Dynamic investment strategies for Chinese pension funds

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Dynamic investment strategies for Chinese

pension funds

Master Thesis

University of Groningen

Faculty of Economics and Business

XIAOFEI YUE

December 2012

Supervisor:

Auke Plantinga

Student name: Xiaofei Yue

Student number: s2188384

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Abstract

This paper examines the feasibility of investing Chinese pension funds into the local stock and bond markets from 2012 to 2021 by using yearly data from 2002 to 2011. I employ the Monte Carlo simulation under three dynamic investing strategies: the constant-mix strategy, the constant-proportion portfolio insurance strategy (CPPI) and the time-invariant portfolio protection strategy (TIPP). The constant-mix strategy following 60/40 stock-bond policy is considered as the benchmark portfolio. In addition, I use the value at risk (VAR) as the measurement of risk. I find that:

1) The CPPI portfolio has the highest average return annually and the highest portfolio value whereas it has the largest VAR among the three strategies.

2) Larger exposures to the stock market result in higher portfolio returns and total portfolio values. However, investors should also undertake higher risks when they set a higher multiplier and a lower floor under the CPPI and TIPP or allocate more to the share market under the constant-mix strategy.

3) The capital injection has a positive relationship with the final values as well as the expected returns of the portfolios, and a negative relationship with VAR.

Keywords: China pension fund, constant-mix strategy, capital injections, CPPI, TIPP, Monte-Carlo

methods, VAR.

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1. Introduction

1.1 Chinese Pension Fund

In the past 10 years, a severe problem (i.e. a rapidly aging population) has appeared due to China’s one-child policy. According to Yangtuan, a deputy director of the Chinese Academy of Social Sciences, as parents of the first generation of the “only-child” continue into old age, it becomes clear that a typical couple of working people need to support four elders and one child, which brings a heavy burden to those couples. What’s more, the migration movement makes this problem worse. On the one hand, for the convenience of education and work, many people move to the “first-tier” cities1 (i.e. Beijing, Shanghai, and Guangzhou) where they may be far away from their hometown. The pension then becomes the only income to support the elderly who can no longer live with their children, as used to be the case in China earlier. On the other hand, China’s pension system is highly fragmented; even within the same region, different rules may be applicable. Employees may get into trouble when they pay their contributions in one city and get the retirement payments in another city. For instance, before 2010, there were no well-established provisions about pension transferred between different regions. Therefore, if a person who worked in Zhengzhou finds a job in Shanghai, he/she may have to give up the accumulated years he/she worked in the previous unit when his/her new employer calculates the pension related to the total number of years he/she has worked.

However, the pension insurance fund system in China, founded since 1991, covers only 55% of the urban residents and a small fraction of rural residents. Even though the number of employees participating in the basic pension insurance system has increased from 2008 to 2010, the collection rate (the ratio between employees paying the contributions continuously and the total number of contributors) has decreased from 25.1% to 17.1% during this period. In other words, the number of individual retirement accounts increased; meanwhile more contributors suspended their premium payment due to changing jobs or moving to another city. According to David (2009) and Haico et al. (2009), the Chinese current pension replacement rate (the percentages of pension payments in terms of pre-retirement wages) is only 19.01%, far less than 45%, the level which was mentioned in Chinese pension insurance regulations.

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The following five characteristics were listed to define a city tier in China on RightSite.com in 2009: • The population should be over five million

•The Provincial GDP should exceed CNY250 billion ,or CNY350 billion in more well-developed provinces

•Strong economic growth is essential

•Geography (cities in Southeast coastal area always have strong economic capabilities, for example, Shanghai, Guangzhou).

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4 Lionel et al. (2012) recommend two methods to solve this problem. One is extending the retirement age; however, currently most of the cohort approaching retirement has a low education level, and employers prefer highly educated young people rather than the elderly. Therefore, if the government extends the retirement age, many old people will have to live without pension with poor chances of getting jobs, which will burden the relief system in China.

A potential solution is to expand the role of retirement savings. Several countries, such as the United Kingdom and Japan, have already extensive retirement saving programs, involving large investments in the stock and bond markets. The question is to what extent such systems can be helpful in China. In addition, it is worthwhile investing the benefits that can be obtained by proper management of the retirement savings portfolios, in particular when comparing it to bank savings. Therefore, I will discuss the feasibility of investing Chinese pension fund into the local stock and bond markets by investigating dynamic investment strategies.

1.2 Dynamic Investment Strategies

The optimal equity allocation of pension fund is controversial, a high percentage investment in stocks results in significant exposure of pension wealth to fluctuations in the equity market. Most of the pension fund beneficiaries are risk averse, because the loss from the stock investment cannot be covered easily by the government or extending the retirement age. However, high risks generate high expected returns. Portfolio insurance strategies, which are characterized by convex payoff functions, focus on maintaining a minimum value of the portfolio, the so-called floor.

Lionel et al (2012) suggest that apart from a floor, pensioners and bondholders can benefit from imposing a cap on the funding ratio which only has a slightly negative influence on equity value. I investigate time-invariant portfolio protection (TIPP) and constant-proportion portfolio insurance (CPPI) strategies which have floors to guarantee a lower risk level. These strategies will be compared with a constant-mix strategy as a benchmark on a risk-adjusted basis. The asset allocation for dynamic strategy can be determined by the risk tolerance level of investors and the risks of the stock market. In order to investigate the differences in asset allocations of dynamic strategies, I change the stock-bond allocation under the constant-mix strategy as well as the multiplier and the pre-set floor under the CPPI and TIPP.

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5 1.3 Structure of This Paper

The rest of the paper is organized as follows. In Section 2, I will discuss Chinese pension fund system and three strategies as well as analyze the asset allocation and the feasibility of the program. In Section 3, the data and methodology of this study will be discussed and in Section 4 the results will be presented. In the last section, the conclusion will be drawn. Furthermore, the limitations of this paper will also be listed.

2. Literature review

2.1 China’s Pension Insurance Fund System

Chinese pension insurance system is composed of three parts: basic old-age security, enterprise complementary endowment insurance (i.e. enterprise annuity) and staff individual save endowment insurance. David (2009) indicates that the current Chinese pension insurance plan, aiming at transforming the defined benefit, the pay-as-you-go system to a multi-pillar scheme, was issued in 1997 and updated in 2005. As one of the main pillars, basic old-age security is composed of two tiers, known as the “Social Pooling” and the “Individual Accounts”. They are both mandatory. The contribution rates vary in different provinces, but in general, the “Social Pooling” and the “Individual Accounts” are on average 20% and 8% of the entire salary respectively. Based on State Council document 38, the target replacement rate of a social pooling pillar is designed as 35% of the citizens’ average wage. And for the 1B pillar (i.e. individual accounts), it should ensure a fixed replacement rate of retirement of 24% of the urban residents’ average pays.

