1
Successful Technical Analysis and
Momentum in US Stock Markets
Tom Janssen
t.l.janssen@student.rug.nl
Student number: s2597950
University of Groningen
Program: MSc Finance
Faculty of Economics and Business Economics
Supervisor: dr. L. Dam
Second evaluator: dr. I. Souropanis
January 11th, 2021
Abstract
This thesis examines whether technical analysis yields abnormal risk-adjusted returns. It looks at all publically listed stocks in all available years in the United States stock market. By constructing portfolios based on technical indicators and testing those portfolios on the well-known factor models in finance, I try to find out whether these returns are abnormal, and also whether if there is a link between technical analysis and momentum. Three indicators give significant negative alphas, while one other indicator seems to earn persistent alphas over time. Doing the exact opposite from those three indicators does also give positive alphas over time. Alphas range from -19 percent up until 23 percent on an annual basis, with most strategies having slightly higher or about the same risk compared to the market.
2
Introduction
Technical analysis in financial markets is the practice of predicting price movements based on (price-) charts and other market statistics. In the academic world, this method has always been met with a lot of scepticism (see Brock et al., 1992). It is common perception that the method of technical analysis is perceived as “patently false” (Malkiel, 1981) in the academic world. However as will be presented further on, many papers have found different kinds of anomalies within the stock market. One of those is the momentum anomaly, which shows portfolios composed based on stock returns in the past can earn extraordinary returns (Jegadeesh and Titman, 1993). Interestingly, one branch of technical analysis constructs many indicators based on past prices of stocks, showing similarity between momentum and technical analysis. Some have argued these strategies can earn extraordinary returns (see for example Levy, 1967; Pruitt and White, 1988), while others state returns are not present and persistent (see for example Jensen and Bennington, 1970; Fama, 1998). This thesis adds further knowledge with respect to technical methods applied to stock markets. It tries to do so in twofold. Firstly, this thesis investigates whether technical price-based methods can earn extraordinary returns over time. Secondly, by linking it to traditional finance based models, this thesis checks whether any of these returns can be explained by systematic risk or common factors, especially with respect to momentum.
Techniques of technical analysis go in against the Efficient Market Hypothesis (EMH), which states that new information on any security is reflected in its price almost immediately (see Fama, 1965 and Fama, 1970). Efficient markets would make it impossible to earn any abnormal returns based on analysis of prices, thus past information. Research within this field is available in abundance1. Fama (1970) concludes evidence in favour of the Efficient Market Hypothesis is extensive. Since then however, the Efficient Market Hypothesis has been debated on fiercely. Jegadeesh and Titman (1993) conclude portfolios of past winning stocks tend to outperform past losing stocks. They select stocks based on the stock’s past return, and find that portfolios of stocks with higher past returns (based on returns of maximally twelve months before) outperform portfolios with stocks that have lower past returns.2 Rouwenhorst (1998) also observed this so-called ‘’momentum’’ effect with internationally diversified portfolios. International momentum returns from Rouwenhorst (1998) correlate with those of the United States found by Jegadeesh and Titman (1993), which suggests a common factor drives momentum returns. Carhart (1997) proposes to add one additional factor to the Fama-French three factor model to capture these momentum effects. DeBondt and Thaler (1985, 1987) find the exact opposite for the long-term: past losers tend to outperform past winners in the US stock
3 market. Debate is still ongoing on whether these anomalies are consistent with market efficiency other market inefficiency3.
Remarkably, momentum and reversal effects found within stock markets show great similarities with respect to technical analysis. Many technical strategies are based on analysing past prices, as is the case with portfolios formed based on past momentum. Based on a survey conducted by the magazine Euromoney, Frankel and Froot (1990) noted a shift in the 1980s in the US from analysis using fundamentals towards analysis using technical indicators by foreign exchange forecasting services. Though in theory, fundamentals can also not be used to predict future prices, they entail metrics which are related to the factor models of Fama and Frech (1996) like firm size and value. Taylor and Allen (1992) report that 90 percent of London foreign exchange traders use some kind of technical analysis. Cheung and Chinn (2001) conclude from their survey 30 percent of traders find technical analysis describes technical trading behaviour the best. Though this research only concerns foreign exchange trading, it does show the higher usage of technical analysis as a tool. This can also be seen in the increasingly amount of technical instruments agencies like Bloomberg, Reuters and most banks provide in the form of chart and price instruments. More research on technical strategies has also come available. Results though are quite mixed (see Nazario et al., 2017, for an extensive review on literature on technical analysis), similarly to the momentum anomaly. Can price-based technical strategies earn extraordinary returns in the stock market? Are these returns explained by systematic risk and other common factors, or can they generate significant alphas? Are these returns similar with respect to strategies based on momentum, and do these returns show signs of positive momentum or negative momentum (reversals)? This thesis tries to answer these questions by linking technical analysis and classical factor based models together.
I focus on the United States stock market to answer these questions. I use all publicly listed stocks in the United States in the period from 1926-2019. From these stocks I create value-weighted market portfolios which are composed based on four different price-based technical indicators. Based on the different strategies given by these indicators, I calculate returns for each portfolio and analyse those returns to evaluate each strategy, also with respect to risk. After that, I will regress the returns on the well-known one factor model as well as the three-and five factor models developed by Fama three-and French (1996 three-and 2015) three-and the four factor model developed by Carhart (1997) to see whether these strategies give risk-adjusted and significant alphas or not. Moreover, we can see whether these returns can be explained by any
3 It still remains unclear whether these excess returns are present because of inefficiencies in markets, or if
4 of the factors present in these models, especially looking for whether the momentum factor has high or low explanatory power.
