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Data on mean and standard deviation of daily returns for buy and sell days, as well as various trading rules such as Simple Moving Average (SMA) and Exponential Moving Average (EMA) with different time periods. The data includes Welch t-statistics to measure the difference between average daily returns on buy and sell days to average daily buy-and-hold returns, and between average daily returns on buy days and average daily sell-day returns.
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Master Thesis in Economics
Author: Dan Gustafsson Tutor: Per-Olof Bjuggren, Louise Nordström
Jönköping May 2012
i
Abstract
In this paper I examine the validity of technical analysis for the Swedish stock index OMXS30 between 2001 - 12 - 28 and 2011- 12 - 30. Results indicate that OMXS30 followed a non-random walk and that technical trading rules had predictive power over future price movements. Results also suggest that technical trading rules could be used to outperform a buy-and-hold strategy.
1 Introduction
In the course of years, literally thousands of research papers have tried to appraise the state of the stock market. In fact, during the past ten decades, few other topics have been so ex- haustively studied. The rewards to those who are able to anticipate the market are enor- mous - no wonder the field has attracted so many financial economist and practitioners.
The intensive research has all tried to answer the investor’s problem of how to behave in the stock market. As a result, two rather different disciplines have arisen. The first disci- pline is commonly referred to as fundamental analysis and the second discipline as tech- nical analysis. Fundamental analysis tries to find the “correct” value of a security and, as the name implies, looks at economic fundamentals to do so. Technical analysis on the other hand, appraises securities with the use of historical price information.
In this paper I will examine the validity of technical analysis for the Swedish stock index OMXS30 and see if a strategy based on technical trading rules could have outperform a buy-and-hold strategy. As such, this paper will be an interesting contribution to the general discussion of market efficiency, behavioral finance and technical analysis.
At a first glance, the use of technical analysis is quite appealing. The primary reason is the anticipation to time and beat the market (buy low and sell high) and spend an inordinate amount of time and research doing so. An investor would no longer need to depend on profit-loss-statements, auditor’s reports and dividend records. Instead, all an investor need is historical price data and a trading rule which generates buy and sell signals. However, finding a trading rule that generates profitable buy and sell signals is easier said than done. As such, to avoid being whipsawed by seemingly erratic market price movements, an inves- tor should first and foremost try to understand the fundamental condition of the stock market before applying technical analysis. For example, if stock markets follow a random walk, market timing would be impossible using technical analysis. As such, a long term in- vestment strategy based on the assumption that stock markets generate good rewards in the long run (from now on called the buy-and-hold strategy), would be superior to any strategy based on technical trading rules. If price movements are predictable, on the other hand, technical analysis should be the obvious choice for any investor when appraising securities.
Previous studies have lent some support to the idea that technical analysis could be used to outperform a buy-and-hold strategy for the Swedish stock exchange (SSE). For example, both Frennberg and Hansson (1992) and Säfvenblad (2000) rejected the random walk hy- pothesis (the first obstacle for technical analysis) for the SSE, finding high levels of auto- correlation. Säfvenblad (2000) suggested that the underlying reason for the SSE’s non- random walk behavior was negative feedback trading^1 (where investors sell after price in-
(^1) Feedback trading is a form of trading strategy including: profit taking, herding and dynamic asset allocation (Säfvenblad, 2000)
creases). An additional study supporting the use of technical analysis for the SSE is Metghalchi, Chang and Marcucci (2005). Findings suggested that simple moving average techniques have had predictive power over future price movements and could outperform a buy-and-hold strategy for the Swedish stock index OMXS30 between 1986 and 2004.
However, except for Metghalchi et al (2005), the validity of technical analysis for the SSE has been notably unexamined until now. Furthermore, as Metghalchi et al findings were based on stock market data between 1986 and 2004, I believe it is high time for a revisit. As such, I will in this paper examine the validity of technical analysis for the Swedish stock in- dex OMXS30 and see if a strategy based on technical trading rules could have outperform a buy-and-hold strategy. To do this I will test the following hypotheses: (1) OMXS30 fol- lowed a non-random walk, (2) technical trading rules did have predictive power over future price movements and (3) strategies based on technical trading could outperform a buy-and- hold strategy.
