Maximizing Returns: Forex Trading And Mining Strategies In Coventry – Optimizing trading strategy parameters with backtesting has one major problem: there are not enough historical trades to achieve statistical significance. Any optimal parameters that are found may suffer from data opacity, and they may not have optimality in the out-of-sample period. For this reason, optimizing the parameters of a trading strategy usually does not add any value. On the other hand, since the input data are prices, not trades, and we have a lot of prices, it is more reliable to optimize time series model parameters (e.g., autoregressive or maximum likelihood fit for GARCH models). Fortunately, it turns out that there are clever ways to take advantage of the ease of optimizing time series models to optimize trading strategy parameters.
An elegant way to optimize a trading strategy is to use stochastic optimal control theory methods – elegant, that is, if you are mathematically sophisticated and able to solve the Hamilton-Jacobi-Bellman (HJB) equation analytically (Cartea et al. ) However However, this will only work when the underlying time series is well known, i.e. the continuous Ornstein-Uhlenbeck (OU) process underlying all mean-reverting price series. This OU process is clearly represented by stochastic differential equations. Furthermore, the HJB equation can often be solved if the objective function has a simple form, such as a linear function. If your price series is clearly represented by the OU process, and your goal is to maximize profits as a linear function of the price series, then stochastic optimal control theory will give you an analytically optimal trading strategy: exact entry and exit thresholds given as a function of the OU process parameters. There is no longer any need to find such an optimal threshold by trial and error during the tedious test of inviting overfitting on a small number of trades. As mentioned above, the parameters of the OU process can be very well tuned, and in fact there is an analytical maximum likelihood solution for this fit given in Leung et. which
Maximizing Returns: Forex Trading And Mining Strategies In Coventry
Many optimization problems turn to simulation when no analytically optimal solution is available. Examples of such methods include simulated annealing and Markov chain Monte Carlo (MCMC). Here we will do the same thing: if we fail to find an analytical solution to the optimal trading strategy, but we can fit our underlying price series fairly well to a standard discrete time series model such as ARMA, we can simulate many examples. base price series. We will retest our trading strategy on each instance of the simulated price series to find the best trading parameters that produce the highest Sharpe ratio. This process is much more robust than applying backtesting to real time series because there is only one real price series, but we can simulate as many price series as we want (all under the same ARMA process). This means we can simulate as many trades as we want and get the optimal trading parameters with as much accuracy as we want. It is almost as good as the analytical solution.
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Here is a small example of this procedure. We want to find an optimal strategy that trades AUDCAD every hour. First, we fit an AR(1)+GARCH(1, 1) model to the data
Medium price. The maximum likelihood adjustment is performed using a one-year moving window of historical prices, and the model is updated monthly. We use MATLAB’s Econometrics Toolbox to set this up. After finding the sequence of monthly patterns, we can use them to predict the expected difference between the average log price and the log return at the end of the time bar. Therefore, a simple trading strategy can be tried: if the expected log return on the next line is K times the expected volatility (square root of the volatility) of the log return, then buy AUDCAD and hold on one bar, and vice versa for shorts. But what is the optimal K?
After fitting the new AR(1)+GARCH(1, 1) model according to the above procedure, we use it.
The registration price of the hourly bar with the next month’s price. In fact, we simulate this 1000 times, generating 1000 time series within a month, each with the same number of time bars. We then iterate through all possible values of K and remember which K produces the highest Sharpe ratio for each simulated time series. We choose K that gives the best Sharpe ratio out of 1000 simulated time series (that is, we
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Of the distribution of optimal K over the simulation series). This is the K sequence (one per month) that we use for our final backtest. Below is the sample distribution of the optimal K for the month and the corresponding distribution of the Sharpe ratio.
Interestingly, the optimal K mode is zero in any month. This certainly makes for a simple trading strategy: buy only when the expected log return is positive, and vice versa for shorts. Assuming zero transaction costs and average pricing, the CAGR is approximately 4.5%. Here is the cumulative yield curve:
You say: “This can’t be optimal because I can trade AUDCAD hourly bars with better returns and Sharpe ratios!” Of course, optimal in this case only means optimal within a particular universe of strategies, assuming the basic AR(1)+GARCH(1, 1) price series model. Our strategic world is very simple: buy or sell regardless of whether the expected return exceeds the expected volatility multiple. But this procedure can be extended to any price series pattern you can think of and any strategy you can think of. In any case, this greatly reduces the possibility of overloading.
We took a similar idea from Dr. Ng’s computational research in condensed matter physics a few months ago and devised this procedure for our own use (see Ng.
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Here or here). However, we later discovered that a similar procedure had already been described in a paper by Carr et al.
Ernie is a popular quantitative hedge fund manager and quantitative finance author. He previously served as IBM T.J. used his experience in machine learning. Watson Research Center’s Human Language Technology Group, Morgan Stanley’s Data Mining and Artificial Intelligence Group, and Credit Suisse’s Horizon Trading Group.
Ray Ng is a Quantitative Strategist at QTS. He received his Ph.D. in Theoretical Condensation Physics from McMaster University.
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