Is information uncertainty a driver for the profitability of the moving
average technical trading strategy?
A comparison of the US REIT market and the NYSE/AMEX
B.A.E. Looij (10688110)
Master Thesis
MSc Finance
Specialization Real Estate Finance
Faculty of Economics and Business
Department of Finance
Supervisor: Dr. J.E. Ligterink
August 2018
Statement of Originality
This document is written by Student Bob Looij who declares to take full responsibility for the content of this document.
I declare that the text and the work presented in this document are 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
This thesis investigates whether information uncertainty is a driver for the profitability of technical trading. The specific technical trading strategy used in this thesis is the moving average trading strategy with a lag length of 10 days. The moving average trading strategy is applied to both US Real Estate Investment Trust stocks and NYSE/AMEX stocks, which are sorted into quintile and decile portfolios based on their underlying volatility. The time period of this study is from January 1991 to December 2016. Firstly, this thesis researches Real Estate Investment Trust stocks, since it is assumed that they are relatively transparent in comparison to other stocks and therefore les information uncertainty is expected. The lower levels of information uncertainty would suggest lower profits from technical trading in comparison to the stocks from the NYSE/AMEX. This thesis indeed did not find any significant evidence of the moving average trading strategy outperforming the buy-and-hold strategy when applied to US Real Estate Investment Trust stocks. However, when the moving average strategy was applied to the NYSE/AMEX portfolios, it did outperform the buy-and-hold strategy for 5 out of 10 portfolios. This suggests that information uncertainty might play a roll in deriving profit from technical trading. Secondly, this thesis investigates whether the
profitability of the moving average trading strategy increases with the volatility of the underlying stock. Volatility is used to proxy information uncertainty. If information uncertainty plays a roll in driving the profitability of technical trading, than the portfolio with higher volatility stocks should have higher returns derived from technical trading than those with lower volatility stocks. For the US Real Estate Investment Trust portfolios this thesis finds no significant positive relationship between volatility and returns derived from the moving average trading strategy. However, for the NYSE/AMEX portfolios, a significantly positive relationship was found.
TABLE OF CONTENTS
1. INTRODUCTION ... 1
2. LITERATURE REVIEW ... 4
2.1 Fundamental analysis versus technical analysis ... 4
2.2 The moving average trading strategy ... 5
2.3 The efficient market hypothesis ... 6
2.4 Explanations for technical trading profits ... 7
2.5 Overview of previous research on technical analysis ... 8
2.6 The real estate and REIT market ... 11
2.7 Development of the research question and hypotheses ... 12
3. METHODOLOGY ... 14
3.1 The moving average trading strategy ... 14
3.2 The REIT quintile portfolios ... 14
3.3 The CRSP NYSE/AMEX decile portfolios ... 15
3.4 Overview of the empirical analysis ... 15
3.5 The statistical significance testing procedure ... 18
4. EMPIRICAL RESULTS ... 20
4.1 Robustness check ... 25
5. DISCUSSION ... 29
6. CONCLUSION ... 31
1. INTRODUCTION
Technical analysis, also known as “charting”, uses past prices and other past statistics to predict future price movements and to make investment decisions. Proponents of technical analysis believe that past data contains information about future price movements. The techniques which try to discover hidden relations in past prices, range from extremely simple to quite elaborate. The modern technique of technical analysis can be traced back to Charles Dow in the late 1800s. By many it is considered to be the original form of investment analysis. It was widely used in the period before financial information was elaborately and fully disclosed which enabled the practice of fundamental analysis. From the moment that Charles Dow introduced the Dow theory, technical analysis has been popular by market participants in the financial industry. For instance, major brokerage firms publish technical commentaries on the markets, and use technical analysis as a foundation for their advisory services. Swager (1993, 1995) interviewed many top traders and fund managers who stated that they use it. In addition Covel (2005) states the use of technical analysis by large and successful hedge funds, which advocate the use excessively without learning any
fundamental information on the market. Within the financial industry technical analysis is both widely used and at the same time controversial.
The opposition against technical analysis is even bigger among some academics. The discipline of technical analysis has not received the level of academic scrutiny and acceptance as more traditional approaches like fundamental analysis. Lo, Mamaysky, and Wang (2000) describe that one of the greatest gaps between academic finance and industry practice is the existing
separation between technical analyst and their academic critics. They continue by stating that contrary to fundamental analysis, which was quickly adopted by the scholars of modern finance, technical analysis has been an orphan from the very start. A representative example of the attitude from academics toward technical analysis is well described by Malkiel (1981, p. 140):
“ Obviously, I am biased against the chartist. This is not only a personal predilection, but a
professional one as well. Technical analysis is anathema to the academic world. We love to pick on it. Our bullying tactics are prompted by two considerations: (1) the method is patently false; and (2) it’s easy to pick on. And while it may seem a bit unfair to pick on such a sorry target, just
remember: it is your money we are trying to save.”
Park and Irwin (2007) state that skepticism by academics towards technical analysis is associated to (1) acceptance of the efficient market hypothesis (Fama, 1970) and (2) negative empirical findings in early and well known studies of technical analysis in the stock market, among others Fama and
Blume (1966), Van Horne and Parker (1967) and Jensen and Benington (1970). However, as stated by Brock, Lakonishok, and LeBaron (1992) the conclusion that technical analysis is useless might be premature in the light of recent studies on the predictability of equity returns from past returns. Indeed, several models, like the random walk, which are based on the conventional efficient market theory, rule out the existence of technical trading profits in speculative markets.
The studies that did find technical analysis to be profitable, have proposed several reasons. Firstly, more recent models such as noisy rational expectation models or behavioral models imply that prices adjust sluggish to new information, due to noise in the market or irrational behavior by investors. Secondly, various empirical factors have also been proposed as the reasons for technical trading profits. Such as central bank interventions, clustering of order flows, time-varying risk premiums, market microstructure deficiencies and temporary market inefficiencies (Park & Irwin, 2004).
In a recent study by Han, Yang, and Zhou (2013) technical trading rules are applied to decile portfolios sorted on variables that reflect information uncertainty. Their investigation into the role of information uncertainty is motivated by the following intuitive reasons. First, they view technical analysis as a trading signal that aid investors in their decision-making. When information about stocks is very uncertain, fundamental signals are likely to be imprecise, and hence investors are likely to rely more on technical signals. Following this reasoning, if technical signals are truly profitable, they are likely to show up more for the more information uncertain stocks. Second, they use a moving average trading rule which is a trend following strategy. The profitability of the strategy relies on whether there are detectable trends in the cross section of the stock market. As argued by Zhang (2006) stock price continuation is due to under-reaction to public information by investors, and this increases in case of greater information uncertainty. Han et al. (2013) find abnormal returns that are of great economic significance derived from their technical trading strategy. They state that the technical trading profitability depends mostly on the information
uncertainty of the stocks. With their findings they have created a new research avenue in the field of technical analysis. They claim to have found a new anomaly in the finance literature and state that it will likely be fruitful to examine the profitability of technical analysis in various markets and assets classes, especially focusing on the role of volatility and other proxies for information uncertainty The contribution of this thesis is to further investigate the relation between information
uncertainty and the profitability of technical analysis by building upon the finding of Han et al. (2013). Thereby adding more scientific research to the newly found anomaly of the relation between information uncertainty and the profitability of technical trading. In addition this thesis contributes to the existing literature because it partly focuses on the Real Estate Investment Trust (REIT) market. A considerable amount of studies, related to technical analysis, have focused on the
stock market, the currency market, and the futures market. However, little research on technical trading has been conducted into the REIT market specifically.