Criticism of technical analysis often derives from academic research supporting the “weak form” efficient market hypothesis as defined by Fama (1970). Specifically, the validity of technical analysis is often dismissed due to the belief that stock markets follow a random walk. Examples of studies supporting the random walk hypothesis are: Fama (1965)^2 , Fama & Blume (1966)^3 and Jensen & Benington (1970)^4. However, numerous of research papers have challenged the random walk hypothesis. In addition to Frennberg & Hansson (1992) and Säfvenblad (2000), empirical evidence supporting non-random walk behavior for stock markets are: Lo and MacKinlay (1988)^5 , Berglund & Liljeblom (1988)^6 , Chan (1993)^7 and Lima & Tabak (2006)^8.
(^2) Fama (1965) examined stock price movements of the Dow Jones Index between 1956 and 1962. Findings suggested that price changes were uncorrelated over time and therefore consistent with the random walk hypothesis.
(^3) Fama & Blume (1966) applied Alexander’s filter technique on closing prices of individual securities of the Dow Jones Index between 1956 and 1962. Fama & Blume concluded that the random walk theory was ad- equate for the average investor due to low serial dependence. (^4) Jensen & Benington (1970) reexamined Levy’s trading rules for the NYSE between 1931 and 1965. Findings suggested that Levy’s trading rules were outperformed by a buy-and-hold strategy and that price move- ments had followed a random walk.
(^5) Lo & MacKinlay (1988) tested the random walk hypothesis by comparing variance estimators for the CRSP return index between 1962 and 1985.Findings strongly rejected the random walk hypothesis.
(^6) Berglund and Liljeblom (1988) examined the Helsinki stock exchange between 1977 and 1982. Findings suggested first order autocorrelation in index returns due to trading procedures.
(^7) Chan (1993) examined the smallest and the largest NYSE deciles between 1980 and 1989. Results indicated serial correlation in stock returns.
(^8) Lima & Tabak (2006) tested the random walk hypothesis for China, Hong Kong and Singapore. Findings rejected the random walk hypothesis for the Singapore stock exchange and B shares for the Chinese stock exchange. Findings supported however the random walk hypothesis for the Hong Kong stock exchange.
low a random walk gained popularity when Malkiel (1973) compared price movements in financial markets to a “drunkard’s unsteady gait”.
Cambell, Lo & MacKinlay (1999) define three different versions of the random walk hy- pothesis. The Random Walk 1 (RW1) model states that all error terms are independent and identically distributed. Hence, past price patterns includes absolutely no information about future price changes. RW1 is considered the strongest form of the random walk the- ory and will be tested with Lo and MacKinlay’s variance ratio test.
The Random Walk 2 (RW2) model states that the distribution of new information, alt- hough independent, can change over time. The underlying theory of the RW2 model is that it is not plausible for security prices to have identically distributed increments over a long time horizon (Cambell, Lo & MacKinlay, 1999).
The Random Walk 3 (RW3) model states that the error terms are uncorrelated. This is to be considered the weakest form of the random walk hypothesis and is often the one tested by financial economists through different serial correlation tests. RW3 is considered the weakest form of the random walk theory since although a trajectory has uncorrelated in- crements, it could still exhibit dependence if the squared increments are correlated (Cam- bell, Lo & MacKinlay, 1999). RW3 will be tested with the Box-Pierce Q-test
From an investor’s point of view, the random walk theory is especially interesting since it contest price predictability. As such, if stock markets follow a random walk, investors can- not use historical prices to establish profitable trading strategies. Hence, the use of tech- nical analysis is futile.
First introduced by Fama (1970), the efficient market hypothesis (EMH) builds upon the assumption that changes in security prices are randomly distributed (follow a random walk). According to Fama (1970), these random price movements are due to the markets incorporation of new information. As new information about companies, industries etc. ar- rives randomly, market reactions should also be random. As such, the EMH do not only assert that financial markets are informationally efficient but also contest the validity of technical analysis. Fama (1970) defines three forms of market efficiency.