The second pillar is the enterprise complementary endowment insurance system, which is built by companies based on their own economic strengths as well as national regulations and conditions. Its nature is a part of salaries or employee’s welfare which is delayed in payment. Only employers are required to contribute but get a tax benefit. Haico et al. (2009) refer that owners of companies can invest directly up to 20% of these annuities in the share market and around 50% in fixed-income securities. This will play a part in releasing financial burdens of companies. However, several problems still exist under this system. For example, due to the intensive adjustments of the enterprise complementary pension insurance policies, many SMEs (small and medium size enterprises) cannot adapt to new changes in time. As a result, several managers and local administrative staff do not know the exact calculation methods of the enterprise complementary pension, and hence they remove it from the employees’ insurance plan.

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6 account for pension insurance, which was set up by the local social insurance institution. Workers can receive the principal and the interest payments in one payment or spread over several times during a specific period after they reach the legal retirement age. If the worker switches to another job or move to another district, the individual retirement savings will be transferred with him/her. Moreover, if employees die before retiring, the money entered into their individual retirement accounts should be collected by designated persons or statutory successors.

2.2 Wealth Gap between Cities in China

In China, the individual wealth has a strong influence on the welfare for periods of unemployment and sickness, especially on the pension system. Meng (2007) mentions that the Chinese government intends to transform the current social welfare system to a new one in which the individual contribution should play a significant role. However, the individual wealth gap in different cities is quite large. For example, in 2011, the GDP per capita in Beijing, one of the first-tier cities, was more than $20,000, while that in a fourth-tier city, such as Lanzhou, was only $4,031.

Herd (2010) has studied the nationwide inequality in China and concluded that even though there is a tendency of faltering growth in the overall inequality in recent years, the geographical inequality remains very high compared with the international situation. He also gives the main reason for the nationwide inequality in China. On the one hand, the institutional factors, particularly the Chinese Hukou system, prohibit Chinese people in various regions or cities from pursuing the equal rights of education and medical insurance. The Chinese Hukou system provides regulated proof and personal information for the purpose of the public order security and the state administration. It is not set for limiting the immigration between cities and regions. However, due to various regulations and policies among cities in China, several regions retain more wealth than others. In order to get higher education and more opportunity for success, more and more citizens prefer to migrate to first-tier or second-tier cities which generate population explosions in relatively developed cities. To protect local residents’ interests, governments set higher barriers on Hukou system, such as only highly educated people are able to apply for Hukou in Beijing, to prevent more people from moving in; on the other hand, higher barriers promote further wealth gaps among the cities of different tiers.

2.3 Asset Allocation

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7 of direct relationship between the benefits of pensions and the returns earned on the investment portfolio has been found till now. Exley (2001) has argued that this characteristic implied that pension funds should invest in a portfolio composed by 100% long-term index-linked bonds and it should exactly match the liability. Campbell and Viceira (2002) also emphasize that long-term investors, such as pension funds, should take substantial positions in bonds. Furthermore, Ziemba (2011) argued that the results cast doubt on the long run wisdom of the common 60/40 stock-bond strategy since all 100% equity strategies investigated had much higher wealth at the end of the sample period.

Economists offered different suggestions for the improvement of Chinese retirement system, both from the beneficiaries and from the revenue stream points of view. For instance, Tamara (2006) suggests elevating Chinese retirement ages because the average life expectancies at birth have increased to 71 years for males and 74 years for females. However, in the year 2012, a poll of a major newspaper in China (The People’s Daily) showed that 93.3% of the participants (sample: 450,000 people) were against the extension of the retirement age claiming that millions of elderly people and lower-educated employees would lose their jobs without getting retirement pension.

Due to a comparatively low interest rate and returns from bond investment, several scholars recommended putting the money in the equity market. Jong (2007) uses a continuous-time long-term investment framework to show that the optimal portfolio consists of two parts, a speculative part and a hedge part in general. The speculative part is a standard stock-bond portfolio with a 50-50 mix for stocks and medium-term nominal bonds, and a 65-35 mix for stocks and long-term index-linked bonds. Additionally, Griffin (1993) presents the procedures of Dutch and English pension funds globally, accounting for the reason why the Dutch invest less than 25% in stocks, whereas the British invest more than 75%. The size of pension funds relative to local stock market capitalization is the most common reason to explain the differences of asset allocation for pension funds in different countries. However, as mentioned in this paper, this is not a usable explanation for the huge difference in asset allocation because of the benefits of international diversifications of equity markets.

2.4 Investment Strategies

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8 Portfolio insurance, constant-proportion portfolio insurance (CPPI) and Reverso2) and find that the CPPI and Reverso are more probable to offer an attractive risk-return spectrum than the benchmark strategy they have set. Scheller and Pezier (2011) examined optimal investment strategies. They prefer CPPI style investment strategy when sponsors take credit risks into consideration. Due to a specific floor adjusted to the share prices, a CPPI can reduce the credit risks to insignificant levels without large influences on the performances of portfolios. They also follow the constant-mix strategy and find the certainty equivalent rises in proportion to increasing market allocations.

2.5 Constant-Mix Strategy

Weert (2010) defines the constant mix strategy as a constant portion of wealth, maintained in risky and riskless assets at the beginning of the investment period. It is a dynamic strategy which means that portfolios should be rebalanced periodically on a continuous basis throughout the entire investment horizon under consideration. However, rebalancing can be disadvantageous due to high costs that come along with it. In order to keep the portion at its original level, Perold and Sharpe (1988) find that this requires the purchase of shares as they fall in value and the sale of risky assets as they rise in price. Because the average costs of securities are less than the average prices of the securities, benefits of the constant-mix strategy are manifested when the market fluctuates. This strategy underperforms when the stock market ends up far from its starting point in a bear market.

The investors can theoretically decide when to rebalance by themselves. Some may rebalance daily or weekly while others may do some adjustments when the price deviation is over a specific percentage. However, in practice, due to different taxes, transaction fees, and other costs, portfolios are not rebalanced continuously, especially not by individual investors.