To investigate the relation between information uncertainty and the profitability of technical trading, this study will investigate and compare technical analysis applied to portfolios that have been sorted on volatility, since volatility is a simple proxy for information uncertainty. The underlying assets for those volatility portfolios will be US REIT stocks in one case and the NYSE/AMEX stocks in the other case. The interest, into the REIT market is because REITs are relatively transparent. REITs are relatively transparent in comparison to other companies because there are regulatory constraints they have to comply with in order to qualify as a REIT. In addition the valuation of a REIT’s stock price is straight forward what leaves little room for information uncertainty. Because REITs are relatively transparent there should be less information uncertainty relatively to other stocks. Therefore if profitability from technical trading is driven by information uncertainty as argued by Han et al. (2013) it is not expect, or to a lesser degree, that technical trading is profitable when applied to the REIT market. If however technical trading is profitable when applied to the REIT market it could mean that it is not driven by information uncertainty. The results of the technical analysis applied to the REIT market will be compared to the results from technical analysis applied to the stocks that are listed on the NYSE/AMEX. The sample period of this study is from January 2, 1991 tot December 30, 2016. The technical trading rule of interest in this study is the Moving Average (MA) indicator. It is the most popular strategy of technical trading analysis and the main focus of most studies in the literature (Han et al., 2013).
The empirical analysis into the profitability of the moving average trading strategy is structured as followed. First, equal weighted quintile portfolios of daily REIT returns sorted on volatility are created. The 10 NYSE/AMEX volatility decile portfolios are readily available from the CRSP. To these portfolios both the moving average strategy and a naïve buy-and-hold strategy will be applied. The difference in returns between the two strategies gives insight to the profitability of the moving average strategy.
This thesis consists of several sub chapters, being: literature review, methodology, empirical results, and lastly the discussion and conclusion. First, the literature review is presented, which starts with an overview of the differences between fundamental and technical analysis. Secondly, the moving average trading strategy and the efficient market hypothesis are introduced. Theories that may explain the profitability of technical analysis are discussed, followed by the analysis of previous researches into technical analysis. In the last part of the literature review the specifics of the REIT market will be discussed followed by the development of the research question and hypothesis of this study. The Methodology consists of how the empirical analysis will be
conducted. The Empirical results of the moving average strategy will be analyzed. Thereafter a robustness check will be carried out. At last, the discussion of the results and the conclusion.
2. LITERATURE REVIEW
The literature review starts with a discussion of fundamental analysis and technical analysis and the differences between both. Secondly, the moving average trading strategy and the efficient market hypothesis are introduced. Thereafter theories that may explain the profitability of technical analysis are put forward. In the last part of the literature review the specifics of the REIT market will be discussed followed by the development of the research question and hypothesis of this study.
2.1 Fundamental analysis versus technical analysis
Technical analysis tries to predict future market prices by exploiting past and current market prices, trading volume and potentially other public available information. Technical analysis is based on the idea that prices move in trends that are determined by changing attitudes of investors toward a variety of economic, monetary, political and psychological factors (Park & Irwin, 2007). There are two forms of technical analysis. The first and oldest form is the graphical approach. Data is plotted on a graph and the analyst tries to visually perceive trends. Among the first and famous technical analyst who used this technique is Munches Homma. He accumulated a huge fortune in the rice market in the 1700s in Japan. His technique is nowadays known as the candlestick pattern. The fact that this technique is based on visual inspection makes it hard to express those judgments in a mathematical manner. In the United States technical analysis is based on the Dow theory developed by Charles Dow and later refined by William Peter Hamilton in the 1800s, it asserts that security markets move in certain phases with predictable patterns (Zhu & Zhou, 2009). The second type of technical analysis uses indicators that are formulated in mathematical relationships. These
indicators generate a trading signal when they perceive a trend. Many consider technical analysis as the original form of investment analysis. It was very popular before the period of extensive and fully disclosed financial information, which enabled the practice of fundamental analysis to develop (Brock et al., 1992).
Fundamental analysis, uses firm specific characteristics like earnings, dividend prospects and riskiness combined with market factors like future interest rates to determine the proper stock
price. It represents an attempt to determine the discounted value of all future payments a stockholder will receive from each share held. That value is then compared to the current stock price to infer a buy or sell indicator. However, fundamental analysis is also based on publicly available information. Hence, by efficient market theory, fundamental analysis is only profitable when the insight into the fundamental value is better than that of the other market participants1. Fama (1970) argues that, by the efficient market hypothesis, the only way to generate excess profit is by the use of fundamental analysis, not from technical analysis. Based on their believe in efficient markets, passive investors do not attempt to outperform the market with a active trading strategy. Instead they use a buy-and-hold strategy and combine securities to match their desired risk and return profile.To the contrary technical analysis is based on the assumption that markets are to some degree inefficient and that historical security prices can provide relevant information for future price changes.
2.2 The moving average trading strategy
There are a wide variety of different technical trading strategies that try to discover hidden relations in security returns. These techniques can range from extremely simple to quite elaborate. However the moving average indicator is the most popular strategy of technical trading analysis and the main focus of most studies in the literature (Han et al., 2013). By employing a moving average trading strategy, a moving average is used as an indicator that shows the average value of a security’s price over a period of time. By calculating a moving average, a mathematical analysis of the security’s average value over a predetermined time period is made. Different predetermined time length, also known as lag lengths, over which the moving average is calculated can be used. The averages move along with the security in time. The average is calculated over the determined lag length prior to the securities current price. As the security’s price changes its moving average changes as well. Also the way in which the average is calculated can vary between different methods. Among others, arithmetic, exponential, triangular, variable and, weighted averages can be used. The moving average trading strategy compares the moving average of the security’s past price with the security’s current price itself. A signal to buy the security is generated when the security’s price rises above its moving average and a sell signal is generated when the security’s price falls below its moving average. The idea of the moving average strategy is for an investor to ride the
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uninterrupted up trend of a risky asset. When the trend is broken the investor should then sell the asset and thereby avoid the downward price trend. The specific details of the moving average strategy applied in this study will be discussed in the methodology.