The weak form market efficiency assumes that all information contained in historical prices is fully reflected into current prices. While fundamental analysis can be used to outperform the market, technical analysis will not be able to produce excess returns.
The semi-strong form market efficiency assumes that all public information is fully reflect- ed into current prices. Investors with information monopoly (insiders) are able to outper- form the market. However, neither fundamental analysis nor technical analysis will work.
The strong form market efficiency assumes that all information, public or private, is fully reflected into current prices. If strong form market efficiency holds, no single investor can outperform the market. As such, investors should follow a buy-and-hold strategy.
Empirical evidence in regard to the EMH has been mixed. In fact, after almost four dec- ades, financial economists and practitioners have not yet reached a consensus as to whether the EMH holds true for most financial markets. One field that challenge the EMH is be- haviour finance.
In contradiction to the EMH that assumes that investors behave with extreme rationality, behaviour economists suggest that financial markets are full of imperfections in the form of psychological biases (Barberis, Shleifer & Vishny, 1998). Specifically, behaviour finance contest the EMH thru commonly observed patterns of choice. Some of the behavioural bi- ases assumed exhibited in financial markets are explained by prospect theory and regret theory.
The prospect theory (Kahneman & Tversky, 1979) is considered one of the cornerstones in behaviour finance. The prospect theory is primarily concerned with how people make choices that involves risk but where the probabilities of outcomes are known. In contradic- tion to the expected utility theory^9 , the prospect theory argues that individuals value losses more than they value gains. Hence, when comparing losses against gains with the same probability, losses tend to dominate. In other words, the prospect theory suggests that in- dividuals are very concerned with small losses. Furthermore, Kahneman et al (1979) sug- gest that individuals tend to distort probabilities by preferring certainty over uncertainty. To be more specific, individuals tend to choose prospects with assured outcomes over pro- spect with uncertain outcomes - even if they offer lower expected utility.
Related to the prospect theory is the regret theory. The regret theory describes how indi- viduals tend to distort probabilities by making decisions based on anticipated feelings of regret (Loomes & Sugden, 1982). By making decisions based on anticipatory regrets, indi- viduals can become either more risk averse or risk loving. That is, some individuals may avoid making an investments if anticipating regret if the value of the investment declines. Other individuals may take on investments based on anticipated regret from missing out on an opportunity. Applied on financial markets, the regret theory can be observed when in- vestors hold on to loosing investments while locking in gains by selling winners (Odean 1998). This strategy is also known as profit taking and is a form of negative feedback trad- ing. In markets that exhibit profit taking, investors should expect price reversals after peri- ods of strong positive gains as investors sell of winning securities.
(^9) The expected utility theory states that individuals will chose between risky prospects by comparing expected utility values. In other words, individuals will value prospects by multiplying expected utility with the re- spective probability and chose the prospect generating the highest weighted value (Barbera, Hammond & Seidl, 2004).
Technical analysis is the study of price behavior and aims to predict future price move- ments on the basis of historical price patterns. The basic premise of technical analysis is that price movements incorporate human behavior and that human behavior is fairly con- sistent over time. In other words, due to the irrational nature of the human psychology (Baumeister & Bushman, 2011), financial markets will be driven by repeated irrational fac- tors. Thus, technical analysis is not purely technical, as the Dow Theory, but has a very close link to behavior finance.
Advocates of technical analysis claim that there is a wide divergence between presumed value and actual price (Edwards & Magee, 1997). I.e. technical traders assume that market values do not only reflect fundamental statistics but also different value opinions based on rational and irrational behavior. As such, the only way to find out the true value of a stock is to observe the characteristics of supply and demand as buyers and sellers trade with each other. The assumption that markets follow irrational behavior and a supply-demand bal- ance would be of little interest however, were it not for the three basic principles of tech- nical analysis, all of which are commonly observed in stock markets (Edwards & Magee, 1997).
