Jensen's Alpha strategy based on momentum effect : empirical research on Chinese securities market

Jensen’s Alpha Strategy Based on Momentum Effect:

Empirical Research on Chinese Securities Market

Name: Gan Liu

Student number: 11450460 Thesis supervisor: Liang Zou Date: 1st _{July 1, 2018}

MSc Finance, specialization Quantitative Finance

Statement of Originality

This document is written by student Gan Liu who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

Abstract

The purpose of this paper is to construct effective Alpha investment strategies based on the obvious momentum effect existing in the Chinese securities market to achieve abnormal returns. With taking the CSI 300 Index and its component stocks as empirical research object, this paper takes two different Alpha investment strategies. Specifically, the first strategy is to use momentum strategy to establish certain stock portfolio with large positive Alpha, while simultaneously utilizing the hedging mechanism of CSI 300 index futures, to eliminate the systematic risk of the portfolio thus obtaining abnormal returns. The second strategy is under the assumption that Chinese securities market allows the short-selling mechanism, aiming to construct the portfolio including not only stocks with positive Alpha at long position but also stocks with negative Alpha at short position, which is also gives the ability to achieve market neutral and to obtain abnormal returns.

From the final research results, both strategies designed in this paper achieved abnormal returns, beating the benchmark returns of CSI 300 Index. During the 21-month empirical period, this paper identifies the profitability of those two Alpha strategies under various market conditions. The better profitable strategy is the Alpha investment strategy based on the short-selling mechanism, the explanation is that such investment strategy not only has the ability to reflect and amplify the upward trend of the benchmark returns but also can get rid of the negative influence of the market with making the market neutral. As for hedging-based Alpha strategy, the abnormal returns during the entire investment period are not significant, but in the down stage of the market, the strategy is able to fully exert the effect of eliminating the systematic risk, subsequently mitigating the fluctuation of the benchmark returns.

Contents

I. Introduction ...5

A. Background and Motivation ...5

B. Objective and Structure ...6

II. Related Theory and Literature Review ...8

A. Efficient-Market Hypothesis ...8

B. Capital Asset Pricing Model ...9

C. Jensen’s Alpha ... 10

D. Momentum Effect and Alpha Strategy ... 10

III. Empirical Study ... 15

A. Methodology and Data ... 15

B. Hypothesis of Empirical Study ... 18

C. Empirical Study Results ... 19

(a) Alpha Strategy with Hedging Mechanism... 19

(b) Alpha Strategy with Short-Selling Mechanism ... 26

(c) Results Discussion ... 29

IV. Conclusion ... 32

I. Introduction

A. Background and Motivation

The concept of Alpha was born in the middle of the 20th century, when nearly 75% of the asset portfolios could not obtain abnormal returns in the market. Scholars believed that such phenomenon stems from the theory of market efficiency. That is, as long as there are arbitrage activities, then investors can only obtain the benchmark return rate of the market in the efficient market but cannot obtain abnormal returns. However, in the following decades, financial derivatives have been continuously developed, in this case, many funds have achieved performance over the market benchmark interest rate. At this point, investors are no longer satisfied with investing in simple market portfolios or stock indices, but rather want to configure more aggressive strategies to achieve returns that exceed market levels. The abnormal returns getting rid of the impact of market is called Alpha, which is used to determine the ability of a security or portfolio overcoming the market. Investors seeking for Alpha believe that they are able to acquire more than market returns through information superiority, technical analysis and rich experience.

The traditional arbitrage strategies mainly rely on the short-term deviation of the market. Under such circumstances, the majority of operating models used by investors will gradually converge, and as the number of arbitrageurs continues to increase, opportunities for arbitrage will gradually disappear. Under the circumstances, Alpha investment strategy mainly depends on the ability of stock selection and asset allocation, so it has stronger initiative and more opportunities to make profit. At present, Alpha strategy is widely applied in the investment field and has been successfully tested in capital markets of major developed countries. However, for the developing country such as China, the securities market is emerging and inefficient, so there may be more opportunities to explore Alpha. In recent years, innovative financial derivatives have been continuously launched, which further provides possibility to obtain abnormal

returns in Chinese securities market. Additionally, this paper intends to use momentum strategy to construct stock portfolio as there is obvious information asymmetry in the Chinese securities market, making the firm value far away from the actual value and pushing the stock price continuously move to favorable direction, so it is feasible to find momentum effect in Chinese securities market and use it to isolate Alpha.

Chinese securities market is an emerging capital market, which means investors face not only the risk of the individual stock but also the systematic risk of the whole market. In the case, empirical research on Alpha strategy has practical significance for Chinese investors. Furthermore, if this paper finally obtains stable Alpha abnormal returns, it could provide evidence for existing research on Chinese securities market efficiency, and it could also verify the theoretical value of the technical analysis in Chinese securities market.

B. Objective and Structure

The research goal of this paper is mainly to use the Alpha investment strategy based on momentum effect to conduct empirical research on the Chinese securities market and explore the practical value of Alpha investment strategy in Chinese securities market. There are four parts in this paper, the first part is an introduction which briefly describes the research background, the purpose of this paper, the main research contents and research methods.

The second part is the related theory and literature review. As the theoretical foundation of Jensen’s Alpha, this paper first reviews the theory of efficient-market hypothesis and the Capital Asset Pricing Model, and then introduces the specific definition and the theoretical derivation of Jensen’s Alpha. Since both the Alpha strategies adopted in this paper are based on the momentum effect of stocks, this part also elaborates the research on the momentum effect of stocks in recent years, which laid the theoretical foundation for the discussion of the empirical results of the following content. Finally, this paper

reviews the rationale and research status of different Alpha investment strategies and compares the advantages and disadvantages of different strategies.

The third part is empirical research. Based on the momentum strategy, this paper adopts two different routes to construct Alpha investment strategies. For the first route, we firstly analyze the original data samples to construct a portfolio consisting of stocks with positive high Alpha (only set long positions). After constructing the stock portfolio, we use the short-selling mechanism of the CSI 300 Index futures to eliminate the systematic risk of the stock portfolio to obtain abnormal returns. For the second strategy, this paper assumes that the Chinese stock market allows the existence of short-selling mechanisms then establishes stock portfolio consisting of not only stocks with large positive Alpha at long position but only stocks with large negative Alpha at short position, meanwhile give them the same weights to construct alternative Alpha investment strategy to obtain abnormal returns.

