The mean reversion trading systems are more appealing to a lot of traders because it tends to have a higher win rate as opposed to the trend following strategies. Even when the markets are in well-established trends, mean reversion happens quite often.
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The mean reversion theory is at the foundation of many trading strategies that involve buying and selling of those asset class prices that have deviated from their historical averages. The idea is that in the long-term prices will return back to their previous average prices and normal pattern.
Our best mean reversion strategy is to trade those price ranges that occur after a severe price markup or markdown. In this case, reversion to the mean implies trading around the middle of the range as our average price.
The best mean reversion strategy you can possibly use is the one that can help you capitalize on choppy or ranging markets. During a consolidation period, the price will get stretched to the upside and downside multiple times. The price will tend to snap back from these overbought/oversold readings.
This research analyzed the effectiveness of Black Swan strategies for the Short-Term Mean-Reversion systems, the risks and rewards profiles of such betting systems based on the S&P500 index. In determining the Black Swan events, the research made use of multiple strategies against two portfolios. By utilizing the python notebooks, signals created by the Black Swan and Bollinger Bands trading strategies were compared for performance against the baseline index (buy-and-hold strategy). This was followed by a validation of how risk mitigation techniques like the stop-loss affect the trading performance. The research concluded that it is possible to construct a Mean-Reverse strategy that outperforms the market over time.Supplemental Materials:
Traditionally in finance, portfolios are often selected according to mean-variance theory (Markowitz 1952, 1959) or its variants, to trade off between return and risk. In recent years, this problem has also been actively studied from a learning to select portfolio perspective, with roots in the fields of machine learning, data mining, information theory and statistics. Rather than trading with a single stock using computational intelligence techniques, learning to select portfolio approach focuses on a portfolio, which consists of multiple assets/stocks. Several approaches for online portfolio selection, often characterized by machine learning formulations and effective optimization solutions, have been proposed in literature (Kelly 1956; Breiman 1961; Cover 1991; Ordentlich and Cover 1996; Helmbold et al. 1996; Borodin and El-Yaniv 1998; Borodin et al. 2000, 2004; Stoltz and Lugosi 2005; Hazan 2006; Györfi et al. 2006; Blum and Mansour 2007; Levina and Shafer 2008; Györfi et al. 2008). Despite being studied extensively, most approaches are limited in some aspects or the other.
Under different scenarios, the proposed PAMR strategy either passively keeps last portfolio or aggressively approaches a new portfolio by following the mean reversion principle. By solving three well formulated optimization problems, we arrive at three simple portfolio update rules. It is interesting to find that the final portfolio update scheme reaches certain trade-offs between portfolio return and volatility risk, and explicitly reflects the mean reversion trading rule. Moreover, we propose a mixture algorithm, which mixes PAMR and other strategies, and show that the mixture can be universal if one universal strategy is included. The key advantages of PAMR are its highly competitive performance and fairly attractive computation time efficiency. Our extensive numerical experiments on various real datasets show that in most cases the proposed PAMR strategy is quite performance efficient in comparison to a number of state-of-the-art portfolio selection strategies under a variety of performance metrics. At the same time, the proposed strategy costs linear time with respect to the product of the number of stocks and trading days, and its computational time in back tests is orders of magnitude less than its competitors, showing its applicability to real-world large scale online applications.
We show that the time complexity of the proposed algorithm is linear with respect to the number of stocks per trading day, and its empirical computational time in the back tests is quite competitive compared with the state of the arts, indicating the proposed strategy is suitable for online large-scale real applications.
For the tth trading day, an investment according to portfolio b t results in a portfolio daily return s t , that is, the wealth increases by a factor of \(\mathbfs_t=\mathbfb_t^\top\mathbfx_t=\sum_i=1^mb_tix_ti\). Since we use price relative, the investment results in multiplicative cumulative return. Thus, after n trading days, the investment according to a portfolio strategy b n results in portfolio cumulative wealth S n , which is increased by a factor of \(\prod_t=1^n\mathbfb_t^\top \mathbfx_t\), that is,
Learning to select portfolio has been extensively studied in information theory and machine learning. Generally, a strategy selects one optimal strategy (it can be market strategy, challenging BCRP strategy, or even Oracle strategy which chooses the best stock every trading day) and tries to obtain the same cumulative return. The regret of a strategy is defined as the gap between its logarithmic cumulative wealth achieved and that of the optimal strategy.