I find that three out of four indicators generate negative returns over time. All strategies return negative alphas ranging from -8.1 percent until -21.4 percent on an annual basis. Moreover, the three-, four- and five- factor models do not seem to explain a higher proportion in returns compared to the simple one factor model. The explanatory power of the momentum factor is not that high, meaning these indicators are not fully capable of picking out the stocks with high momentum returns, though the economic effect is substantially higher compared to the other factors. Systematic risk seems to be quite similar compared to the market for most indicators. One indicator gives positive alphas over time. This indicator also has comparable risk with respect to the market, as well as the highest amount of explanatory power. As this indicator trades based on expectations returns will reverse (contrary to the other three indicators who expect momentum to be positive), this finding could hint the effect of reversals yields positive returns in the stock market. Doing the exact opposite of all strategies confirms this, where opposite-based strategies based on the first three indicators yield positive alphas ranging from 3.4 percent until 24 percent on an annual basis. The last indicator yields negative returns in this ‘’opposite’’ case.
5
Literature review
Technical analysis
Theoretically, technical analysis is based on two concepts; the Dow Theory developed by Charles Dow and the Elliot Wave Principle developed by Ralph Elliot. The Dow Theory suggests the market follows certain ‘’bull’’ and ‘’bear’’ trends (Brown, Goetzmann and Kumar, 1998), though short-term deviations are present. However, by charting past price movements, an analyst is able to identify and predict which trend the market is going to follow. The Elliot Wave Principle proposes that market foundations are based on social principles and prices unfold in certain patterns, what Elliot called ‘’waves’’ (Collins, Frost and Prechter, 1999). Stock markets are divided into multiple short and long term cycles, which makes it able to predict which trend the market is going to follow. It also develops itself as a Fibonacci sequence (also known as the golden ratio), a mathematical sequence which can be found in many forms within society. More recently, technical analysis has been named together with Chaos Theory, a theory which suggests systems are predictable up until a certain moment, and afterwards become random (for more on this see Peters, 1994). Whereas the Efficient Market Hypothesis is built on the notion of rationality and efficiency, these three theories take a more psychological form of view found in socioeconomics and behavioural economics. They both build upon uncertainty and irrationality of people’s behaviour. The intuition behind al theories is similar: the guiding principle for technical analysis is ‘’to identify and go along with the trend’’ (Chew, Manzur and Wong, 2010)
6 technical analysis is that it would be a self-fulfilling prophecy. With respect to the Elliot Wave Principle, analysts would count backwards and ‘’bend’’ the correct amount of waves to fit the theory all the time, making it unreliable for predictions considering the future. In practice, buy signals would lead to increasing levels of volume of stocks being bought, increasing the price automatically (the same logic applies to sell signals). Frankel and Froot (1990) suggested that the overpricing of the US Dollar in the 1980s might have been caused by technical analysis. Froot et al. (1992) found that this behaviour created speculative bubbles. Shiller (1987) concluded based on a questionnaire that many investors were influenced by technical analysis considerations from computer programs, which partly caused the 1987 stock market crash.
Despite the criticism, evidence has been found which might support technical analysis. Irwin and Park (2004) find in their review that technical trading strategies were profitable in foreign exchange markets and future markets, but not in stock markets until the 1980s. The majority of studies (around 63 percent) found positive results, with 26 percent of studies on the negative side, and about eleven percent of studies indicating mixed results. Levy (1967) was one of the first to test and find that stocks who trade at current prices that are higher than their past average prices generate significant abnormal returns. Jensen and Bennington (1970) criticized his work as they found out his data was influenced by selection bias and/or data snooping. Shiller (1984) concludes that markets exhibit excessive volatility due to irrational investor behaviour, which might be implemented by technical analysts to gain advantage without extra risk. Brown, Goetzmann and Kumar (1998) refute the previously mentioned conclusions by Cowles (1933). After reviewing his work, they determine that the analysis based on the Dow Theory yielded positive risk-adjusted returns. Brock et al. (1992) find that using moving averages yield positive returns and provide strong support for technical strategies. Moreover, four tested random walk based models are not consistent with the positive returns they find from their strategies. Pruitt and White (1988) claimed their CRISMA system (which is based on the indicators cumulative volume, relative strength and moving average) can outperform the market over a long time period with almost 2 percent, even after accounting for trading costs and controlling for risk. Chew, Manzur and Wong (2010) investigated the timing of market entry and exit based on technical indicators on the Singapore Stock Exchange, and concluded one can earn substantial profits by applying technical indicators as moving averages and relative strength indices. Moreover, as technical analysts claim, there is also many evidence present which rejects the Efficient Market Hypothesis (see, for example, Basu, 1977; Zarowin, 1989). This would imply there is room for technical analysis to be implemented as a successful strategy.
Momentum
7 stock performance. This contradicts the theory of market efficiency, these portfolios cannot earn extraordinary returns even within the weakest form of market efficiency. However, empirical research shows these returns are possible to achieve. Reasoning from this perspective, momentum could be seen as a form of technical analysis. Though technical analysis does often build on momentum, momentum is not considered as a form of it. Academic literature describes momentum as the observable effect, whereas technical analysts use indicators to estimate any momentum present in the market. The effect of momentum is based on past prices, technical analysts make calculations based on past prices and construct indicators from those prices.
With respect to momentum, the most leading paper within this field would be the paper by Jegadeesh and Titman (1993). Their framework consists of composing portfolios based on their past performance, which results in portfolios of losing stocks and portfolios of winning stocks. They construct portfolios based on J-months, where J would range from three to twelve months. A ‘’winners’’ portfolio would be constructed from the best performing stocks, as well as a ‘’losing’’ portfolio from the worst performing stocks. A long position would be taken in the winners-portfolio, in addition to a short position in the losers-portfolio. These positions would have the length of K months, where J and K would be equal for each portfolio. The main findings of this strategy is that significant momentum returns are found from the period of 1965 until 1989. Their follow up research later (Jegadeesh and Titman, 2001) confirmed their previous results. Evidence of momentum returns continued in the 1990’s. The paper also presents evidence of behaviour models explaining effects of momentum returns, though they state it should be taken into account with caution. Rouwenhorst (1998) considers the effect of momentum returns in an international context. This paper finds that medium-term winners outperform medium-term losers by more than one percent per month (corrected after risk). It also finds that return continuation is negatively related to firm size, emphasizing the outcomes from Fama and French (1993). Chan, Jegadeesh and Lakonishok (1996) find that the drift of future returns are understated in regard to past information due to under reaction of the market. Market risk, size and book-to-market effects do not explain any drifts for the future. This evidence would contradict the principle of the weak-from efficiency of markets, as markets only gradually react to information from the past instead of instantly. DeBondt and Thaler (1985, 1987) find that over longer time horizons returns reverse. Portfolios of firms that performed poor over three- to five- year time horizons earn higher average returns compared to portfolios of firms that performed well in the past.