Essentially, the three principals of technical analysis are directly related to tenant 1, 2 and 5 of the Dow Theory. The first principle is that financial markets follow trends. Hence, a large part of technical analysis is to analyze, recognize and exploit assumed trends. As ad- vocates of technical analysis assume that markets follow irrational behavior and pursue a supply-demand balance, different trends will occur due to changing price responses to- wards the market. As price responses are assumed to be composed of two phases: an ac- cumulation or distribution phase and a public participation phase, trends are assumed to be fairly consistent. Hence, the second principle of technical analysis is that trends persist. The third principle is that volume follows the trend. As such, in a bull market, there should be an increase in volume as the price level goes up. A mirror image occurs for a bear market.
There is however no universal trading rules that can be applied on all financial markets. In fact, as mentioned above, technical analysis is only useful if the stock markets exhibit non- random walk behavior. Moreover, even between financial markets that exhibit a non- random walk, trading results based on the same trading rules may differ. Investors should therefore be careful and evaluate the fundamental condition of the stock market before ap- plying technical analysis.
3 Research method
In this chapter I intend to give a thorough description of the tests and models used to examine the validity of technical analysis for OMXS30. The chapter is divided into two parts. The first part will concentrate on two random walk tests: the Box-Pierce Q-test and Lo & MacKinlay’s single variance ratio test. The second part will focus on technical trading rules related to financial theory and previous studies.
As technical analysis asserts that successive returns are dependent, I seek evidence support- ing the first hypothesis: that OMXS30 followed a non-random walk between 2001 - 12 - 28 and 2011- 12 - 30. I will evaluate the random walk hypothesis with two random walk tests: the Box-Pierce Q-tests and Lo & MacKinlay’s single variance ratio tests.
3.1.2 The Box-Pierce Q-test
The Box-Pierce Q-test (Box & Pierce, 1970) is a method to test for serial correlation in a time series. I will use the Box-Pierce Q-statistic to test the weakest form of the random walk hypothesis (RW3) with a null hypothesis of no serial correlation. The Q-statistic is a linear equation of equally weighted squared autocorrelation coefficients and is asymptoti- cally distributed as the chi-squared distribution. As defined by Box & Pierce (1970) the sta- tistic is calculated as:
( ) (^) ∑
where n is the sample size, m is the number of autocorrelation coefficient and the vari- ous squared autocorrelation coefficients. is calculated as:
( ) ∑ ∑
The Box-Pierce Q-statistic assumes that the innovations are normally distributed. It turns out that this assumption is a bit problematic since many stock markets exhibits a lep- tokurtic distribution. Nonetheless, since the asymptotic normality of the autocorrelation coefficients does not require that the innovations are normally distributed (Anderson & Walker, 1964) the Box-Pierce Q-statistic should still be considered a useful tool to detect serial correlation.
( )̂ ( ) (^ ( )(^ ) )
The second test statistic is the robust z-statistic in the case of heteroscedasticity. Since hetroscedasticity can explain the rejection of the random walk hypothesis (RW1), the ro- bust test statistic is of great importance. In other words, if the robust z-statistic is signifi- cant, the rejection of the random walk hypothesis is not due to changing variances because of heteroscedasticity (time varying variances). The robust test statistic is calculated as:
( ) ( ) √^ ( ̅ ( )) √ ̂( )
where ̂( ) is the heteroscedasticity-consistent estimator of the asymptotic variance of ̅ ( ) which can be defined as:
( ) ̂( ) ∑ [ ( ) ] ̂( )
where ( ) is the heteroscedasticity-consistent estimator of the variance of the autocorrela- tion coefficient estimator. (^ )^ is computed as:
( ) ( )
∑ ( ̂) ( ̂) [∑^ ( ̂) ]
where ̂ is the average return. In this paper, I will use observation intervals (q) of 2, 4, 8 and 16.
