What Are the Best Tips for Evaluating Index Fund Performance?

Fund performance evaluation is a fair and objective evaluation of the investment ability of fund managers on the premise of excluding the general market return rate, the market risk of the fund, and the contingency of earnings.

Fund Performance Evaluation

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Fund performance evaluation is a fair and objective evaluation of the investment ability of fund managers on the premise of excluding the general market return rate, the market risk of the fund, and the contingency of earnings.

Fund performance evaluation is a complex issue. It not only involves objective and effective measurement methods for measuring performance, but also relates to factors such as the sustainability of fund performance and performance attribution analysis. Judging from the current situation, China's research on fund performance evaluation is still very weak, not only in theoretical research, but also basically staying at the theoretical level abroad in the 1990s, and it is relatively lacking in empirical research.

The theoretical research and practice in foreign countries in recent decades show that quantitative analysis methods have been widely introduced into fund performance evaluation. With the continuous development of modern financial theory, fund performance evaluation has conducted many empirical analyses under the guidance of theoretical research, and the results of empirical analysis have in turn verified relevant financial theories and assumptions. In fact, many controversial assumptions in the financial investment theory community can still be found in the field of fund performance evaluation.

Foreign research on fund performance evaluation has a long history, a relatively complete theoretical system, and a large number of empirical studies, but China is still basically at the beginning stage. This is because securities investment funds have been in China for a relatively short time, even if they are calculated from the irregular establishment of funds in various places in the early 1990s (such as the Blue Sky Fund, Tiancheng Fund, and GF Fund, etc.), it is only over 10 years. It is only a few years from the establishment of the first closed-end fund (fund Jintai, fund Kaiyuan) in March 1998. Because the fund size (shares) of closed-end funds does not change with the performance of the fund, the issuance of closed-end funds has been in a situation of over-subscription for a long time. In addition, holders mainly obtain spread income through closed-end fund transactions rather than net value growth. Capital gains, so the research on fund performance evaluation by management companies, holders, regulators and independent third parties is not systematic and thorough. Since Hua'an Fund Company issued the first open-end fund in the Chinese market in 2001, as of December 28, 2005, a total of 217 securities investment funds have officially operated, of which 163 are open-end funds and 54 are closed-end funds. According to the statistics of the Securities Regulatory Commission at the end of November, the current net value of securities investment funds has reached 500 billion yuan; there are 52 fund management companies, of which 49 are officially managed funds; compared with the rapidly growing fund market, China's The theoretical research and empirical analysis of performance evaluation are still far behind.

Performance evaluation abroad has a long history. The portfolio theory, capital asset pricing model, and stock price behavior theory of the 1960s laid the cornerstone of modern fund evaluation theory. In particular, Sharpe / Lintner's capital asset pricing model (CAPM) is the foundation of fund performance evaluation. Treynor, Sharpe, and Jensen each proposed risk-adjusted fund performance evaluation methods at the same time, which enabled performance evaluations to be compared at the same level of risk. Although they choose different indicators to measure risk (the Sharpe index uses all risks). The CPAM model has a long history and is still widely used (eg Malkiel, 1995 and Ferson, Schadt, 1996). However, this theory has also been strongly opposed (RichardRoll 1977, 1978, Admatiand Ross, 1985, and Dybvigand Ross, 1985a, b). For example, the use of securities market lines for performance evaluation is "uncertain." Using this method to judge performance is sometimes viewed as "hopeless" (AdmatiandRoss, 1985, p. 16) and "anything is possible overall." (DybvigandRoss, 1985a, p. 383)

In response to the above criticisms, some improved indicators have been proposed. For example, the information rate, which is the improved Jensen index, evaluates the fund's investment performance through the extraordinary return of unit non-systematic risk. The 1997 Nobel Prize winner Franco Modigliani and his granddaughter Leah Modigliani introduced treasury bonds into the actual asset portfolio of securities investment, constructing a virtual asset portfolio, with its total risk equal to the risk of the market portfolio, by comparing the average return on the virtual asset portfolio with the market portfolio Evaluation of fund performance, this method is named M2.