8 by Jegadeesh and Titman (1993), DeBondt and Thaler (1985 and 1987) and Rouwenhorst (1998) versus papers based on technical analysis by Levy (1967), Brock et al. (1992) and Chew, Manzur and Wong (2010). Whereas the first three papers based all take returns as their metric for research, the last three all use past prices as metrics for estimation, showing the methodological overlap between momentum and technical analysis. With respect to the technical papers, all find significant positive excess returns when technical trading strategies are executed. From current literature, we can expect technical trading strategies to yield positive returns within stock markets.
9
Research method and methodology
Indicator definitions
Technical analysis can be broadly divided into two categories: chart analysis and statistical analysis (Nazario et al., 2017). In this thesis, I focus on price analysis due to its similarity with the momentum anomaly found in classical finance papers. I will focus on statistical analysis by investigating four popular indicators. As has been mentioned in the literature review, the basic intuition of technical analysis is to go along with the trend. Papers who research technical strategies use simple moving averages in abundance (see Levy, 1967; Brock et al., 1992; Chem, Manzur and Wong, 2010). Moreover, based on Chew Manzur and Wong (2010), I will use the relative strength index as an indicator. These will be complemented by two indicators commonly used in practice in recent times.
As such we will consider three trend indicators: the Simple Moving Average (SMA), Exponential Moving Average (EMA) and Moving Average Convergence Divergence (MACD). These indicators have as expectation that the momentum effect will be positive within stocks. We will also look at one counter-trend indicator, the relative strength index (RSI). This is the one indicator which trades based on the expectation of the price of the stock to reverse. For the SMA and RSI, this thesis follows a similar definition given by Chew, Manzur and Wong (2010). Exponential Moving Averages and the Moving Average Convergence Divergence are slight modifications of the Simple Moving Average. In this thesis, I will follow a similar methodology compared to that of Jegadeesh and Titman (1993), who form strategy-based portfolios and test them for systematic risk and effects of other common factors. I will basically do the same in this thesis, where I form portfolios based on technical strategies and test those returns on classical finance models.
10 Here 𝑆𝑀𝐴𝑡,𝑛 is a Simple Moving Average for n-days at time t, 𝐶𝑖 is the closing price for period i4. If 𝐶𝑡−1≥ 𝑆𝑀𝐴𝑡−1,𝑛, this would trigger a buy signal, meaning B = 1. If 𝐶𝑡−1< 𝑆𝑀𝐴𝑡−1,𝑛, this would trigger a sell signal, meaning B = 0. This will be lagged one day as I am using closing prices as data. This means I assume at the end of each day, it will be determined if the stock will be hold long or sold. Selling would then occur against the last known closing price immediately on the next day. If the stock price would move along a clear trend, this indicator would work well. However, if the price would be moving sideways or if there would be high volatility, this indicator could trigger false signals. Based on common use by practitioners, we will trade stocks using moving averages in the form of common 10, 20, 50, 100 and 200 day Simple Moving Averages. I will only consider having long positions throughout this thesis.
The Exponential Moving Average (EMA) is built based upon the SMA. Unlike the SMA, the EMA contains (several) multipliers which give more weight to more recent price changes, making it react quicker to recent (large) changes in price. This second indicator is defined in this thesis as follows:
𝐸𝑀𝐴𝑡,𝑛 = 𝐶𝑡∗ 𝑚 + 𝐸𝑀𝐴𝑡−1∗ (1 − 𝑚). (2)
Here 𝐸𝑀𝐴𝑡,𝑛 is a Exponential Moving Average for n-days at time t, 𝐶𝑡 is the closing price at time t5. One can see the last closing price gets a higher share in the EMA compared to the SMA, by multiplying this price with a factor 𝑚. This multiplier is calculated as:
𝑚 = 𝑆
𝑛 + 1
(3)
Here 𝑆 is the so-called ‘smoothing factor’, which in most cases is set to two. As one can see, increasing the amount of 𝑆 would give even more weight to the recent price. Again, if 𝐶𝑡−1≥ 𝐸𝑀𝐴𝑡−1,𝑛, this would trigger a buy signal, meaning B = 1. If 𝐶𝑡−1< 𝐸𝑀𝐴𝑡−1,𝑛, this would trigger a sell signal, meaning B = 0. Just like with the SMA, we focus on the value of the common 10, 20, 50, 100 and 200 day Exponential Moving Averages in this thesis. The smoothing factor will be set to the accepted standard of two.
4 The first observation of the n-day SMA is only possible after passing an amount of time equal to n days in the
future.