The last part is the discussion and comparison of the results of the two investment strategies. This paper compares the returns obtained by both investment strategies with the benchmark returns of the CSI 300 Index to evaluate the effectiveness of those two investment strategies. Not only that, we also give reasonable explanations for the different performances of both investment strategies during the entire investment period.

II. Related Theory and Literature Review

A. Efficient-Market Hypothesis

In 1965. Eugene Fama published a thesis entitled " The Behavior of Stock Market

Prices", proposed an efficient market theory which became one of the basic theories of the modern financial market. The problem of market efficiency refers to whether the market price fully reflects market information sets. According to efficient-market hypothesis, efficient markets can be specifically divided into three types: weak efficiency, semi-strong form, and strong-form. In weak-form efficient markets, securities prices have fully reflected the information sets from historical transaction data; In semi-strong form efficient markets, securities prices have fully reflected all public available information sets; In strong-form efficient markets, securities prices have fully reflected all relevant information, including not only historical transaction data information and public available information, but also inside information only for the company insider.

Efficient-market hypothesis believes that investors can rationally judge market information sets in most cases; Irrational judgments and behaviors generated in a few cases will hedge against mutually; Market deviations caused by irrational behaviors will be leveled by market rational arbitrageurs. Therefore, nobody can obtain abnormal returns when the market is efficient because securities price can fully reflect information sets of the market. However, efficient-market hypothesis has also been questioned by scholars and investors. In particular, some famous hedging funds have obtained long-term and amazing returns by different investment strategies, mercilessly rejecting the conclusion of the efficient-market hypothesis, verifying that they could obtain abnormal returns. In fact, if all the investors in the market cannot obtain abnormal profits, the market will lose its attractiveness as abnormal returns are the charm of the securities market. After twenty-six years from putting forward efficient-market hypothesis, Eugene Fama concluded by reviewing what he learned from the

work on efficiency, and where it might go in the future, finally re-describe the market efficiency as event studies, private information and return predictability.

B. Capital Asset Pricing Model

In 1964, William Sharp proposed the CAPM model. The core concept of the CAPM model can be stated as follows: The returns of an asset portfolio are positively related to the systematic risk of the asset, and it assumes the systematic risk will obtain the risk premium compensation corresponding to the average return of the market. The mathematical formula of the CAPM model is as:

𝐸(𝑅$) = 𝑅'+ 𝛽$*𝐸(𝑅+) − 𝑅'-

The description of the CAPM model is as follows:

(a) The expected return of an individual security consists of both the risk-free rate of return and the risk premium corresponding to the risk assumed;

(b) The size of the risk premium is related to the Beta value. The larger the Beta value, the higher the risk of the securities and the greater the risk premium required;

(c) Beta measures systematic risk.

The CAPM model is able to predict the relationship between the systematic risk and the expected rate of return on the assets. In actual investment activities, investors always use this model to balance the relationship between systematic risk and returns as well as estimate the overall future investment returns in advance. However, in the real securities market, due to various reasons such as the asymmetric information dissemination and irrational judgments of investors on the return of securities, in most cases the actual returns are always deviate from the expected returns, which leads to the topic of the Jensen’s Alpha theory below.

C. Jensen’s Alpha

The CAPM only elaborates the impact of systematic risk on the expected returns of the portfolio as wells as uses the Beta coefficient to reflect the sensitivity of the portfolio to systematic risk. In this way, the stock price should be stabilized at the value obtained by the CAPM. However, the fact is far from this. In 1968, Michael C. Jensen published "The Performance of Mutual Funds in the Period 1945-1964". Based on the Capital Asset Pricing Model, this paper groundbreaking proposed to use the Jensen index (Alpha) to measure the performance of a portfolio since the Alpha is the abnormal part which equals to the actual return of the portfolio minus the expected return from the CAPM. According to the definition, Alpha is an index of measuring the relative performance of the portfolio (whether it can overcome the market). After that, how to explore stable Alpha and adopt appropriate strategy to acquire abnormal returns in capital markets become a hot spot. The specific formula of Jensen’s Alpha is as follows:

𝛼 = 𝐻𝑃𝑅 − 𝐸(𝑅_$) = 𝐻𝑃𝑅 − 𝑅_'− 𝛽_$*𝐸(𝑅₊) − 𝑅_'-

As indicated above, 𝛼 is the abnormal return of the portfolio, HPR is the actual returns of the portfolio during holding period, and 𝐸(𝑅_$) is the expected return of the portfolio. In practice, it proves that equity funds can obtain abnormal return higher than the market average through proactive asset allocation and active management. With the development and maturity of the securities market, the concept of Alpha was gradually implemented into the practical operations which reflected in fund managers try to take active management to obtain abnormal returns. Specifically, this approach does not rely on the judgment of the whole market but focuses on the relative investment value of the stock portfolio, in an attempt to obtain abnormal returns, and the related strategies are collectively referred to as Alpha strategy.

According to the classical theory, the fluctuation of stock prices is random and independent, with no tendency and memory. However, in the actual securities market, the change in the stock price not only has a tendency, but also has a certain memory to some extent. The specific performance is that stocks have risen consecutively in the previous period would continue to rise for a certain period of time; Similarly, stocks have fallen consecutively in the previous period would continue to fall for a certain period of time. Such trend for the stock price is often referred to the momentum effect. In fact, not only a single stock has a momentum effect, but an industry in the securities market also has momentum effect. That is, certain industry indices are able to continue to increase in one year or even longer, while some industry indices are possible to fell continuously in the longer term.

The traditional efficient market hypothesis cannot give a reasonable explanation for the momentum effect, but behavioral finance theory believes that such phenomena are related to the investors' deviation of reaction to the information. Behavioral finance theory assumes that the company has private information which is unknown by investors and that the behavior of investors is not completely rational. When the private information of firms is disclosed in the open market, on the one hand, investors have different channel of information will come into contact with such information at different time and then gradually respond. On the other hand, due to under-reaction or over-reaction, investors are likely to gradually adjust their reactions in the follow-up period. For these two reasons, the price change in the stock market will appear as a continuous process, which is explained as momentum effect.