2.6 Constant-proportion Portfolio Insurance

Perold and Sharpe (1988) propose the constant-proportion portfolio insurance (CPPI) to prevent losses from falling under a predetermined value, the so-called floor. This value should be less than the asset value at the start of the investment activities. The difference between the asset value and the floor is regarded as a “cushion” which leaves a space for the investors who have different risk preferences. Bertrand and Prigent (2002) compare the Option Based Portfolio Insurance (OBPI) with the CPPI and show that the more risks investors can bear the lower floor they prefer. In addition, the higher the

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9 multiplier is, the faster the portfolio value can reach the floor in falling markets, and the allocation to risky assets will be zero when the value of the portfolio reaches the floor. Reallocations are not caused by the elapsed time, but by the market development.

Basically, we consider such a strategy buying shares when they rise and selling stocks when they fall as a convex strategy. Black and Rouhani (1989) analyze payoffs and the role of expected and actual volatilities of OBPI and CPPI. They point out that the CPPI method performs comparatively well in a relatively constant-trend market without too many reversals and works relatively poorly in a volatile market, because only when the market shows a turnaround, they will sell into weakness, and buy on strength only to see the market sluggishness. The CPPI protects effectively when a decline starts because the strategy will be initialized simultaneously with the decline of the portfolio value. With the decrease in stock prices, the amounts of risk-free investments take the place of those on shares till the exposure to stocks reaches zero. Therefore, under the CPPI strategy, investors can get a guarantee from the existing floor even in a severe bear market. However, we cannot take the wealth growths generated by market changes during rebalancing period into consideration. When the portfolio’s value grows faster than the pre-set floor, the protection will not participate in the subsequent market rise promptly. In addition, bad performances still exist when investors do not have enough time to rebalance before the market drops.

2.7 Time-Invariant Portfolio Protection

Estep and Kritzman (1988) introduced the Time-Invariant Portfolio Protection (TIPP) strategy. It aims at adjusting the protected floor as a function of insured portfolio performance. In their research, TIPP has the following features:

i. In general, the portfolio value cannot fall below the pre-set floor which will be adjusted as a result of changes to a specified percentage of the highest value of the portfolio, i.e. when the portfolio value increases, the floor will also increase, and when the portfolio value declines, the floor will maintain the same value as before;

ii. The initial floor of the portfolio should be lower than the current portfolio value; iii. The portfolio values can be protected through the pre-set floor without ending dates; iv. The calculation is simple and the Black-Scholes formula is not necessary;

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10 Estep and Kritzman (1988) also find that TIPP has the ability of capturing the profits earned once the economy picks up and protecting against severe drops during volatile years.

3. Data and Methodology

3.1 The Simulation Model and the Initial Investment

This study uses Monte Carlo simulation to evaluate the performance of a collection of dynamic asset allocation strategies.

A Monte Carlo simulation is a technique to sample random outcomes for a stochastic process. It is used to analyze the influence of uncertainty on the outcome of an investment strategy. It is impossible to foresee with certainty what the actual outcome will be, but with forecasting by making use of historical data or past experience, the Monte Carlo method can provide a range of possible values rather than a single estimate.

I have simulated sequences of stock returns by drawing random numbers from a normal distribution. The mean and standard deviation of this distribution is given in Table I, and is based on the average return and standard deviation of the Shanghai Composite Index from 2002 to 2011. Each sequence of returns considers a period of 10 years. I have performed 2,000 simulation runs in order to construct confidence intervals regarding the outcomes of the investment strategy.

In Table I, the average returns of the Shanghai Composite Index ranged from -65.39% in 2008 to 130.43% in 2006. From 2002, the average return jumped from -17.52% to 10.27% in 2003, and then reduced rapidly to -15.40% in 2004. Due to the influence of the subprime crisis in the U.S. in 2007, this data started to decrease from the highest (i.e.130.43%) to 96.66% in 2007, and then plummeted around 167% towards -65.39%, which has been the lowest during ten years. Even with an increase to 79.98% in 2009, the stock returns remained negative in 2010 and 2011. The average yearly return of the Shanghai Composite Index is 17.47% even though it has only showed a positive return for 4 years out of the 10 years.

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11 average standard deviation in the five years is 21.78%, 6.35% lower than that from 2007 to 2011. Furthermore, the average standard deviation in ten years is 24.96%.

Table I

The average stock returns and standard deviation of index (SSE) and the risk-free rate

This table reports the average returns and standard deviations of the Shanghai Composite Index per year in China. The yearly standard deviation is calculated by the monthly standard deviation multiplied by square root of the number of observations. Moreover, the risk-free rate of the government bond is assumed to be constant over time. The sample period is from 2002 to 2011.

In addition, in order to compare the performance of hedging, I used a ten-year government bond index issued in March, 2002 on the Shanghai stock exchange. The government bond yield varied from 2.87% in 2009 to 4.53% in 2005. Myers and Turnbull (1976) assume that the risk-free rate of interest is constant over time when they use the capital asset pricing model. In this paper, I also assume that the government bond yields a constant rate of 3.60% per year.

According to the China pension report published in 2011, the total number of retirees in a year increased from 42.39 million in 2006 to 56.12 million in 2010 with an average growth rate of 7.74%. Therefore, I assume that in the next ten years, the growth rate of retirees in China will stay the same, which means that in 2021, the total number of people that will retire will be around 127.43 million. Meaning that in 2011, there are around 127.43 million people who became 50 years old, which covers 65.74% of the overall insured employees. Moreover, through this report, the average increasing rate of the Chinese pension fund individual balance is 18.34%, which means that, if this pace is maintained for the rest of the year, till 2011, the aggregate amount of this account is 23.19 trillion Yuan. At last, I assume that the percentage of the insured 50 years old group related to all the fund participants has a positive correlation with the proportion of the balance of the individual accounts held by 50 years old people compared to that held by the whole pension-fund contributors. As a result, each insured individual has an

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12 average insurance of 11,963.08 Yuan in his/her individual pension fund account when he/she is 50 years old. In this paper, I will use this number as the initial investment in different portfolio strategies.

