My Research on Social Security Fund of China

ContentsIntroduction.................................................................................................................................................2

Choosing Proxies.........................................................................................................................................3

Markowitz Mean Variance Model...............................................................................................................7

Capital Allocation in Reality of the Social Security Fund............................................................................13

Conclusion.................................................................................................................................................15

IntroductionAccording to UN criterion, those societies whose population at age 65 or higher makes up more than 7 percentage of total population are defined as aged society. In 2013, population at age 65 or higher is 9.7 percentage of total population in China, which means China has already stepped into stage of aged society. Those aged population need enough income, medical services and many other social arrangements to live better lives after they contribute their time to the whole society when they are able to work. China has the world’s largest population and the aged population is tremendous. This puts a huge financial stress to China’s social security system, especially the pension system. Society security fund (hereinafter referred as the fund) must find efficient ways to realize enough appreciation to meet the fast increasing need of aged people. In 2000, the State Department approved to establish the National Council for the Social Security Fund (NCSSF) whose main responsibility is to manage the fund which was set in the same year. The fund consists of basic pension insurance fund, unemployment insurance fund, basic medical care insurance fund, work injury insurance fund, and maternity insurance fund. Pension insurance fund is the majority of the fund and counts for approximately 70 percentage of the fund.

Table 1 shows the historical data about the fund’s income from investments, rate of return, and inflation rate from 2000 to 2014. The yearly average rate of return from 2000 to 2014 is 8.36 percentage, higher than the yearly average inflation rate during the same period, 2.42 percentage.

YearIncome from Investments

(in CNY 100 million)

Rate of Return (%)

Inflation (%)

2000 0.17 − −2001 7.42 1.73 0.72002 19.77 2.59 -0.82003 44.71 3.56 1.22004 36.72 2.61 3.92005 71.22 4.16 1.82006 619.79 29.01 1.52007 1453.5 43.19 4.82008 -393.72 -6.79 5.92009 850.43 16.12 -0.72010 321.22 4.23 3.32011 74.6 0.86 5.42012 654.35 7.1 2.62013 685.87 6.2 2.62014 1392 11.43 2Total 55801 8.362 2.423

1. The number is adjusted based on changes of accounting principles2. Geometric mean of historical data3. Geometric mean of historical dataTable 1: History data of social security fundSource: National Council for Social Security Fund, PRC

Regulated by Interim Policy of Managing Society Security Fund and several other following laws, the fund can spread its capital into cash in banks, bonds, stocks, entrusted loans, and equity investments. All investment instruments have restrictions relative to total asset of the fund: Cash in banks should be more than 10 percentage of total invested capital of the fund; sum of treasury bonds and cash in banks should be more than 50 percentage; Finance Bonds and corporate bonds rated as investment level or higher should be less than 10 percentage; stock investments should be less than 40 percentage; entrusted loans should be less than 5 percentage; equity investments should be less than 30 percentage. Table 2 shows the details of restrictions to each investment instruments.

Investment Instruments Restriction 1 Restriction 2

Treasury Bonds>= 50%

Cash in banks >= 10%Finance Bonds

<=10%Corporate BondsStocks <= 40%Direct Equity Investments <= 20%Equity Investment Funds <= 10%Entrusted Loans <= 5%Table 2 :Restrictions on investment instrumentsSource: Compiled from data from National Council for Social Security Fund, PRC

Under these restrictions, what is the optimal weight assigned to each asset? Is 8.36 percentage a good investment returns? Should the regulations loosen these restrictions? I will use the famous Markowitz Mean-Covariance model to answer these questions theoretically.

Choosing ProxiesThe result from the model will be much more concise if I can get the real investments details of the fund. Unfortunately, these details are almost impossible to be acquired. The published data only depict a vague picture of the fund investments. To overcome the problem, using some proxies from markets is the one feasible approach. I use 8 proxies to represent the investment instruments. Table 3 shows all the proxies for all investment instruments.