5 Note that for the first ever EMA to be calculated, we need to have one more observation than with the SMA,
11 Thirdly, we will look at the MACD-indicator. This metric combines three different EMA-indicators to look for any upward or downward trends. These different EMA curves can be calculated using equation (2). The standard used in practice is to subtract a 12-day EMA from a 26-day EMA:
𝑀𝐴𝐶𝐷𝑡 = 𝐸𝑀𝐴𝑡,26− 𝐸𝑀𝐴𝑡,12. (4)
If 𝑀𝐴𝐶𝐷𝑡> 0, this would point towards an upward (downward) trend. Practitioners than look for a conformation of this trend by comparing this difference with a ‘signal’ line, which in practice often is a 9-day EMA of the calculated MACD:
𝑆𝐼𝐺𝑁𝐴𝐿𝑡= 𝑀𝐴𝐶𝐷𝑡∗ 𝑚 + 𝑀𝐴𝐶𝐷𝑡−1∗ (1 − 𝑚), (5)
with 𝑚 = 𝑆
9+1. This approach will also be followed in this thesis: if 𝑀𝐴𝐶𝐷𝑡−1 ≥ 𝑆𝐼𝐺𝑁𝐴𝐿𝑡−1 , this will be interpreted as a buy signal, meaning B = 1 and conformation of an upward trend. If 𝑀𝐴𝐶𝐷𝑡−1< 𝑆𝐼𝐺𝑁𝐴𝐿𝑡−1, this will be interpreted as a sell signal, meaning B = 0 and conformation of a downward trend.
At last, we will look at the Relative Strength Index (RSI). One could say this indicator is the ‘’odd one out’’, as it is the only indicator which trades based on the expectation a trend will reverse. It is calculated as follows:
𝑅𝑆𝐼𝑡,𝑖 = 100 − 100 1 + 𝑅𝑆𝑡,𝑖
(6)
Here 𝑅𝑆𝐼𝑡,𝑖 is the value if the RSI at time t for period i. 𝑅𝑆𝑡,𝑖 represents the relative strength and is calculated as follows:
𝑅𝑆𝑡,𝑖 = 𝑈̅𝑡,𝑖 𝐷̅𝑡,𝑖
(7)
12 a sell signal since the market in question would be interpreted as an overbought market. Low readings of the RSI would then lead to buy signals in an oversold market, showing the RSI’s purpose as a countertrend indicator. According to the standard, a period of 14 days is used to calculate the RSI. Moreover, after the first 14 days, a smoothing procedure is followed where the average upward or downward movement of observation t-1 is multiplied by 13, then adding the new upward or downward movement and dividing by 14 again. I will also follow this procedure in this thesis.
With respect to determining the buy and sell signals, I will follow the ‘’crossover’’ method, as well as the ‘’retracement’’ method. With respect to the first method, a buy signal is noted if the RSI falls below a certain level, and a sell signal is noted if the RSI rises above a certain level. In this thesis, I will test a crossover level of 50, as well as combined crossover levels of 30 and 70. With the latter, a buy signal is noted if the RSI falls below 30, and a sell signal is noted if the RSI rises above 70 (Chew, Manzur and Wong, 2010).
The second method tries to take into account a fundamental problem of using technical indicators. When using technical indicators, there will often be the problem of them giving false signals. Within a trending market, moving averages could give false buy (sell) signals if the price of a stock would move above (under) its moving average, though it is still in an downward (upward) trend with respect to the longer term. When using the RSI, one can try to take into account such false signals using the “retracement’’ method. This will mean that a buy (sell) signal is only acted upon, if the RSI crosses over (under) the 30 (70) level, after it has regularly moved below (above) the 30 (70) level. With this method, speculators try to “confirm” an upward or downward trend. This “retracement” method will also be investigated in this thesis.
Research design
Based on the buy and sell signals given by these indicators, I will calculate returns for each stock given by these different strategies using daily stock data. (details on the which stock data is used will be given in the next section). The calculation of these individual stock returns is given by equation (8):
𝑅𝑖𝑡 = (𝑃𝑖𝑡− 𝑃𝑖, 𝑡−1) + 𝐷𝑖𝑡 𝑃𝑖, 𝑡−1
(8)
13 SMA-strategies, five EMA-strategies, one MACD strategy and three RSI-strategies), meaning there are a total of fourteen different portfolios. The individual returns of all portfolios are summarized in equation (9): 𝑅𝑝𝑡 = ∑(𝑅𝑖𝑡 ∗ 𝑀𝑉𝑖𝑡 𝑇𝑀𝑉𝑡 ) 𝑛 𝑖=1 (9)
Here 𝑅𝑝𝑡 is the return for portfolio p at time t. MV is the total market value of stock i at time t, and TMV is the total value of the market as a whole at time t. For each portfolio, I would then take the average on a monthly basis so I can perform regression analysis with those returns.
Having calculated the monthly portfolio returns, I regress the returns on the Capital Asset Pricing Model developed by Sharpe (1964) and Lintner (1965). I further regress the returns on the three- and five-factor models proposed by Fama and French (1996 and 2015) and the four-factor model proposed by Carhart (1997). These models, with the returns of the momentum portfolios as dependent variables, are given by the equations (10)-(13):
𝑅𝑝𝑡 − 𝑅𝑓𝑡 = 𝛼𝑝+ 𝑏𝑝(𝑅𝑀𝑡− 𝑅𝑓𝑡) + 𝑠𝑝𝑆𝑀𝐵𝑡+ ℎ𝑝𝐻𝑀𝐿𝑡+ 𝑚𝑝𝑀𝑂𝑀𝑡+ 𝜀𝑡 (13)
Here 𝑅𝑝𝑡 − 𝑅𝑓𝑡 represents the excess return on a strategy portfolio and 𝑅𝑀𝑡− 𝑅𝑓𝑡 the excess return on the market portfolio. Equation (10) is the standard Capital Asset Pricing Model. Equation (11) is the three-factor model developed by Fama and French (1996), equation (12) being their more recent addition known as the Fama-French five-factor model (2015). Here, 𝑆𝑀𝐵𝑡 represents the difference between returns from diversified portfolios of small stocks minus big stocks, 𝐻𝑀𝐿𝑡 is the difference between the returns on diversified portfolios of high and low book-to-market stocks. 𝑅𝑀𝑊𝑡 captures the difference between returns on diversified portfolios of stocks with weak and robust profitability, and 𝐶𝑀𝐴𝑡 covers differences between
𝑅𝑝𝑡 − 𝑅𝑓𝑡 = 𝛼𝑝+ 𝑏𝑝(𝑅𝑀𝑡− 𝑅𝑓𝑡) (10)
𝑅𝑝𝑡 − 𝑅𝑓𝑡 = 𝛼𝑝+ 𝑏𝑝(𝑅𝑀𝑡− 𝑅𝑓𝑡) + 𝑠𝑝𝑆𝑀𝐵𝑡+ ℎ𝑝𝐻𝑀𝐿𝑡 + 𝜀𝑡 (11)
14 returns on diversified portfolios of conservatively and aggressively investing firms. In equation (13), 𝑀𝑂𝑀𝑡 represents the momentum factor in the model proposed by Carhart (1997).