In 1993, Narasimhan Jegadeesh and Sheridan Titman used the data of the New York Stock Exchange and the American Stock Exchange from 1965 to 1989, first discovered and demonstrated momentum effect which would generated the abnormal returns, namely, Alpha. The strategy adopted by them is to buy stocks that have performed well and sell stocks that have performed badly in the past. This portfolio generated a

significant positive return during the three to twelve months in the holding period. Furthermore, they found that the abnormal returns of this portfolio were not due to systematic risk or delays in the reaction of stock prices to public information in the market. After eight years, Jegadeesh and Titman reassessed various explanations that why the momentum effect of stocks can be used to make profit. Their updated evidence showed that the benefits from the momentum effect in the 1990s can continue to increase, indicating that the empirical results of eight years ago were not due to sample bias. According to the theory of behavioral finance, they also believe that the existence of momentum effects is due to over-reaction or delay in response by investors. On the other hand, their research results also further supplement and support the theory of behavioral finance.

Jennifer Conrad and Gautam Kaul (1998) not only applied the momentum effect theory to construct Alpha strategy, but also compared the momentum Alpha strategy and the contrarian Alpha strategy. They took a much wider range of data, including data on all stocks in the United States stock market from 1926 to 1989, and empirical results showed that less than half of the 120 strategies enacted could yield returns significantly different from zero. The number of successful momentum Alpha strategies and contrarian Alpha strategies are almost the same. In terms of time, the momentum Alpha strategy is more effective in 3-12 months while the contrarian Alpha strategy is more effective in less than 1 month and 3-5 years. More importantly, their research results further showed that the cross-sectional changes in the average returns of various securities have a huge impact on their profitability, that is, changes in cross-section may potentially explained the profitability of the momentum effect strategy, and it was also responsible for reducing the return on price reversal to a long-term reversal strategy.

Meanwhile, Kalok Chan, Allaudeen Hameed and Wilson Tong (2000) examined the profitability of the momentum strategy implemented by the international stock market indices. Their results provided statistically significant evidence of profits caused by momentum effects. Not only that, they also found that the profit brought by the

momentum effect mainly comes from the time series predictability of the stock market indices, but only a small part comes from the predictability in the currency market. On the other hand, they also found that the momentum effect caused by the momentum effect would be higher in the active trading market, which indicated that as the transaction volume increases, the continuity of returns is stronger, confirming the informational role of volume and its applicability in technical analysis. Moreover, Cooper, Gutierrez and Hameed (2004) found that whether or not they could utilize momentum strategy to obtain profits mainly depends on the market conditions. A six-month momentum portfolio can only be profitable after the market gains, and as the lagged market returns increased, the profit caused by momentum effects also increased. In addition, under a high level of lagged market returns, profits would reduce but not eliminate, suggesting that there is a long-run reversal of momentum profits. Moreover, they found that macroeconomic factors could not explain momentum profits after simple methodological adjustments to take account of microstructure concerns.

However, above literature merely focus on developed markets. In developing markets, Rouwenhorst (1998) first used 1750 stocks transaction data from 20 developing countries in the world to do the empirical study, the conclusion was that the stock momentum effect obviously exists. More importantly, they found that the returns caused by momentum effects in the securities markets of various countries were likely to be related to the strength of the momentum effect in the US stock market, indicating that common factors existing in different markets could promote the profitability of the momentum strategy. In 2004, Allaudeen Hameed and Kusnadi Yuanto found that there are medium-term return continuations caused by momentum effects in six Asian countries securities markets. However, due to unstable returns and high volatility in the market, the unrestrained momentum strategy would not bring significant and sustained returns. They further found that the scale of the company and the volume of transactions in the market could also distinctly affect the magnitude of the momentum effect. That is, unless specific factors are combined, it is difficult to find significant momentum effects in emerging markets. Especially, for the Chinese market, Tony Naughtona and

Cameron Truong investigated the magnitude of the momentum effect of stocks listed on the Shanghai Stock Exchange. The results showed that from 1995 to 2000 there was significant momentum effect in the Chinese securities market and there was no strong link to the past trading volume. In addition, they found that investors could invest in strategies that are unrelated with market movements to obtain abnormal returns. Their research also showed that due to the weak efficiency of Chinese securities market and the overreaction or under-reaction of investors to public market information, it was feasible to use momentum effect strategies to obtain abnormal returns.

In addition to using the traditional Alpha strategy to obtain abnormal returns, some scholars have proposed the portable Alpha strategy, referring to the process of separating Alpha from Beta and then applying it to other portfolios. Compared with the traditional Alpha strategy, portable Alpha strategy is able to make the investment funds more effectively, and this part of the funds would be invested in Alpha position. Without changing the systematic risk, portable Alpha strategy are mainly relied on increasing the funds invested in the Alpha position to promote the returns on the portfolio.

Edward Kung and Larry Pohlman (2004) explored the effects of implementing portable Alpha strategy under various investment scenarios and discussed the advantages and disadvantages of portable Alpha strategy. Their results showed that portable Alpha strategy is an active Alpha strategy that would have a profound impact on asset allocation and could be widely applied to traditional portfolio management.

III. Empirical study

A. Methodology and Data

This paper intends to construct stock portfolio by momentum strategy, in which both the formation period and holding period are three months. The reasons for choosing three months is that if the time span is to short, such as one week, two weeks or one month, the uptrend caused by the sudden bullish quotes or the downtrend caused by sudden bearish quotes will have a great influence on the regression calculation of Alpha of individual stocks during the formation period. Moreover, it is inevitable to adjust constituent stocks in the portfolio frequently because of short holding period, leading to liability and high transaction costs; If the period is too long, such as six months or one year, the Alpha would disappear gradually. So, choosing three months as the time interval will be a comprehensive decision after considering the stability of the stock portfolio and the persistence of the momentum effect. Specifically, the process of constructing Alpha strategy based on momentum effect is as follows:

1. Choose appropriate stocks to the stock pool

2. Set the time span length T、K for formation period and holding period respectively 3. Calculate the Alpha of the selected stock during the formation period

4. Trading rules: If the stock in the stock pool has a positive Alpha, it will be added to the portfolio with a certain weight. The portfolio will be held for K trading days. After maturity, we will adjust the portfolio according to Alpha at the due date: removing stocks with negative Alpha and adding stocks with positive Alpha.