Investment Instrument ProxyTreasury Bonds ChinaBond Treasury Bond Aggregate Full Price IndexFinance Bonds ChinaBond Finance Bond Aggregate Full Price IndexCorporate Bonds ChinaBond Corporate Bond Aggregate Full Price IndexStocks Shanghai Shenzhen CSI 300 IndexDirect Equity Investments Finance Index of Shanghai Stock Exchange

Equity Investment FundsHigh-Tech Index of Shanghai Stock ExchangeEmerging Index of Shanghai Stock Exchange

Entrusted Loans Monthly Official Interest Rate of Loans of Financial InstitutionsTable 3: Proxies chosen for investment instruments

Treasury Bonds

Treasury bonds are the commonest instruments for pension fund all over the world. For the fund, safety comes before profitability. Given the lowest default risk of treasury bonds, they become a fixed part in the fund’s portfolios. I use ChinaBond Treasury Bond Aggregate Full Price Index, provided by China Government Securities Depository Trust & Clearing Co Ltd (CDC), as the proxy of Treasury bonds.

Finance Bonds and Corporate Bonds

Finance bonds and corporate bonds are bonds issued by financial institutions and corporates. These two bonds have higher risks than Treasury bonds but have higher yields, which are attractive to increase total return of the fund’s investment instruments. Actually, finance bonds have almost the same, low default risk with Treasury Bonds in China. Financial fields are the only several fields that still are not fully opened to society. All the financial institutions have earned huge monopoly profits after China’s economic reformation. So bankruptcy for banks in China is almost impossible, making finance bonds a safe and profitable investment instrument to the fund. Compared with finance bonds, corporate bonds have higher default risk with higher yields. It is a good choice to further increase investment return.

The risks of holding bonds are mainly the interest rate risk. The changes of interest rate have a direct influence on bond prices. So, in turn, the changes of bond prices can reflect the risks of holding bonds. Therefore, the three bond aggregate full price indices are good indicators of risks of holding bonds.

Stocks

Because of the regulations, NCSSF cannot directly buy stocks from market. However, it can allocate its capital to different sub-funds which are managed by financial institutions. These financial institutions must comply with the NCSSF’s guides, which require that financial institutions seek medium- and long-term investment opportunities in certain stocks that have adequate liquidities and rate of dividends. Moreover, corporate issuing these stock should reach certain economy of scale to be qualified as potential targets of sub-funds. Here I choose Shanghai Shenzhen CSI 300 Index as the proxy. The index is the first index published by both Shanghai Stock Exchange and Shenzhen Stock Exchange in 2004. The index is made up of 300 out of approximately 2750 listed companies in the two exchanges. These component companies hold more than 60 percentage of total market capitalization and are the most frequently traded securities. Even though sub-funds neither allocate their stock portfolio fully mirroring the index nor only trade stocks incorporated in the index, sub-funds frequently change components of their portfolio by continuously buying and selling certain securities, most of which are component of the index. So Shanghai Shenzhen CSI 300 Index is a good proxy for stocks investments of the fund for most component securities are sub-funds’ long-term target.

Equity Investment

NCSSF can make equity investment in two ways: directly buying equity from certain corporates and buying shares in certain equity investment funds managed by financial institutions. Specially, direct equity investment should be less than 20 percentage and equity investment funds should be less than 10 percentage.

The direct equity investments basically focus on financial areas. Started from 2007, NCSSF made equity investments in several giant financial institutions in China. NCSSF invested CNY 15.5 billion in Agricultural Bank of China, CNY 10 billion in Bank of Communication, CNY 10 billion in Bank of China, CNY 10 billion in Industrial and Commercial Bank of China, CNY 10 billion in China Development Bank, and CNY 10 billion in People’s Insurance Company of China, and CNY 5 billion in

China Cinda Asset Management Co., LTD. NCSSF also made other equity investment in small amount in other financial institutions and corporates, such as Beijing-Shanghai High-speed Rail Co., LTD with CNY 10 billion. Financial Index of Shanghai Stock Exchange contains 30 securities, including 14 banks, 8 securities companies and 4 insurance companies. The index is an overall market indicator of financial areas in China. So I use the index as the proxy of the direct equity investments.

To spread risks and increase investment return, NCSSF also “hire” certain equity investment funds to manage its capital. These equity investment funds are managed by the best asset management companies with professional managers. All these funds mainly set their feet in high-tech and emerging industry, not only because these industries have the highest profit potential but also because the regulations require that social security support such industries. Some of companies funded by the equity investment funds are publicly traded, but some are not. To reflect the changes of these two industries, I choose two related indices in Shanghai Stock Exchange, High-tech Index and Emerging Index. The intuition behind is that these two indices can give us an overall view about the market expects on these two industries, which will in turn affect all companies, private or public, in the two industries.