3.2 The Investment Strategies

The 20-80 stock-bond allocation is the current investment pattern for the basic old-age security. Furthermore, Dai Xianlong, president of the National Council for Social Security Fund, asserts that the contribution of stock investment to the total benefits is over 40% despite that only 20% of the basic old age security is invested into the Chinese share market. However, he also pointed out that with an increasing number of retirees, the total benefits are still beyond the reach of the demand, and hence the Chinese government intends to invest 40% of the pension in the stock market. Therefore, in this paper, I choose the constant-mix strategy with 40-60 stock-bond allocation as a benchmark strategy.

In general, the CPPI method uses a basic portfolio strategy to distribute assets dynamically over time. This method contains, in principle, two assets: the riskless one, with a constant interest rate r (the government bond index with the average yearly interest rate of 3.60%) and the risky one (the Shanghai Composite Index is applied here). For the constant proportion portfolio insurance strategy, I follow the formula suggested by Perold and Sharpe (1988):

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where Ws is the allocation in stocks, m is a fixed multiplier, A is the total assets and F denotes the

floor.

Under this formula, investors intend to recover a fixed percentage of the initial investment V0 during the period [0, T]. Thus, they need to keep the portfolio value Vt above the floor F= V0 at any

time t during the known period, or the final result VT may be less than the insured amount V0, which will overrun the investors’ risk tolerance. For this purpose, the amount of risky investments is based on the fixed multiplier m, and the difference between the current assets and the floor (i.e. the cushion). Generally speaking, the larger the multiplier the larger the share of risky assets is. Therefore, the possibility of larger fluctuations in risky assets increases. To the contrary, a higher level of the floor results in less risky investment. In short, a risk taker who believes stock prices will increase in the future sets lower floors and a large multiplier, and a risk avoider prefers a higher floor and a smaller multiplier in order to reduce losses when stock prices decrease.

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13 (4)

where Ws denotes the amount of dollars invested in stocks, m is a fixed multiplier, A is the total assets, F

is the initial floor and f is the pre-determined insured proportion of the portfolio value that the investor has to sign.

Investors can use the product of the portfolio’s value as well as the fixed floor percentage, and then compare the results with the previous floor. The larger one will be the new floor; otherwise, they need to keep the original one. After rebalancing the floor, investors could adjust the proportion of risky and riskless assets of their portfolios using the same way as in the CPPI method.

For CPPI and TIPP, a pre-set floor is necessary which can represent portfolio managers’ risk tolerance before they choose risky and riskless assets. I set an initial floor as 90% of the initial investment and adjust it in different scenarios in order to make sure that most Chinese people can benefit from this investment after they retire.

Ameur and Prigent (2007) suggest that the multiplier can be chosen based on the distribution of the past asset returns and volatility. Portfolio managers can adopt a multiplier less than 5 when they expect their maximal daily historical drop (e.g. -20%) will occur. For instance, the sterling protected profits fund3 chooses a multiplier of 3.5. Thus is in contrast to the Chinese stock markets which are less regulated and more unpredictable to reduce risks. By performing the investment strategies, CPPI and TIPP, I employed the multiplier of 2 which is also used by Société Générale for the Swiss pension funds.

3.3 Rebalancing with Different Contribution Levels

Thanks to the rebalancing, portfolio managers can make better portfolio strategies available involving in static frameworks as these movements can be considered as an expansion of the opportunity sets. In order to understand the influence on portfolio values of rebalancing with capital addition, the annual individual contribution of pension fund based on personal incomes is used as an input of rebalancing.

The mainland of China comprises 23 provinces, 5 minority autonomous regions and 4 municipalities. In this respect, huge gaps of wealth standards, salary levels and potential saving levels among different cities should be taken into consideration. In order to deal with the large regionalism within China, typical cities which can represent most cities in terms of the wealth levels and pay rates are picked. I choose Beijing,

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14 Shanghai as the representatives of first-tier cities in the mainland of China and Chengdu, Tianjin as representatives of Chinese second-tier cities. In addition, Zhengzhou is picked to stand for the rest of the cities.

The table below shows the wage gaps in five cities in China within a decade. Beijing and Shanghai, as typical cities of first-tier cities, have offered relatively high individual salaries since 2002. Interestingly, the income per capita in Beijing was CNY 20,728 in 2002 and increased to CNY 44,715 in 2008 with an average growth rate of 16.95%. However, the average salaries in Shanghai seem not to be satisfactory. In 2002, the general staff can only get CNY 17,764 per year, which is around 3,000 Yuan less than the staff can get in Beijing. Even though in 2008, the pay rate grew by 17.38%, the best in these ten years, salary levels in these two cities still had a staggering gap.

With the average wage growth rates of 13.22% and 13.47% in Tianjin and Chengdu respectively, the annual individual salary in Tianjin increased CNY 28,388 from CNY 13,852 to CNY 42,240 in ten years. However, as a representative of second-tier city, companies in Chengdu can only pay on the average 34,008 Yuan in 2011 for workers, which is 1,533 Yuan less per year compared with enterprises in Zhengzhou.

Even though Zhengzhou had the lowest wage standard among five cities in 2004, with the fastest average growth rate of 14.09% in ten years and improved significantly in 2004 (i.e. 21.7%) and in 2007 ( i.e. 22.08%), the salary level for general employees in Zhengzhou has emulated that in Chengdu since the year of 2002.

In addition, several assumptions should be made to determine the individual pension fund contributions. i. The percentage of individual monthly contributions to the individual retirement account will

remain unchanged over time, because this proportion was revised several times under different pension regulations published in different cities. For example, Beijing changed it from 11% to 8% in 2007, while Shanghai has updated it since the year of 2011;

ii. The staff individual’s premium used in the simulation is listed below:

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where P is the staff individual’s premium per year and S is the average individual annual salary

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15 iv. The retirement age in China is currently 60 years old for men and 55 years old for female civil servants, but for the convenience of calculation, the retirement age is assumed to be 60 years old for both Chinese males and females.