2.3 The efficient market hypothesis
The resistance of academics against the possible profitability of technical analysis can be attributed to the acceptance of the efficient market theory. The efficient market hypothesis describes the behavior in speculative markets and has long been the dominant paradigm. The fundamental of the efficient market hypothesis is that prices reflect all available information (Fame, 1970).
Jensen (1978) stated that he believed that there was no other proposition in economics which had more solid empirical evidence than the efficient market hypothesis and gave a more practical definition: “ A market is efficient with respect to information set θt if it is impossible to make economic profits by trading on the basis of information set θt”. By economic profits is meant, the risk adjusted returns net of all costs. Based on the definition of information set θt, Jensen
presented three various testable versions of the efficient market hypothesis;
1. Weak form efficiency, where the information set θt is limited to the information contained in the past price history of the market as of time t;
2. Semi-strong form efficiency, where the information set θt is all information that is publicly available at time t (this includes, of course, the past history of prices so the weak form is just a restricted version of the semi-strong form);
3. Strong form efficiency, where the information set θt is all public and private information available at time t (this includes the past history of prices and all other public information, so weak and semi-strong forms are simply restricted versions of the strong form).
Thus, by applying the moving average trading strategy we can test for the validity of the weak form efficiency in the market. Because the moving average strategy tries to use past price history to make economic profits from trading. If one assumes markets to be efficient, and therefore that all
available information is impounded in current prices, there would be no possibility to profit from technical analysis or trading rules. In the sense, that past information or currently available information cannot provide grounds for profitable trades.
2.4 Explanations for technical trading profits
Some modern studies have found proof for the profitability of technical trading rules. If one assumes markets to be efficient there would be no possibility to profit from technical analysis or trading rules. In the sense, that past information cannot provide profitable trades. However, there are some reasons and theoretical models proposed that aim to explain the profitability of technical trading rules, which will be discussed next.
The efficient market theory implicitly assumes that market participants are rational and have homogenous beliefs about information. In contrast, noisy rational expectation equilibrium models assume that current prices do not reflect all available information because of noise in the current equilibrium price. Noise is then defined as the unobserved part of either current supply of risky assets or information quality. Therefore the markets are inefficient and prices do not instantly adjust to new information, creating possibilities for profitable trading (Park en Irwin, 2007). Other models that could explain the profitability of technical analysis are behavioral models. Shiller (2003) argues that academic finance has evolved from the theory that market efficiency was considered to be proven without a doubt. In contradiction with the theory of market efficiency behavioral finance was develop in the early 1990s which approaches finance from a broader social science perspective including psychology and sociology. Behavioral finance can account for market anomalies, which the efficient market theory could not do. The efficient market theory assumes that every investor is a rational optimizer. However, Shiller (2003) argues that it is merely a metaphor for the world around us. He states that it is an absurd claim to assume that everyone knows how to solve complex stochastic optimization models and that for the efficient market theory to hold it must be the case that some small element of ‘sophisticated’ investors can offset the ‘foolishness’ of many. Therefore the behavioral finance models assume that there are two types of investors. The fist type of investor is the sophisticated investor also called, smart money, arbitrageur or marginal trader. The second type is called noise trader, feedback trader or liquidity trader. Black (1986) defines arbitrageurs as investors who have fully rational expectations of security returns, whereas noise traders are investors who trade irrationally on noise as if it were information.
One of the behavioral finance theories is the so-called feedback model. It reasons that when speculative prices go up and creates returns for some investors it attracts public attention. The enthusiasm of the rising prices creates high future expectation and creates demand that leads to further prices increases, away from the fundamental price. The high prices are not sustainable since they are based on expectations of future price increases and not on the fundamentals. The feedback can also work in the other way, by which price decreases cause pessimism. The pessimism leads to more downward price movement to unsustainable low prices not in line with fundamentals.
Existence of the feedback model could cause technical trading rules to be profitable. Shleifer and Summers (1990) argue that the prior discussed feedback model or behaviouralist approach is then based on two assumptions. Fists, the noise traders, are not fully rational and their demand for risky assets is affected by their beliefs or sentiment that do not fully rely on fundamental news. Second, the trading of arbitrageurs, which is fully rational and not subject to such sentiment, is risky and therefore limited. Both assumptions together imply that changes in investor sentiment are not fully countered by arbitrageurs and so affect security returns. They argue that this approach is in many ways superior to that of the market efficiency paradigm. It can be reasoned that when markets for risky assets are assumed to follow the behavioral models instead of the model for market efficiency some forms of technical trading can be profitable.
2.5 Overview of previous research on technical analysis
Empirical studies have investigated the use of technical analysis in a variety of markets. The purpose of these studies was to either discover profitable trading strategies or investigating the market efficiency hypothesis, or both. Numerous studies have investigated the profitability of technical trading rules is both emerging and mature markets leading to conflicting conclusions (Park en Irwin, 2004). Although this current study focuses on the moving average trading rule applied to stocks, the broader literature of technical trading will be examined since they are based on the same assumptions and theories.
Park and Irwin (2007) reason that studies on technical analysis can be categorized into two groups: early studies (1960-1987) and modern studies (1988-2004) based on the types of testing procedures they used. Starting with the earlier work. In most early studies technical trading rules along with statistical test where used to investigate price movements in several speculative markets. Before technical analysis was used to test market efficiency, researchers made use of statistical analysis like serial correlation. Fame and Blume (1966) make a case for directly testing the technical trading rules. They state that there is no obvious relation between the size of the serial correlation coefficient and the expected profit from technical trading rules. Furthermore, they argue that the simple linear relationship of the serial correlation model is far to unsophisticated to identify the complicated patterns a chartist would see in the stock prices. Moreover, it is difficult to apply transactions cost and risk elements into statistical analysis. Fama (1970) states that it is hard to infer the possibility for substantial profit from trading rules by looking at the degree of serial correlation in prices. He then further explains that there are types of nonlinear dependencies that imply the profitability of trading systems and yet do not imply nonzero serial covariance. Thereby for many
reasons the case is made for directly testing the profitability of various trading rules. Therefore in most of the earlier studies, technical trading rules are applied directly in accordance with statistical analysis to avoid the above-mentioned restrictions of statistical analysis.
A representative early study is that of Fama and Blume (1966). They used daily closing prices of 30 securities in the Dow Jones Industrial Average from 1956-1962. Although the authors find that some of the examined trading rules outperform the buy-and-hold strategy, they argue that in practice this would probably not be the case due to transaction costs. Van Horne and Parker (1967) test the moving average trading rule with a variety of lag lengths on 30 industrial stocks listed on the New York Stock Exchange from 1926-1966. They conclude that technical analysis cannot outperform the buy-and-hold strategy, not even when transaction cost are ignored. James (1968) reached the same conclusion by applying a monthly moving average to individual stock of the New York Stock Exchange from 1926-1960. Jensen and Benington (1969) also found evidence against the profitability of technical analysis. They applied trading rules based on moving averages and relative strength systems to individual securities of the New York stock exchange from 1926-1966.