Entrusted Loans

In 2007, China Ministry of Finance and Ministry of Labor and Social Security (now Ministry of Human Resources and Social Security) approved NCSSF to invest the fund into entrust loans underwritten by banks. Then major borrowers are Ministry of Railways, State Grid Corporation, and China Guodian Corporation, a state-owned corporation in power generation industry. All borrowers have very high creditworthiness to guarantee the collection of interest and principal. The basic risk involving in entrusted loans is the changes of interest rate of loan determined by the Central Bank. These entrusted loans are usually medium- or long-term, so I take the official 5-year or more interest rate of loan of financial institutions as the indicator of entrusted loans. And the expected rate of return is the weighted average interest rate of loan where days of interest rate applied are the weight (see worksheet Rf, Rm & int rate of loan). To get the interest rate of loan applied to each month, I simply take the yearly interest rate of loan divided by 12.

Cash in Banks

All investment instruments have risks that could earn negative returns. If all the capital are invested for certain term, the liquidity will decrease and will impair the fund’s ability of pay and lives of insurant. So across the world, the fund should reserve certain portion of cash in case of any emergencies. A portion of the reserved cash will be saved as demand or fixed-term deposit in banks. The regulations require the fund reserve certain cash equal to two-month defrayment and the rest be saved as one-year fixed deposit. The latter one is the majority of the cash. So I take the one-year deposit interest rate as the indicator of cash in banks. The expected rate of return is the weighted average interest rate, where days of interest rate applied are the weight (see worksheet Rf, Rm & int rate of loan). To get the interest rate applied to each month, I simply take the yearly interest rate of loan divided by 12.

Risk Free Rate

Unlike the financial market in U.S., financial market in China is far less capitalized and transparent. A large amount of social resources are not publicly traded or only traded between private sectors. The lack of transparency leads to severe rent-seeking, illegal insider trading, and financial scandal. The two factors together make it difficult to find an efficient indicator of the overall risk free rate. Chinese scholars mainly choose between two benchmark rates as risk free rate: yields of Treasury Bonds and interest rate of fixed-term deposit. Treasury Bonds have low default risk for they are backed by the government.

However, the current volume of Treasury Bonds is not large enough to reflect the risk free rate to the whole market. Compared with many developed counties and even certain developing countries, China has a high saving rate, because most people still regard saving as the best investment ways against inflation. Hence the interest rate of deposit has the widest application in financial fields. Given the changes of macroeconomic conditions, the central bank frequently adjust the interest rate of deposit with various terms. Additionally, deposits in bank have the same default risk as Treasury Bonds because all banks are government backed in China. The wide application, timeliness, and low default risk make the interest rate of deposit a better indicator than yields of Treasury Bonds. Specially, I choose the interest rate of one-year deposit as the risk free rate. On one hand, long time span can capture the interest rate more concisely; on the other hand, data from long ago are not valid to reflect the recent economy. Choosing 1999 as the beginning point is the compromise of the two considerations (actually, all data used in the model start after 1999). I calculate the weighted average interest rate of one-year deposit started from 1999(see worksheet Rf, Rm & int rate of loan).

Beta

Among the 8 proxies, 4 are stock index. In order to get the expected return of relative investment instruments, it is essential to calculate their Betas. Here I use the same method which is used to calculate Beta of certain stock: running a regression between changes of stock prices and changes of benchmark market index. Specially, to get the Beta of Shanghai Shenzhen CSI 300 Index, I run regression between changes of Shanghai Shenzhen CSI 300 Index and changes of Shanghai Composite Index and Shenzhen Component Index. Then I take the average of two coefficients from two regressions as the Beta of Shanghai Shenzhen CSI 300 Index. The intuition is that all component securities of Shanghai Shenzhen CSI 300 Index come from the two benchmark market indices and running regression between changes of Shanghai Shenzhen CSI 300 Index and changes of either benchmark market index can’t fully reflect the volatility of Shanghai Shenzhen CSI 300 Index. Alternatively, I calculate Betas of the other three stock indices (see worksheet Beta).

Bond Yields

Treasury Bonds in China have an unbalanced term structure. Short-term and medium-term Treasury Bonds are made up a large portion of total Treasury Bonds (see worksheet Treasury Bonds Term Structure). The fund seeks long-term investment in Treasury Bonds while retail investors tend to buy the short-term and institutional investors prefer the mixture of the short-term and the medium-term. So I choose the average yield of 10-year Treasury Bonds to represent the fund’s rate of return form Treasury Bonds investments.

