Trend following with momentum versus moving averages: a tale of differences

Despite the ever-growing interest in trend following and a series of publications in academic journals, there is a dearth of theoretical results on the properties of trend-following rules. Our paper fills this gap by comparing and contrasting the two most popular trend-following rules, the momentum (MOM) and moving average (MA) rules, from a theoretical perspective. We provide theoretical results on the similarity between different trend-following rules and the forecast accuracy of trading rules. Our results show that the similarity between the MOM and MA rules is high and increases with the strength of the trend. However, compared to the MOM rule, the MA rules exhibit more robust forecast accuracy for the future direction of price trends. In this paper, we also develop a hypothesis about uncertain market dynamics. We show that this hypothesis, coupled with our analytical results, has far-reaching practical implications and can explain a number of empirical observations. Among other things, our hypothesis explains why the empirical performance of the MA rules is better than that of the MOM rule. We broaden the appeal and practical importance of our theoretical results by offering various illustrations and real-world examples.     

Testing moving average trading strategies on ETFs

The evidence for the profitability of MA strategies documented in the literature is usually based on non-tradable indices or portfolios/factors and the use of the zero return or risk-free rate as the benchmark. In this paper we implement MA strategies using ETFs and examine the performance of such strategies using a variety of risk-adjusted performance measures. We find that relative to the buy-and-hold strategy, MA strategies have lower average returns and Sharpe ratios, but fare better under factor-adjusted performance measures such as the CAPM alpha. We also find that MA strategies become less profitable when they are implemented using ETFs than using their underlying indices. In addition, we propose a quasi-intraday version of the standard MA strategy (QUIMA) that allows investors to trade immediately upon observing MA crossover signals. The QUIMA strategy outperforms the standard one that only trades at the close of a trading day, when the long-term MA lag length is no more than 50 days.     

Detailed study of a moving average trading rule

We present a detailed study of the performance of a trading rule that uses moving averages of past returns to predict future returns on stock indexes. Our main goal is to link performance and the stochastic process of the traded asset. Our study reports short-, medium- and long-term effects by looking at the Sharpe ratio (SR). We calculate the Sharpe ratio of our trading rule as a function of the probability distribution function of the underlying traded asset and compare it with data. We show that if the performance is mainly due to presence of autocorrelation in the returns of the traded assets, the SR as a function of the portfolio formation period (look-back) is very different from performance due to the drift (average return). The SR shows that for look-back periods of a few months the investor is more likely to tap into autocorrelation. However, for look-back larger than few months, the drift of the asset becomes progressively more important. Finally, our empirical work reports a new long-term effect, namely oscillation of the SR and proposes a non-stationary model to account for such oscillations.     

Is smarter better? A comparison of adaptive, and simple moving average trading strategies

This study examines the comparative performance of an Adaptive Moving Average (AMA) on the Australian All Ordinaries, Dow Jones Industrial Average, and Standard and Poor's 500 stock market indices. The theoretical advantage of the Adaptive Moving Average over fixed length Simple Moving Average (SMA) trading systems is its ability to automatically respond to changing market conditions dependant upon the level of volatility in the market. While the strategy is confirmed to have some market timing ability, the overall results show returns to the Adaptive Moving Average cannot compensate for the cost of trade therefore lending support for the use of a long run passive strategy.     

Time series momentum trading strategy and autocorrelation amplification

This paper investigates why general Moving Average (MA) trading rules are widely used by technical analysts and others. We assume general stationary processes for prices and we derive the autocorrelation function for an MA trading rule. Based on our results, we conjecture that autocorrelation amplification is one of the reasons why such trading rules are popular. Using simulated results, we show that the MA rule may be popular because it can identify price momentum and is a simple way of assessing and exploiting the price autocorrelation structure without necessarily knowing its precise structure. This paper then, provides empirical evidence of autocorrelation amplification using 15-year daily price data for 11 major international stock indices.     

Profitability of time series momentum

We propose a continuous-time heterogeneous agent model consisting of fundamental, momentum, and contrarian traders to explain the significant time series momentum. We show that the performance of momentum strategy is determined by both time horizon and the market dominance of momentum traders. Specifically, when momentum traders are more active in the market, momentum strategies with short (long) time horizons stabilize (destabilize) the market, and meanwhile the market under-reacts (over-reacts) in short-run (long-run). This provides profit opportunity for time series momentum strategies with short horizons and reversal with long horizons. When momentum traders are less active in the market, they always lose. The results provide an insight into the profitability of time series momentum documented in recent empirical studies.     