In 2000, Muralidhar believed that the Sharp value, information rate, and M2 method were not sufficient to effectively perform portfolio construction and fund performance ranking. The key to the problem was insufficient adjustment of the standard deviation between the portfolio and the benchmark, and ignored the "relationship between the portfolio and the benchmark." "Sex" often leads to misordering and evaluation. In view of this, Muralidhar proposed the M3 measurement method. Stutzer (2000) based on the theory of loss aversion, assuming that investors choose to avoid the risk as much as possible, and constructed a new evaluation index, namely the Probability of DecayRate. The biggest feature of this index is that it allows the rate of return to converge to various distributed. When the yield rate converges to the non-normal distributed attenuation degree, the sensitivity to skewness and kurtosis is high, and the risk of funds with positive skewness becomes smaller.

In addition, securities selection and timing, performance attribution, performance continuity, fund style, consistency of performance evaluation, effectiveness of benchmark portfolios, and asset allocation analysis are also hot topics in recent foreign fund performance evaluation studies.

The quadratic equation model (TM model) first proposed by Treynor & Mazuy (1966) can be used to test the timing ability of fund managers. Timing ability refers to the ability of a fund manager to predict whether the return on risky assets will be higher or lower than the risk-free interest rate. Heriksson & Merton (1981) proposed adding a binomial random variable to the CPAM model, which is called the double beta model (HM model). Bhattacharya & Pfleiderer's (1983) research on the HM model shows that their improved model can judge whether fund managers have correctly used the correct information. Connor & Kora jczyk (1991) research shows that when there is a co-skewness between the fund portfolio and market returns, the TM and HM models will get wrong conclusions. Grinblatt & Titman (1989, 1994) proposed a PositivePeriodWeightingMeasure (PPW) model for this situation. This model calculated the weighted rate of return of the excess rate in each period of the period, and gave a comprehensive test result of stock selection and timing. In addition, Chang & Lewellen (1984) proposed a new inspection method based on the APT model. Introduce the variables 1 and 2, and calculate the difference to determine the timing ability of the asset manager.

Fama (1972) first conducted attribution analysis on fund performance and proposed the famous Fama model. Fama's model is built on the premise that the CAPM model is valid. He divides the excess return of the asset portfolio into "selective returns" (consisting of diversified returns and net selective returns) and "risk returns" (by investor risk returns and managers) Risk and reward components) two parts. The BHB model proposed by Brinson, Hood & Beebower (1986) attributes the differences between the asset portfolio and the benchmark portfolio to timing, stock selection, and interaction. However, their findings have also been criticized, such as Hensel, Ezra & Ilkiw (1991), John Nuttall (1998), and others.

Persistence of performance is another major research aspect of performance evaluation. If the performance of the fund is continuous, the results of the performance evaluation are of practical significance to investors. Although research on performance sustainability is often contradictory, many recent studies have tended to believe that the performance of funds is more significant. For example, Brown & Goetzmann (1995) believes that the fund is sustainable in the short term. The more commonly used test methods include the half-period average rank difference test and the cross product ratio (CPRCrossProductRadio) method. The half-period average rank difference test method is to divide the fund into two parts with equal time before and after, and calculate its rank separately. If the ranks of the two paragraphs are equal, it indicates that the performance of the fund has remained stable in the ranking of all funds, and its performance has long-term stability. The CPR method compares the performance of a fund over a certain period with the median value of all funds, marking those with a higher comparison result as W (win) and those with a lower median value as L (lost). Define CPR = WW LL / (WL LW). The value range of CPR is (0, + ). If the performance persistence is worse, the CPR value is closer to 0; otherwise, if the persistence is stronger, the CPR value is closer to positive infinity. According to Carhart (1997), the continuity of short-term fund performance should be attributed to the good or bad stocks held, while the long-term continuity is due to the different design of the fee structure.