Another promising direction for portfolio selection is wealth maximization approach, which is based on the notion of approaching the Oracle as the optimal strategy. This idea was followed by Borodin et al. (2004) in their proposal of a non-universal portfolio strategy named Anti-Correlation (Anticor). Unlike the regret minimization approaches, Anticor strategy takes advantage of the statistical properties of financial market. The underlying motivation is to bet on the consistency of positive lagged cross-correlation and negative autocorrelation. It exploits the statistical information from the historical stock price relatives and adopts the classical mean reversion trading idea to transfer the wealth in the portfolio. Although it does not provide any theoretical guarantee, its empirical results (Borodin et al. 2004) showed that Anticor can outperform all existing strategies in most cases. Unlike the greedy algorithm by the Anticor strategy, Li et al. (2011b) very recently proposed Confidence Weighted Mean Reversion (CWMR) strategy to actively exploit the mean reversion property and the second order information of a portfolio, which produces better performance than Anticor.
Besides the main stream of learning to select portfolio, another type of trading strategy is based on switching between various strategies, that is, maintaining a probability distribution among the strategies. Singer (1997) proposed Switching Portfolios (SP), which aims to deal with changing markets by taking into account the possibility that the market changes its behavior after each trading day. It switches among a set of basic investment strategies and assumes the a priori duration of using one basic strategy is geometrically distributed. Levina and Shafer (2008) proposed Gaussian Random Walk (GRW) strategy, which is a Markov switching strategy. GRW switches among the basic investment strategies as a Gaussian random walk in the simplex of portfolios.
One popular trading idea in reality is trend following or momentum strategy, which assumes that historically better-performing stocks would still perform better than others in future. Some existing algorithms, such as EG and ONS, approximate the expected logarithmic daily return and logarithmic cumulative return respectively using historical price relatives. Though this idea is easy to understand and makes fortunes to many of the best traders and investors in the world, trend following is very hard to implement effectively. In addition, in the short-term, the stock price relatives may not follow previous trends as empirically evidenced by Jegadeesh (1990) and Lo and MacKinlay (1990).
In a word, both trend following and mean reversion can generate profit in the financial markets, if appropriately used. In the following, we will propose an active mean reversion based portfolio selection method. Though simple in update rules, it empirically outperforms the above existing portfolio selection strategies in most cases. The success of the proposed portfolio selection strategy indicates that it appropriately takes advantage of the mean reversion trading idea and generates significantly high profits in the back tests with real market data.
To further illustrate why aggressive reversion to the mean can be more effective than a passive one, let us continue the example in Table 1 that has a market going to nowhere but actively fluctuating. We show that in such markets, the proposed strategy is much more powerful than BCRP in hindsight, a passive mean reversion trading strategy. Table 2 compares the two trading strategies. As the motivating example shows, the growth rate of BCRP is \((\frac54)^n\) for a n-trading period, while at the same time, the growth rate of the proposed PAMR strategy is \(\frac54\times(\frac32)^n-1\) (the details of the calculation/algorithm will be presented later). We intuitively explain the success of PAMR below.
Assume the threshold for PAMR update is set to 1, that is, if portfolio daily return is below 1, we do nothing but keep the existing portfolio. Our strategy begins with a portfolio \((\frac12, \frac 12 )\). For the 1st trading day, the return is \(\frac54>1\). Then at the beginning of the 2nd trading day, we rebalance the portfolio to satisfy the condition that approximate portfolio daily return based on last price relatives is below the threshold 1, and the resulting portfolio is \((\frac 23, \frac13 )\). Although it seems that we build a portfolio such that the approximate portfolio return is below the threshold, in practice, as the reversion to the mean suggests, we are maximizing the portfolio return in the next trading day. As we can observe, the return for the 2nd trading day is \(\frac32>1\). Then following the same rule, we will rebalance the portfolio to \((\frac13, \frac23 )\). As a result, in such a market, the growth rate of the proposed strategy is \(\frac54\times (\frac32 )^n-1\) for a n-trading period, which is much more superior to that of BCRP, that is, \((\frac54 )^n\). 2ff7e9595c
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