This paper first determines the general scope of stock selection: That is, we focus on Chinese national strategic emerging industries such as information technology industry, biotechnology industry, new energy technology industry, transportation industry, etc., excluding high-energy-consumption industry, high-pollution industry and real estate

industry, etc. Within this general stock selection scope, we will use momentum strategy to construct stock portfolio for further empirical study.

Based on the set-up of time span, we regress the daily returns of the CSI 300 Index on the daily returns of all the stocks within the previous scope during the formation period to get the Alpha and Beta (calculated by Excel). After calculation, we firstly sort the Alpha of all the stocks thus select the top 40 stocks into the stock pool. The reason for choosing 40 stocks is that such quantity of stocks ensures that the stocks with obvious positive Alpha will be included into stock pool and keeps the transaction cost at a low level, providing convenience for further empirical study; Secondly, we need to remove the stocks that have a longer time suspension for asset reorganization or suddenly resume trading during the formation period as these stocks are possible to bring special unreliable high Alpha. Finally, the remaining stocks are regarded as the certain portfolio. Meanwhile, the investments funds will be equally allocated to each constituent stock in the constructed portfolio, providing convenience for calculating the average value of Beta of each stock (regarded as the Beta of the portfolio) and the average returns of the portfolio at the end of holding period.

While completing the construction of the stock portfolio, we regard the average Beta of the stock portfolio as the optimal hedge ratio to short the CSI 300 Index futures, which is capable of eliminating the systematic risk of the stock portfolio. We intend to choose the monthly current CSI 300 Index futures contract, with considering: First, compared to forward contracts, the monthly current contracts are more active thus are able to reduce the impact costs caused by inactive transactions; Secondly, at the end of the holding period, the monthly current contract is more closely aligned with the CSI 300 Index, making the effect of hedging more realistic. Since the holding period are three months, we need two rollovers during each holding period before the delivery date. Of course, the rollover will increase transaction costs correspondingly.

calculated by regressing the daily return of the CSI 300 Index on the daily returns of each stock during the formation period. This paper uses the Beta of each stock directly to calculate the Beta of the stock portfolio, and the average Beta of the stock portfolio is regarded as the optimal hedge ratio. In fact, there are two Betas: One is the Beta between the stock and the CSI 300 Index, and the other is the Beta between the CSI 300 Index and the monthly current CSI stock index futures contracts. Since the CSI 300 Index keeps close convergence with the monthly current consecutive CSI 300 Index futures contracts, it can be similarly considered that the Beta between CSI 300 Index and monthly current consecutive CSI 300 Index futures contracts is close to 1, so this paper directly replaces the Beta between the CSI 300 Index and monthly current consecutive CSI 300 Index futures contracts with the Beta between stock portfolio and CSI 300 Index.

While setting up the stock index futures hedging positions, we must also consider the funds allocation problem of the stock index futures. In order to avoid risks, most futures companies set the actual margin level around 15%. Because the stock index futures price will fluctuate during the holding period, additional margin needs to be reserved aside to prevent forced liquidation due to insufficient margin.

The time span starts from July 1st_{, 2016 and ends at March 31}th_{, 2018, in total one year} and nine months. It is divided into 6 phases, each contains one formation period and one holding period.

Formation period of Alpha Holding period of portfolio

1 01/07/2016 - 30/09/2016 01/10/2016 - 31/12/2016

2 01/10/2016 - 31/12/2016 01/01/2017 - 31/03/2017

4 01/04/2017 - 30/06/2017 01/07/2017 - 30/09/2017

5 01/07/2017 - 30/09/2017 01/10/2017 - 31/12/2017

6 01/10/2017 - 31/12/2017 01/01/2018 - 31/03/2018

B. Hypothesis of Empirical Study

We assume that the initial investment funds are $20 million, with the stock portfolio and CSI index futures are allocated in a ratio of 3:1. That is, the funds allocated to the stock portfolio are $15 million, while the funds allocated to the stock index futures margin account are $5 million that higher than $2.25 million which are needed for shorting $15 million stock index futures contract. Theoretically, such set-up can afford the 12% increase in stock index futures during the holding period, avoiding forced liquidation. If stock index futures increased by more than 12%, then the margin can be replenished according to the specific circumstances. In order to guarantee the convenience of calculation, we assume that CSI index futures can be infinitely subdivided.

Transaction costs and impact costs: At present, the stamp tax for stock transactions is unilaterally charged by 0.1%, and the rate of service charge is bidirectionally charged by 0.05%. So, the rate of transaction cost for each holding period is 0.2% in total. Because the transaction amount of each stock is less than $400,000, the impact cost is negligible. On the other side, the rate of service charge of stock index futures is bidirectionally charged by 0.03% of the value of the contract. Since there will be three times stock index futures transactions during the holding period (the first transaction mentioned above plus the two shift positions during the period), the rate of transaction costs is 0.18% in total. In addition, we also ignore the impact cost of the stock index futures contracts due to the small transactions amount.

Transaction price set-up: In order to make the empirical results more realistic, we regard the opening price of the first trading day as the bid price during the period, similarly, the ask price is based on the closing price of the last trading day during the holding period. For the stock index futures contract, the opening price of the first trading day is the ask price during the holding period, and the closing price is the settlement price of the last trading day during the holding period.

Calculate returns during the holding period: Let 𝑅 be total returns, 𝑅1 is the logarithmic return of stock portfolio, 𝑅₂ is the logarithmic return of shorting CSI 300 Index futures, then 𝑅 = 𝑅1+ 𝑅2. After the end of each holding period, we will take out the proceeds (or make up the losses), restoring the investment fund to $20 million, restarting the empirical study in the next period.

