Estimating the profits from trading strategies

Price improvement is the difference between the execution priceof an order and the quoted bid or ask when the order was submitted.We show that expected price improvement falls off dramaticallyas the size of the order approaches the quoted depth, and becomesnegative for larger orders. This is particularly important forsmall firms because the quoted depths are low. Using quotedspreads and depths and our estimate of expected price improvement,we show that trading strategies that attempt to exploit theweekly predictability of small-firm returns would be swampedby transaction costs.     

No arbitrage conditions for simple trading strategies

Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the losses are not assumed to be bounded from below.) We show that for a class of non-negative strict local martingales, the strong Markov property implies the no arbitrage property with respect to the class of simple trading strategies. This result can be seen as a generalization of a similar result on three dimensional Bessel process in Delbaen and Schachermayer (Math Finance 4:343–348, 1994). We also provide no arbitrage conditions for stochastic processes within the class of simple trading strategies with shortsale restriction.     

Asymmetric return dynamics and technical trading strategies

We investigate the profitability of technical trading strategies based on an asymmetric reverting property of stock returns. We identify an asymmetry in return dynamics for daily returns on the S&P 500 index. Return dynamics evolve along a positive (negative) unconditional mean after a prior positive (negative) return. The trading strategies based on this asymmetry generate a positive return for buy signals, a negative return for sell signals, and a positive return for the spread between buy and sell signals. Our results imply that the observed asymmetry in return dynamics is the main source of profitability for the implied strategies, thereby corroborating arguments for the usefulness of technical trading strategies.     

S&P 500 trading strategies and stock betas

This paper shows that S&P 500 stock betas are overstatedand the non-S&P 500 stock betas are understated becauseof liquidity price effects caused by the S&P 500 tradingstrategies. The daily and weekly betas of stocks added to theS&P 500 index during 1985-1989 increase, on average, by0.211 and 0.130. The difference between monthly betas of otherwisesimilar S&P 500 and non-S&P 500 stocks also equals 0.125during this period. Some of these increases can be explainedby the reduced nonsynchroneity of S&P 500 stock prices,but the remaining increases are explained by the price pressureor excess volatility caused by the S&P 500 trading strategies.I estimate that the price pressures account for 8.5 percentof the total variance of daily returns of a value-weighted portfolioof NYSE/AMEX stocks. The negative own autocorrelations in S&P500 index returns and the negative cross autocorrelations betweenS&P 500 stock returns provide further evidence consistentwith the price pressure hypothesis.     

Constant-collateral pyramiding trading strategies in futures markets

This paper introduces constant-collateral pyramiding trading strategies, which can be implemented in the futures markets. For these strategies, expressions are derived for effective constraints on the number of futures contracts in the trader’s portfolio and on the trader’s wealth. Implications of the results are drawn regarding the degree of pyramiding adopted by a subgroup of noise traders who underestimate the probability of receiving a margin call when they engage in positive feedback strategies. Suggestions are made regarding how market regulators can use margin requirements to encourage these traders to adopt less aggressive pyramiding strategies.     

Dynamic mode decomposition for financial trading strategies

We demonstrate the application of an algorithmic trading strategy based upon the recently developed dynamic mode decomposition on portfolios of financial data. The method is capable of characterizing complex dynamical systems, in this case financial market dynamics, in an equation-free manner by decomposing the state of the system into low-rank terms whose temporal coefficients in time are known. By extracting key temporal coherent structures (portfolios) in its sampling window, it provides a regression to a best fit linear dynamical system, allowing for a predictive assessment of the market dynamics and informing an investment strategy. The data-driven analytics capitalizes on stock market patterns, either real or perceived, to inform buy/sell/hold investment decisions. Critical to the method is an associated learning algorithm that optimizes the sampling and prediction windows of the algorithm by discovering trading hot-spots. The underlying mathematical structure of the algorithms is rooted in methods from nonlinear dynamical systems and shows that the decomposition is an effective mathematical tool for data-driven discovery of market patterns.     

Return enhancement trading strategies for size based portfolios

Recent theoretical work suggests that definitions of market efficiency that allow for the possibility of time-varying risk-premia will generally lead to return sign predictability. Consistent with this theory, we show that a logit model based on the lagged value of the market risk premium is useful for successfully predicting the return sign for CRSP small decile portfolio returns, but not large ones. We additionally employ this model in market timing simulations of micro-cap mutual funds in which investment can actually be made. The results indicate that a market-timing strategy based on our return-sign forecasting model outperforms a buy-and-hold strategy for 13 of 14 micro-cap funds studied. On average, the buy-and-hold strategy produces an average compound return of 11.98% per annum versus an average of 16.60% for the market-timing strategy. Nevertheless, trading restrictions make the return-sign forecasting model more practical to employ by the micro-cap fund portfolio manager rather than the individual fund investor.