Table II

The average annual salary levels in five cities from 2002 to 2011

This table reports the average annual salary levels in Beijing, Shanghai, Tianjin, Chengdu, and Zhengzhou, respectively. The currency unit is Chinese Yuan (CNY). The sample period is from 2002 to 2011. The data were collected from local Bureaus of Statistics in those five cities.

year/city Beijing Shanghai Tianjin Chengdu Zhengzhou 2002 20,728 17,764 13,852 10,930 10,960 2003 24,045 19,473 15,706 12,344 12,400 2004 28,348 22,160 17,810 15,023 14,357 2005 32,808 24,398 20,196 16,694 16,630 2006 36,097 26,823 22,740 18,861 19,215 2007 39,867 29,569 26,700 23,025 23,098 2008 44,715 34,707 31,200 26,476 24,691 2009 48,444 39,502 33,516 29,837 27,272 2010 50,415 42,789 37,540 32,779 30,515 2011 56,064 46,757 42,240 35,541 34,008 3.4 Transaction Costs

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16 and CPPI strategies, the floors change with the rate of return of the riskless asset or have to be adjusted as a specified ratio of the highest value the portfolio achieves. In practice, if we continue to rebalance the strategy to adjust to floating target, transaction costs may be very expensive.

However, the rules for transaction costs in China are complex. For example, in 2001, the stamp tax decreased from 0.4% to 0.2% and continued to decline to 0.1% in 2005, however, after two years, in 2007, China’s State Tax Bureau increased the stamp tax to 0.3% again and in 2008, it was lowered to 0.1%. Therefore, in this model, I will not consider the impacts of transaction costs as well as asset management costs, because they vary in pension funds and are difficult to evaluate.

3.5 Evaluation Criteria

Value at Risk (VAR), is applied to measure the risk of loss for the four portfolios of financial assets mentioned in this paper. Theoretically, the VAR technique is defined as a probability of portfolio losses from “systematic risk” as opposed to all risk for a given portfolio, probability and time horizon. In general, VAR is used by portfolio managers to reflect the potential loss in value of their investments from adverse market movements over a fixed time period. It deals with the problem “how bad can things get?” Based on the definition, the formula of VAR can be expressed as:

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where Vp is the initial market value in the portfolio, the typical sample period is set from one day to one

week or more. In this paper, for the convienece of calculation, I will use one year. The µp is the expected

value of the portfolio, and the value of the parameter α depends on the confidence level, which ranges from 1% to 10% generally. Futhermore, p is the standard deviation of the portfolio.

4. Simulation Results

In this section, the results of pension fund investing under different strategies are analyzed. Without additional capital, a constant mix strategy formed with 40% of stocks and 60% of bonds serves as benchmark for the investment strategies.

4.1 Investment Strategies with General Annual Rebalancing

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17 that has 40% allocated to stocks and invests 60% in government bonds ranks second; its total portfolio value is 28,510.07 Yuan from 2012 to 2021. Furthermore, the third column shows the average return of three strategies during the sample period. For example, TIPP has a total portfolio value of 22,111.00 Yuan, which is the lowest among the three strategies after ten years, and it offers the lowest yearly return that is 6.33% on average, while the CPPI portfolio with a multiplier of 2 has the highest average annual return of 9.70% in 10 years.

However, in general, high potential returns are associated with high levels of uncertainty, so VAR is also considered as a selection criteria of dynamic investment strategies. For the benchmark strategy, from 2012 to 2021, the one year 99% VAR ranges from -146.80 to -134.18, and its average value is -141.34, which means that portfolio managers who choose constant-mix strategy and allocate 40% of their investment in stocks as well as 60% in government bonds have 1% of chance of losing 141.34 Yuan out of the whole portfolio value or more per year in the following ten years. Moreover, the CPPI portfolio has an average VAR which is around 47 less than that of the constant-mix strategy. Besides of that the percentage of the total VAR to the CPPI portfolio value is the lowest (i.e. -6.21%). In other words, at the same confidence level, investors choosing CPPI will lose more money. On top of that, compared with CPPI and constant- mix strategy, the TIPP has the minimum VAR (i.e. -52.67), implying that it has the lowest risk under 99% confidence level among three strategies.

Table III

The total portfolio value, average return and the average VAR of three strategies from 2012 to 2021

This table reports the total portfolio value, the average return, the average 99% VAR per year and the percentage of the total VAR to the total portfolio value under three strategies. The sample period is ten years that is from 2012 to

2021. The constant-mix strategy with an allocation of 40% to the risky assets, and 60% to the riskless assets is considered as the benchmark portfolio. The CPPI has a multiplier of 2. The TIPP has a multiplier of 2 and a pre-set

floor that is 90% of its initial investment. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

Strategy/index Total portfolio value Average expected return

Average VAR4 in ten years

Total VAR/ Total portfolio value CMS(40-60) 28,510.07 9.07% -141.34 -4.96% CPPI (m=2) 30,279.02 9.70% -188.08 -6.21% TIPP (90% floor) 22,111.99 6.33% -52.67 -2.38% 4

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18 According to Table III, all the strategies cannot guarantee a 100% profit for investors. However, for the risk averter, TIPP portfolio has the lowest VAR and the lowest ratio of the total VAR to the total portfolio value, which means that in the same circumstances, TIPP performs better in controlling the risk, i.e. portfolio managers have the minimum losses if they choose TIPP. Additionally for investors who enjoy taking risk can choose CPPI with a multiplier of 2. Interestingly, in this sample, the total losses of the constant-mix strategy, the CPPI and the TIPP are only around 4.95%, 6.21% and 2.38%, respectively. As can be seen the portfolio value differences among the dynamic strategies are relatively large. Therefore, although pension fund investors are risk avoiders who intend to make a profit without taking a high risk, CPPI can still obtain the highest portfolio value even though it is being exposed to the maximum loss.

4.2 Asset allocations in constant-mix strategy and different multipliers and initial floors in CPPI and TIPP

William (2011) doubts whether the common 60/40 stock-bond strategy is the best strategy for the long-term investment, so in this part, I examine the influences of different allocations to the risky assets on portfolio values, returns and the risk level by using the constant-mix strategy.

Table IV shows that the allocation of risky assets in the constant-mix strategy has a positive relationship with portfolio values during the sample period. For instance, when people use the benchmark strategy, the constant-mix strategy following 40/60 stock-bond policy in 2012, they will obtain 28,510.07 Yuan in 2021 and a relatively low VAR of -141.34 per year for the next ten years. However, people who invest 20% of pension on stocks and put the rest on bonds will get 46,542.15 Yuan in total, which increases by 63.24% from 28,510.07 Yuan, and a higher VAR that is around 1.25 times more than the VAR under the benchmark strategy. And when investors allocate more in the stock market, the absolute value of the total VAR to the total portfolio value also increases. Generally speaking, investors benefit from the high volatility under the constant-mix strategy. In addition, people can have a positive VAR from 2012 to 2021 only when they invest all their money in the government bond.