Park and Irwin (2007) give an overview of previous literature and evidence of the profitability of technical analysis. They conclude that the results from the earlier studies vary greatly between markets. In general these studies failed to find evidence for the profitability of technical trading rules in stock markets. However, technical trading rules where often found to achieve considerable net profits in foreign exchange and future markets. Indicating that stock markets were more efficient relative to exchange and future markets in the time period of those studies. The early studies however had some considerable limitations in their testing procedures. The more modern studies, that will be discussed later, tried to overcome those limitations.
Now the limitations of the earlier studies will be discussed. Park and Irwin (2004) sum up the general limitations of the testing procedures of the early studies. One of the limitations is a model selection problem. Jensen (1967) refers to the problems of sampling error and selection bias also known as data snooping. He pointed out that one should pay close attention to the danger of data snooping that can arise in the testing procedure of technical analysis. Data snooping occurs when technical models are being optimized on the same data as they are being tested on. In other words if various technical trading rules are tested with enough variants on a body of data, profitable trading rules might be discovered due to chance, which leads to the misjudgment of the genuine predictive power of those rules by the researcher. To counter the problems arising from data snooping, Jensen (1967) proposes out of sample testing where the first half of the data is used to uncover the best trading rules, which should than be validated on the second half of the data. If the results on the two data sets are in line this would strengthen the case that the results were not due to
random chance. Another limitation of earlier studies is that the risk-return element of the trading rules was often ignored. As Jensen and Bennington (1970) point out, if investors are risk-averse they command extra return if they take on more risk. Therefore profits from technical trading rules do not automatically discard market efficiency since the returns may be driven by greater risk. It is thus important that when the returns from the trading rules are compared with a benchmark their corresponding riskiness is taken into account or adjusted for. Most early studies failed to
statistically test the technical trading returns and if they did they used conventional statistical tests. Moreover, early studies often studied several trading rules and reported the results as an average across all the trading rules without emphasizing the most and least profitable trading rule, which reduces the possibility to interpret them.
More modern studies tried to resolve the above-described testing problems of the earlier studies in several ways, which will be discussed next. The more modern studies vary in how they address the issues of data snooping, transaction costs, risk, parameter optimization, out of sample testing and statistical tests. Park and Irwin (2007) categorize the study of Lukac, Brorsen and Irwin (1988) to be the first modern study because they provide a more comprehensive analysis than the early studies. The authors conducted an out-of-sample test, performed statistical significance test and took the riskiness of the returns and transaction cost into account. They tested various trading rules in multiple future markets between 1975-1984 and reported statistically significant returns after transaction cost ranging from 1.89% to 2.78%. One of the most influential modern study was conducted by Brock et al. (1992). They applied a moving average and the trading range breakout rule to the DJIA between 1897-1986 and conclude that technical analysis outperformed the buy-and-hold strategy, excluding transaction cost. Additionally, their study shows that the time series could not be explained by a; Random Walk (with drift), an AR(1) or (E)GARCH model. In a follow up study on Brock et al. (1992), Bessembinder and Chan (1995) attribute the forecasting power of technical analysis to measurement errors arising from non-synchronous trading. Ready (2002) even goes further and claims that the profitability of trading rules in Brock et al. (1992) are due to a spurious result of data snooping. However, Sullivan, Timmerman, and White (1999) apply White’s Reality Check and state that Brock et al. (1992) results are robust to data snooping and even
perform better in their out-of-sample test. Lo et al. (2000) test a large set of technical indicators on a large number of U.S. stocks from 1962 to 1996 and found some predictive ability especially for the moving average rule.
Han et al. (2013) investigate a moving average strategy applied to NYSE/AMEX decile portfolios which they sorted on variables that proxy information uncertainty. As proxies for
information uncertainty they used, volatility, size, distance to default, credit rating, analyst forecast dispersion, and earnings volatility. However, their main interest is in the decile portfolios, which are
sorted on volatility. They conclude that the moving average strategy based on the volatility decile portfolios substantially out perform the buy-and-hold strategy. Especially for the high-volatility portfolios, the abnormal returns, relative to the capital asset pricing model and the Fama-French 3-factor models, are of great economic significance. Similar results hold for the portfolios sorted on the other proxies for information uncertainty. In the same spirit, Glabadanidis (2015) conducts a thorough study and applies the moving average trading strategy to US decile portfolios sorted by market size, book-to-market and momentum on seven international markets as well as 18,000 individual US stocks in the sample period of 1960-2011. He finds the moving average trading strategy to be profitable with risk-adjusted returns in a range of 3% to 7% after transaction costs.
The, to my knowledge, only study that specifically investigates the market timing power of the moving average in the U.S. REIT market is that of Glabadanidis (2014). He investigates monthly returns of both 20 US REIT indexes and 274 individual REITs over the period 1980 - 2010. The moving average trading strategy applied in his study dominates the buy-and-hold returns of the underlying assets in a mean-variance sense.
2.6 The real estate and REIT market
This thesis investigates if technical trading is profitable when applied to the REIT market and to what extend the profitability depends on information uncertainty. The interest, of this study, in the REIT market is because REITs are relatively transparent entities and therefore one would expect less information uncertainty. REITs have to oblige to some regulatory constraints, which make them relatively transparent in comparison to other companies. For instance, at least 75 percent of a REIT’s total assets must be real estate, mortgages, cash or federal government securities, and 75 percent or more of the REIT’s yearly income must be derived directly or indirectly from real
property. Additionally their income (at least 75 percent) must be from primarily passive sources like rents and mortgages interest, as distinct from short-term trading or sale of property assets. Also, at least 90 percent of a REIT’s annual taxable net income must be distributed to shareholders as dividends each year2. Therefore, the valuation of a REIT is in essence very straightforward. The main task is to estimate the value of all the properties currently held by the REIT, as these
properties would currently be valued in the private property market. Then adjust for the non-asset-based value the REIT might have and subtract the value of the current liabilities. This gives the net asset value (NAV) of the REIT. Dividing by the number of shares outstanding, gives the REIT’s
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NAV per share3. Because REITs are relatively transparent there should be less information uncertainty relatively to other stocks. Therefore if profitability from technical trading is driven by information uncertainty as argued by Han et al. (2013) it is not expected, or to a lesser degree to find, that technical trading is profitable when applied to the REIT market. However, if technical trading is profitable it could mean that it is not driven by information uncertainty.
2.7 Development of the research question and hypotheses
The author has set up the following research question:
Is information uncertainty a driver for the profitability of the moving average technical trading strategy?
Han et al. (2013) state that they have found a new anomaly in the finance literature, which is the relationship between information uncertainty and the profitability of technical analysis. This thesis further investigates the role of information uncertainty in technical trading profits. To investigate if information uncertainty plays a role in driving the profitability of technical trading, several portfolios with different underlying assets are sorted on their volatility. The portfolios are sorted on volatility since volatility is a proxy for information inefficiency.
