

meanwhile

treasury bond

enterprise bond

60.13

36.00

14.32

51.27

37.87

8.17

41.87

22.65

12.36

66.5

43

235

fund 10.74 7.34 15.9 9.6

stock 10.12 0.05 0 8.9

5 conclusions


18/23

From the comparison of practical portfolio and theoretical investment portfolio of

these three companies we can see that:

5.1 Analysis of deposits and treasury bonds investment of China insurance companies

The investment funds of insurance companies are mostly liabilities to the insured,

because the funds must be paid to them after the insurance accidents. Therefore, to

maintain an adequate solvency, insurance investment must strictly follow the principle

of security. So the majority of domestic insurance company's funds mainly invested to

the bank deposits and treasury bonds. But the rates of return of them are lower than

other securities correspondingly. If domestic insurance companies decide to raise the

yield of investment, it is necessary to increase the investment of enterprise bonds and

other high return securities.

5.2 Actual investment proportion of enterprise bonds is lower than the theoretical one

In 2006, enterprise bond investments proportion of Ping An reached 12.51%, with a

30% increase for the last three years. Enterprise Bonds become favored mainly

because their returns were significantly higher than that of treasury bonds and

financial bonds. Currently the rate of return of the top three enterprise bonds in China

are 5.64%,5.61% and 5.19%.In addition, the scale of China enterprise bonds issuing

expanded rapidly. In 2006 China issued a total of 101.5 billion Yuan enterprise bonds.

In 2007, China National Development and Reform Commission will continue to

expand the enterprise bonds issuance, with an increase of no less than 55%.

5.3 The actual proportion of securities investment funds is a little lower

An important reason for the low proportion of securities investment funds is that

China securities investment funds market is still in its early stage of development,

which makes the insurance companies puzzled by high market risk and fluctuations of

rates of returnthe performance of market from 2000 to 2006 is the best proof.

In China, policy influenced the stock market apparently, so systematic risk in stockmarket is significantly higher than that in other mature stock markets. That is even the

nonsystematic risks can be transferred, the investors will have to take on plentiful

systematic risk.

Furthermore the insurance funds can directly invest in stock market, so insurance

companies do not need security investment funds to help them invest in stocks. This is

another reason for the low percentage of security investment funds.

5.4 Stock investment grows rapidly and approaches the policy ceiling


19/23

After the exploration in 2005, China insurance funds started to increase the scale of

direct investment in stock in 2006. By the end of August 2006, the investment

proportions of stocks get to 49.903 billion Yuan, and accounted for 3.14% of the total

investment funds. In 2006, stock investment of PICC was 7.9 billion Yuan, accounting

for 10.12% of its total assets. The proportion of stock investment of New China Lifeinsurance Company and Tai kang Life insurance Company has nearly reached the

ceiling.

China insurance companies have to increase investment return to meet rapid growth

of the total assets. And in the last two years, lots of banks, telecommunications and

other large capitalization stocks have listed, therefore the insurance industry will

continue to invest in the stock market substantially.

Although the good news from the stock market is really exciting, the insurance

industry should be conscious of the risks of the stock market. In the past four years,the bear market has brought many losses to institutional investors, so the insurers

should control the amount of stock investment. It is reported that regulation of

insurance venture capital investment management has been draw up already.

5.5 The overall use of insurance capital from the analysis

It can be seen from table 8, 9 and 10, the sum of deposit and Treasury bond accounted

for majority of the investment funds, and the sum match the theoretical results very

well. That means, China insurance companies think much of investment security. And

we can learn from table 7 that with the return of portfolio increase, the proportion of

enterprise bonds maintained, and the proportions of Treasury bond and stock

increased, whereas the proportion of deposit decreased. Therefore, if China insurance

companies want to obtain a higher investment return, they need to reduce the

investment of bank deposit and enhance the investment of security funds and stocks

under effective risk control.