For the safety purposes, the fund should prudently invest in finance and corporate bonds because of the bonds’ higher risks. I choose the interbank finance and corporate bonds both rated AAA to reflect the rate of return from the two bonds.

All the monthly yields for the three bonds come from China Government Securities Depository Trust &Clearing Co Ltd (CDC) (see worksheet Bond Yield).

Markowitz Mean Variance ModelMarkowitz mean variance model deals with the problem about how to allocate capital to each security (asset) in a risky portfolio. The model treat the variance as a measure of the risk. Markowitz argued that it is not a security’s own risk that is important to an investor, but rather the contribution the security makes

to the variance of his entire portfolio --- and that this was primarily a question of its covariance with all the other securities in his portfolio(Mark Rubinstein, 2002). The sum of one security’s covariance with all other securities in the risky portfolio is this security’s contribution to the variance of the risky portfolio. In the same way we can also calculate the rest sum of covariance for all other securities in the risky portfolio. Then we can get the variance of the risky portfolio. Using computer program, we can set a goal of return and request the computer to find the weights to each security that can minimize the variance of the risky portfolio. The weights are the optimal capital allocation plan under the goal of return. And the weighted average return is the optimal return with the minimum variance. Setting different goals of return, we can get a group of weights with minimized variances. Charting all these returns and the corresponding minimized variances, we can get the famous efficient frontier of risky assets. Now we have solved the problem about how to spread out capital to different securities in the risky assets.

As required by the model, we should constitute a portfolio with risk free assets and risky assets. Now we can use the capital allocation line (CAL) to get the optimal return of the risky portfolio. CAL depicts all the risk-return combinations available to us. The slope of CAL is called the Sharpe ratio, a ratio reflecting the incremental return per incremental risk. Then we adjust the slope of CAL until CAL is tangent to the efficient frontier. The risky portfolio, constituted by the securities with weights indicated by the tangent point, is the optimal risky portfolio that is feasible to us. Finally, the expected return of the complete portfolio depend on our preference on the mixture between the risk free assets and the risky assets. More risk free assets in the portfolio will result a lower expected return.

Data Range

Data used in the model are ChinaBond Treasury Bond Aggregate Full Price Index, ChinaBond Finance Bond Aggregate full price index, ChinaBond Corporate Bond Aggregate full price index, Shanghai Shenzhen CSI 300 Index, Finance Index of Shanghai Stock Exchange, High-Tech Index of Shanghai Stock Exchange, Emerging Index of Shanghai Stock Exchange, Monthly Official Interest Rate of Loans of Financial Institutions, Shanghai Composite Index, Shenzhen Component Index (see worksheet Historical Data). All data are used either as direct inputs (such as monthly changes of ChinaBond Treasury Bond Aggregate Full Price Index) to the model or as inputs to generate certain properties, such as Beta and risk free rate. Data range should be as large as possible to reflect historical fluctuations. But data too long ago cannot reflect the current conditions. The objective of the model the NCSSF, which was established in 2000. Too be consistent with this fact, data used to generate properties start from 2000 (see worksheet Historical Data) and the data used as direct inputs to the model start from January, 2009 (see worksheet Selected Range for the Model), if the series can be tracked before 2009. All data end at January, 2015.

Application of the Model

In the previous paragraph, I present all the restrictions on all the investment instruments, included the risk free asset, Certificate of One-year Deposits, and the other risky assets. In Markowitz mean-variance model, the risk free asset is isolated from the model computation. So for all the risky asset, I recalculate their restrictions. To simplify the computation, I assume that the capital invested as Certificate of One-year Deposits is fixed at 10 percentage, the lowest bound set by the Interim Policy of Managing Society Security Fund, and thus the capital invested in Treasury Bonds is 40 percentage or higher. In terms of the risky portfolio only, the new restrictions are recalculated relatively to each instrument in the risky portfolio. For example, the new restriction for Treasury Bonds in the risky portfolio should be 40%/90%=44.44% or higher. Only in this way can I get the 100 percentage weight when add the risk free and risk assets together. The new restrictions are shown in table 4.