From a theoretical approach it is interesting to investigate the relation between volatility and the returns resulting from the moving average strategy. Rational models, such as Brown and
Jennings (1989) show that investors can gain from forming future expectations based on historical prices, and this gain increases with the volatility of the asset. In addition stock price continuation might be an effect of the under-reaction by investors to public information, the effect will increase with greater information uncertainty (Zhang, 2006). If the profitability of the technical trading strategy increases along with the sorted variable in each quintile portfolio, it would mean that the performance of the technical trading strategy has a relation with that variable. The technical trading rule of interest in this study is the Moving average indicator. It is the most popular strategy of technical trading analysis and the main focus of most studies in the literature (Han et al., 2013, p1437). Technical trading is only useful if it can outperform the market. Therefor the moving average trading strategy is compared to the buy-and-hold strategy.
For the portfolios sorted on volatility two different underlying asset categories are used. The first asset category is REIT stocks and the second assets category is stocks from the NYSE/AMEX.
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The difference in underlying asset allows for the comparison of the profitability of technical trading applied to the different asset categories. The interest of this study in the REIT market is because REITs are relatively transparent. REITs are relatively transparent because there are regulatory constraints they have to comply with in order to qualify as a REIT. In addition the valuation of a REIT’s stock price is straight forward what leaves little room for information uncertainty. Because REITs are relatively transparent there should be less information uncertainty relatively to other stocks. Therefore if profitability from technical trading is driven by information uncertainty as argued by Han et al. (2013), it is not expected, or to a lesser degree, to find technical trading to be profitable when applied to the REIT market. If however technical trading is profitable when applied to the REIT market it could mean that it is not driven by information uncertainty. To further
investigate the relation between information uncertainty and the profitability of technical analysis. The moving average strategy is also applied on portfolios sorted on volatility with stocks of the NYSE/AMEX as underlying assets. If profitability from technical trading is driven by information uncertainty it is expected that technical analysis applied to the high-volatility portfolios will provide excess returns above the buy-and-hold strategy. This thesis investigates the relation between
information uncertainty and the profitability of technical analysis applied to both portfolios comprised of REIT stocks and portfolios comprised of NYSE/AMEX stocks.
To investigate the above the author has set up the following research hypotheses:
1. The moving average trading strategy outperforms the buy-and-hold strategy on average when applied to a portfolio comprised of REIT/-NYSE/AMEX stocks.
2. The profitability of the moving average trading strategy increases with the volatility of the underlying stocks.
3. METHODOLOGY
The methodology section starts with the introduction of the technical trading rule that will be tested. Thereafter, the underlying data and construction of the REIT quintile portfolios and the 10
NYSE/AMEX decile portfolios will be presented. This will be followed by a stepwise overview of the empirical analysis. The empirical analysis of this study is mainly based on the methodology used by Han et al. (2013). Finally, the statistical significance testing procedure of the results will be presented.
3.1 The moving average trading strategy
As noted by Brock et al. (1992) there is a substantial danger of detecting spurious patterns if technical trading strategies are both discovered and tested on the same database of security prices. To circumvent the possible danger of data snooping, the best trading rule is not selected ex-post in the data set. Although there are a lot of different technical trading rules, only the moving average trading rule will be applied. A moving average is a lagged indicator that is used to smooth a data series. In general, as the lag length increases the moving average becomes smoother. The longer the lag of the moving average the less sensitive it becomes to small price changes. Therefore the longer the lag length is, the more it smooths out the small cycles present in the index. The longer moving average follows the long-term trends and the shorter moving average follows the short-term trends. Following Han et al. (2013) the lag length used in the research for the moving average window will be 10 days.
3.2 The REIT quintile portfolios
The dataset for the empirical analysis consist of daily US REIT prices and returns between January 2, 1991 and December 30, 2016. The underlying assets for the technical analysis will consist of quintile portfolios that are sorted by their volatility. More specifically, the volatility quintile portfolios are constructed based on the REIT stocks and sorted into 5 groups (quintiles) by their annual standard deviation estimated by daily returns within the prior year. The REIT stocks that exhibit the lowest volatility will be sorted into the lowest quintile portfolio and the REIT stocks that exhibit the highest volatility will be sorted in the highest quintile portfolio. The portfolios are rebalanced each year at the end of the previous year. Once the stocks are assigned to a quintile
portfolio, daily portfolio index (price) levels and returns will be calculated by equal weighting. The quintile portfolios sorted on volatility are constructed since volatility is a simple proxy for
information uncertainty. There is a positive relation between the uncertainty of future information and the volatility of the stock. So by looking at the quintile portfolio sorted on volatility we can investigate if the returns from the moving average strategy are driven by information inefficiency.
3.3 The CRSP NYSE/AMEX decile portfolios
The NYSE/AMEX decile portfolios are available from the Center for Research in Security Prices (CRSP). 10 volatility decile portfolios are used as the underlying asset for the technical analysis. The decile portfolios are constructed based on the NYSE/AMEX stocks. By their annual standard deviation estimated from daily returns within the prior year, the NYSE/AMEX stocks are assigned to a decile portfolio. The stocks that exhibit the lowest volatility have been sorted into the lowest decile portfolio and the stocks that exhibit the highest volatility have been sorted in the highest decile portfolio. The portfolios are rebalanced each year at the end of the previous year. The daily portfolio index (price) levels and returns are readily available from CRSP and are calculated by equal weighting. The sample period for volatility decilice portfolios is from January 2, 1991 and December 30, 2016.
3.4 Overview of the empirical analysis
For the technical trading analysis a comparison of the 10 NYSE/AMEX decile portfolios and the 5 REIT quintile portfolios are made. The REIT stocks are sorted into 5 quintile portfolios because if they would be sorted into 10 decile portfolios there would not be enough stocks in each portfolio to make a reasonable statistic analysis. However, the technical analysis applied to both the REIT quintile portfolio and NYSE/AMEX decile portfolios is identical, only the number of portfolios the stocks are sorted into differs.
Starting with the buy and hold return. For the 10 NYSE/AMEX decile portfolios the daily price levels and returns are readily available from CRPS. For the REIT quintile portfolios the price levels and returns needed to be calculated. The daily return for the buy and hold returns of the portfolios are calculated the following way:
1 𝑟! = log ( 𝑃! 𝑃!!!)
Where 𝑟! is the return at time t, log is denoted as the natural logarithm, 𝑃! is the price at time t, and 𝑃!!! is the price at time t-1. The return of the buy and hold strategy will be analyzed based on the mean, the standard deviation, the skewness, and the Sharpe ratio.