Asymmetry,tail risk and time series momentum

In this paper, we investigate how to improve the time series momentum strategy by using partial moments. We find that reversals of time series momentum can be partly predicted by tail-distributed upper and lower partial moments derived from daily returns of commodity futures. Based on such information, we propose rule-based approaches to improve the trading signals suggested by the time series momentum strategy. The empirical results based on Chinese commodity futures document statistically significant improvements of the Sharpe ratio in the out-of-sample period. These improvements are robust to different look-back windows.     

Predictability of the simple technical trading rules: An out‐of‐sample test

In a true out-of-sample test based on fresh data we find no evidence that several well-known technical trading strategies predict stock markets over the period of 1987 to 2011. Our test safeguards against sample selection bias, data mining, hindsight bias, and other usual biases that may affect results in our field. We use the exact same technical trading rules that Brock, Lakonishok, and LeBaron (1992) showed to work best in their historical sample. Further analysis shows that this poor out-of-sample performance most likely is not due to the market becoming more efficient – instantaneously or gradually over time – but probably a result of bias.     

Chasing trends: recursive moving average trading rules and internet stocks

The recent rise and fall of Internet stock prices has led to popular impressions of a speculative bubble in the Internet sector. We investigate whether investors could have exploited the momentum in Internet stocks using simple moving average (MA) trading rules. We simulate real time technical trading using a recursive trading strategy applied to over 800 moving average rules. Statistical inference takes into account conditional heteroscedasticity and joint dependencies. No evidence of significant trading profits is found. Most Internet stocks behave as random walks; this, combined with high volatility, may be the reason for the dismal performance of the moving average rules.     

Time series reversal in trend-following strategies

This paper empirically studies the reversal pattern following the formation of trend-following signals in the time series context. This reversal pattern is statistically significant and usually occurs between 12 and 24 months after the formation of trend-following signals. Employing a universe of 55 liquid futures, we find that instruments with sell signals in the trend-following portfolio (‘losers’) contribute to this type of reversal, even if their profits are not realised. The instruments with buy signals in the trend-following portfolio (‘winners’) contribute much less. A double-sorted investment strategy based on both return continuation and reversal yields to portfolio gains which are significantly higher than that of the corresponding trend-following strategy.     

Efficient willow tree method for European-style and American-style moving average barrier options pricing

Moving average options are widely traded in financial markets, but exiting methods for pricing this type of option are too slow. This paper proposes two efficient willow tree methods for pricing European-style and American-style moving average barrier options (MABOs). We first solve the finite-dimensional partial differential equation model for discretely monitored MABOs by willow tree methods, and then compute the value of continuously monitored MABOs by Richardson’s two-point extrapolation. Our new willow tree method employs the interpolation error minimization technique to reduce complexity. The corresponding convergence rate and error bounds are also analyzed. It shows that our proposed methods can provide the same accuracy as the binomial tree approach and Monte Carlo simulation, but require much less computing time. The numerical experiments support our claims.     

Idiosyncratic momentum and the cross‐section of stock returns: Further evidence

In this article, we evaluate the profitability and economic source of the predictive power of the idiosyncratic momentum effect, by using five popular asset pricing models to construct the idiosyncratic momentum. We show that all five idiosyncratic momentum strategies produce similar return predictability and consistently outperform the conventional momentum strategy in the cross‐sectional pricing of equity portfolios and individual stocks. This positive effect of idiosyncratic momentum on returns is consistent with the investment capital asset pricing model (CAPM). Further analysis reveals that the firm‐level idiosyncratic momentum effect cannot extend to the aggregate stock market.     

The intra-day performance of market timing strategies and trading systems based on Japanese candlesticks

Abstract

We develop market timing strategies and trading systems to test the intra-day predictive power of Japanese candlesticks at the 5-minute interval on the 30 constituents of the DJIA index. Around a third of the candlestick rules outperform the buy-and-hold strategy at the conservative Bonferroni level. After adjusting for trading costs, however, just a few rules remain profitable. When we correct for data snooping by applying the SSPA test on double-or-out market timing strategies, no single candlestick rule beats the buy-and-hold strategy after transaction costs. We also design fully automated trading systems by combining the best-performing candlestick rules. No evidence of out-performance is found after transaction costs. Although Japanese candlesticks can somewhat predict intra-day returns on large US caps, we show that such predictive power is too limited for active portfolio management to outperform the buy-and-hold strategy when luck, risk, and trading costs are correctly measured.     