In theory, the coefficients 𝑏𝑝, 𝑠𝑝, ℎ𝑝 𝑚𝑝, 𝑟𝑝, 𝑐𝑝 should capture all the variation in returns across its time series, making 𝛼𝑝 equal to zero in expectation. 𝜀𝑡 is then a random error in all models. These models have proven to be very useful, with the three-factor model explaining over 90% of the returns on diversified portfolios, compared to 70% for the original CAPM. Important to note is that with the five-factor model, the HML factor can be completely explained by the other factors (Fama and French (2015)).
Furthermore, because of the binary division in returns from either buy (B = 1) or sell (B = 0), I also have the availability of returns of doing all strategies in exactly the opposite way. This would mean instead of buying the stock when 𝐶𝑡−1≥ 𝑆𝑀𝐴𝑡−1,𝑛, one would sell the stock with this SMA-indicator. Note that I only consider returns from long positions in this thesis, so a stock must have been bought first, by means of the signal of 𝐶𝑡−1 ≤ 𝑆𝑀𝐴𝑡−1,𝑛. This also holds for all the other indicators and accessory strategies/portfolios. I will analyse these returns in the same way as the original approach. As can be seen later and already from the introduction, these returns suggests some strategies could be done better by doing them the exact opposite way.
Additionally, I will use the Sharpe, Sortino and Treynor ratio to provide some additional preliminary analysis based on each portfolios raw average return:
𝑆ℎ𝑎𝑟𝑝𝑒 𝑅𝑎𝑡𝑖𝑜 = 𝑅𝑝 − 𝑅𝑓 𝜎𝑝
(14)
15
Data and descriptive statistics
The data used in this thesis is from the Chicago Research in Security Prices (CRSP) database of the Wharton Research Data Services (WRDS) website. WRDS is well-known, it is used widely as a data source among academics as well as practitioners in the field of finance for practical as well as research purposes. CRSP is one of their databases, containing a comprehensive set on applicable variables for financial markets such as, security prices, volumes and returns.
I use the daily stock file as the data source for this thesis’s dependant variable. This includes the daily closing price, company specific identification numbers, daily returns and number of shares outstanding. Definitions of the most important variables from this original dataset can be found in appendix A1. I took all data which for which full year data was available, meaning the dataset consists if data starting in January 1926 running all the way up until December 2019. By looking at such a long dataset, forms of selection bias and/or data snooping are minimized. Papers who come in the neighbourhood of such a long dataset are DeBondt and Thaler (1985 and 1987) with data from 1926 until 1982, and Brock et al. (1992), with data running from 1897 until 1986. I took all listed companies on NYSE, AMEX and NASDAQ and Arca stock markets, meaning I basically take all publically listed shares in the United States stock market. This results in a dataset consisting of data from 94 years, containing data from over 29000 companies and over 33000 different types of shares. A short summary of information is presented in Table 1 below.
Table 1. Information regarding the original sample selection procedure
Period Markets Number of
16 By taking such a high number of companies and including every available firm, this should make the free from any survivorship bias. I first create each technical indicator with all corresponding days and strategies, resulting in fourteen indicators in total. Based on a dummy variable I determine all buy and sell signals for each strategy. This results in fourteen different trading strategies and corresponding returns for every different share. I then create a value-weighted (see equation (9)) portfolio of the entire market based on each strategy. For all those portfolios I calculate arithmetic monthly returns for each day based on the daily returns that were given by the dataset of CRSP. I constructed averages on a monthly basis, based on the amount of business days which were present each month within the first dataset. This resulted in the monthly returns I will use in this thesis to perform my analysis and use as my dependent variable.
At first I would like to show what would have happened if one would have invested one dollar at the beginning of 1926 according to each strategy. Figure 1 and Figure 2 give an example for each indicator. Figure 1 gives the values of following the strategies according to executing the traditional way (hereafter to be named as the ‘’pro-approach” or “pro-strategies” or “pro”), Figure 2 gives the values of indexes from strategies according to executing them the exact opposite way (hereafter to be named as the “contra-approach” or “contra-strategies” or “contra”). As has been stated in the introduction and methodology section, the chosen methodology enables analysis of returns which are generated in exactly opposite ways of traditionally executing all strategies.
Figure 1 shows the SMA, EMA and MACD indicator show an one dollar investment in those strategies would have accumulated to a lower value compared to the market (the negative value is because of the logarithmic adjustment). Figure 1 also shows the RSI strategy would have resulted in an one dollar investment accumulating to a higher value compared to the market. Figure 2 shows exactly the opposite happens compared to Figure 1.
17 I extracted the data for the Fama-French portfolios from their own website. The three factor portfolio consists of the excess return on the market, 𝑅𝑀𝑡− 𝑅𝑓𝑡, of a value weighted portfolio of all listed CRSP firms minus the one month US Treasury bill rate. Moreover, the factor 𝑆𝑀𝐵𝑡 represents the average return of three small portfolios minus the return of three big portfolios. 𝐻𝑀𝐿𝑡 represents the average return of two high book-to-market portfolios minus the average return of two low book-to-market portfolios. 𝑅𝑀𝑊𝑡 is the average return of two robust profitable portfolios minus the average return of two weak profitable portfolios, whereas 𝐶𝑀𝐴𝑡 has the same principle of 𝑅𝑀𝑊𝑡, though this factor takes returns of conservative versus aggressive firms as average returns. 𝑀𝑂𝑀𝑡 also comes directly from their website, Table 2 gives some summary statistics of those factors, also including the return on the market.
