Advanced trading strategies

A new factor model consisting of the market factor, an investment factor, and a return-on-equity factor is a good start to understanding the cross-section of expected stock returns. Firms will invest a lot when their profitability is high and the cost of capital is low. As such, controlling for profitability, investment should be negatively correlated with expected returns, and controlling for investment, profitability should be positively correlated with expected returns. The new three-factor model reduces the magnitude of the abnormal returns of a wide range of anomalies-based trading strategies, often to insignificance. The model's performance, combined with its economic intuition, suggests that it can be used to obtain expected return estimates in practice.

We study the performance of mean-variance optimized (MVO) equity portfolios for retail investors, in various markets in the U.S. and around the world. Actively managed equity mutual funds have relatively high fees and tend to underperform their benchmark. Index funds such as ETFs still charge appreciable fees, and only deliver the performance of the benchmark. We find that an MVO is relatively easy to manage by a retail investor, and that they tend to outperform their benchmark or, at worst, equal its performance, even after adjusting for risk. Moreover, we show that the performance of these funds is not particularly sensitive to the frequency at which they are rebalanced so that, in the limit, an investor might have to rebalance her portfolio only once per year. This last finding translates into very low trading costs, even for a retail investors. Thus, we conclude that MVOs offer an easy, cheap alternative for a retail investors to invest in the world’s equity markets.

Implementations of the Standard Initial Margin Model (SIMM) and the Sensitivity Based Approach (SBA) in the Fundamental Review of the Trading Book (FRTB), both call for the calculation of sensitivities with respect to a standardised set of risk factors. Since standard factors are generally collinear and pricing functions are possibly rough, finding sensitivities qualifies as a mathematically ill-posed problem for which analytical derivatives do not provide a robust solution. Numerical instabilities are particularly problematic since they hamper reconciliation and make collateral optimisation strategies inefficient.

In this article, we introduce a method for calculating sensitivities based on ridge regressions to keep sensitivities small and stable. We find that a drift term and FX cross-gammas significantly improves the accuracy of the P&L explain achieved in the SIMM methodology. The method implies rigorous upper bounds on errors in P&L explain, on which basis we adjust Initial Margin conservatively in order to pass back-testing benchmarks.

Inspired by visualization techniques à la Feynman, we introduce Stochastic Flow Diagrams (SFDs), a new mathematical approach to represent complex dynamic systems into a single weighted digraph. This topological representation provides a way to visualize what otherwise would be a morass of equations in differences. SFDs model the propagation and reverberation that follows a shock. For example, reverberation explains how a shock to a financial system can initiate a sequence of events that lead to a crash long after the occurrence of the shock. SFDs can simulate systems in stable, steady or explosive state. SFDs add Topology to the Statistical and Econometric toolkit. We believe that SFDs will help policy makers, investors and researchers communicate and discuss better the complexity of dynamic systems.

Academics and practitioners have extensively studied Value-at-Risk (VaR) to propose a unique risk management technique that generates accurate VaR estimations for long and short trading positions and for all types of financial assets. However, they have not succeeded yet as the testing frameworks of the proposals developed, have not been widely accepted. A two-stage backtesting procedure is proposed to select a model that not only forecasts VaR but also predicts the losses beyond VaR. Numerous conditional volatility models that capture the main characteristics of asset returns (asymmetric and leptokurtic unconditional distribution of returns, power transformation and fractional integration of the conditional variance) under four distributional assumptions (normal, GED, Student-t, and skewed Student-t) have been estimated to find the best model for three financial markets, long and short trading positions, and two confidence levels. By following this procedure, the risk manager can significantly reduce the number of competing models that accurately predict both the VaR and the Expected Shortfall (ES) measures.

In this thesis, problems in the realm of high frequency trading and optimal market making are established and solved in both single asset and multiple asset economies. For an agent that is averse to holding large inventories for long periods of time, optimal high frequency trading strategies are derived via stochastic control theory and solving the corresponding Hamilton-Jacobi-Bellman equations. These strategies are analyzed and it is shown that both inventory control and accounting for adverse selection play critical roles in the success of an algorithmic trading strategy.

In the single asset problem, a market maker actively modifies her limit quotes in an economy with asymmetric information. She attempts to keep her inventory small and posts her limit orders in the limit order book at a depth that mitigates her adverse selection risk, while not posting too deep in the book as to generate no trade flow. In addition to this behaviour, a profit maximizing investor trading in multiple assets also seeks out statistical arbitrage opportunities and acts aggressively via the submission of market orders when it is deemed optimal to do so.

Throughout this thesis, numerical and practical considerations are made a priority. Full scale calibration and estimation methods are given in detail, as well as dimensional reductions for large scale numerical procedures, where appropriate. The bridge from abstract mathematical theory to practical real-time implementation is made complete as an entire chapter is dedicated to applications on real data.

Technical Analysis (TA) is a security analysis methodology based on the study of past market data. Although it has been criticized by academics and the profitability of many related strategies has been statistically rejected, TA remains highly popular among practitioners and retail investors, in particular. We analyze the role of TA for retail investors trading structured products (knock-outs and warrants) on Stuttgart Stock Exchange. We find a 35% increase in trading activity on days of chart pattern trading signals and an 11% increase for moving average signals. The increase in activity typically reverses on the following trading days. Furthermore, we identify trading characteristics of round-trip trades and find that trades associated with TA trading signals differ. First, we find significantly higher raw returns in TA-related trades while leverage levels at purchase as well as holding duration appear to be lower. Second, the shape of the realized return distribution of trades in accordance to TA signals is distinct from their peer groups. Specifically, realized returns are significantly less left-skewed (more right-skewed). In this regard, retail investors using TA methods might be less prone to the disposition effect due to the system-based trading approach. If we assume a general gambling intention with respect to the considered products, then TA-related trades tend to reach this goal more effectively.

We test a Wall Street investment strategy, pairs trading, with daily data over 1962-2002. Stocks are matched into pairs with minimum distance between normalized historical prices. A simple trading rule yields average annualized excess returns of up to 11 percent for selffinancing portfolios of pairs. The profits typically exceed conservative transaction costs estimates. Bootstrap results suggest that the pairs effect differs from previously-documented reversal profits. Robustness of the excess returns indicates that pairs trading profits from temporary mis-pricing of close substitutes. We link the profitability to the presence of a common factor in the returns, different from conventional risk measures.