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19 Table IV

The impact of different asset allocations on the constant-mix portfolio from 2012 to 2021

This table reports the impact of different asset allocations on the total portfolio value, the average return, the average VAR per year and the percentage of the total VAR to the total portfolio value under the constant mix strategy. The currency unit is Chinese Yuan (CNY). The initial investment is 11,963.08 Yuan. The sample period is from 2012 to 2021.

Stock-bond allocation/variables

Total portfolio value in 2021

Average expected return

Average VAR from 2012 to 2021

Total VAR/ Total portfolio value CMS (100-0) 58,961.57 17.27% -407.34 -6.91% CMS (80-20) 46,542.15 14.54% -318.67 -6.85% CMS (60-40) 36,533.82 11.80% -230.01 -6.30% CMS (50-50) 32,297.77 10.44% -185.67 -5.75% CMS (40-60) 28,510.07 9.07% -141.34 -4.96% CMS (20-80) 22,111.99 6.33% -52.67 -2.38% CMS (0-100) 17,038.86 3.60% 36.00 2.11%

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20 Table V

The impact of the multiplier on the CPPI and TIPP portfolio from 2012 to 2021

This table reports that the multipliers of CPPI and TIPP affect the total portfolio value, the average return, the average VAR per year and the percentage of the total VAR to the total portfolio value from 2012 to 2021. The multiplier ranges from 2 to 5. The initial floors for both strategies remain unchanged. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

Finally, I also examine the influence on adjusting initial floors for CPPI and TIPP. With the same multiplier (i.e. m=2) in both strategies, we can see that the changes of initial floor has a positive effect on the average VAR. For instance, under the CPPI, when the floor value increases from 10,766.77 Yuan to 11,364.93Yuan, the annual VAR increases from -188.08 to -90.42. In other words, the portfolio value is restricted to losing less per year when investors set a higher CPPI floor. Besides, when the floor value moves down to 8,374.16 Yuan, the yearly VAR declines by 619.46 to -709.88. However, high risk results in high return. With the changing pre-set floor, the average returns of the CPPI portfolio ranges from 6.42% to 15.03%, the total portfolio value also increases as the floor value declines.

The value of Multiplier/variables

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21 Table VI

The impact of the initial floor on the CPPI and TIPP portfolios from 2012 to 2021

This table reports that the initial floors of CPPI and TIPP affect the total portfolio value, the average return, the average VAR per year and the percentage of the total VAR to the total portfolio value from 2012 to 2021. For CPPI, the initial floor varies from 8,374.16 Yuan to 11,364.93 Yuan, and for TIPP, the initial floor changes from 70% of the initial investment to 95%. Furthermore, the multipliers for both strategies remain unchanged. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

Under TIPP, the average VAR grows to -8.33 when the percentage of the floor increases to 95%, and decreases to -230.01 if the percentage of the floor value drops to 70%. Moreover, the percentage of the total VAR to the total portfolio value is only -0.43% which means that in 2021, investors can get over 99% of the expected total portfolilo value if they set their floor percentage at 95%. The TIPP portfolio contains less risk when the initial floors of CPPI and TIPP have the same trend of variability. Based on Table VI, the initial floor value has a negative relationship with portfolio values and returns. Generally speaking, when investors set a lower floor under their strategies, the cushion of the portfolio increases, leading to a larger allocation to risky assets, in other words, portfolio managers will face more risks when the stock prices change. On the other hand, higher risks are related to more profits, hence investors will benefit more from taking higher risks.

The value of floors/variables

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22 4.3 Investment Strategies with Yearly Rebalancing and Capital Addition

Table VII

Consumption indices in five typical cities

This table reports the average consumption level, the average growth rate of the consumption level and the expected living expenses in 2021 for people who live in Beijing, Shanghai, Tianjin, Chengdu, and Zhengzhou. The data are collected from the statistical bureau of Beijing, Shanghai, Tianjin, Chengdu and Zhengzhou. The currency unit is Chinese Yuan (CNY).

Table III illustrates that the highest total portfolio value in 2021 is 30,279.02 Yuan, offered by a CPPI portfolio with a multiplier of 2. However, considering the capital demands after ten years from 2011(see Table VII), a resident living in Zhengzhou which is a typical third-tier city, requires at least 47,931.50 Yuan in 2021, which is around 17,000 Yuan more than the highest portfolio value without adding capital. Besides of that, if we consider the gap in consumption levels in different cities, the living costs will be much higher. For example, the average annual growth rate of consumption level in Shanghai from 2006 to 2011 is about 9.00% and the average consumption level in 2011 is around 21,984 Yuan. Then the total portfolio values needed after a decade can be estimated as 72,522.08 Yuan that is over 1.4 times higher than the highest portfolio value listed in Table III. Furthermore, the average Chinese life expectancy will be around 73 years in 2020, listed in the United Nations World Population Prospects report. Thus after retiring, people will still live 13 years on average. Without salaries, the Chinese people can only rely on the pension and the saving deposits that they have accumulated through the years. The portfolio values in Table III are far less than the basic living needs of most people.

The investment strategies with capital injections are taken into consideration. For people who live in Beijing, Shanghai, Tianjin, Chengdu and Zhengzhou, the annual individual contribution to pension

Cities/indices Average consumption level in 2011

Average growth rate from 2006 to 2011

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23 savings based on personal incomes is used as the input of rebalancing . From Table VIII, even though the premium contribution in 2012 is the lowest in Zhengzhou due to the highest growth rate of individual salary level, it increases to 10,622.07 Yuan in 2021 , which is almost the same as the premium payment in Shanghai in 2021, that is 10,997.05 Yuan. However, employees in Beijing still have the highest normal premium payment because of a relatively high growth rate and the highest initial value in 2012. Furthermore, as representations of the second-tier cities, Chengdu performs worse than Tianjin due to a smaller growth rate in terms of individual salary level as well as fewer premium contributions in 2021.

Table VIII

The expected yearly normal premium payment in Beijing, Shanghai, Tianjin, Chengdu and Zhengzhou from 2012 to 2021

This table reports the expected normal premium payments from 2012 to 2021 in Beijing, Shanghai, Tianjin, Chengdu, and Zhengzhou. The currency unit is Chinese Yuan (CNY). The expected normal premium payment is calculated based on the average yearly individual salary and the contribution factor.