This section seeks evidence supporting the second hypothesis that technical trading rules did have predictive power over future price movements of OMXS30 between 2001 - 12 - 28 and 2011- 12 - 30. I will assume that OMXS30 follow trends in the primary market move- ment. I therefore adopt two trend determinants: the standard moving average (SMA) and the exponential moving average (EMA). Following Säfvenblad’s (2000) findings that OMXS30 exhibit negative feedback trading, where investors sell after price increases (profit taking), I also introduce two oscillators: the relative strength index and the RSIstoch. As these oscillators measures the power of directional price changes, they might be a useful tool to detect price reversals generated from profit taking behaviour. In addition, I have al- so followed up on successful trading rules for OMXS30 examined by Metghalchi et al (2005): the Arnold and Rahfeldht moving average technique and price relative to an SMA. For brevity, descriptions for the two trading rules are found in the appendix (section 1.1).
To evaluate the different trading rules I will use the Welch t-statistic. The Welch t-test is employed when population variances are assumed to be different and when the sample siz- es are not equal. A description of the Welch t-statistic is found in the appendix (section 2.2). All trading rules will be tested at the 5% significance level. Furthermore, I will assume that the index level remains stable during the last few minutes of trading. An investor will therefore be able to place next day’s market position at the close.
3.2.1 Standard Moving Average
Standard Moving Average (SMA) techniques are some of the most popular trend calcula- tions (Kaufman, 2003). The main use of the SMA is to smooth out day-to-day fluctuations in security prices and by that identify assumed trends. The standard moving average takes the average from past closing prices over a predetermined time period and is calculated as:
( ) ∑
is the number of days in the predetermined time period and is the price level. Alt- hough the 200-day moving average seems to be the benchmark, investors can choose themselves how long or short the time period should be. There are no specific rules in re- gard to that. However, while shorter time periods tends to be more responsive to price changes, longer time periods will provide more reliable estimates on the long-term trend.
In this paper, a “buy-signal” is generated when a short SMA moves above a long SMA. Likewise, a “sell-signal” is generated when a short SMA moves below a long SMA. The main reason for using a short SMA instead of the index price level is to avoid being whip- sawed by erratic price movements.
3.2.2 Exponential Moving Average
While the SMA assign equal weights to past observations, the exponential smoothening ef- fect incorporated in the exponential moving average (EMA), assign exponentially decreas- ing weights to past observations over time. Hence, EMA brings the exponential value clos- er to the last closing price by assigning greater importance to recent data. The starting value of the EMA is usually the simple moving average for N days. The following values of the EMA are calculated as:
( ) (^) ( )
is the last known price and the smoothing factor. When assigning the smoothing factor it is important to remember that while smaller values of tends to produce trend values more responsive to price changes, larger values of will provide more reliable estimates on the long-term trend. I will however adopt a more common practice and calculate the smoothing factor with the following formula:
where is the lowest low for the RSI for the given time period and the highest high for the RSI for the given time period. Investors can choose themselves how long or short the time period should be. I will however use the same time period as for the RSI of 14 trading days.
As for the RSI, the RSIstoch will not be used as a single indicator. The RSIstoch will in- stead be used to detect potential market entry and exit points once a positive trend has been established using SMAs and EMAs. I will assume that the index will rebound and thereby exit the market once the RSIstoch is above 0.80.
I will use closing prices from OMXS30. OMXS30 is an index which involves OMX Stock- holm’s most traded stocks and should provide a good general picture of the Swedish stock exchange. Furthermore, using the OMXS30 index I will mitigate biases related to illiquidity. In other words, an investor should be able to buy and sell shares quickly without seeing a relevant change in price. The data I will use is taken from NasdaqOMX. The time period I will examine is between 2001- 12 - 28 and 2011- 12 - 30. I have chosen this time period since it includes periods of both high and low volatility. In addition, I believe that a time period of ten years is substantial for examining the topic at hand.
4 Empirical Results
This chapter will be divided into three parts. The first part will summarize empirical results from two random walk tests. The Box-Pierce Q-test and Lo & MacKinlay’s single variance ratio test. The second part will summarize the results from different trading rules to assert if technical trading rules could have been used to predict recurring price patterns. The third part will summarize which trading strategies, if any, could have been adopted to outperform the buy-and-hold strategy.
This section summarizes the results from two different random walk tests: the Box-Pierce Q-test and Lo & MacKinlay’s single variance ratio test. I seek evidence rejecting the ran- dom walk theory for OMXS30.