Fund style research is a study of the characteristics of fund investment and returns. With the deepening of financial innovation and the intensification of product design competition, many types and styles of funds have gradually appeared in the market. Therefore, the research on the style of the fund has great practicality. The methods of fund style research can be divided into factor analysis and characteristic analysis. The earliest style research method is the so-called HBS (HoldingsBasedStyleAnalysis) method. This method is performed by analyzing all the shareholding information disclosed by the fund. The disadvantage is that "disclosure day modification" behavior cannot be effectively eliminated. In 1992, Sharpe adopted a 12-factor model (the 12 factors are short-term bills, medium-term government bonds, long-term government bonds, corporate bonds, mortgage securities, large-cap value stocks, large-cap growth stocks, medium-cap stocks, small-cap stocks, non- U.S. bonds, Japanese equities, and European equities). This method is called RBS (ReturnBasedStyleAnalysis). The RBS method decomposes fund returns into style returns and choice returns. The selection of factors in the model follows the principles of exclusivity, omission and easy availability. At present, more and more various factor models appear. The characteristic analysis method includes MSB (MorningstarStyleBox) method. The Morning Star Style Box Method (MSB) was proposed by the famous Morning Star company in 1992 and improved in 2002. It first divides each stock in the asset portfolio into large, medium, and small caps, then calculates its value and growth score based on a defined algorithm in each divided market cap interval, and finally positions it to the fund style Different locations in the box.

Golloand Lockwood (1999) studied changes in performance, risks, and investment styles of mutual funds that changed managers during 1983-1991. When reclassifying funds by company size, value / growth, it was found that more than 65% of funds have changed their investment style after changing management.

The consistency of performance evaluation is the difference in the results of research and comparison of fund performance evaluation methods. However, there has been relatively little research in this area. At present, only Wang Cong (2001) has introduced some concepts such as multiple comparisons. The test methods for assessing consistency include Spearman rank correlation test, Kendall collaborative test and multiple comparison method. The Spearman rank correlation test method judges whether the two methods are consistent through the correlation of the order columns formed by the two performance evaluation methods. If the ranks (squares of the differences in ranking) of the two methods are small, it indicates that the two methods are consistent in the evaluation of funds. The Kendall collaborative test is developed on the correlation coefficient test. The Kendall coordination coefficient is defined as 12S / m2n (n2-1). The value of W ranges from 0 to 1. The larger the value of W, the stronger the consistency of performance evaluation methods. In the extreme, a value of W indicates that all performance evaluation methods have the same results. After Kendall's collaborative test, consistent funds can use multiple comparison methods to evaluate overall performance.

Domestic research on fund performance evaluation is still relatively small. Judging from published articles and collected data, domestic research is still limited to the introduction and empirical research of foreign theories, and more on a single theory or perspective. There is a lack of overall and systematic research and lack of Theoretical innovation.

1.Introduction to the Sharpe Index

American economist William Sharp published the article "Community Fund Performance" in 1966, proposing that the fund's performance should be measured by the excess return brought by the fund's total unit risk (including systemic risk and non-systematic risk). This is the Sharpe Index . The Sharp Index measures the fund's performance by the ratio of the average return of the fund's investment portfolio over the risk-free rate of return to the standard deviation of the fund's rate of return during a certain evaluation period. The calculation formula is:

Sp = (rp-rf) / p

Among them, Sp is the Sharpe index, rp is the actual return of the fund portfolio, rf is the risk-free rate of return, and p is the standard deviation of the fund's rate of return.

The theoretical basis of the Sharp Index is the capital asset model (CAPM model), with the capital market line (CML) as the base point for evaluation. If the Sharp index of the fund's securities portfolio is greater than the Sharp index of the market's portfolio M, the fund portfolio is located in the CML. On the contrary, it indicates that it performs better than the market; on the contrary, if the Sharp index of the fund's investment portfolio P is smaller than the Sharp index of the market's securities portfolio M, the fund portfolio is located below the CML, indicating that its performance is worse than the market. Therefore, it can be considered that the larger the Sharp Performance Index, the better the fund performance; otherwise, the worse the fund performance.

2.Introduction to the Treynor Index

Jack Treynor published a paper "How to Evaluate the Management of Investment Funds" in 1965, arguing that a sufficient portfolio of securities can eliminate the non-systematic risk of a single asset, then the systematic risk can better describe the risk of the fund, that is, the change with the return rate The linkage should be systemic risk. Therefore, the Treynolds Index uses the average

The method of comparing risk compensation with its systematic risk to evaluate the performance of investment funds. This is the Reynolds Index, which is equal to the ratio of the fund's excess returns to its systemic risk measure .