C. Empirical Study Results

(a) Alpha Strategy with Hedging Mechanism

This part aims to short CSI 300 Index futures to hedge the systematic risk of the stock portfolio, and ultimately only obtain Alpha. With the method of constructing the Alpha strategy model and the indispensable preconditions, we now start the empirical study. At first, this paper will use ordinary least squares to estimate Beta and Alpha of constituent stocks. The mathematical derivations are following:

From Capital Asset Pricing Model:

𝐸(𝑅_$) = 𝑅_'+ 𝛽_$*𝐸(𝑅₊) − 𝑅_'-

𝐸(𝑅_$) is the expected return of the portfolio, 𝑅_' is the risk-free rate of interest, 𝛽_$ is the sensitivity of the expected excess portfolio returns to the expected excess market

returns, 𝐸(𝑅₊) is the expected return of the market.

From Jensen’s Alpha model:

𝛼 = 𝑅_$ − 𝐸(𝑅_$) 𝐸(𝑅_$) = 𝛽_$∗ 𝑅₊+ 𝜖 R$ = α + 𝛽$∗ 𝑅++ 𝜖

So, there is a linear relation between the realized return of the portfolio and the realized return of the market. Suppose all the data are stationary, we can use ordinary least squares to estimate 𝛽_$, the independent variable is the realized return of the market and the dependent variable is the realized return of the portfolio. The intercept is the Alpha which we need. All the data were form Wind and all the calculations were completed in Excel.

Table 1. Portfolio information in Period 1 (sorted by Alpha)

Constituent

Code Constituent Name Beta Alpha Returns

300033.SZ Hithink Royalflush Information

Network Co., Ltd. 0.2591 0.0149 3.4012%

600061.SH SDIC Capital Co., Ltd 0.4579 0.0143 -0.0640% 000792.SZ Qinghai Salt Lake Industry Co., Ltd 0.2984 0.0106 0.0525%

601611.SH China Nuclear Engineering

Corporation Limited 0.0940 0.0102 15.5121%

600959.SH

Jiangsu Broadcasting Cable Information Network Corporation

Limited

0.0713 0.0084 7.5334%

601186.SH China Railway Construction Co.,

Ltd 0.2237 0.0084 26.2364%

002065.SZ DHC Software Co., Ltd. 0.1080 0.0082 10.2979% 601901.SH Founder Securities Co., Ltd 0.4924 0.0081 2.2622%

002304.SZ Jiangsu Yanghe Brewery

Joint-Stock Co., Ltd 0.2977 0.0081 3.0634%

601985.SH China National Nuclear Power Co.,

Ltd. 0.6764 0.0078 5.2338%

600115.SH China Eastern Airlines Corp Ltd 0.2664 0.0074 13.2925%

002008.SZ Han's Laser Technology Industry

Group Co., Ltd. 0.2279 0.0073 3.4207%

600011.SH Huaneng Power International Inc 0.1866 0.0068 -0.5658%

601766.SH CRRC Corporation Limited 0.5072 0.0067 7.4344%

000876.SZ New Hope Liuhe Co., Ltd 0.3621 0.0066 -1.3572%

601555.SH Soochow Securities Co., Ltd 0.3509 0.0066 0.6805%

000166.SZ Shenwan Hongyuan Group Co., Ltd 0.0355 0.0065 -2.6837%

300124.SZ Shenzhen Inovance Technology

600703.SH Sanan Optoelectronics Co., Ltd 0.0188 0.0063 10.8769% 000776.SZ GF Securities Co., Ltd. 0.3825 0.0063 0.8937% 601288.SH Agricultural Bank of China Co., Ltd 0.4014 0.0062 -1.6000%

600887.SH Inner Mongolia Yili Industrial

Group Co., Ltd 0.2214 0.0060 8.8459%

601992.SH BBMG Corporation 0.0109 0.0058 4.1196%

601328.SH Bank of Communications Co., Ltd 0.3493 0.0058 2.9905%

600038.SH AVIC Helicopter Co., Ltd. 0.2651 0.0057 14.3435%

002252.SZ Shanghai RAAS Blood Products

Co., Ltd 0.0096 0.0056 3.2573%

000060.SZ Shenzhen Zhongjin Lingnan

Nonfemet Co., Ltd 0.2093 0.0056 7.6387%

601006.SH Daqin Railway Co., Ltd 0.3028 0.0056 8.7011% 600369.SH Southwest Securities Co., Ltd 0.5920 0.0055 -2.4932%

601169.SH Bank of Beijing Co., Ltd 0.0293 0.0054 6.7823%

601099.SH The Pacific Securities Co., Ltd 0.0165 0.0054 3.7591%

600682.SH Nanjing Xinjiekou Department

Store Co., Ltd 0.1723 0.0054 30.1823%

002044.SZ Meinian Onehealth Healthcare

Holdings Co., Ltd. 0.0797 0.0054 -6.3210%

002624.SZ Perfect World Co., Ltd. 0.1514 0.0053 -16.3743% 600886.SH SDIC Power Holdings Co., Ltd. 0.3140 0.0053 0.6015%

600332.SH Baiyunshan Pharmaceutical Holding

Co., Ltd. 0.3217 0.0053 -4.5648%

600893.SH AVIC Aviation Engine Corporation

PLC. 0.2339 0.0052 -6.6750%

600029.SH China Southern Airlines Co., Ltd 0.2021 0.0051 -0.5682%

Taking the first period as example: On the first trading day, we divide the $15 million investment amount into 40 shares in order to average the positions of the above 40 constituent stocks to form a stock portfolio, and use the average Beta (0.2637) value of above 40 constituent stocks in the formation period as the optimal hedging ratio to short CSI 300 Index futures contracts with a value of $ 15 𝑚𝑖𝑙𝑙𝑖𝑜𝑛 ∗ 0.2637 = $3.955 𝑚𝑖𝑙𝑙𝑖𝑜𝑛. Then we can calculate the average returns of the stock portfolio in the first holding period which equals to 3.8432% (including transaction costs), and the returns of CSI 300 Index returns is 0.7085%. So, the hedging strategy actually results in 0.7085% ∗ 0.2637 = 0.1868% loss. Overall, the data shows that the portfolio under Alpha strategy with hedging in the first holding period achieves abnormal returns. According to the same procedure, we can calculate the returns of other portfolios for each holding period.