2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 Beijing 5,012,74 5,602,42 6,261.48 6,998.07 7,821.30 8,741.39 9,769.69 10,918.97 12,203.45 13,639.04 Shanghai 4,166,49 4,640,93 5,169,38 5,758.01 6,413.67 7,143.98 7,957.46 8,863.56 9,872.85 10,997.05 Tianjin 3,825,97 4,331.82 4,904.54 5,552.98 6,287.15 7,118.40 8,059.54 9,125.11 10,331.57 11,697.53 Chengdu 3,087.00 3,502.69 3,974.36 4,509.55 5,116.80 5,805.83 6,587.63 7,474.72 8,481.26 9,623.34 Zhengzhou 3,243,83 3,700.82 4,222.18 4,816.99 5,495.59 6,269.80 7,153.07 8,160.77 9,310.44 10,622.07

As we can see from Table IX, TIPP portfolio has the lowest total portfolio values in 2021 in the five scenarios (i.e. Beijing, Shanghai, Tianjin, Chengdu and Zhengzhou), but its VAR remains positive. In other words, a positive VAR simply means that the worst consequence at the specified level of confidence is a profit, rather than a loss. For this reason, TIPP seems to be the best strategy for employees who invest their individual pension into the stock market.

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24 With similar input for different strategies, investors in Shanghai are also recommended to utilize the CPPI strategy. In panel b, the CPPI with a mutiplier of 2 also has a negative average VAR at -610.12 but the highest total portfolio value. Hence even with the maximum loss for ten years, the final value of CPPI portfolio is still the highest. In additon, risk averters in Shanghai can also choose the constant-mix strategy with the 40/60 policy, because they will have chance to gain a profit of 4.16 Yuan per year and the portfolio value in 2021 is relatively high. For investors applying TIPP, they will get far less investment incomes although the portfolio value has 1% chance to move up to 118,962 Yuan after ten years.

The difference under this scenario is the reduction of three variables which is due to the decline of the normal premium payments. For example, from 2012 to 2021, the total capital injection in the Beijing scenario is around 87,000 Yuan, and the final values of the three portfolios are 161,896.41 Yuan, 203,373.58 Yuan, and 139,112.41 Yuan respectively. While during the same period, the total capital injection in Shanghai scenario is nearly 71,000 Yuan, and the final values of the three portfolios are 137,637.42 Yuan, 188,597.81 Yuan, and 117,765.84 Yuan.

Lower inputs in Tianjin Scenario lead to lower VARs regarding the three strategies, indicating that with the same initial portfolio values, the lower the capital injection is, the higher the risk we need to take. In this scenario, the total portfolio value and the average return have small changes, and TIPP portfolio still maintains the highest positive one year 99% VAR. Moreover, the yearly reduction of VAR under TIPP is only 1 Yuan, which is the lowest reduction among the three strategies. The contrast shows that TIPP does better in reducing risks. However, investors applying TIPP should also pay attention to the huge differences of the final portfolio values between the TIPP portfolio and the CPPI portfolio. Negative VAR does not have a large influence on the portfolio value. Even taking the highest risk, CPPI investors can still get the highest portfolio value after ten years. Consequently, CPPI is the most ideal strategy for investors in Tianjin.

Since the annual input of Chengdu is the least; so are the figures that come along with it, which can be seen from Table IX. For example, the highest expected total portfolio value in Chengdu scenario is 151,283.91 Yuan, offered by CPPI with a multiplier of 2. Compared with the results in Beijing scenario, investors earn 52,090 Yuan less in 2021. Furthermore, under the same market conditions, TIPP and the constant-mix strategy perform worse than the CPPI.

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25 from a loss instead of a profit from 2012 to 2021 if they apply the constant-mix strategy to invest 40% in the stock market and 60% in the government bonds. As a result, in spite of the highest average return and portfolio value, the risk averters in Chengdu can still choose the CPPI with a multiplier of 2.

Table IX

Indices under different investment strategies with rebalancing and the capital injection

This table reports the total portfolio value in 2021, the average return per year, the VAR in ten years with the capital injection in Beijing, Shanghai, Tianjin, Chengdu, and Zhengzhou and the percentage of the total VAR to the total portfolio value. The capital injection is estimated based on the normal premium payments. The constant-mix strategy with an allocation of 40% to the risky asset, and 60% to the riskless asset is considered as the bench mark portfolio. The CPPI has a multiplier of 2. The TIPP has a multiplier of 2 and a pre-set floor that is 90% of its initial investment. The sample period is from 2012 to 2021. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

Strategies/Indices Total portfolio value in 2021

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26 Among all the five cities used in the sample, Zhengzhou has the highest annual income growth rate. Due to the lower contribution of pension funds, the portfolio value and average annual return are still below the level of Shanghai, Beijing and Tianjin; however, it does not differ significantly. For instance, the average yearly return under the CPPI in Zhengzhou scenario is 28.30% (see panel e), and it is 32.14% in Beijing scenario and 30.02% in Shanghai scenario. In addition, the highest portfolio value in 2021 is 158,659.89 Yuan that is nearly 11,000 Yuan less than the final value of the CPPI portfolio in the Tianjin scenario.

In panel e, variables of the benchmark strategy and TIPP are similar; whereas investors will prefer the constant-mix strategy in Zhengzhou due to a higher portfolio value. From the perspective of pension fund investors, the CPPI implies a relatively high risk to take, i.e. -830.66, but far more profits in the future. In other words, in 2021, people can get at least 150,353 Yuan. The total portfolio value of the CPPI is still higher than the total portfolio value of the other two strategies. To conclude, the CPPI is the best choice not only in Zhengzhou scenario but for all other scenarios.

Finally, with the reductions of the capital injection in the different scenarios, the final portfolio value and the average return will decrease, while the risk level will increase. The CPPI performs the best in terms of the final portfolio value and average yearly returns. Interestingly, the VAR of the TIPP has a positive relationship with the normal premium payment. It remains a positive trend in ten years among five scenarios, which means that after adding the premium payments for each year, only TIPP retains potential not to lose money. However, its final portfolio value is still much lower than that of the CPPI and the constant-mix strategy even with the largest increment of 106.89 Yuan per year. At last, as the capital injection declines, the percentage of the total VAR to the total portfolio value under the three strategies all decrease.

5. Conclusion and limitations

5.1 The Conclusion

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27 also able to make the greatest profit. These results are consistent with the outcomes of the studies conducted by Ammann and Zingg (2006) and Scheller and Pezier (2011).