Figure 1. Indexed values of all pro-strategies
This figure gives an indexed value of one dollar invested at the beginning of 1926 for all pro-strategies for the period of 1926-2019. I took the logarithm of each index so they could be compared
18 .
Table 2. Summary statistics of all factor variables used in the regression analysis This table presents summary statistics for all factor variables used in the regression analysis for the period 1926-2019. For each factor, this table gives its average excess return, volatility (standard deviation), Sharpe, Sortino and Treynor ratio. The market risk premium, SMB and HML factor start in July 1926. The momentum factor starts in January 1927, and the RMW and CMA factors both start in July 1963. Source: https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
Factor Average annual return Annual volatility Sharpe ratio Obs.
𝑅𝑀𝑡− 𝑅𝑓𝑡 7.73% 17.18% 0.45 1122 𝑆𝑀𝐵𝑡 1.72% 10.21% 0.17 1122 𝐻𝑀𝐿𝑡 3.88% 10.05% 0.39 1122 𝑅𝑀𝑊𝑡 3.13% 7.51% 0.42 678 𝐶𝑀𝐴𝑡 3.34% 6.90% 0.48 678 𝑀𝑂𝑀𝑡 65% 15.29% 0.57 1116
Figure 2. Indexed values of all contra- strategies
This figure gives an indexed value of one dollar invested at the beginning of 1926 for all contra-strategies for the period of 1926-2019. I took the logarithm of each index so they could be compared
19 Looking at Table 3 one can already see some preliminary risk-return characteristics of the portfolios. Following the strategies based on the first three indicators according to the traditional approach all seem to give negative average returns. Following both the SMA and EMA according to standard, buying (selling) stocks when prices cross over (under) average values appear to give a negative pay-out. Following this strategy for a 50-day SMA would lead to an average negative return of around 12.6%. For a 50-day EMA strategy it is even worse, making an even higher negative average return of 13.4% on a yearly basis. The exponential composition of the EMA seems to worsen the overall effect of the moving average strategy. Moreover, it looks like a peak in negative returns is reached following a strategy of somewhere between 50 and 100 days. This might give an indication on how long it would take for a trend on average to reverse.
The RSI-strategies give positive average excess returns. As has been stated before, the RSI indicator is the only indicator that says you should execute trades based on expectations of reversals. Both the 50 crossover and 30-70 crossover strategies give positive returns of about 35 and 17 percent per year on average. Moreover, the 50-crossover strategy has one of the highest Sharpe ratios of 2.35. Comparing this to the Sharpe ratio of the market of 0.45 (see Table 2), the difference seems quite significant. This is also confirmed by looking at all the other contra-strategies. All contra-strategies yield positive average excess annuals returns for the first three indicators. All these strategies also seem to have high Sharpe and Sortino ratios. Furthermore, the higher Sharpe ratios for shorter term EMA’s might suggest this reversal often occurs on a shorter term basis, which could be puzzling in comparison with the pro-strategy approach where the peak of average returns seems to be somewhere between 50 and 100 days, a longer time horizon.
20 Table 3. Descriptive statistics of all strategies for the period of 1926-2019 in the US stock market This table contains descriptive statistics of each strategy for the period of January 1926 until December 2019. These portfolios and resulting statistics are calculated based on all listed stocks on the NYSE, AMEX, NASDAQ and Arca stock markets in the United States. For each strategy, this table gives its average excess return, volatility (standard deviation), Sharpe, Sortino and Treynor ratio, the daily average of assets in each portfolio and the daily average of transactions in each portfolio. All returns, corresponding volatilities and ratios are annualized in this table. Pro or contra indicates whether the strategy is followed (pro) or the exact opposite is executed (contra).
22
Results
I present estimation results for each indicator, taking the 50-day SMA, 50-day EMA, MACD and RSI 50-crossover as a base. I discuss the results for each indicator, discussing both the outcomes of the pro strategy as well as the contra strategy. Full estimation results can be found in Appendix B, with Table B3 until Table B12 showing all results, for each different n-day indicator used for the Simple Moving Average as well as the Exponential Moving Average, the MACD-strategy as well as all three RSI-strategies.
Simple Moving Average (SMA) and Exponential Moving Average (EMA) indicators
Table 4 on the next page shows the results for both 50-day SMA strategies. Following the strategy according to theory and practice seems to give a negative alpha in all cases. Within the simple one factor model, the average alpha earned per month equals a negative premium of -1.80 percent, which equals -19.6 percent on an annual basis. This result is consistent including both the three factor and momentum factor model, with alpha decreasing slightly to about -1.82 percent and -1.90 percent. The risk of this strategy seems to be a bit higher compared to the market, having a beta of around 1.10 until 1.12. Moreover, this implies that a 1 percentage point increase in the premium earned in the market will give about a 1.1 until 1.2 increase in the return of this strategy. Both alpha and beta seem to be significant across all models. The three- four- and five- factor models do not add significant extra explanatory power, with r-squared values only marginally increasing. Looking at Table B3 and Table B4 in the appendix, results are consistent over different numbers of days used for the indicator.
23 The estimation results of the contra-strategy give positive and significant alphas. These display significant positive alphas across all four models. Again, the explanatory power does not increase significantly when adding more factors. The average premium earned lays between about 1.56 percentage points and about 1.63 percentage points, which translates to an average of 20.45 percent on an annual basis. Risks of these portfolios are quite similar compared to the pro-strategy version, laying only slightly higher between values of about 1.11 until 1.13. Alphas and betas seem to be most significant. Also noticeable is the high significance from the momentum model across all different days (see appendix b, tables B8 and B9. This effect is negative, which makes sense because of the exact opposite this strategy is executed towards momentum.