Investment Instruments In Risky Portfolio Restriction 1 Restriction 2

Treasury Bonds >=44.44% Finance Bonds

<=11.11Corporate Bonds Stocks <= 44.44% Direct Equity Investments <= 22.22% Equity Investment Funds <= 11.11% Entrusted Loans <= 5.55% Table 4: Adjusted Restrictions on Investment InstrumentsSource: Compiled from data from National Council for Social Security Fund, PRC

Under all the restrictions, the optimal expected return of the risky portfolio is 4.372 percentage, resulting an expected return, 4.192 percentage, of the complete portfolio (see worksheet Efficient Frontier with restric). The result is much lower than the reported figure, 8.36 percentage. At the same time, I recalculate the optimal expected return of the risky portfolio without restriction (the weight of risk free asset is still 10 percentage). Without restrictions, the optimal expected return of the risky portfolio is 5.631 percentage, which brings the optimal expected return of the complete portfolio to 5.326 percentage (see worksheet Eff Fro Without Restrictions). After the adjustment, the optimal expected return goes up but still is much lower than 8.36 percentage.

In the model, I use CAPM, which takes the Beta of Shanghai Shenzhen CSI 300 Index into the formula, to calculate the expected rate of return from investment in stock market. In this way, the changes of annual return of the index relative to the benchmark index determine the expected rate of return from stock market. However, the annual return is an overall indicator of the average return of investors in the market whose portfolios fully mirror the index. In term of certain investor, we should also take some other factors, such as the amount of investors’ capital and investors’ degree of specializations, into consideration. Actually, given the fund’s huge amount of capital (sub-funds managed by financial institutions) invested in the stock market and the high degree of specialization provided by financial institutions, the fund’s overall rate of return from stock market should be higher than the market average. According to available published information, the fund’s average rate of return from stock market from 2003 to 2011 is 18.61 percentage (geometric mean), which is higher than 9.936 percentage. The result is understandable. Once the huge amount of capital flows into certain stock, many other relative smaller investors will follow the fund’s step, bidding up the stock prices. With high degree specialization, the sub-funds have more accurate judges on the market trend, hence guaranteeing significant profits and limited losses.

Shanghai Shenzhen CSI 300 index went up for approximately 42 percentage after 2011, generating a yearly geometric mean of approximately 12.39 percentage. And it is highly possible that the fund earned higher-than-average profits. Here I assume that the fund’s rate return from stock market is high enough to support a same rate of return as from 2003 to 2011. In my new calculation, I set the expected rate of return from stock market at 18.61 percentage. Using the new data, I calculate the optimal expected return of the risky portfolio and the complete portfolio under all restrictions (see worksheet Eff Fro With Restri & Higher Re) and no restrictions (see worksheet Eff Fro With Higher Re & No Res).

The summary of results under different circumstances is shown in table 5 and 6. Efficient frontier for each circumstances is shown in figure 1 to 4.

Treasury Bonds

Finance Bonds

Corporate Bonds

StocksDirect Equity

Investments

Equity Investment

Funds in High-Tech Industry

Equity Investment

Funds in Ererging Industry

Entrusted Loansl

Weight 0.7756919 0.0000000 0.1111000 0.0564192 0.0000000 0.0000000 0.0012888 0.0555000Optimal Standard Deviation of Risky Portfolio 2.911%Optimal E( r ) of Risky Portfolio 4.372%Max Sharpe ratio 0.616Weight 0.0000000 0.3952029 0.2022345 0.0237442 0.0000000 0.0000000 0.0000000 0.3788185Optimal Standard Deviation of Risky Portfolio 2.256%Optimal E( r ) of Risky Portfolio 5.777%Max Sharpe ratio 1.417Weight 0.7388429 0.0000000 0.1111000 0.0945571 0.0000000 0.0000000 0.0000000 0.0555000Optimal Standard Deviation of Risky Portfolio 3.450%Optimal E( r ) of Risky Portfolio 5.425%Max Sharpe ratio 0.825Weight 0.0000000 0.4423138 0.1693122 0.0387375 0.0000000 0.0000000 0.0000000 0.3496364Optimal Standard Deviation of Risky Portfolio 2.321%Optimal E( r ) of Risky Portfolio 6.142%Max Sharpe ratio 1.535

Table 5: Summary of calculations under different circumstances for risky portfolio