Table 2. Average returns of portfolio in six time periods (including transaction costs)

Time Span Average return of portfolio

01/10/2016 - 31/12/2016 3.8432% 01/01/2017 - 31/03/2017 6.0415%

01/04/2017 - 30/06/2017 5.0680% 01/07/2017 - 30/09/2017 8.8239% 01/10/2017 - 31/12/2017 8.9274% 01/01/2018 - 31/03/2018 5.2115%

Table 3. Returns of CSI 300 Index futures in six periods

Time Span Closing Price Closing price Market Type Returns 01/10/2016 - 31/12/2016 3,319.20 3,342.80 Fluctuation 0.7085% 01/01/2017 - 31/03/2017 3,352.80 3,464.00 Up-market 3.2628% 01/04/2017 - 30/06/2017 3,457.60 3,521.00 Up-market 1.8170% 01/07/2017 - 30/09/2017 3,738.00 3,834.20 Up-market 2.5410% 01/10/2017 - 31/12/2017 3,924.40 3,987.60 Up-market 1.5976% 01/01/2018 - 31/03/2018 4,290.80 4,082.00 Down-market -4.9886%

Table 4. Returns of hedging in six periods (including transaction costs)

Time Span Average returns of portfolio Returns of stock index futures Hedging ratio Returns of hedging 01/10/2016 - 31/12/2016 3.8432% 0.7085% 0.2637 -0.2048% 01/01/2017 - 31/03/2017 6.0415% 3.2628% 0.2845 -0.9461% 01/04/2017 - 30/06/2017 5.0680% 1.8170% 0.2520 -0.4759% 01/07/2017 - 30/09/2017 8.8239% 2.5410% 0.1738 -0.4596% 01/10/2017 - 31/12/2017 8.9274% 1.5976% 0.1027 -0.1820% 01/01/2018 - 31/03/2018 5.2115% -4.9886% 0.1650 0.8049%

for each holding period:

Table 4. Returns of portfolio in six periods

Time Span Income of portfolio Income of hedging Income in total Returns in total

01/10/2016 - 31/12/2016 0.5765 -0.0307 0.5458 2.7288% 01/01/2017 - 31/03/2017 9.0622 -0.1419 0.7643 3.8215% 01/04/2017 - 30/06/2017 0.7602 -0.0714 0.6888 3.4441% 01/07/2017 - 30/09/2017 1.3236 -0.0689 1.2546 6.2732% 01/10/2017 - 31/12/2017 1.3391 -0.0273 1.3118 6.5590% 01/01/2018 - 31/03/2018 0.7817 0.1207 0.9025 4.5123% Sum 5.4678 27.3388%

As shown in the Table 4, Alpha strategy with hedging obtains $5.4678 million in total, the cumulative returns reach to 27.3388%. Meanwhile, the returns of CSI 300 Index in six periods are showing in the Table 5. In the next step, we will compare the returns by Alpha strategy with the returns of the CSI 300 Index during the whole investment period:

Table 5. Returns of CSI 300 Index in six periods

Time Span Closing Price Closing price Market Type Returns 01/10/2016 - 31/12/2016 3293.87 3310.08 Fluctuation 0.4910% 01/01/2017 - 31/03/2017 3342.23 3456.05 Up-market 3.3488% 01/04/2017 - 30/06/2017 3503.89 3666.80 Up-market 4.5444% 01/07/2017 - 30/09/2017 3650.85 3836.50 Up-market 4.9602% 01/10/2017 - 31/12/2017 3882.21 4030.85 Up-market 3.7575% 01/01/2018 - 31/03/2018 4087.40 3898.50 Down-market -4.7318%

Sum 12.3700%

Figure 1. Accumulative return of portfolio and CSI 300 Index

From Figure 1 we can see that after adopting the mechanism of hedging, the trend of the returns of portfolio is more stable than that of the CSI 300 Index. However, the mechanism of hedging eliminated the systematic risk of the portfolio at the expense of the premiums brought by systematic risk. In particular, since the market as a whole is bullish in the first five periods, the CSI 300 Index futures all take a positive return, so the hedge would inevitably bring losses to the portfolio. But it is worth noting that in the sixth period, since the market was in a downward phase, neither the CSI 300 Index nor the CSI 300 Index futures achieved negative returns. Under this circumstance, due to the mechanism of hedging has escaped the impact of the market downturn, it has been able achieved considerable positive returns, demonstrating that the Alpha strategy with hedging is effective in this situation.

(b) Alpha Strategy with Short-Selling Mechanism

In the previous section, in order to obtain abnormal return, we use the short-selling 0.0000% 5.0000% 10.0000% 15.0000% 20.0000% 25.0000% 30.0000% 1 2 3 4 5 6 Time period

Accumulative Return Rate

mechanism of stock index futures to hedge the systematic risk of the portfolio. Since systematic risk will be hedged, we also cannot obtain the benefits from systematic risk premiums, so the return on investment portfolios will decline in the bullish market. In order to explore a better profit model, this article assumes that the Chinese securities market allows short-selling, that is, based on the existence of the short-selling mechanism, to further construct more effective Alpha investment strategy.

In the first part of the empirical study, we need to select stocks with large positive Alpha to construct investment portfolio, but under short-selling conditions, stocks with large negative Alpha also have high investment value. Therefore, in this section, while stocks with a positive Alpha are selected, stocks with large negative Alpha are also selected, which together constitute the portfolio we needed. It is worth noting that stocks with positive and negative Alpha in the portfolio have different directions of operation, that is, we give positive weights to the stocks with positive Alpha (long position) and give negative weights to the stocks with negative Alpha (short position).

