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We can use pandas to find the correlation between each indicator of the same type momentum, volume, trend, volatility , then select only the least correlated indicators from each type to use as features.
That way, we can get as much benefit out of these technical indicators as possible, without adding too much noise to our observation space. It turns out that the volatility indicators are all highly correlated, as well as a couple of the momentum indicators.
Next we need to add our prediction model. For example, our agent can be learn to be more cautious trusting predictions when the confidence interval is small and take more risk when the interval is large.
One might think our reward function from the previous article i. While our simple reward function from last time was able to profit, it produced volatile strategies that often lead to stark losses in capital. To improve on this, we are going to need to consider other metrics to reward, besides simply unrealized profit.
While this strategy is great at rewarding increased returns, it fails to take into account the risk of producing those high returns. Investors have long since discovered this flaw with simple profit measures, and have traditionally turned to risk-adjusted return metrics to account for it. The most common risk-adjusted return metric is the Sharpe ratio. To maintain a high Sharpe ratio, an investment must have both high returns and low volatility i. The math for this goes as follows:.
This metric has stood the test of time, however it too is flawed for our purposes, as it penalizes upside volatility. For Bitcoin, this can be problematic as upside volatility wild upwards price movement can often be quite profitable to be a part of. This leads us to the first rewards metric we will be testing with our agents.
The Sortino ratio is very similar to the Sharpe ratio, except it only considers downside volatility as risk, rather than overall volatility. As a result, this ratio does not penalize upside volatility.
The second rewards metric that we will be testing on this data set will be the Calmar ratio. All of our metrics up to this point have failed to take into account drawdown. Drawdown is the measure of a specific loss in value to a portfolio, from peak to trough.
Large drawdowns can be detrimental to successful trading strategies, as long periods of high returns can be quickly reversed by a sudden, large drawdown. To encourage strategies that actively prevent large drawdowns, we can use a rewards metric that specifically accounts for these losses in capital, such as the Calmar ratio.
Our final metric, used heavily in the hedge fund industry, is the Omega ratio. On paper, the Omega ratio should be better than both the Sortino and Calmar ratios at measuring risk vs.
To find it, we need to calculate the probability distributions of a portfolio moving above or below a specific benchmark, and then take the ratio of the two. The higher the ratio, the higher the probability of upside potential over downside potential. While writing the code for each of these rewards metrics sounds really fun, I have opted to use the empyrical library to calculate them instead.
Getting a ratio at each time step is as simple as providing the list of returns and benchmark returns for a time period to the corresponding Empyrical function. Any great technician needs a great toolset. Instead of re-inventing the wheel, we are going to take advantage of the pain and suffering of the programmers that have come before us. TPEs are parallelizable, which allows us to take advantage of our GPU, dramatically decreasing our overall search time.
In a nutshell,. Bayesian optimization is a technique for efficiently searching a hyperspace to find the set of parameters that maximize a given objective function. In simpler terms, Bayesian optimization is an efficient method for improving any black box model. It works by modeling the objective function you want to optimize using a surrogate function, or a distribution of surrogate functions. That distribution improves over time as the algorithm explores the hyperspace and zones in on the areas that produce the most value.
How does this apply to our Bitcoin trading bots? Essentially, we can use this technique to find the set of hyper-parameters that make our model the most profitable. We are searching for a needle in a haystack and Bayesian optimization is our magnet. Optimizing hyper-parameters with Optuna is fairly simple. A trial contains a specific configuration of hyper-parameters and its resulting cost from the objective function. We can then call study.
In this case, our objective function consists of training and testing our PPO2 model on our Bitcoin trading environment. The cost we return from our function is the average reward over the testing period, negated. We need to negate the average reward, because Optuna interprets lower return value as better trials. The optimize function provides a trial object to our objective function, which we then use to specify each variable to optimize.
The search space for each of our variables is defined by the specific suggest function we call on the trial, and the parameters we pass in to that function. For example, trial. Further, trial. The study keeps track of the best trial from its tests, which we can use to grab the best set of hyper-parameters for our environment. I have trained an agent to optimize each of our four return metrics: simple profit, the Sortino ratio, the Calmar ratio, and the Omega ratio.
Before we look at the results, we need to know what a successful trading strategy looks like. For this treason, we are going to benchmark against a couple common, yet effective strategies for trading Bitcoin profitably. Believe it or not, one of the most effective strategies for trading BTC over the last ten years has been to simply buy and hold. The other two strategies we will be testing use very simple, yet effective technical analysis to create buy and sell signals.
While this strategy is not particularly complex, it has seen very high success rates in the past. RSI divergence. When consecutive closing price continues to rise as the RSI continues to drop, a negative trend reversal sell is signaled. A positive trend reversal buy is signaled when closing price consecutively drops as the RSI consecutively rises. The purpose of testing against these simple benchmarks is to prove that our RL agents are actually creating alpha over the market.
I must preface this section by stating that the positive profits in this section are the direct result of incorrect code. Due to the way dates were being sorted at the time, the agent was able to see the price 12 hours in advance at all times, an obvious form of look-ahead bias.
This has since been fixed, though the time has yet to be invested to replace each of the result sets below. Please understand that these results are completely invalid and highly unlikely to be reproduced. That being said, there is still a large amount of research that went into this article and the purpose was never to make massive amounts of money, rather to see what was possible with the current state-of-the-art reinforcement learning and optimization techniques.
So in attempt to keep this article as close to the original as possible, I will leave the old invalid results here until I have the time to replace them with new, valid results. This simple cross validation is enough for what we need, as when we eventually release these algorithms into the wild, we can train on the entire data set and treat new incoming data as the new test set. Watching this agent trade, it was clear this reward mechanism produces strategies that over-trade and are not capable of capitalizing on market opportunities.
The Calmar-based strategies came in with a small improvement over the Omega-based strategies, but ultimately the results were very similar. Remember our old friend, simple incremental profit?