Economic policy uncertainty and momentum

We show that a news‐based measure of economic policy uncertainty (EPU) negatively forecasts momentum. A 1‐standard‐deviation increase in EPU is associated with a 1.11% decrease in risk‐adjusted momentum returns. The predictive power of EPU is robust after controlling for previously documented economic state variables and macroeconomic uncertainty. We provide an explanation for these results from the perspective of a fund flow‐induced trading mechanism and offer direct empirical support. The literature documents that momentum can be partially attributed to performance‐chasing mutual fund flows. We find that this flow‐induced mechanism functions more effectively in low EPU states, thereby generating stronger stock momentum.     

Clustering financial time series with variance ratio statistics

This study introduces a new distance measure for clustering financial time series based on variance ratio test statistics. The proposed metric attempts to assess the level of interdependence of time series from the point of view of return predictability. Simulation results show that this metric aggregates time series according to their serial dependence structure better than a metric based on the sample autocorrelations. An empirical application of this approach to international stock market returns is presented. The results suggest that this metric discriminates stock markets reasonably well according to size and the level of development. Furthermore, despite the substantial evolution of individual variance ratio statistics, the clustering pattern remains fairly stable across different time periods.     

Estimating correlation and covariance matrices by weighting of market similarity

We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for the similarity of previous market conditions to the present situation. The resulting estimators are less biased and show lower variance than either unweighted or exponentially weighted estimators. The weighting scheme is based on a similarity measure that compares the current correlation structure of the market to the structures at past times. Similarity is then measured by the matrix 2-norm of the difference of probe correlation matrices estimated for two different points in time. The method is validated in a simulation study and tested empirically in the context of mean–variance portfolio optimization. In the latter case we find an enhanced realized portfolio return as well as a reduced portfolio risk compared with alternative approaches based on different strategies and estimators.     

News implied volatility and disaster concerns

We construct a text-based measure of uncertainty starting in 1890 using front-page articles of the Wall Street Journal. News implied volatility (NVIX) peaks during stock market crashes, times of policy-related uncertainty, world wars, and financial crises. In US postwar data, periods when NVIX is high are followed by periods of above average stock returns, even after controlling for contemporaneous and forward-looking measures of stock market volatility. News coverage related to wars and government policy explains most of the time variation in risk premia our measure identifies. Over the longer 1890–2009 sample that includes the Great Depression and two world wars, high NVIX predicts high future returns in normal times and rises just before transitions into economic disasters. The evidence is consistent with recent theories emphasizing time variation in rare disaster risk as a source of aggregate asset prices fluctuations.     

Volatility forecasts and at-the-money implied volatility: a multi-component ARCH approach and its relation to market models

This article explores the relationships between several forecasts for the volatility built from multi-scale linear ARCH processes, and linear market models for the forward variance. This shows that the structures of the forecast equations are identical, but with different dependencies on the forecast horizon. The process equations for the forward variance are induced by the process equations for an ARCH model, but postulated in a market model. In the ARCH case, they are different from the usual diffusive type. The conceptual differences between both approaches and their implication for volatility forecasts are analysed. The volatility forecast is compared with the realized volatility (the volatility that will occur between date t and t + ΔT), and the implied volatility (corresponding to an at-the-money option with expiry at t + ΔT). For the ARCH forecasts, the parameters are set a priori. An empirical analysis across multiple time horizons ΔT shows that a forecast provided by an I-GARCH(1) process (one time scale) does not capture correctly the dynamics of the realized volatility. An I-GARCH(2) process (two time scales, similar to GARCH(1,1)) is better, while a long-memory LM-ARCH process (multiple time scales) replicates correctly the dynamics of the implied and realized volatilities and delivers consistently good forecasts for the realized volatility.     

Rating Migrations: The Effect of History and Time

We examine the effect of rating history and the passage of time on the rating migration hazard for corporate debt issuers. Controlling for industry effects and the evolution of business and political cycles, the results consistently show that the next change of rating depends more strongly on rating history than it does on the current rating. However, there are significant interactions between the main effects of rating history and the duration of the current rating. The result is substantial decay in the effects of rating history the longer a rating remains unchanged. This decay effect is stronger for downgrades and for ratings in the speculative category.