Lessons from the evolution of foreign exchange trading strategies

The adaptive markets hypothesis posits that trading strategies evolve as traders adapt their behavior to changing circumstances. This paper studies the evolution of trading strategies for a hypothetical trader who chooses portfolios from foreign exchange (forex) technical rules in major and emerging markets, the carry trade, and US equities. The results show that a backtesting procedure to choose optimal portfolios improves upon the performance of nonadaptive rules. We also find that forex trading alone dramatically outperforms the S&P 500, with much larger Sharpe ratios over the whole sample, but there is little gain to coordinating forex and equity strategies, which explains why practitioners consider these tools separately. Forex trading returns dip significantly in the 1990s but recover by the end of the decade and have been markedly superior to an equity position since 1998. Overall, trading rule returns still exist in forex markets—with substantial stability in the types of rules—though they have migrated to emerging markets to a considerable degree.     

An examination of the benefits of dynamic trading strategies in U.K. closed-end funds

We examine the after-cost out-of-sample performance of the unconditional mean–variance (UMV) strategy in the presence of conditioning information (Ferson and Siegel (2001)) using portfolios of U.K. equity closed-end funds. We find that the performance of the UMV strategy significantly improves when using lagged information variables with the highest persistence (first-order autocorrelation) levels and reduces turnover. This strategy is able to outperform alternative dynamic trading strategies and performs well across different subperiods. At low levels of trading costs, the UMV strategy is able to deliver significant value added to investors.     

Efficient trading strategies in the presence of market frictions

We provide a price characterization of efficient contingentclaims - that is, chosen by at least a rational agent - in multiperiodeconomies with market frictions. Frictions include market incompleteness,transaction costs, short-selling, and borrowing costs. We characterizethe inefficiency cost of a trading strategy - its required investmentminus the largest amount necessary to obtain the same utilitylevel - and we propose a measure of portfolio performance. Weshow that arbitrage bounds cannot be tightened based on efficiencywithout restricting preferences or endowments. We observe commoninvestment strategies becoming inefficient with market frictionsand others rationalized by them.     

Trend-following trading strategies in commodity futures: A re-examination

This paper examines the performance of trend-following trading strategies in commodity futures markets using a monthly dataset spanning 48 years and 28 markets. We find that all parameterizations of the dual moving average crossover and channel strategies that we implement yield positive mean excess returns net of transactions costs in at least 22 of the 28 markets. When we pool our results across markets, we show that all of the trading rules earn hugely significant positive returns that prevail over most subperiods of the data as well. These results are robust with respect to the set of commodities the trading rules are implemented with, distributional assumptions, data-mining adjustments and transactions costs, and help resolve divergent evidence in the extant literature regarding the performance of momentum and pure trend-following strategies that is otherwise difficult to explain.     

Heterogeneous real-time trading strategies in the foreign exchange market

The foreign exchange (FX) market is worldwide, but the dealers differ in their geographical locations (time zones), working hours, time horizons, home currencies, access to information,transaction costs, and other institutional constraints. The variety of time horizones is large: from intra-day dealers, who close their positions every evening, to long-term investors and central banks. Depending on the constraints, the different market participats need different strategies to reach their goal, which is usually maximizing the profit, or rather a utility function including risk. Different intra-day trading strategies can be studied only if high-density data are available. Oslen & Associates (O & A) has collected and analysed large amounts of FX quotes by market makers around the clock (up to 5000 non-equally spaced prices per day for the German mark against US$). Based on these data, a set of real-time intra-day trading models has been developed. These models give explicit trading recommendations under realistic constraints. They are allowed to trade only during the opening hours of a market, depending on the time zone and local holidays. The models have been running real-time for more than three years, thus leading to an ex ante test. The test results, obtained with a risk-sensitive performance measure, are presented. All these trading models are profitable, but they differ in their risk behaviour and dealing frequency. If a certain profitable intra-day algorithm is tested with different working hours, its success can considerably change. A systematic study shows that the best choice of working hours is usually when the most important markets for the particular FX rate are active. All the results demonstrate that the assumption of a homogeneous 24-hour FX market with identical dealers, following an identical ‘rational expectation’, is far from reality. To explain the market dynamics, a heterogeneous model of the market with different types of dealers is more appropriate.     

