Convert index trading to option strategies via LSTM architecture

AbstractIn the past, most strategies were mainly designed to focus on stocks or futures as the trading target. However, due to the enormous number of companies in the market, it is not easy to select a set of stocks or futures for investment. By investigating each company's financial situation and the trend of the overall financial market, people can invest precisely in the market and choose to go long or short. Moreover, how to determine the position size of the transaction is also a problematic issue. In the past, many money management theories were based on the Kelly criterion. And they put a certain percentage of their total funds into the market for trading. Nonetheless, three massive problems cannot be overcome. First, futures are leveraged transactions, and extra funds must be deposited as margin. It causes that the position size is hard to be estimated by the Kelly criterion. The second point is that the trading strategy is difficult to determine the winning rate in the financial market and cannot be brought into the Kelly criterion to calculate the optimal fraction. Last, the financial data are always massive. A big data technique should be applied to resolve this issue and enhance the performance of the framework to reveal knowledge in the financial data. Therefore, in this paper, a concept of converting the original futures trading strategy into options trading is proposed. An LSTM (long short-term memory)-based framework is proposed to predict the profit probability of the original futures strategy and convert the corresponding daily take-profit and stop-loss points according to the delta value of the options. Finally, the proposed framework brings the results into the Kelly criterion to get the optimal fraction of options trading. The final research results show that options trading is closer to the optimal fraction calculated by the Kelly criterion than futures trading. If the original futures trading strategy can profit, the benefits after converting to options trading can be further superior

Practical implementation of the Kelly criterion: optimal growth rate, number of trades, and rebalancing frequency for equity portfolios

We develop a general framework to apply the Kelly criterion to the stock market data, and consequently, to portfolio optimization. Under few conditions, using Monte Carlo simulations with different scenarios we prove that the Kelly criterion beats any other approach in many aspects. In particular, it maximizes the expected growth rate and the median of the terminal wealth. We also show that, under a normal distribution of returns, the Kelly criterion has the best performance in the long run. Next, we optimize a portfolio with the Kelly criterion with no leverage and no short selling conditions and show that this portfolio lays in the mean-variance efficient frontier and has higher expected return and higher variance, although it is less diversified, respect to the tangent portfolio optimized under the Markowitz approach. Finally, we implement a dynamic strategy applied on the European stock market data and compare the results between the tangent and the optimal Kelly portfolios. In a dynamic setting, the rolling Kelly portfolio outperforms competitors particularly in the case of rebalanced portfolios optimized with a 2-years window width

How to lose money in derivatives: examples from hedge funds and bank trading departments

What makes futures hedge funds fail? The common ingredient is over betting and not being diversified in some bad scenarios that can lead to disaster. Once troubles arise, it is difficult to take the necessary actions that eliminate the problem. Moreover, many hedge fund operators tend not to make decisions to minimize losses but rather tend to bet more doubling up hoping to exit the problem with a profit. Incentives, including large fees on gains and minimal penalties for losses, push managers into such risky and reckless behavior. We discuss some specific ways losses occur. To illustrate, we discuss the specific cases of Long Term Capital Management, Niederhoffer’s hedge fund, Amaranth and Société Genéralé. In some cases, the failures lead to contagion in other hedge funds and financial institutions. We also list other hedge fund and bank trading failures with brief comments on them

Trading foreign exchange carry portfolios

Foreign exchange carry trades involve buying high yielding currencies while selling low yielding currencies. Contrary to the implications of the uncovered interest parity condition, carry trades have generated consistent profits in the past decades. As foreign exchange has gained increased relevance as an asset class in its own, the carry trade emerged as a major driver of foreign exchange market turnover. Given the widespread use and ease of implementation of carry strategies, active currency managers should be evaluated relative to a benchmark which incorporates a proxy for carry trade returns. Within this thesis we study the profitability of various carry portfolio strategies on a very recent data set ranging from the 1st of January 1999 to the 5th of March 2010. Within three distinct empirical chapters we analyse whether different asset allocation, market-timing and money management methodologies have the potential to improve the performance of a simple carry portfolio, such as the one implemented by the Currency Harvest exchange traded fund by Deutsche Bank. Three main findings emerge from our investigation on carry trade portfolios. First, we find that a simple carry trade proxy is difficult to outperform with asset allocation and market-timing techniques. Nevertheless, we would not conclude that professional currency managers should cease to implement carry strategies, since they can add value to the investment process by successfully addressing the issue of optimal leveraging for carry trades. Second, we find that the portfolio flows of carry traders do uncover pockets of predictability in the FX market. Strategies which aim at front-running the trades of carry strategies, do generate positive returns with low correlations to traditional carry trade strategies and therefore offer good diversification vehicles for carry portfolios. Lastly, we find that while profitable market-timing seems feasible on historical backtests, the results are strongly dependent on the correctly timing the credit crisis. Thus, we note that our results are affected by a lookback bias. We posit that before the credit crisis, portfolio managers would not have had the foresight to select the correct market-timing indicators. We thus advocate a broad diversification of risk indicators for carry trade timing