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Appendix

Table 1 Underwriting Profit Margin of China life Insurance Group 2000-20062006 2005 2004 2003 2002 2001 2000 average

underwritingprofit

-13821 -4665 -516 -4168 -574 -1101 -266 -

underwritingincome

182680 80253 65075 51354 128781 81313 65164 -


21/23

unearnedpremiumreserves

483 67 623 547 409 276 264

Underwritingprofit margin

-0.0759 -0.0581 -0.008 -0.0820 -0.0045 -0.0140 -0.0041 -0.0352

Table2: Proportion of Investment Asset to Total Asset of China Life Insurance Group

2000-2006

2006 2005 2004 2003 2002 2001 2000 average

investmentasset

594879 494356 374890 156516

128649

94351 72038 -

total asset 684515 559219 433671 455781

299898

220966

159769

-


0.870 0.884 0.864 0.343 0.429 0.427 0.451 0.61

Table 3: Variance-Covariance Matrix of return of risk assets and underwriting profit

marginChina Life Insurance Group

treasury bond enterprisebond

investmentfunds

stock underwritingprofit margin

treasury bond 0.418980 0.933010 0.165752 0.222950 0.172876

enterprisebond

0.933010 0.370900 -0.019922 0.038324 0.084338

investmentfunds

0.165752 -0.019922 668.5224 0.937298 -0.440753

stock 0.222950 0.038324 0.937298 3056.934 -0.461198


0.172876 0.084338 -0.440753 -0.461198 0.001245

Table 4: Efficient Portfolio of China Life Insurance Group

rate ofreturn

1 2 2.5 3 3.5 4 4.5 5

variance 3.742 9.907 18.050 26.660 30.049 40.281 49.036 53.142

deposit 0.846 0.697 0.558 0.463 0.302 0.234 0.181 0.153

treasurybond

0.011 0.069 0.167 0.233 0.375 0.402 0.411 0.426


22/23

enterprise bond

0.113 0.168 0.190 0.207 0.209 0.210 0.210 0.210

funds 0.015 0.033 0.042 0.048 0.059 0.087 0.120 0.130

stock 0.015 0.033 0.043 0.049 0.055 0.067 0.078 0.081

Table 5 Underwriting Profit Margin of PICC insurance Group 2000-2006

2006 2005 2004 2003 2002 2001 2000 average

underwriting profit 535 1766 465 1486 1045 1502 833 -

underwriting income 24792 49802 50628 58111 41478 39297 36803 -

unearned premiumreserves

3512 -227 1500 2613 1340 1480 660

long-term unearnedpremium reserves

0 337 600 915 0 0 0

Underwriting profitmargin

-0.025 -0.034 -0.009 -0.027 -0.026 -0.039 -0.023 -0.0264

Table 6: the Proportion of Investment Asset to Total Asset of PICC Insurance Group

2000-20062006 2005 2004 2003 2002 2001 2000 average

investmentasset

38068 36128 34989 10933 14771 7560 4200 -

gross asset 106124 95112 90757 75956 59443 52593 48954 -


0.359 0.380 0.386 0.144 0.248 0.144 0.086 0.250

Table 7: Variance-Covariance Matrix of return of risk assets and underwriting profitmarginPICC

treasury bond enterprisebond

investmentfunds

stock underwritingprofit margin

treasury bond 0.418980 0.933010 0.165752 0.222950 0.172876

enterprisebond

0.933010 0.370900 -0.019922 0.038324 0.084338

investment

funds

0.165752 -0.019922 668.5224 0.937298 -0.440753


23/23

stock 0.222950 0.038324 0.937298 3056.934 -0.461198


0.802480 0.800420 -0.072187 0.135461 0.029420

Table 8: Efficient Portfolio of PICC

rate ofreturn

1 2 2.5 3 3.5 4 4.5 5

variance 2.176 10.811 16.007 23.240 31.998 40.802 45.769 89.261

deposit 0.733 0.621 0.538 0.462 0.301 0.255 0.151 0.026

treasurybond

0.057 0.113 0.172 0.217 0.353 0.362 0.430 0.460

enterprise bond

0.182 0.196 0.201 0.220 0.231 0.235 0.235 0.235

funds 0.014 0.035 0.044 0.050 0.057 0.077 0.103 0.186

stock 0.014 0.035 0.045 0.051 0.058 0.071 0.081 0.093

Documents

4207An Empirical Analysis of Investment Portfolio of China Insurance Company Hao Jia