Table 4. Regression results for the pro and contra 50-day SMA strategy from 1926 until 2019 in the US stock market.
This table displays the regression results for both the pro and contra 50-day SMA strategy. For each strategy we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
50-day SMA (pro) 50-day SMA (contra)
24 This all might suggest the overall return on the contrarian based strategy is higher compared to the pro version of the SMA strategy. Designing a technical strategy according to an SMA, which follows the theoretical foundations of momentum, yields lower returns compared to doing the exact opposite, following a contrarian based strategy.
The estimation results with respect to the Exponential Moving Average are very similar. Alphas are slightly lower with the original strategy, and slightly higher based on the contra approach. This seems the be accompanied by slightly higher levels of risk, thus beta. The exponential component seems to exaggerate all numbers slightly compared the Simple Moving Average. The effect of momentum is also similar. For full estimation results, see Table B5, B6, B9 and B10 in Appendix B.
Moving Average Convergence Divergence (MACD)
For the MACD strategy, estimation results can be seen in Table 6. The pro MACD strategy also shows a negative alpha, showing slightly lower negative premiums with values ranging from minus 0.95 percentage points until minus 1.102 percentage points, which averages -11.9 percent on a yearly basis. Again the three- four- and five-factor models do not seem to bring extra explanatory power compared to the simple one factor model. Risk is completely comparable to the market though with values of beta ranging around 1, suggesting this might be an improvement compared to the SMA and EMA indicators. What disappears is the significance of the momentum factor. This would make the MACD incapable of pick out stocks that exhibit momentum returns. The contra strategy suggests again a positive alpha can be earned by doing the exact opposite of the original MACD strategy. The average alpha per month is about 1.24 percent for this strategy. However this strategy does come with an 8 till 9 percentage point higher risk compared to the market and its counterpart, looking at its beta.
Relative Strength Index (RSI)
25 momentum factor is significant, especially among the pro versions of the RSI strategy (see table B7). The sign here is negative which makes sense, as RSI strategies tend to act oppositely compared to momentum strategies. A one percentage point increase in the return on the momentum portfolio decreases the return on this RSI strategy with about 0.06 percentage points, which shows a weak economic effect.
This effect does get bigger with the RSI-30-70-crossover and 50-retracement strategy (see table B7). The RSI strategies also show high explanatory power, with r-squared values reaching values of approximately 87 till 92 percent with these two strategies. The RSI-30-70-crossover seems attractive. It averages an alpha of around 0.7 percent per month, which is equal to an average annual return of about 8.9 percent. Combined with beta very close to 1 and high explanatory power, this strategy could give stable risk-adjusted excess returns.
Table 6. Regression results for the pro and contra MACD strategy from 1926 until 2019 in the US stock market.
This table displays the regression results for both the pro and contra MACD strategies. For each strategy we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
MACD (pro) MACD (contra)
26 If an individual/investor would want to, it is possible to (come relatively close) to secure alpha. By going long in the regressed portfolio, which are in this case the own constructed technical strategies, and short the factors by the amount of the coefficients, one basically creates a minimum variance portfolio with an expected return of alpha. It would be best to use models that have the highest significance. In the case of the 30-70 crossover strategy, it is most attractive to use the four factor momentum model because of the high significance across all factors.
Results seem to be significant and consistent across all indicators. For the Simple Moving Average, Exponential Moving Average and Moving Average Convergence Divergence, average returns are negative across all stocks in the whole period on which data is available in the United States. These three indicators do not seem to be a good predictor of future stock price movements. This is in contradiction with technical papers from Chew, Manzur and Wong (2010) and Brock et al. (1992) and also Levy (1969). These papers both conclude Simple Moving Averages based strategies earn positive returns, according to Brock et al. (1992) also risk-adjusted. This can be due to a difference in market characteristics, with Brock et al. (1992) only using Dow Jones Industrial Average firms and Chew, Manzur and Wong testing the Singapore stock market. These results also contradict momentum based research from Jegadeesh and Titman (1993) and Rouwenhorst (1998). Both claimed positive momentum returns are present in stock markets, also internationally.
27 Table 7. Regression results for the pro and contra RSI-50-crossover strategy from 1926 until 2019 in the US
stock market.
This table displays the regression results for both the pro and contra RSI-50-crossover strategies. For each strategy we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
RSI-50-crossover (pro) RSI-50-crossover (contra)
28
Conclusion
This thesis examined whether technical analysis could yield positive risk-adjusted abnormal returns on the United States stock market. It does so by looking back at the entire known history of all publicly listed stocks in the United States for the entire period from 1926 until 2019. By looking at four different prise based technical indicators, I determined trading activity for each portfolio on a daily basis. By calculating average returns for each portfolio I analysed if returns were present and consistent by consistently following different technical trading rules. By regressing these returns on the well-known factor models from classical finance theory, I tried to see whether any coincidence could be found in the returns of the other popular factor portfolios, especially the similar and also price based momentum portfolio.
It seems technical analysis can earn extraordinary returns, however in an unexpected way. Technical indicators based on Simple Moving Averages, Exponential Moving Averages and a combination of Exponential Moving Averages known as the MACD, perform quite badly with negative returns, higher risk compared to the market and negative alphas. The RSI indicator is the indicator which generates positive alphas consistently over time. One strategy of these RSI strategies is able to generate positive alphas while having an almost completely similar amount risk in relation to the market. When following exact opposite based strategies based on Simple Moving Averages, Exponential Moving Averages and the MACD, it is possible to generate positive alphas. It remains questionable how valid these results are due to the lower explanatory power of the models. The three- four- and five- factor models do not add many explanatory power across all strategies.