The calculation formula is:

Tp = (rp-rf) / p

Among them, Tp is the Treynolds index; p represents the coefficient of the fund's investment portfolio, which is the system risk that the investment portfolio should bear.

The theoretical basis of the Treynor Performance Index is also the capital asset pricing model (CAPM model), but based on the evaluation of the securities market line (SML), when the market is in equilibrium, all asset portfolios fall on SML, that is, The slope represents the Treynor index of the market's portfolio of securities. When the fund s Treynolds index is greater than the slope of the SML, the portfolio is above the SML line, indicating that it performs better than the market. On the contrary, when the fund s Treynolds index is less than the slope of the SML, the investment The fund's portfolio is below the SML line, indicating that its performance is worse than the market performance. Therefore, the larger the Treynor Performance Index, the better the fund's performance; on the contrary, the worse the fund's performance.

3.Introduction to the Jensen index

The American economist Michael Jensen published the article "Performance of Mutual Funds from 1945 to 1964" in 1968, and proposed an absolute index for evaluating fund performance, namely the Jensen Index. He believes that the additional income of the fund's investment portfolio can measure the value of the additional information of the fund, and therefore can measure the investment performance of the fund. The calculation formula is:

Jp = rp- [rf + p (rm-rf)]

---- Jp is the Jensen Index.

The Jensen Performance Index, also known as the alpha value, reflects the performance difference between the fund and the market as a whole. The Jensen Index is also based on the capital asset pricing model and estimates the fund's excess return based on SML. Its essence is to reflect the difference between the return rate of the securities investment portfolio and the equilibrium return rate calculated according to the coefficient of the portfolio. Of course, the larger the difference, the larger the Jensen coefficient, the better the effect of the fund's operation. If it is positive, it means that the fund manager has extraordinary stock selection ability. Compared with the market, the evaluated fund is higher than the market average and the investment performance is good. If it is negative, it means that the fund manager's stock selection ability is not good and cannot run. After the index, the performance of the evaluated fund is inferior to the market as a whole; a value of zero indicates that the fund manager's stock selection ability is average and can only be equal to the index.

The above three indicators are classic methods for measuring fund performance. However, in actual operation, inconsistent evaluation may occur for the same data. The reason is that each indicator has its own characteristics in the measurement of risk and return. It's different.

This section starts from the different measures of risks and returns of various indicators, and analyzes the shortcomings and deficiencies of the Sharp Index, the Treynor Index, and the Jensen Index based on the decomposition of fund returns.

1.Flaws and shortcomings of the Jensen Index

According to the regression model rp-rf = p + p (rm-rf) + , p is the size of Jp. According to the analysis of the securities market line, the Jensen index measures the portion of the risk premium that is higher than the average market return of the securities portfolio, that is, the difference between the total return of the investment portfolio and the returns of the securities portfolio located on the securities market line. According to the Fama fund portfolio income decomposition above, it can be seen that the Jensen index measures the return of the investment portfolio selection, and does not evaluate the market timing grasping ability. It can be seen that although the Jensen index is one of the most widely used evaluation methods so far, its evaluation of fund returns is not comprehensive enough.

Secondly, since SML is used as the base point for research, the assumption of the overall benefit of the fund using the Jensen index and the Treynor index implies a hypothesis that the non-systematic risk of the fund has been completely dispersed through the investment portfolio, which is often not the case , Especially for those investment funds using active management strategies are not applicable. It can also be said that these two methods ignore the number of securities contained in the fund's investment portfolio, that is, the breadth of the fund's investment portfolio, and only consider the size of the excess return, which is the depth of the fund's investment portfolio. This is another flaw.

2.The shortcomings and shortcomings of the Reynolds index

There are two main flaws in the Treynor Index:

First of all, it is clear from its calculation formula Tp = (rp-rf) / p that, as mentioned in the previous article, the measurement of risk in the Treynor index is only the systemic risk of the portfolio, which assumes Non-systematic risks are completely dispersed. However, in actual operation, the risk selected by the fund is not completely decentralized, so the system risk and the overall risk are not equal, but there may be large errors.