Optimal Risky Portfolio

Restrictions

No Restrictions

Higher Expected Rate of Return of

Stocks and Restrictions


Stocks but No Restrictions

Treasury Bonds

Finance Bonds

Corporate Bonds

StocksDirect Equity

Investments

Equity Investment

Funds in High-Tech Industry

Equity Investment

Funds in Ererging Industry

Entrusted Loansl

Cash in Banks

Weight 0.6981227 0.0000000 0.0999900 0.0507773 0.0000000 0.0000000 0.0011599 0.0499500 0.1000000

Optimal Standard Deviation of Complete Portfolio 2.620%

Optimal E( r ) of Complete Portfolio 4.192%

Weight 0.0000000 0.3556826 0.1820110 0.0213698 0.0000000 0.0000000 0.0000000 0.3409366 0.1000000



Weight 0.6649586 0.0000000 0.0999900 0.0851014 0.0000000 0.0000000 0.0000000 0.0499500 0.1000000



Weight 0.0000000 0.3980824 0.1523810 0.0348638 0.0000000 0.0000000 0.0000000 0.3146728 0.1000000


Optimal E( r ) of Complete Portfolio 5.786%Table 6: Summary of calculations under different circumstances for complete portfolio

Optimal Complete Portfolio

Restrictions

No Restrictions


Stocks and Restrictions


Stocks but No Restrictions

0.000% 2.000% 4.000% 6.000% 8.000% 10.000% 12.000% 14.000% 16.000% 18.000%0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

Figure 1: Efficient frontier with restriction

Efficient Frontier CAL

Standard Deviation

Expe

cted

Ret

urn

0.000% 5.000% 10.000% 15.000% 20.000% 25.000% 30.000%0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

18.0%

Figure 2: Efficient frontier without restriction


Standard Deviation

Expe

cted

Ret

urn

0.000% 2.000% 4.000% 6.000% 8.000% 10.000% 12.000% 14.000% 16.000%0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

Figure 3: Efficient frontier with restrictions and a higher expected return of stock


Standard Deviation

Expe

cted

Ret

urn

0.000% 5.000% 10.000% 15.000% 20.000% 25.000% 30.000% 35.000%0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

18.0%

20.0%

Figure 4: Efficient frontier with a high expected return but without restrictions


Standard Deviation

Expe

cted

Ret

urn

I find a very interesting results from my calculations. The benefits of no restrictions are obvious. Without restrictions, the optimal expected returns of risky and complete portfolios increase while the optimal standard deviations of risky and complete portfolios decrease. The maximum Sharpe ratios also significantly increase without restriction compared to with restrictions. Higher Sharpe ratios mean more incremental return per incremental risk. The result proves that restrictions on investment instruments impair the overall performances of the fund.

Some investment instruments have significant fluctuations in their weights when I eliminate all restrictions. The optimal weights of Treasury Bonds with restrictions are more than 65 percentage which, however, will be 0 percentage without restrictions. The optimal weights of stock also go down. The optimal weights of finance and corporate bonds and entrusted loans dramatically increase if eliminating all restrictions. The results are consistent with my expectations. Even though Treasury Bonds are the safest investment instrument, their low returns make them inferior instruments. The high risk of stock also make stock less attractive to the fund. Excess investments with low risks in the portfolio increase the need of high risk investments, as what happens to the changes of stock weight in the portfolio. Finance and corporate bonds and entrusted loans have adequate expected returns with relative low risks (see worksheet Efficient Frontier with restric). This kinds of investment instruments are indispensable parts of any portfolios, because all portfolio managers are working hard to find ways to earn as much profits as possible under as low risks as possible.

So far, my calculations are all based on the assumption that weight of cash in banks is fixed at 10 percentage. Table 7 shows the optimal E(r) and standard deviation of complete portfolio and maximum Sharpe ration with different weights of cash in banks in complete portfolio under all restrictions and the higher expected return from stocks. The optimal E (r) and standard deviation of complete portfolio go up when weights of cash in banks go down. It is consistent with my expectations that adding more risk free asset into complete portfolio will lower the optimal E(r) and standard deviation of complete portfolio. What surprise me is that the maximum Sharpe ratio gradually increases, indicating that, adding more risk free asset into complete portfolio, decreases of the optimal standard deviation exceed decreases of expected excess return (optimal E(r) of risky portfolio minus risk free rate). From this perspective, risk free asset will help improve the performance of the fund. But this is counterintuitive to the fund’s goal, increase the investment return of the fund with acceptable and controllable risk. The goal requires that the fund not sacrifice investment return for the safety purpose.