Forecasting stock market return with nonlinearity: a genetic programming approach

The issue whether return in the stock market is predictable remains ambiguous. This paper attempts to establish new return forecasting models in order to contribute on addressing this issue. In contrast to existing literatures, we first reveal that the model forecasting accuracy can be improved through better model specification without adding any new variables. Instead of having a unified return forecasting model, we argue that stock markets in different countries shall have different forecasting models. Furthermore, we adopt an evolutionary procedure called Genetic programming (GP), to develop our new models with nonlinearity. Our newly-developed forecasting models are testified to be more accurate than traditional AR-family models. More importantly, the trading strategy we propose based on our forecasting models has been verified to be highly profitable in different types of stock markets in terms of stock index futures trading

Behaviour of futures markets and implication for portfolio choice

First, we document the co-existence of the time series momentum and of the term structure factors in the global commodity futures market. We demonstrate that the strategies based on the joint time series momentum and term structure trading signal outperform time series momentum only strategies and term structure only strategies. Second, we propose a Multivariate Volatility Regulated Kelly strategy, which imposes extra variance penalization compared to the Kelly criterion. We furthermore demonstrate the superiority of our method in relatively low correlated portfolios, relative to the fractional Kelly and full Kelly strategies. The simulation results and Chinese commodity future empirical results strongly support our method. Third, we combine the shrinkage theory and CUSUM change point detection in order to improve the covariance estimators. The change point embedded covariance estimator can pe1jorm better than any shrinking covariance estimators in the portfolio management. We empirically test different shrinkage estimators based portfolios in global futures markets

ESSAYS IN MATHEMATICAL FINANCE AND MACHINE LEARNING

This dissertation consists of three independent essays. Chapter 1, “Exploring Machine Learning in Fixed Income Market” designs a decision support framework that can be used to provide suggested indications of future U.S. on-the-run 10Y Treasury market direction along with the associated probability of making that move. My primary innovation is proposing a framework for applying machine learning methods to U.S. fixed income market. The framework includes a newly proposed performance metric that combines profitability and randomness to select proper outperform models and a sliding window cross-validation method for streaming data learning. I find the Random Forest method provides a decent Sharpe ratio for trading U.S. 10Y Treasury in a “quarantined” testing set but underperforms on Spread trading (10Y Treasury and an asset swap) and Volatility trading (1M10Y Swaption Straddle). Chapter 2, “A Robust Trend Following Framework: Theory and Application” constructs a trend-following signal based on statistical theory and analytically analyzes its properties. I manage to reconcile our model's theoretical results with stylized facts about trend-following investing – the presence of a "CTA smile". Leveraging on the theoretical results, we proposed a prototype trend-following framework that is diversified across time-frames and assets. I also discuss the portfolio and risk management of the trend-following strategy. I illustrate the risk-budgeting approach can be used to enhance the trend-following framework. Different approaches to control the costs have also been discussed. Chapter 3, “Markov Modulated Bilateral Gamm Mean Reversion Model” proposed a Markov modulated Bilateral gamma mean-reversion model. Market practitioners argue the market has high volatility regimes and low volatility regimes. I argue the model can capture the mean reversion, asymmetries of returns of up moves and down moves, and other empirical regularities. I derived the characteristic function and provide preliminary parameter estimates by calibrating the model to VIX Index upon the assumption of stationary distribution to avoid using filter methodologies

The statistical properties of technical trading rules

A portfolio of 200 heterogeneous technical trading rules is tested for their directional predictabilities on the DJIAI from 1988 to 1999. We also explore several nonparametric techniques designed for brain research, and detected possibly other forms of dependencies more significant than the traditional linear autocorrelation for the time series. The overall conditional mean directional predictability is 46%. 36 percent of the rules have more than 50% directional predictability, and the top 20 percent rules has a 73% directional predictability, whereas the bottom 80 percent has a directional predictability of 40%. Buy signals consistently generate higher predictability than sell signals but do not commensurate with their respective risk levels. The relationship between two sub-periods is not stable, while the difference between the conditional mean directional predictability of buy only and sell only signals is highly significance. The belief that most successful rules have a directional predictability of 25% to 50% coincides with the mode of distribution. We observe counter intuitive relationship between volatility and directional predictability. The results of directional predictability in a downtrend concur with the argument that buy-and-hold strategy is not a suitable benchmark. Attempts are made to tackle the issues of small sample bias, data snooping, size of test window, bootstrap or t-test, and homogeneity. Issues are discussed on empirical testing for their real world applications, statistical and non-statistical interpretations; also randomness test; physical or biological science approach