Table 1 summarize the statistical results from the Box-Pierce Q-test. To test the validity of the random walk hypothesis (RW3), Q-statistics are calculated for lags 1 – 10. For daily ob- servations we cannot reject the null hypothesis of no serial correlation at the 5% signifi- cance level for lag m = 1 and m = 2. However, there is a clear rejection of the null hypoth- esis of no serial correlation for m = 3 to m = 10. The main source of high autocorrelation seems to be generated from lag 3. For weekly observations there is a strong rejection of the null hypothesis of no serial correlation for all lags. The main source of high autocorrelation
comes from lag 1. Hence, using the Box Pierce Q-test, both weekly and daily samples reject the weak-form random walk hypothesis (RW3) at the 5% significance level.
Table 1 Statistical results for the Box-Pierce Q-test M Q statistic M Q statistic Panel 1: Daily data 1 1,00250 6 26,1525* (0.317) (0.000) 2 2,2756 7 26,2936* (0,321) (0.000) (^3) 17,8339* 8 27,7251* (0.001) (0.001) 4 23,8478* 9 27,9557* (0.000) (^) (0.001) 5 23,8478* (^10) 29,9458* (0.000) (^) (0.001) Panel 2: Weekly data 1 14,5787* 6 27,9422* (0.000) (0.000) 2 14,8097* 7 36,7125* (0.001) (0.000) 3 17,4523* 8 38,8313* (0.001) (0.000) 4 19,9496* 9 40,2186* (0.001) (0.000) 5 23,4009* 10 42,2689* (0.000) (0.000) m correspond to the number of lags, Q is the Box-Pierce Q-statistic. Reported below the Box-Pierce Q-statistic are the corresponding p- values. Numbers marked with asterisks are significant at the 5% significance level.
q correspond to aggregation values, VR is the Variance Ratio, M(q) is the Variance Ratio estimator, N is the number of observations. Reported below the Z-statistics are the corresponding p-values. Numbers marked with asterisks are significant at the 5% significance lev- el.
Table 2 Statistical results for Lo & MacKinlay VR test Q VR M (q) Z Robust Z N Panel 2: Daily data 2 0,98053 - 0,01947 - 0,9768 - 0,6990 2516 (0.329) (0.485) 4 0,91039 - 0,08961 - 2,4024* - 1,6701 2516 (0.016) (0.095) 8 0,80362 - 0,19638 - 3,3274* - 2,2665* 2512 (0.001) (0.0234) 16 0,75265 - 0,24735 - 2,8164* - 1,9192 2512 (0.005) (0.055) Panel 1: Weekly data 2 0,00878 - 0.12247 - 3,7525* - 2,3545* 520 (0.000) (0.018) 4 0,81117 - 0,18883 - 2,3016* - 1,5843 520 (0.021) (0.113) 8 0,84475 - 0,15525 - 1,1968 - 0,8725 520 (0.231) (0.383) 16 1,0872 0,018722 0,0962 0,0712 512 (0.923) (0.943)
This part will summarize the results from different technical trading rules. Knowing that OMXS30 did not follow a random walk, I seek evidence that technical analysis could have been used to predict recurring price patterns.
For comparison, between 2001-12-28 and 2011-12-30, the average daily return for the buy- and-hold strategy was 0.0184%, the standard deviation 0.016 and the total number of trad- ing days 2517. Given the average daily return, the standard deviation and the number of trading days, the t-statistic for the buy-and-hold strategy, using the one sample t-test (see Appendix, section 2.1), is 0.
√
Compared with the critical value of 1.96 at the 5% significance level, the average daily re- turn for the buy-and-hold strategy is not significantly larger than zero. Interestingly, this implies that a buy-and-hold strategy have not provided positive average daily returns be- tween 2001-12-28 and 2011-12-30.