In order to make the market neutral and to maintain the same number of stocks as the previous two methods, we therefore take the top 20 stocks with positive Alpha and bottom 20 stocks with negative Alpha into stock pool.All the stocks still have the same weight, and the other assumptions mentioned above are still valid. However, in the empirical process, we find that the number of stocks with negative Alpha in the third to fifth time period did not reach twenty. Given this situation, for those three time periods, we take the same action as the previous part, that is, only select the top 40 stocks with positive Alpha. The real returns excluding transaction costs of the stock portfolio for six periods are showing in Table 6:

Table 6. Average returns of portfolio in six periods (including transaction costs)

Time Span Average returns of portfolio 01/10/2016 - 31/12/2016 5.4694%

01/01/2017 - 31/03/2017 9.6561% 01/04/2017 - 30/06/2017 5.0680% 01/07/2017 - 30/09/2017 8.8239% 01/10/2017 - 31/12/2017 8.9274% 01/01/2018 - 31/03/2018 7.3635%

Next, we can calculate the investment income by Alpha strategy with short-selling mechanism for each holding period:

Table 7. Returns of portfolio in six periods

Time Span Income of portfolio Returns in total

01/10/2016 - 31/12/2016 1.0939 5.4694% 01/01/2017 - 31/03/2017 1.9312 9.6561% 01/04/2017 - 30/06/2017 1.0136 5.0680% 01/07/2017 - 30/09/2017 1.7648 8.8239% 01/10/2017 - 31/12/2017 1.7855 8.9274% 01/01/2018 - 31/03/2018 1.4727 7.3635% Sum 9.0617 45.3083%

As shown in the Table 7, the Alpha strategy with short-selling mechanism obtains 9.0617 million in total, the cumulative returns reach to 45.3083%. We will also compare the returns of the Alpha strategy with short-sellingmechanism with the returns of the CSI 300 Index during the whole period:

Figure 2. Accumulative return of portfolio and CSI 300 Index

From Figure 2, we can see that due to the short-selling mechanism, the portfolio can obtain returns from both long and short directions, thereby increasing profitability. However, since there are less than twenty stocks with negative Alpha in the third to fifth period, we can only analyze the effect of this strategy as a whole. No matter how, we still know from the chart that in the first, second, and sixth period which combine the short-selling mechanism, our strategy has achieved remarkable returns that greatly exceed the first strategy. In general, the Alpha strategy with the short-selling mechanism has better profitability than Alpha strategy with hedging mechanism, so we reasonably assume that if the Chinese securities market allow the existence of short-selling in the future, Alpha strategy could be applied more widely.

(c) Results Discussion

From the above empirical results, both strategies have achieved abnormal returns, while our empirical objective is to explore the practical value of different Alpha investment

0.0000% 10.0000% 20.0000% 30.0000% 40.0000% 50.0000% 1 2 3 4 5 6 Time period Accumulative Return Rate

strategies under different situations. Therefore, in order to compare these two strategies, we put the accumulative returns obtained by them and the CSI 300 Index on the following figure:

Figure 3. Accumulative returns of three strategies

From the curve of cumulative returns obtained by both investment strategies in the empirical study, we directly conclude that both investment strategies designed in this paper have the ability to obtain abnormal returns in the long-term investment of twenty-one months. Specifically, the Alpha strategy based on the short-selling mechanism has extremely strong profitability, and regardless of how the benchmark returns fluctuates, the strategy always far exceeds the benchmark returns. As this strategy can not only reflect the volatility of the benchmark returns, but also can amplify the volatility of the benchmark returns to a positive direction. On the other hand, the hedging-based Alpha strategy performs worse. Since systematic risk would be hedged, we also cannot obtain the benefits from systematic risk premiums, the return on investment portfolios will decline even if the hedging mechanism has an irreplaceable role from the perspective of risk management. Such strategy suffers losses during the up stage of the market therefore affecting the overall return. The conclusion is that in the bullish market, the

0.0000% 10.0000% 20.0000% 30.0000% 40.0000% 50.0000% 1 2 3 4 5 6 Time period

Accumulative Return Rate

Alpha strategy with hedging is not an effective strategy. However, in the down stage of the market, the profit from the mechanism of hedging can make up for the losses caused by the stock-trading, so the strategy still maintains stable profitability. Therefore, in the bearish market, the Alpha strategy with hedging is an effective hedge to some extent.

We can also analyze the applicability of different strategies from the perspective of market conditions: When the market goes up, the Alpha investment strategy based on hedging has lower profitability as the sharp increase of benchmark index causes the losses of short positions thus affecting the overall return of the portfolio. However, the Alpha investment strategy based on the short-selling mechanism shows the strong profitability as this strategy could reflect the fluctuation of the benchmark index in advance and will amplify this fluctuation. When the market goes up, we can see that the Alpha strategy based on hedging could maintain stable returns. Similarly, the Alpha strategy with short-selling also shows strong profitability during the down period of the market. Similar to the rules found in the above paragraph, such strategy is able to identify and amplify the stock index volatility. From the perspective of long-term holding, the two kinds of profitability are also worthy of recognition.

IV. Conclusion

The first conclusion of this paper is that the momentum effect of stock is quite obvious in Chinese securities market. It is feasible to use the momentum effect to construct a suitable Alpha investment strategy in the Chinese securities market. In this paper, the success of Alpha strategies proves that under the current situation where the Chinese securities market is not efficient, the Alpha strategy based on momentum effect is capable of achieving abnormal returns beyond the average returns of the market. Due to the existence of momentum effect, stocks with large positive Alpha are able to maintain their upward trend in both bearish and bullish markets. In the bullish market, this strategy mainly relies on the momentum effect to continuously capture the most profitable portfolio, ensuring that abnormal returns would be achieved. In the bearish market, even if most of the stock prices are falling, the Alpha strategy still ensures the construction of profitable stock portfolios due to the continuity of the rising trend of the previous profitable stocks.

Specifically, hedging-based Alpha strategy is lower than the Alpha strategy based on short-selling mechanism in terms of profitability, but the most significant feature of such strategy is to eliminate the systematic risk that the market brings to the portfolio. Especially in the down period of the market, this strategy is able to get rid of the negative impact of the market, maintaining stable returns. Our conclusion is that this strategy is applicable to risk-averse investors as well as investors with high liquidity requirements as the strategy ensures that investors can obtain decent abnormal returns even if they withdraw from the downward market.