Secondly, the returns of the portfolios sorted on volatility under the moving average trading strategy have to be calculated. The following definition of the moving average used in this study follows that of Han et al. (2013). Let Rjt (j = 1,…,5/10) be the return on, the by volatility sorted portfolio J at time t, and Pjt ( j = 1,...,5/10) the corresponding portfolio prices (index levels). The moving average for portfolio j at time t of lag L is then defined as:
2
Ajt, L =
( P
jt−L+1+ P
jt−L+2𝐿
+. . . + P
jt−1+ P
jt)
The way in which the moving average strategy is implemented is to compare closing price Pjt at the end of every day to the moving average Ajt, L. If the closing price is above the moving average it triggers a signal to invest in the volatility portfolio J (or to stay invested if already invested in t-1) in the next day t+1. If the closing price at the end of the day is lower than the moving average it is a signal to leave the risky investment of the volatility portfolio and invest in the risk-free rate for the next day (or to stay invested in the free rate if already invested in t-1). The proxy for the risk-free rate will be the return on the 30-day US Treasury Bill. The idea of the moving average strategy is for an investor to ride the uninterrupted up trend of a risky asset. When the trend is broken the investor should then sell the asset and thereby avoiding the downward price trend.
The formal return of the moving average strategy, in absence of any transaction cost derived from switching between the portfolio and the risk-free rate, can be expressed as:
(3) R
!",!=
R
!",
if P
!"!!> A
!"!!,!;
𝑟
!", 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Where R!",! is the return of the moving average strategy, Rjt is the return on the jth quintile or decile portfolio on day t and rf is the return on the risk-free asset. Rjt will be calculated in the same way as the buy and hold return, see formula 1.
To give a representative insight into the possibility of a profitable moving average stagey, one should take into account the transactions costs of switching between the quintile portfolio and the risk-free rate. In this research there are no transactions cost applied when buying or selling the risky or the risk-free asset. Previous conducted studies by Balduzzi and Lynch (1999) suggest that 1
to 50 basis points, is an appropriate value to account for transaction cost. This empirical methodology will not impose any transaction cost for the calculations of returns.
The performance of the moving average strategy will be measured relative to the buy-and-hold strategy of the underlying portfolios. The focus is whether the moving average strategy outperforms the buy-and-hold portfolio. The interest of this study is the difference between the returns of the buy-and-hold portfolios and the moving average strategy. This can be written as:
Rjt, L - Rjt. The difference in the return between the buy-and-hold portfolio and the moving average
strategy is represented by the Moving Average Portfolio (MAP). The performance of the MAP depends on the usefulness of the moving average trading signal. For each volatility portfolio the MAP is constructed, which can be generalized into the form of:
5 MAP
!",!= 𝑅
!",!− 𝑅
!",
j = 1, . . . ,5/10.
The profitability of the moving average timing strategy can be derived from the performance of the MAPs. The presence of significant returns resulting from the MAPs can be interpreted as the superiority of the moving average trading strategy above the buy-and-hold strategy of the underlying assets.
To investigate if information uncertainty plays a role in driving the profitability of the moving average strategy, the portfolios sorted on volatility are analyzed. If the profitability of the moving average strategy increases along with the sorted variable in each volatility portfolio, it would mean that the performance of the moving average strategy has a relation with that variable. The performance of the MAPs will be analyzed with the use of summary statistics like the average return, standard deviation, Sharpe ratio, and the skewness. Although we can infer from this whether the moving average strategy outperforms the buy-and-hold strategy, it is unclear whether the returns from the MAPs can be explained by a risk-based model. To this end Han et al. (2013) regresses the return from the different MAPs on the Capital Asset Pricing Model and the Fama and French 3 factor model. This current study will however not examine the returns of the MAPs in the context of factor models.
3.5 The statistical significance testing procedure
The fist hypothesis, whether a moving average trading strategy outperforms a buy and hold strategy applied to the underlying stocks of US REITs and the NYSE/AMEX can be answered by looking at the MAPs. The MAPs represents the difference in return between the two strategies and is created by subtracting the return of the buy-and-hold portfolio from the moving average strategy (see formula 4). Therefore the return of the MAP depends on the profitability of moving average signal. To answer the first hypothesis a statistical test should be performed to see whether the mean return of the MAP decile portfolios is statistically greater than zero. The following hypotheses need to be tested.
H0: The difference in return between the buy and hold strategy and the moving average strategy is equal to zero at a 5% significant level.
𝐻! = 𝑀𝐴𝑃!",! = 𝑅!",! − 𝑅!" = 0, (𝑗 = 1, … ,5/10. )
H1: The difference in return between the buy and hold strategy and the moving average strategy is greater than zero.
𝐻! = 𝑀𝐴𝑃!",! = 𝑅!",! − 𝑅!"> 0, (𝑗 = 1, … ,5/10. )
The above hypothesis should be tested for all MAPs. So for each US REIT quintile portfolio and for each NYSE/AMEX decile portfolio sorted on volatility.
In order to draw a conclusion about the above hypothesis, the statistical significance of the MAPs return have to be tested. To test the statistical significance of the MAPs returns a one-tailed t-test will be performed to see if the mean return of the moving average portfolios is significantly different from the mean return of the buy and hold portfolios.
The value of the t-statistic will be calculated using the following formula:
6 𝑡 − 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 =
!!"#,!!!! !!"#,!!!"#,!
, ( j = 1, … ,5/10)
Where, 𝑟!"#,! is the mean return of the jth quintile/decile portfolio sorted on volatility, 𝑟! is the
mean return under the null hypothesis, 𝑠!"#,! is the standard deviation of the returns of the jth quintile/decile portfolio sorted on volatility, 𝑛!"#,! is the number of observations of the returns from the jth quintile/decile portfolio sorted on volatility. The empirical t-statistic will be compared
to its critical value at a 5% significance level. If the t-statistic is larger than the critical 5% significance level, the null hypothesis (H0) can be rejected in favor of the alternative hypothesis (H1). A one-tailed t-test is used because the outperformance of the moving average strategy in comparison to the buy and hold strategy is of interest. Therefore, t-values that exceed 1.645 are significant.
For the second research hypothesis, the statistical significance testing procedure is quite similar. The hypothesis: Is information inefficiency a driver for the profitability of technical trading? Is the following:
H0: The mean return of the highest volatility portfolio is equal to the lowest volatility portfolio.
𝐻! = 𝑀𝐴𝑃!/!"!,!"# − 𝑀𝐴𝑃!!,!"# = 0
H1: The mean return of the highest volatility portfolio is statistically significant higher than the lowest volatility portfolio.
