Part 1 Back Testing Quantitative Trading Strategies

Transcription

1 Part 1 Back Testing Quantitative Trading Strategies A Guide to Your Team Project 1 of 21 February 27, 2017

2 Pre-requisite The most important ingredient to any quantitative trading strategy is data that are compatible with the nature of the strategy. For example, for intra-day trading strategy, you need at least one-minute bar data. For HFT, you need at leas tick data for backtesting. For ulta HFT, you need low-level messages received by the exchanges. 2 of 21 February 27, 2017

3 Data Example S/N Date Period Time1 Time2 Open High Low OF_ Close Trades Volume Trades OF_ Vol :00:00 7:00:00 7:00: :01:00 7:00:57 7:00: :02:00 7:02:19 7:02: :03:00 7:03:32 7:03: :04:00 7:03:32 7:03: :05:00 7:03:32 7:03: :06:00 7:03:32 7:03: :07:00 7:03:32 7:03: :08:00 7:08:20 7:08: Period: 1-minute interval Time 1: time at which the first trade in the 1-minute interval occurs Time 2: time at which the last trade in the 1-minute interval occurs OF_Trades: order flow in number of trades over 1minute OF_Vol: order flow in signed volume over 1 minute 3 of 21 February 27, 2017

4 Intra-Day BackTesting on One-Minute Data? You have a trading strategy, and it has a parameter denoted by θ. You have historical data of futures (or any other financial instruments). Suppose in your historical data, your trading strategy finds 200 trading signals to short (or to long). Suppose the parameter θ is the holding period before squaring off your position. You separate the 200 signals into two portions: o o Say, 70% of the signals are used for finding an optimal value of θ such that it gives the best in-sample performance in this 70%. Fix this optimal θ, and measure the out-of-sample performance of the trading strategy in the other 30% of the signals. 4 of 21 February 27, 2017

5 Buying and Selling in Back-Testing Ideally, you should have the best bid price and the best ask price at the beginning and also at the end of every minutes. When selling one contract at the beginning of t+1, you sell at the best bid price. When buying one contract at the end of t+1+θ, you buy at the best offer price. Your task is to find an optimal θ that gives the best performance after all costs such as commissions and clearing fees (if any). For the project, the per-contract commission is assumed to be 500 yens. 5 of 21 February 27, 2017

6 In-Sample Training of θ For every signal, the size of your position is one contract. You need to know the commission for trading one contract (assumed to be 500 yens per contract). When the signal is generated at time t, you cannot trade at time t but at (the beginning of) time t+1. As a risk management policy, you must square off any outstanding position before the trading session closes. At time t, you short, and at time t+1+θ, you square off your short position. Your task is to find an optimal θ that gives the best performance. 6 of 21 February 27, 2017

7 Specifically>>>> You let θ equal to 1 minute. Measure the performance for the 70% in-sample signals. You let θ equal to 2 minute. Again measure the insample performance. Do likewise, for θ up to 20 minutes. Obviously, as θ becomes larger, the number of tradable signals is smaller as time t+1+θ could be after the end of the trading session 7 of 21 February 27, 2017

8 What is a good performance measure? Before answering the question, look at the numbers generated by back-testing. A sequence of P&Ls after round-trip commission costs and other costs Based on the P&Ls, categorize the signals as correct and incorrect Count the numbers of correct and incorrect signals, which are denoted by N c and N i, respectively. The winning probability is p = N c N c + N i Obviously, higher p is better. 8 of 21 February 27, 2017

9 Reward-to-Risk Ratio Compute the average positive P&Ls of correct signals. Do likewise for incorrect signals. Let these averages be A c and A i, respectively. So A c can be interpreted as the average gain when the signal is correct, and A i is the average loss amount if the signal is incorrect. The reward-to-risk ratio is r = A c A i Obviously, higher r is better. 9 of 21 February 27, 2017