The Alpha strategy based on short-selling mechanism has better profitability, but due to the influence of Chinese trading rules and the real situation of Chinese securities market, this paper does not fully reflect the advantages of such strategy. However, from the empirical results we can reasonably infer that the existence of the short-selling mechanism is expected to improve the Alpha strategy as well as bring more benefits to

investors.

As both strategies designed in this paper have different risk and return characteristics, it is necessary for investors to make a choice with taking market conditions into account. Since Chinese securities market temporarily does not allow short-selling, the Alpha strategy based on the short-selling mechanism lacks of the realistic soil. However, we still reasonably imagine that regardless of market conditions, it will be feasible to use various Alpha strategies to achieve abnormal returns in Chinese securities market and Alpha strategies will be applied more widely in the securities market of developing countries in the future.

Reference List

Michael C. Jensen, 1968. The Performance of Mutual Funds in the Period 1945-1964. The Journal of Finance, Vol. 23, No. 2, (May., 1968), pp. 389-416.

N.Jegadeesh and S.Titman, 1993. Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. The Journal of Finance, Vol. 48, No. 1. (Mar., 1993), pp. 65-91.

N.Jegadeesh and S.Titman, 2001. Profitability of Momentum Strategies: An Evaluation of Alternative Explanations. The Journal of Finance, Vol. 56, No. 2. (Apr., 2001), pp. 699-720.

China Securities Regulatory Commission 2015 Annual Report.

Daniel, Kent, David Hirshleifer, and Avanidhar Subrahmanyam, 1998, Investor psychology and security market under- and overreactions, Journal of Finance 53, 1839-1886.

George, Thomas J., and Chuan-Yang Hwang, 2004, The 52-week high and momentum investing, Journal of Finance 59, 2145-2176.

Grinblatt, Mark, and Matti Keloharja, 2000, The investment behavior and performance of various investor types: a study of Finland’s unique data set, Journal of Financial Economics 55, 43-67.

Liu, Xiaolei Laura and Lu Zhang, 2008, Momentum profits, factor pricing, and macroeconomic risk, Review of Financial Studies 21, 2417-2448

Lowenstein, Louis, 2006, Searching for rational investors in a perfect storm: a behavioral perspective, Journal of Behavioral Finance 2: 66-74.

Mei, Jianping, Jose A. Scheinkman, and Wei Xiong, 2009, Speculative trading and stock prices: evidence from Chinese A-B share premia, Annals of Economics and Finance 10, 225-255.

Nofsinger, John R., and Richard W. Sias, 1999, Herding and feedback trading by institutional and individual investors, Journal of Finance 54: 2263-2295.

K. Geert Rouwenhorst, 1998. International Momentum Strategies. The Journal of Finance. Vol. 53, No. 1 (Feb., 1998), pp. 267-284.

Financial Studies. Vol. 11, No. 3 (Jul., 1998), pp. 489-519.

Chan, K.; A. Hameed; W. Tong. 2000. "Profitability of Momentum Strategies in the International Equity Markets." Journal of Financial and Quantitative Analysis 35, no. 2: 153-172.

Cooper, M.J.; R.C. Gutierrez; and A. Hameed. 2004. "Market States and Momentum." Journal of Finance 59, no. 3: 1345-1365.

A. Hameed and K. Yuanto. Momentum Strategies: Evidence from the Pacific Basin Stock Marketsf [J]. Working Paper,2000.

T.Naughton and C.Truong. Momentum strategies and stock returns: Chinese evidence. Pacific-Basin Finance Journal. Vol 16, No. 4. (Sept., 2008), pp.476-492

E Kung and L Pohlman, 2004. Portable Alpha. Journal of Portfolio Management Spring 2004.

Chordia Tarun and Lakshmanan Shivakumar, 2002, Momentum, business cycle, and time-varying expected returns, Journal of Finance 57, 985-1019.

Chui, Andy C.W., Sheridan Titman, and K.C. John Wei, 2010, Individualism and momentum around the world, Journal of Finance 65, 361-392.

Arnott, Robert D. 2002. “Risk Budgeting and Portable Alpha.” Journal of Investing, summer: 15-22.

Asness, Cliford., Robert Krail., and John Liew. 2001. “Do Hedge Funds Hedge?” Journal of Portfolio Management, Fall: 6-19

Bernstein, Peter L. 2003. “Points of Inflection: Investment Management Tomorrow.” Financial Analyst Journal, Vol. 59, No. 4 (July/August): 18-23.

Jensen, Greg., and Jason Rotenberg. 2003. “Hedge Funds Selling Beta as Alpha.” Working paper, Bridgewater Associates, Inc.

Litterman, Bob. 2003. “Active Alpha Investing.” P&I, August 18: 12-13.

Barras, L., O. Scaillet, and R. Wermers. “False Discoveries in Mutual Fund Performance: Measuring Luck in Estimated Alphas.” Working paper, Swiss Finance Institute and University of Maryland (2008).

Bogle, J. “The Implications of Style Analysis for Mutual Fund Performance Evaluation.” The Journal of Portfolio Management 24, no. 4 (Summer 1998), pp. 34-42.

Carhart, M. “On Persistence in Mutual Fund Performance.” Journal of Finance 52, pp. 57-82.

Davis, J. “Mutual Fund Performance and Manager Style.” Financial Analysts Journal 57 (January/February 2001), pp. 17-26.

de Silva, H., S. Sapra and S. Thorley. “Return Dispersion and Active Management.” Financial Analysts Journal 57, No. 5 (September/October), 29-42.

Duan, Y., G. Hu, and R.D. McLean. “When Is Stock Picking Likely to Be Successful?” Financial Analysts Journal 65, No. 2 (March/April 2009), 55-66.

Malkiel, B. and A. Saha. “Hedge Funds: Risk and Return.” Financial Analysts Journal 61, no. 6 (Nov./Dec. 2005), pp. 80-88.

Pojarliev, M. and R. M. Levich. “Do Professional Currency Managers Beat the Benchmark?” Financial Analysts Journal 64, no. 5 (2008), pp. 18-32.