Percentage of Certificate of Deposits in Complete Portfolio

Optimal E( r ) of Complete

Portfolio

Optimal Standard Deviation of

Complete Portfolio

Maximum Sharpe Ratio

10% 5.140% 3.104% 0.82515% 4.996% 2.904% 0.83220% 4.853% 2.705% 0.84025% 4.711% 2.508% 0.85030% 4.570% 2.311% 0.86135% 4.425% 2.112% 0.87440% 4.285% 1.917% 0.88945% 4.145% 1.724% 0.90850% 4.007% 1.534% 0.930

Table 7: Results under different weight of cash in banks

Capital Allocation in Reality of the Social Security FundWe should notice that, in my optimal calculations, the fund shall never use some investment instruments, such as finance bonds and direct equity investments. I get this result because all I have done so far are model analysis. However, the fund has certain amount of capital invested in the two instruments in reality. If I can use these more realistic data in my model, I can take a more precise glimpse on how well the fund’s performances are. Unfortunately, except capital allocation across several broad classes of assets, published information has never mentioned how much capital of the fund is invested in each investment instrument (see worksheet Assets Details From 2008-2013). For example, depend on holder’s initial attitude toward an asset, an asset can be classified as financial assets held for trading, financial asset available for sale, or investments held to maturity. In the balance sheets of the fund, they only provide total amounts to each major asset item without any information about standards used to classify assets, such as their initial attitude to a certain investment instrument. Moreover, switching to the new accounting principles has put another barrier in the way to reveal the true capital allocations. Balance sheets before 2008 provided more details on investment instruments but the switching makes tracking old data before 2008 meaningless.

NCSSF released an explanation on 2013 annual report, which pertained to some details about its capital allocations to several investment instruments. As of 2013, cash in banks, entrusted loans, equity investments, state-owned shares shifted (can be regarded as stock investments), and index investments (can be regarded as stock investments) are 26.08 percentage, 3.36 percentage, and 14.17 percentage, 6.63 percentage, and 3.71 percentage, respectively, of total asset. The explanation also presented some detail about return of certain investment instruments: CNY 20.557 billion from domestic stock investments, CNY 7.712 million from international stock investments (neglected in my model), CNY 16.616 million from equity investments, CNY 22.974 million from fixed income investments (can be regarded as bond investments), and CNY 0.728 million from cash and cash equivalent (can be regarded as cash in banks).

To generate the almost real weight to each investment instrument, I directly use weights of cash in banks and entrusted loans from the explanation. For weights of direct equity investments and equity investment funds, I assign 2/3 of 14.17 percentage to direct equity investments and the rest 1/3 to equity investment funds, because the maximum percentage of direct equity investment is twice as that of equity investment funds. Then I take the profit from domestic stock investment divided by the average rate of stock investment return from 2003 to 2011 to get the capital which is managed by authorized financial institutions. This part of capital counts for approximately 8.9 percentage of total asset in 2013. Adding 8.9 percentage with 6.63 percentage and 3.71 percentage, I get the total capital of the fund invested in stock market, 19.24%. Weights of the fixed income investments will counts for the rest, 37.16 percentage. Before switching to the new accounting principles, Treasury Bonds hold the most part of the fixed income instruments (according to data I collect, more than 95 percentage of fixed income instrument is Treasury Bonds). To simplify, I allocate 95 percentage to Treasury Bonds, which is 35.29 percentage, and 2.5 percentage to both finance bonds and corporate bonds, which is 0.93 percentage. I also transform these weights in to weights when cash in banks is taken out of the risky portfolio. The new weights are shown in table 8.