𝐻! = 𝑀𝐴𝑃!/!"!,!"# − 𝑀𝐴𝑃!!,!"# > 0
In order to draw a conclusion about the above hypothesis, the statistical significance of results have to be tested. A one-tailed t-test will be performed to see if the mean return of the highest quintile MAP portfolio is different from the mean return of the lowest quintile MAP portfolio. In this case there is a comparison of means of different populations, namely the return of the highest and the lowest decile portfolios. The value of the t-statistic will be calculated using the following formula:
7 𝑡 − 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 =
!!"#!/!"!!!"#! !!! !!"#!/!"! !!"#!/!"! !!"#!! !!"#!Where, 𝑟!"#!/!" is the mean return of the 5th quintile or 10th decile MAP sorted on volatility, 𝑟!"#! is the mean return of the 1st quintile/decile MAP sorted on volatility, 𝑑! is the value under the null hypothesis, which is equal to 0,
𝑠
!"#!/!"! is the standard deviation of the returns of the 5th quintile or 10th decile portfolio sorted on volatility, 𝑠!"#!! is the standard deviation of the returns of the 1st quintile or decile portfolio sorted on volatility, 𝑛!"#!/!" is the number of observations of thereturns from the 5th quintile or 10th decile portfolio sorted on volatility, 𝑛
!"#! is the number of
observations of the returns from the 1st quintile/decile portfolio sorted on volatility. The empirical t-statistic will be compared to its critical value at a 5% significance level. If the t-t-statistic is larger
than the critical 5% significance level, the null hypothesis (H0) can be rejected in favor of the alternative hypothesis (H1). A one-tailed t-test is used because the outperformance of the highest decile portfolio sorted on volatility in comparison to the lowest decile portfolio is of interest. Therefore, t-values that exceed 1.645 are significant.
One should keep in mind that the t-test assumes a normal distribution of the returns of the underlying assets. Therefore the t-test might give biased results in case of a non-normal distribution of the returns.
4. EMPIRICAL RESULTS
This section starts with a discussion of the results from the empirical analysis, which are also presented in table form. Secondly the robustness check, in which the period of the real estate crisis is omitted, is discussed.
Table 1 and Table 2 report the basic return characteristics of the different trading strategies applied to the 5 quintile portfolios of the REIT stocks and the 10 decile portfolios of NYSE/AMEX, respectively. The last row (high-low) in the table provides the difference between the highest
volatility portfolio and the lowest volatility portfolio. Panel A of Table 1 and 2 provides the average return, the standard deviation, the skewness, and the Sharpe ratio of the buy-and-hold strategy across the volatility portfolios. In Panel B of Table 1 and 2 the 10-day moving average strategy is reported. Panel C reports the results from the MAPs, which are the differences of the buy-and-hold strategy and the day moving average strategy. From these portfolios the effectiveness of the 10-day moving average strategy in comparison to the buy-and-hold strategy can be inferred. The results are annualized and in percentages. In the last column of Panel C the success rate of the moving average timing strategy is reported. The success rate is defined as the fraction of trading days when the moving average timing strategy is on the “right” side of the market, that is, it is out of the market when the return of the volatility portfolios are lower than the risk-free rate; and it is in the market when the return of the volatility portfolios are higher than the risk-free rate.
Starting with technical analysis applied to the US REIT market.
Table 1, Panel A provides the average return, the standard deviation, the skewness, and the Sharpe ratio of the buy-and-hold strategy across the 5 volatility quintile portfolios. The average returns range between 4,47% and 22,46%, all are positive and significant, however they are not an increasing function of the volatility quintiles. This becomes clear from the negative return of -16,42% in the high-low row. In Panel B the 10-day moving average strategy is reported. All the
average returns are positive and range between 1,50% and 13,67%. They are significant except for the return of the highest volatility quintile. The returns do not uniformly increase with volatility quintiles as can been inferred from the negative return of -11,99% in the high-low row. Furthermore for each volatility quintile the returns of the 10-day moving strategy in Panel B are lower than that of the buy-and-hold strategy in Panel A. However, the standard deviations of the returns for each volatility quintile in Panel B are all smaller than those of Panel A. The corresponding Sharpe ratios can give more insight in the risk-return trade-off. The Sharpe ratios are higher for the volatility quintiles in Panel A in comparison with Panel B. Panel C reports the results from the MAPs. All the returns of the volatility quintiles are negative ranging from -10,27% to 5,59%, therefore none of them is significantly positive. Also the returns do not appear to be an increasing function of the volatility quintiles. Contrary to Panel A and B the difference between the highest and lowest volatility quintile portfolio is positive, however not significant. In the last column of Panel C the success rate of the moving average timing strategy is reported. Across the quintile portfolios the success rate is in the range of 30% to 35%, which indicates that only about one third of the time the strategy is on the right side of the market and thereby indicating a bad timing performance of the moving average timing strategy. The results from Table 1 clearly show that the moving average timing strategy does not perform well. The moving average portfolios underperform the buy-and-hold portfolios with lower returns and lower Sharpe ratios. The MAP portfolios all have negative returns and a success rate of around 30% to 35%. These results are however not in accordance, with the study of Glabadanidis (2014) in that study the moving average strategy is applied on US REIT indices and individual US REIT stocks. He found that the moving average strategy substantial outperformed the buy-and-hold strategy in a mean-variance sense, with both a higher annualized returns and a lower standard deviation. He concluded that the moving average strategy had great market timing performance.
Secondly, the technical analysis applied to the 10 NYSE/AMEX portfolios reported in Table 2. Panel A in Table 2, provides the average return, the standard deviation, the skewness, and the Sharpe ratio of the buy-and-hold strategy across the 10 volatility decile portfolios. The average returns are roughly an increasing function of the decile portfolios, with a return difference of 41,22% between the lowest and highest decile portfolios. The returns range from 8,76% for the lowest decile to 49,88% for the highest decile portfolio. The moving average strategy reported in Panel B show similar results. Here the average returns are also roughly an increasing function of the on volatility-sorted portfolios, ranging from 14,75% to 56,27% per year. The average returns of Panel B in comparison to Panel A are significantly higher for 5 out of 10 decile portfolios. However, the standard deviations of the moving average decile portfolios in Panel B are
to be higher for each portfolio in Panel B. Panel C reports the results from the MAPs, which are the difference of the buy-and-hold strategy and the 10-day moving average strategy portfolios. The average returns from the MAPs do no appear to be a monotonically increasing function of the decile portfolios. However, the difference between the return of the highest and lowest portfolio is
significantly positive with a difference in returns of 15,15%. Additionally, 5 out of the 10 portfolios do have significantly positive returns, especially the three decile portfolios with the highest
volatility. The success rate of the moving average strategy reported in the last column of Panel C, ranges between 53% and 61% and thereby indicates a good timing ability of the moving average strategy. The results are mostly in accordance with the study of Han et al. (2013). However, they did find a more consistence relationship between the increasing decile volatility portfolios and the average returns from the moving averages strategy.