10 Sharpe Ratio and t statistic Compute the average P&L from the sequence of n number of P&Ls. Denote it by M n. Compute the unbiased standard deviation, denoted by S n. Sharpe ratio is simply the risk-adjusted P&L Sharpe = M n S n Given the null hypothesis of zero mean P&L, the t- statistic is, with n being the total number of signals in the sample, t = n M n 10 of 21 February 27, 2017 S n

11 THE Performance Measure The t statistic is a statistically sound measure. It shows the level of significance of the average P&L against the amount of variation in the in-sample P&L. Therefore, you mainly use the t statistic as the benchmark. You want to find θ * such that t is the largest possible. In other words, you are solving this maximization problem: M n θ * arg max n Sn 11 of 21 February 27, 2017

12 An Example of In-Sample Performance Holding Time Number of Total P&L Average Average Probability Trades (after comms) Gain Loss of win 3 70 $2, $ $ $3, $ $ $3, $ $ $3, $ $ $3, $ $ $3, $ $ $3, $ $ $4, $ $ $3, $ $ $3, $ $ $4, $ $ $4, $ $ $4, $ $ $4, $ $ t- statistic 12 of 21 February 27, 2017

13 What is the Performance of the Trading Strategy? It is the performance of the trading strategy on out-ofsample signals. Typically, in-sample performance measure is higher than that of out-of-sample. If the t statistic of out-of-sample performance is bigger than 2, then the quantitative trading strategy may generate consistent alpha. 13 of 21 February 27, 2017

14 When does a trading strategy stop working? No trading strategy will work forever. A good strategy may deteriorate over time! When to pull the plug? As a rule of thumb, look at the rolling 30-signal t statistic. If it becomes statistically insignificant, stop the trading strategy. 14 of 21 February 27, 2017

15 Equity Curve From the in-sample subsequence of P&Ls, x t, you can construct an equity curve as follows: In other words, C 1 = x 1, C 2 = C 1 + x 2 = x 1 + x 2, C 3 = C 2 + x 2 = x 1 + x 2 + x 3, and so on C t x s s 1 C n = C n-1 + x n = x 1 + x x n t 15 of 21 February 27, 2017

16 Illustration of Equity Curve and Drawdown or longest Source: Quantitative Trading: How to Build Your Own Algorithmic Trading Business (2009) 16 of 21 February 27, 2017

17 Performance Metrics: Maximum Drawdown The maximum drawdown characterises the largest peak-to-trough drop in the equity curve over a particular time period (usually annual). This is most often quoted as a percentage. LFT strategies will tend to have larger drawdowns than HFT strategies, due to a number of statistical factors. A historical backtest will show the past maximum drawdown, which is a good guide for the future drawdown performance of the strategy. 17 of 21 February 27, 2017

18 Sensitivity Analysis Sound, fundamental reasoning for parameter choices should, with all other factors considered, lead to a smoother parameter curve or surface. If you have a very jumpy performance surface, it often means that a parameter is not robust. There is a vast literature on multi-dimensional optimisation algorithms and it is a highly active area of research. 18 of 21 February 27, 2017

19 Examples of Sensitivity Analysis Good example: Parameter Sharpe Ratio 10.0% 10.3% 11.1% 11.5% 14.2% 12.8% 10.9% 9.2% 8.7% Sharpe ratio increases then decreases Bad example Parameter Sharpe Ratio 11.0% 6.3% 16.0% -5.5% 19.4% 2.0% 11.9% 19.2% 9.7% Sharpe ratio appears random 19 of 21 February 27, 2017

20 Project Administration What you need to prepare as a team: a project report and a set of presentation slides. Each team member will evaluate the performance and contribution of other members in the team, so as to be fair to the hard working, and persons with brilliant idea and strong skillset. If you are not presenting, you are to evaluate the presentation performance of the other teams. 20 of 21 February 27, 2017

21 Additional Incentives My ex prop firm is looking for a full-time quantitative researcher. Other boutique hedge funds are also looking for quantitative researchers. Usually a quant researchers, if doing exceptionally well, can transit to the role of a trader after a few years. If you worry too much about your academic grade, you probably won t survive in the jungle of trading. 21 of 21 February 27, 2017