Investment Instruments Weights

Weights Without Cash in Banks

Treasury Bonds 35.29% 47.74%Finance Bonds 0.93% 1.26%Corporate Bonds 0.93% 1.26%Stocks 19.24% 26.03%Direct Equity Investments 9.45% 12.78%Equity Investment Funds in High-Tech Industry 2.36% 3.19%Equity Investment Funds in Emerging Industry 2.36% 3.19%Entrusted Loans 3.36% 4.55%Cash in Banks 26.08% N/A

Total 100.00% 100.00%

Table 8: Capital allocation across different investment instruments

Using this group of weights, I get an expected return of complete portfolio, 6.895 percentage, a little higher than the reported return, 6.2 percentage. Through calculation by setting the return target to 8.418 percentage, the optimal standard deviation of risky portfolio is 8.511 percentage, lower than 12.444 percentage. Alternatively, setting the standard deviation of risky portfolio to 12.444 percentage generates an optimal expected return, 10.466 percentage, higher than 8.418 percentage. The results are because the real complete portfolio of the fund has to contain certain level of instruments with relative low returns and relative high risks. Also note that the Sharpe ratio here, which is 0.469, is lower than those in any different circumstances talked previously

Risky PortfolioTreasury

BondsFinance Bonds

Corporate Bonds

Stocks Direct Equity InvestmentsEquity Investment Funds in

High-Tech Industry

Equity Investment Funds

in Ererging Industry

Entrusted Loansl

Weight 0.4774000 0.0126000 0.0126000 0.2603000 0.1278000 0.0319000 0.0319000 0.0455000Standard Deviation of Risky Portfolio 12.444%E( r ) of Risky Portfolio 8.418%Sharpe ratio 46.916%

Complete PortfolioTreasury

BondsFinance Bonds

Corporate Bonds

Stocks Direct Equity InvestmentsEquity Investment Funds in

High-Tech Industry

Equity Investment Funds

in Ererging Industry

Entrusted Loansl

Certificate of Deposits

Weight 0.3528941 0.0093139 0.0093139 0.1924138 0.0944698 0.0235805 0.0235805 0.0336336 0.2608000Standard Deviation of Complete Portfolio 9.198%E( r ) of Complete Portfolio 6.895%Table 8: Summary of calculations on real capital allocation

ConclusionCompared with my calculation, the rate of return reported by the fund is higher. But the fund seem to be radical to its certain investment instruments. It should cut its capital invested in equity investments, which have relative high risks. At the same time, to increase the safety of its investments, the fund should allocate more capital to entrusted loans, which have adequate rate of return with a risk as low as Treasury Bonds. For the stock investment, the fund should increase its invests, because even though stocks have the almost highest risk among all the investment instruments used by the fund, plenty of return can be generated without bearing too much risk due to the high degree of specializations of financial institutions, which manage sub-funds, and large amount of capital the fund owns. Fixed income instruments are essential parts of the fund’s portfolio, because they provide high securities on the future returns, which is important to lower the overall risk of the fund’s portfolio. Compared with Treasury bonds, finance and corporate bonds hold really small weights. Actually, in the long run, the fund should invest more in finance and corporate bonds to increase the return contribution from fixed income instruments. But all the finance and corporate bonds invested have to have high ratings.

Results generated by the model more or less deviate from the reported results. Major reasons behind can be summarized as the follows;

1. Accuracy and representativeness of choosing proxies. To quantify the risks and expected returns of each investment instrument, I choose several proxies from the financial market, such as indices and interest rate. But the accuracy and representativeness of choosing them are hard to testify. For example, I use Shanghai Shenzhen CSI 300 Index as the proxy of stock investments. The implied assumption is that the fund can only trade securities that are incorporated into the index. But the fund does trade a lot of securities out of the index range. Moreover, the frequency of trading and holding periods are impossible to track.

2. Limited information published by NCSSF. As the only agency responsible for the social security fund, NCSSF have all the information about all aspects of the fund. Unfortunately, NCFFS only open a small portion of information to the public, resulting in excess assumptions in the model.

3. Applicability of Markowitz Mean Variance Model. The model is mainly based on the estimations of the expected rate of return and expected risk of each investment instruments. If all the estimations are error free, the model will be perfect applicable in allocating capital in a portfolio. But the estimation errors can never be eliminated. Estimation errors can make weights allocated to certain instruments much higher than another even if the former one only slightly better performs than the latter one. Furthermore, the model assume the standard deviation is the measure of the risk. But a lot of academic and empirical work prove that the standard deviation as the measure of the risk is appropriate only when the returns are normal distribution. Obviously, returns from entrusted loans and cash saved in banks are not normal. Finally, the model will better perform if the fund only makes one-period investment. That means that fund will never change its asset allocation once it is chosen. But the fund have been changing and adding investment instruments and limitations on them for years.

Documents

My Research on Social Security Fund of China