An agent-based model of corporate bond trading

We construct an heterogeneous agent-based model of the corporate bond market and calibrate it against US data. The model includes the interactions between a market maker, three types of fund, and cash investors. In general, the sensitivity of the market maker to demand and the degree to which momentum traders are active strongly influence the over- and under-shooting of yields in response to shocks, while investor behaviour plays a comparatively smaller role. Using the model, we simulate experiments of relevance to two topical issues in this market. Firstly, we show that measures to reduce the speed with which investors can redeem investments can reduce the extent of yield dislocation. Secondly, we find the unexpected result that a larger fraction of funds using passive investment strategies increases the tail risk of large yield dislocations after shocks.     

Combining mean reversion and momentum trading strategies in foreign exchange markets

The literature on equity markets documents the existence of mean reversion and momentum phenomena. Researchers in foreign exchange markets find that foreign exchange rates also display behaviors akin to momentum and mean reversion. This paper implements a trading strategy combining mean reversion and momentum in foreign exchange markets. The strategy was originally designed for equity markets, but it also generates abnormal returns when applied to uncovered interest parity deviations for five countries. I find that the pattern for the positions thus created in the foreign exchange markets is qualitatively similar to that found in the equity markets. Quantitatively, this strategy performs better in foreign exchange markets than in equity markets. Also, it outperforms traditional foreign exchange trading strategies, such as carry trades and moving average rules.     

Efficiency of football betting markets: the economic significance of trading strategies

Prior studies of the Australian Rugby League betting market report a degree of predictability well in excess of that attributable to chance. However, two important recent changes in the structure of the market facilitate an unambiguous assessment of the statistical significance of predictability and the economic significance of returns to betting strategies. The present paper reexamines the efficiency of the Australian Rugby League betting market under the revised market structure. In addition, a set of measures of the economic significance of trading strategies are developed and implemented. Relative to prior studies, the out‐of‐sample success of the predictive model has diminished notably under the revised market structure; although a naïve strategy betting on home underdogs still performs significantly better than can be attributed to chance. Simulation experiments suggest that the documented level of predictability from several strategies generates economically significant returns.     

The space of outcomes of semi-static trading strategies need not be closed

Semi-static trading strategies make frequent appearances in mathematical finance, where dynamic trading in a liquid asset is combined with static buy-and-hold positions in options on that asset. We show that the space of outcomes of such strategies can have very poor closure properties when all European options for a fixed date \(T\) are available for static trading. This causes problems for optimal investment, and stands in sharp contrast to the purely dynamic case classically considered in mathematical finance.     

Informed momentum trading versus uninformed “naive” investors strategies

We construct a zero net-worth uninformed “naive investor” who uses a random portfolio allocation strategy. We then compare the returns of the momentum strategist to the return distribution of naive investors. For this purpose we reward momentum profits relative to the return percentiles of the naive investors with scores that are symmetric around the median. The score function thus constructed is invariant and robust to risk factor models. We find that the average scores of the momentum strategies are close to zero (the score of the median) and statistically insignificant over the sample period between 1926 and 2005, various sub-sample periods including the periods examined in [Jegadeesh and Titman, 1993] and [Jegadeesh and Titman, 2001]. The findings are robust with respect to sampling or period-specific effects, tightened score intervals, and the imposition of maximum-weight restrictions on the naive strategies to mitigate market friction considerations.     

Convergence of trading strategies in continuous double auction markets with boundedly-rational networked traders

This paper considers the convergence of trading strategies among artificial traders connected to one another in a social network and trading in a continuous double auction financial marketplace. Convergence is studied by means of an agent-based simulation model called the Social Network Artificial stoCk marKet model. Six different canonical network topologies (including no-network) are used to represent the possible connections between artificial traders. Traders learn from the trading experiences of their connected neighbours by means of reinforcement learning. The results show that the proportions of traders using particular trading strategies are eventually stable. Which strategies dominate in these stable states depends to some extent on the particular network topology of trader connections and the types of traders.     

The profitability of pairs trading strategies: distance,cointegration and copula methods

We perform an extensive and robust study of the performance of three different pairs trading strategies—the distance, cointegration and copula methods—on the entire US equity market from 1962 to 2014 with time-varying trading costs. For the cointegration and copula methods, we design a computationally efficient two-step pairs trading strategy. In terms of economic outcomes, the distance, cointegration and copula methods show a mean monthly excess return of 91, 85 and 43 bps (38, 33 and 5 bps) before transaction costs (after transaction costs), respectively. In terms of continued profitability, from 2009, the frequency of trading opportunities via the distance and cointegration methods is reduced considerably, whereas this frequency remains stable for the copula method. Further, the copula method shows better performance for its unconverged trades compared to those of the other methods. While the liquidity factor is negatively correlated to all strategies’ returns, we find no evidence of their correlation to market excess returns. All strategies show positive and significant alphas after accounting for various risk-factors. We also find that in addition to all strategies performing better during periods of significant volatility, the cointegration method is the superior strategy during turbulent market conditions.