Table 6 and 7 (Appendix, section 3) reports trading results based on multiple SMA rules and multiple EMA rules. The trading rule was to enter the market when the short moving average moved above the long moving average and exit the market when the short moving average moved below the long moving average. Findings are not spectacular. Although all trading rules provide positive average daily returns on buy-days and negative average daily returns on sell-days, only MA (50-200) is able to generate significant t-statistics for buy-sell returns. These findings give some support that OMXS30 follow trends. However, return correlation do not seem to be strong enough to provide strong price predictions.
Table 8 and 9 (Appendix, section 3) show trading results based on multiple SMAs and mul- tiple EMAs in combination with the RSI. The trading rule was to enter the market when the short moving average moved above the long moving average while the RSI was below
Table 10 and 11 (Appendix, section 3), reports trading results based on multiple SMA rules and multiple EMA rules in combination with the RSIstoch. The trading rule was to enter the market when the short moving average moved above the long moving average while the RSIstoch was below 0.80. I would exit the market when the short moving average moved below the long moving average or when the RSI moved above 0.80. As for the combination with the RSI, a majority of the trading rules provide average daily buy-day re- turns that are significantly larger than average daily sell-day returns. As expected, the intro- duction of the more sensitive RSIstoch generates more trades than the RSI. However, since the RSI provides higher t-statistics it is possible to consider the RSIstoch as oversensitive for OMXS30.
Interestingly, the introduction of the RSI and the RSIstoch (which indicates the strength of directional price changes) seems to have an impact on price predictability. It is clear that OMXS30 exhibit price reversals after periods of positive returns and that these price rever- sals are exploitable. I view these results as further evidence supporting Säfvenblads (2000) suggestion that the Swedish stock market exhibit negative feedback trading (which include profit taking). Something which can also explain OMXS30’s non-random walk behaviour (Säfveblads, 2000).
Table 12 and 13 (Appendix, section 3) summarize trading results based on price relative to an SMA and Arnold and Rahfeldt’s moving average technique. In contrast to Metghalchi et al (2005) findings, none of the trading rules are able to outperform average daily returns of the buy-and-hold strategy. In addition, none of the strategies are able to provide average daily buy-day returns significantly larger than average daily sell-day returns. In fact, trading based on Arnold and Rahfeldt moving average technique provide negative buy-sell t- statistics. This new failure to predict stock returns for the two trading rules can reflect ei- ther (1) the market has become efficient or (2) trend patterns has changed. Since both the random walk tests and technical trading rules support a non-random walk for OMXS30, I conclude that trend patterns can change over time. This could be a result from changes in stock market volatility. As changes in stock market volatility can relate to changes in ex- pected returns (Merton, 1980), trend behaviour might have shifted.
A summary of trading rules with significantly larger average daily buy-day returns than sell- day returns are reported in table 3. Overall findings lend support to the assumption that technical analysis can be used to predict future price movements. If technical analysis could not predict future price movements, average daily buy-day returns would not be significant- ly larger than average daily sell-day returns. As such, I cannot reject my second null hy- pothesis that technical trading rules did have predictive power over future price move- ments. Interestingly, all trading rules reported in table 3 provide negative returns for sell days. Due to an even weighted number of buy and sell days, this cannot be explained by seasonal effects (Brock et al, 1992). Instead, the predictability of price movements should provide further support that OMXS30 follow an exploitable non-random walk. Equally in- teresting is how all trading rules report higher volatility on sell-days than on buy-days. The- se findings are consistent with the asymmetric volatility phenomenon which suggests that volatility tends to be high following negative returns and low following positive returns (Dufour, Garcia & Taamouti, 2012). Possible explanations for asymmetric volatility are: leverage effects^11 and volatility feedback^12 (Bekaert & Wu, 2000). As such, price predictabil- ity of OMXS30 is not only associated with higher returns but also lower risk.
(^11) The leverage effect occurs when the price of a corporate security falls. As the equity of the firm decreases the leverage increases. As such, the security will become more risky which increases its price volatility (Bekaert & Wu, 2000). (^12) The volatility feedback theory assumes that there exist a positive relationship between expected return and volatility. As increased volatility increase expected returns and lower stock prices, good news will cause vol- atility to go down and bad news will cause volatility to go up (Bekaert & Wu, 2000).