The impact of different allocations between risky and riskless assets under the constant-mix strategy has also been analyzed. As a result, the more people invest in stocks, the higher risk level they have to undertake, yet the more they can benefit. In addition, I cannot prove that the constant-mix strategy following a 60/40 policy performs worse than investing all the money into riskless assets in a long-term period, because even with a negative VAR, investors can still get much more compared with the payoff from the government bond.

On top of that, different multipliers and initial floors in CPPI and TIPP are also discussed in this paper. The values of multipliers are positively related to the portfolio values for both strategies, which can be explained by the fact that a larger multiplier generates more exposure to risky assets, and higher risks are also related to more benefits. Furthermore, the portfolio values and the average returns change negatively with the value of initial floors. In these scenarios, TIPP performs better as it keeps the VAR increasing in a small range.

In order to obtain more accurate results, I rebalance three investment strategies per year with 5 different capital injections. The capital injections are calculated based on the normal premium payments. In those scenarios, people who choose TIPP can always have the opportunity to make a profit. Besides, larger capital injections result in higher portfolio values and lower risks.

5.2 The limitations

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28

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29 Lionel Martellini, Vincent Milhau and Andrea Tarelli, 2012, Dynamic investment strategies for corporate

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Appendix

Appendix I

The portfolio value, the expected return and the VAR of three strategies from 2012 to 2021

This table reports the portfolio value, the expected return and the one year 99% VAR under three strategies. The sample period is from 2012 to 2021. The constant-mix strategy with an allocation of 40% to the risky assets and 60%

to the riskless assets is considered as the benchmark strategy. The CPPI has a multiplier of 2. The TIPP has a multiplier of 2 and a pre-determined floor that is 90% of its initial investment. The initial investment is 11,963.08

Yuan. The currency unit is Chinese Yuan (CNY).

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31 Appendix II

The impact of different asset allocations on the constant-mix portfolio from 2012 to 2021

This table reports the impact of different asset allocations on the portfolio value, the expected return, and one year 99% VAR under the constant-mix strategy. The currency unit is Chinese Yuan (CNY). The initial investment is 11,963.08 Yuan. The sample period is from 2012 to 2021.

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32 VAR -55.16 -50.07 -52.61 -51.81 -49.64 -54.75 -55.40 -49.09 -53.20 -54.95 Panel g: CMS(0-100) Portfolio value 12,393.75 12,839.93 13,302.16 13,781.04 14,277.16 14,791.14 15,323.62 15,875.27 16,446.78 17,038.86 Expected return 3.60% 3.60% 3.60% 3.60% 3.60% 3.60% 3.60% 3.60% 3.60% 3.60% VAR 36.00 36.00 36.00 36.00 36.00 36.00 36.00 36.00 36.00 36.00 Appendix III

The impact of the multiplier on the CPPI portfolio from 2012 to 2021

This table reports that the multipliers of CPPI affect the portfolio value, the expected return and the one year 99%VAR per year from 2012 to 2021. The multiplier ranges from 2 to 5. The initial floors for both strategies remain unchanged. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

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33 Appendix IV

The impact of the multiplier on the TIPP portfolio from 2012 to 2021

This table reports that the multipliers of TIPP affect the portfolio value, the expected return and the one year 99%VAR per year from 2012 to 2021. The multiplier ranges from 2 to 5. The initial floors for both strategies remain unchanged. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

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34 Appendix V

The impact of the initial floor on the CPPI portfolio from 2012 to 2021

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35 Appendix VI

The impact of the initial floor on TIPP portfolios from 2012 to 2021

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36 Appendix VII

Indices under different investment strategies with rebalancing and the capital injection in Beijing

This table reports the portfolio value, the expected return, and the one year 99% VAR from 2012 to 2021 with the capital injection in Beijing. The capital injection is estimated based on the normal premium payments. The constant-mix strategy with an allocation of 40% to the risky asset, and 60% to the riskless asset is considered as the bench mark portfolio. The CPPI has a multiplier of 2. The TIPP has a multiplier of 2 and a pre-set floor that is 90% of its initial investment. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

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37 Appendix VIII

Indices under different investment strategies with rebalancing and the capital injection in Shanghai

This table reports the portfolio value, the expected return, and the one year 99% VAR from 2012 to 2021 with the capital injection in Shanghai. The capital injection is estimated based on the normal premium payments. The constant-mix strategy with an allocation of 40% to the risky asset, and 60% to the riskless asset is considered as the bench mark portfolio. The CPPI has a multiplier of 2. The TIPP has a multiplier of 2 and a pre-set floor that is 90% of its initial investment. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

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38 Appendix IX

Indices under different investment strategies with rebalancing and the capital injection in Tianjin

This table reports the portfolio value, the expected return, and the one year 99% VAR from 2012 to 2021 with the capital injection in Tianjin. The capital injection is estimated based on the normal premium payments. The constant-mix strategy with an allocation of 40% to the risky asset, and 60% to the riskless asset is considered as the bench mark portfolio. The CPPI has a multiplier of 2. The TIPP has a multiplier of 2 and a pre-set floor that is 90% of its initial investment. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

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39 Appendix X

Indices under different investment strategies with rebalancing and the capital injection in Chengdu

This table reports the portfolio value, the expected return, and the one year 99% VAR from 2012 to 2021 with the capital injection in Chengdu. The capital injection is estimated based on the normal premium payments. The constant-mix strategy with an allocation of 40% to the risky asset, and 60% to the riskless asset is considered as the bench mark portfolio. The CPPI has a multiplier of 2. The TIPP has a multiplier of 2 and a pre-set floor that is 90% of its initial investment. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

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40 Appendix XI

Indices under different investment strategies with rebalancing and the capital injection in Zhengzhou

This table reports the portfolio value, the expected return, and the one year 99% VAR from 2012 to 2021 with the capital injection in Zhengzhou. The capital injection is estimated based on the normal premium payments. The constant-mix strategy with an allocation of 40% to the risky asset, and 60% to the riskless asset is considered as the bench mark portfolio. The CPPI has a multiplier of 2. The TIPP has a multiplier of 2 and a pre-set floor that is 90% of its initial investment. The initial investment is 11,963.08 Yuan. The currency unit is Chinese Yuan (CNY).

Dynamic investment strategies for Chinese pension funds