The findings are in line with literature from for example Chew, Manzur and Wong (2010). Trading based on a Relative Strength Index gives extraordinary risk-adjusted returns. This also partly confirms research by DeBondt and Thaler (1985 and 1987), they find momentum in stock markets based on negative momentum, i.e. reversals of stock prices. However, in this thesis these reversals seem to be present on a short-term basis, while in their research they find stock price reversals on a long time horizon. At the same time, findings in this thesis are also in contradiction with Chew, Manzur and Wong (2010) as well as Brock et al. (1992), finding Simple Moving Averages cannot explain positive returns in the traditional way found in their papers.
29 maximum of around thirty percent in one regression. It does have the highest coefficient compared to other factors outside beta and alpha. Whether technical analysis and momentum are similar remains questionable, though both factors are constructed based on past price information. Outcomes do also seem to contradict the positive momentum evidence found by Jegadees and Titman (1993), based on the negative returns momentum based technical strategies produce.
This thesis has its limitations. Another type of methodology could have been used by taking Fama-Macbeth regressions, which might take better into account the variation in errors in the cross section of returns. In this thesis, I tried to overcome this problem by taking monthly arithmetic averages of the returns of the value-weighted market portfolio, which might have been overestimating returns. Moreover, this thesis only takes into account a few technical indicators out of the massive amounts of indicators which are being used, making it hard to draw conclusions for all technical analysis based trading. Also, not one practitioner will look and act according to one indicator only, making the portfolios returns not completely representable compared to the actual behaviour of those persons using those indicators, though it does explain if someone would trade fully based on one of these rules. I tried to make the results robust by taking into account different amounts of days for each indicator, running multiple regressions and looking at multiple indicators. This could be improved further by extending the number of indicators even more, or looking more into depth at different sub samples in time. Or by looking at sub samples of similar kinds of firms.
30
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33
Appendix A: definitions
Table A1. Definitions of variables in the original dataset
This table presents all definitions from the original data set. Definitions were taken from the description of variables in the CRSP database on the WRDS website.
Variable Definition
PERMCO PERMCO is a unique company level identifier
that remains unchanged throughout the whole term of a company’s existence, even if the company changed names.
PERMNO PERMNO is a unique stock level identifier. This
is a unique number which is assigned to each different type of share class, meaning each type of share from each company has a unique PERMNO.
PRC PRC is the closing price or the negative bid/ask
average for a trading day. If the closing price is not available, the value of PRC is equal to the average bid/ask price on a particular day.
RET RET is the return including possible cash
adjustments (dividends) on a particular day for the applicable period. In this case this is daily data, meaning returns are given for each day relative to the previous day.
SHROUT SHROUT is the number of publicly held shares,
recorded in thousands.
34 Table B1. Descriptive statistics of all pro-strategies for the period of 1926-2019 in the US stock market.
35 Table B2. Descriptive statistics of all contra-strategies for the period of 1926-2019 in the US stock market.
This table contains descriptive statistics of each contra strategy for the period of January 1926 until December 2019. These portfolios and resulting statistics are calculated based on all listed stocks on the NYSE, AMEX, NASDAQ and Arca stock markets in the United States. All returns, corresponding volatilities and ratios are annualized in this table.
36 Table B3. Regression results of all pro- shorter/medium term SMA strategies for the period of 1926-2019 in the US stock market.
This table displays the regression results for all shorter and medium term SMA strategies. For each strategy we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
10-day SMA 20-day SMA 50-day SMA
37 Table B4. Regression results of all pro- longer term SMA strategies for the period of 1926-2019 in the US
stock market.
This table displays the regression results for all longer term SMA strategies. For each strategy we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
100-day SMA 200-day SMA
38 Table B5. Regression results of all pro- shorter/medium term EMA strategies for the period of 1926-2019 in the US stock market.
This table displays the regression results for the shorter and medium term EMA strategies. For each strategy we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
10-day EMA 20-day EMA 50-day EMA
39 Table B6. Regression results of the pro- MACD and all longer term EMA strategies for the period of 1926-2019 in the US stock market.
This table displays the regression results for the MACD and all longer term EMA strategies. For each strategy, we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
MACD 100-day EMA 200-day EMA
40 Table B7. Regression results of all pro-RSI-strategies for the period of 1926-2019 in the US stock market.
This table displays the regression results for all RSI strategies. For each strategy, we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
RSI-50-crossover RSI-30/70-crossover RSI-30/70-retracement
41 Table B8. Regression results of all contra shorter/medium term SMA strategies for the period of 1926-2019 in the US stock market.
This table displays the regression results for all contra shorter and medium term SMA strategies. For each strategy we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
10-day SMA 20-day SMA 50-day SMA
42 Table B9. Regression results of all contra longer term SMA strategies for the period of 1926-2019 in the US
stock market.
This table displays the regression results for all contra longer term SMA strategies. For each strategy we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
100-day SMA 200-day SMA
43 Table B10. Regression results of all contra shorter/medium term EMA strategies for the period of 1926-2019 in the US stock market.
This table displays the regression results for all contra shorter and medium term EMA strategies. For each strategy we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
10-day EMA 20-day EMA 50-day EMA
44 Table B11. Regression results of the contra MACD and all contra longer term EMA strategies for the period of 1926-2019 in the US stock market. This table displays the regression results for the contra MACD and all contra longer term EMA strategies. For each strategy, we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
MACD 100-day EMA 200-day EMA
45 Table B12. Regression results of all contra RSI-strategies for the period of 1926-2019 in the US stock market.
This table displays the regression results for all contra RSI strategies. For each strategy, we run four different regressions. Model (1) represents the CAPM-model, model (2) represents the Fama-French three factor model, model (3) represents the Fama-French five factor model, and model (4) represents the Carhart four factor model, all run on the dependant variable 𝑅𝑝𝑡 − 𝑅𝑓𝑡. The first number represents the calculated coefficient, the standard errors are in parentheses. The value of alpha is given in percentage points. ***, ** and * represent significance at the 1%, 5% and 10% level respectively. The bottom three rows give r-squared values as well as the number of observations.
RSI-50-crossover RSI-30/70-crossover RSI-30/70-retracement