The differences in the results from the moving average strategy applied to the US REIT market and the NYSE/AMEX, reported in Table 1 and Table 2, respectively, will be discussed next. The moving average trading strategy appears to perform much better when applied to the
NYSE/AMEX portfolios than when it is applied to the US REIT portfolios. For the NYSE/AMEX portfolios the moving average strategy outperforms the buy-and-hold strategy in terms of both the returns and the standard deviation most of the time. Leading to higher Sharp ratios for all portfolios in Panel B in comparison to Panel A. This is in sharp contrast to the moving average strategy applied to the US REIT stocks. In that case the moving average strategy under performs the buy-and-hold strategy. The moving average strategy generates lower returns and slightly lower standard deviations than the buy-and-hold return. However, the Sharp ratios are for each moving average portfolio lower in Panel B than for the buy-and-hold portfolios in Panel A. Furthermore, the positive relationship between the increasing volatility of the portfolios and the corresponding returns from the moving average strategy that seems to be present for the NYSE/AMEX does not seems to exist for the US REIT portfolios. This becomes clear from the high-low variable in the last row of tables 1 and 2. For the NYSE/AMEX portfolios the difference between the returns from the highest and lowest volatility portfolios is for each panel significantly positive. However, For the US REIT portfolios, none of those differences is significantly positive. Lastly, the success rates of the moving average strategy ranges between 53% and 61% for the NYSE/AMEX portfolios and only between 31% and 35% for the US REIT portfolios. This indicates that the timing performance of the moving average strategy did work well when applied to the NYSE/AMEX, however not when applied to the US REIT stocks.
Table 1
Summery Statistics of the REIT Quintile Portfolios
Rank, indicates the subject quintile portfolio sorted on volatility constructed out of the Zittman REIT database. The 10-day moving average (MA) is calculated each 10-day, using the last 10 10-days’s closing prices including the current closing price. The daily MA price is compared with the current quintile portfolio price and functions as a timing signal. If the current price is above the MA price, it is an in-the-market signal, and the strategy invests in the quintile portfolios for the next trading day; otherwise it is an out-of-the-market signal, and the strategy invests in the 30-day risk-free T-bill for the next trading day. I report the average return (Return), the standard deviation (Std Dev), and the skewness (Skew) for the buy-and-hold benchmark quintile portfolios (Panel A), the MA timing quintile portfolios (Panel B), and the MA portfolios (MAP) that are the differences between the MA timing portfolios and the buy-and-hold portfolios (Panel C). The results are annualized and in percentages. I further report the annualized Sharpe ratio (SR) for the buy-and-hold portfolios and the MA timing portfolios, and the success rate for the MAPs. The success rate is defined as the fraction of trading days when the MA timing strategy is on the “right” side of the market, that is, it is out of the market when the return on the quintile portfolios are lower than the risk-free rate; it is in the market when the return on the quintile portfolios are higher than the risk-free rate. The sample period is from January 2, 1990, to December 30, 2016. The t-statistics are in parenthesis.
Table 2
Summery Statistics of the NYSE/AMEX Decile Portfolios
Rank, indicates the subject decile portfolio. The returns and index levels of the 10 NYSE/AMEX volatility decile portfolios are readily available from CRSP. The 10-day moving average (MA) is calculated each day, using the last 10 days’s closing prices including the current closing price. The daily MA price is compared with the current decile portfolio price and functions as a timing signal. If the current price is above the MA price, it is an in-the-market signal, and the strategy invests in the quintile portfolios for the next trading day; otherwise it is an out-of-the-market signal, and the strategy invests in the 30-day risk-free T-bill for the next trading day. I report the average return (Return), the standard deviation (Std Dev), and the skewness (Skew) for the buy-and-hold benchmark decile portfolios (Panel A), the MA timing decile portfolios (Panel B), and the MA portfolios (MAP) that are the differences between the MA timing portfolios and the buy-and-hold portfolios (Panel C). The results are annualized and in percentages. I further report the annualized Sharpe ratio (SR) for the buy-and-hold portfolios and the MA timing portfolios, and the success rate for the MAPs. The success rate is defined as the fraction of trading days when the MA timing strategy is on the “right” side of the market, that is, it is out of the market when the return on the quintile portfolios are lower than the risk-free rate; it is in the market when the return on the quintile portfolios are higher than the risk-free rate. The sample period is from January 2, 1990, to December 30, 2016. The t-statistics are in parenthesis.
4.1 Robustness check
As robustness check the period of the real estate crisis was omitted from the dataset after which the different strategies were applied again. The period from the beginning of 2007 until the end of 2012 were deleted to see whether the real estate crisis had a significant effect on the returns of the trading strategies. Table 3 and 4 reports the same basic return characteristics of the different trading
strategies applied to the volatility portfolios as Table 1 and 2, however the crisis period was excluded from the dataset.
Starting with the US REIT portfolios, which are reported in Table 3. Panel A provides the average return, the standard deviation, the skewness, and the Sharpe ratio of the buy-and-hold strategy across the volatility quintile portfolios. In Panel A the average returns are all positive and significant, however they are still not an increasing function of the volatility quintiles. In
comparison to Table 1 all the returns are lower except for the highest volatility quintile. The
standard deviations in in Table 2 are all lower than those in Table 1. The Sharpe ratios in Panel A of Table 2 are all higher in comparison to Table 1. Panel B reports the 10-day moving average
strategy. In comparison to Table 1, for each volatility quintile the returns are higher and standard deviation are lower, which leads to higher Sharpe ratios, this is however not true for the highest volatility quintile. By excluding the period of the real estate crisis the 10-day moving average strategy performed better. However still not better than the buy-and-hold return. Also there is still no increasing function between the volatility quintiles and the returns. As can be seen in Panel C, the returns of the MAPs are still negative for each volatility quintile however much closer to zero. Also the success rates are still in the range of 30% to 35%. The returns do get better for the moving average strategy by excluding the real estate crisis from the data set. However the timing signals from the strategy do not get better. Therefore, the results from Table 1 can be seen as robust in relation to the effect of the real estate crisis.
Secondly, a comparison of the moving average strategy applied to the 10 NYSE/AMEX portfolios with and without the period of the real estate crisis, which are reported in Table 2 and 4, respectively. With the real estate crisis omitted the buy-and-hold strategy performs better. In Panel A the returns are higher and the standard deviation lower for each decile portfolio, leading to higher Sharp ratios. For the moving average strategy, reported in Panel B, this is not the case. The returns for each decile portfolio is lower in comparison to Table 2. The returns are however still a roughly increasing function of volatility. The returns are accompanied by lower standard deviations as well. Therefore, 7 out of 10 Sharp ratios are higher. In Panel C, the MAPs are reported which are the difference between the buy-and-hold strategy and the moving average strategy. The profitability of the moving average strategy in comparison to the buy-and-hold strategy does not anymore appear to
be function of volatility. Also, for 7 out of 10 decile portfolios the moving average strategy underperforms the buy-and-hold strategy. From this can be concluded that the moving average strategy relative to the buy-and-hold strategy did perform worse when the real estate crisis was omitted. However, this is not per se proof for the results in Table 2 not being robust. Because as noted earlier, the idea of the moving average strategy is for an investor to ride the uninterrupted up trend of a risky asset. When the trend is broken the investor should then sell the asset and thereby avoid the downward price trend. This could be an explanation as to why the moving average strategy did perform less relatively to the buy-and-hold strategy when the real estate crisis was omitted from the dataset.