Second, in addition, the return E (rp-rf) used by the Treynolds Index is the overall return of the fund, which does not exclude factors of market conditions. However, people often cannot defeat the market. Market factors may play a large role in the returns, rather than due to the operating ability of the fund manager. For example, the same fund does not adjust the systemic risk (p) according to market conditions. In a bull market, the Treynor index will also be larger than in a bear market. At this time, because the unit price of market risk is high, it does not reflect the strong operating ability of the fund manager. It can be seen that if the market conditions are different, it is meaningless to use the Treno index to evaluate performance.

On the one hand, it is the total return of the fund's investment portfolio, and on the other hand, it is the level of systemic risk assumed by the fund manager. When the two are divided, the obtained Treynor index to evaluate fund performance is likely to be inconsistent with the actual situation.

3. Deficiencies and shortcomings of the Sharp Index

When considering the risk factors, the Sharp Index takes into account not only systemic risks but also non-systematic risks, but it still has irrationality:

First of all, when measuring returns, it is the same as the Trenox index, and it does not take market factors into account.

Secondly, because it is a relative indicator, both the Sharp Index and the Trenox Index can only be used for comparison and ranking, and cannot reflect the specific value of the fund's performance over the market portfolio.

In addition to the quantitative analysis indicators of fund evaluation cannot be mechanically copied, but must be combined with the actual situation of China's securities market, the evaluation of China's securities investment funds should also pay attention to the following issues:

(I) Non-quantitative factors

Fund evaluation indicators are all quantitative. In the process of actual selection of funds, comprehensive evaluation should be conducted in conjunction with other aspects of the fund. For example, during the fund evaluation period, there may have been some changes in management and management style. In addition, the economic environment and the industry trend of funds involving securities, etc., are difficult to obtain a fair judgment based on the analysis of the digital level alone. For example, certain types of stocks have trended upward in the past few years. Any fund that holds these stocks in heavy positions will perform well on these indicators, and when the class of stocks goes lower, the values of these indicators will also increase. It is likely to follow. Therefore, investors should use the comparison of evaluation indicators to narrow the horizon of optional funds, and then combine factors such as the fund's management team, investment style, transaction fee structure, potential risk of the investment portfolio, and suitability of the investment portfolio in hand. Consider and then make a more comprehensive assessment of the target fund.

(2) Persistent performance issues

The evaluation of securities investment funds should adhere to performance as the core, while paying attention to the sustainability of performance. Judging from the operation of foreign funds, the performance stability of most funds is relatively poor. The reason is that the outstanding performance of the fund may come from the superb investment skills or good luck of the fund manager. If the fund's performance is not sustainable, past performance cannot be used to predict the future. Therefore, the stability of fund performance is also an important principle for fund evaluation and investor selection of funds. In actual evaluation, it is also necessary to choose a longer evaluation period, because, in a certain sense, the longer the evaluation period, the more the evaluation indicators can truly reflect the performance of the fund.

(C) the choice of benchmarks

To compare fund performance with market conditions, a reasonable and comprehensive reference standard is needed. However, China does not yet have a unified and authoritative market index. The method of comparing the fund with the Shanghai Stock Exchange Index or Shenzhen Stock Exchange Index to reflect the performance of the fund is not objective enough. Because, on the one hand, neither the Shanghai Stock Exchange Index nor the Shenzhen Stock Exchange Index is a unified index of the two markets, and the fund invests in both markets. The index is based on total equity rather than tradable equity. Therefore, the evaluation of fund performance by the Shanghai or Shenzhen index seems to be ineffective. Some people think that the weighted average of the two should be used as a benchmark, or the two indexes should be adjusted appropriately, but there are certain difficulties in actual operation.

(IV) Comparability of funds

According to different standards, funds can be divided into many types, and different types of funds have different characteristics. It can be divided into corporate and contract based on different legal foundations and organizational forms; it can be divided into open and closed based on different realization methods; it can be divided into growth and income based on different investment objectives. Therefore, in fund evaluation, the principle of similar comparison must be adhered to, and different types of funds must have corresponding prerequisites when comparing.

1 Kang Yuan. Comparison and selection of risk-adjusted return indicators for fund performance evaluation (D). Beijing: Renmin University of China. 2004 ^[1]