7. Analysis of performance of trading strategies

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Presentation transcript:

7. Analysis of performance of trading strategies 7.1 Basic concepts “It is hard to make predictions, especially about the future” (Mark Twain) => standard disclaimer of asset management institutions : “Past investment performance does not guarantee future returns”. Back testing: prediction models are fitted (in-sample) and tested (out-of-sample) using past empirical data. Walk-forward testing: for 10-year sample, 1-5-year in-sample, 6th year out-of-sample (1-5,6); then (2-6, 7), etc. Usually, variance-stationary models. More is better? What’s S&P 500? Regime shifts caused by macroeconomic events or changes in regulatory policies (e.g. introduction of Euro in 1999, changes in the up-tick rule, etc.) => Markov-switching models (Tsay (2005)).

7. Analysis of performance of trading strategies 7.1 Basic concepts (continued) Danger of over-fitting: “too good to be true” in-sample accuracy => disaster out-of-sample (fitting the noise). MLE-based Akaike information criterion (AIC): AIC = -2 ln[L(n, N)]/N + 2n/N L(n, N) is likelihood for N points in sample and n model parameters. For ARMA(p, q) with Gaussian noise, AIC(p, q, N) = ln(σp,q2) +2(p+q)/N. Optimal ARMA(p, q) yields minimal AIC. Alas, optimal ARMA(p, q) in-sample may not be optimal out-of-sample (Hansen (2010)). Data snooping bias: the best predictor in the UN database for the S&P 500 stock index is production of butter in Bangladesh (Sullivan et al (1999)). Resampling!!!

7. Analysis of performance of trading strategies 7.2 Performance measures Performance is studied for a time interval >> round-trip transaction. Market imperfections: bid/ask spread, finite liquidity, transaction fees. - Realized (!) total (compound) return – ultimate benchmark R = (1 + r1)(1+r2)… - 1 Is this just luck? - Percentage of winning trades p - Ratio of average winning amount to average losing amount r - Kelly’s criterion for estimating the optimal fraction of trading capital, f, to be used in each trade: f = (pr – 1 + p)/r – valid only asymptotically (be careful!.. (Thorp (2006), Poundstone (2006)).

7. Analysis of performance of trading strategies 7.2 Performance measures (continued) - Multiple trades => probability distribution => comparing strategies - If distribution ~ N(µ, σ), t-value t = Check null hypothesis (µ = 0) using t distribution with N-1 degrees of freedom. - Comparing two strategies (or buys and sells (LeBrock et al (1992)): t = Usually not N(µ, σ)... Hence Wilcoxon (Mann-Whitney) test for medians and Kolmogorov-Smirnov test.

7. Analysis of performance of trading strategies 7.2 Performance measures (continued 2) - Sharpe ratio => Sortino ratio (only negative returns are counted in σ). - Informational ratio for comparing with (buy-and-hold) index strategy: IR = (E[ri] - E[r0])/σi0 - Maximum drawdown: maximum price drop after its peak MD = max[ max X(s) - X(t) ] t [0, T] s [0, t] For random walk with no drift (Magdon-Ismail & Atiya (2004)) : E[MD] = 1.2533σ - Calmar ratio: Sharpe ratio with σ => MD - Number of consecutive losing trades: no strategy works forever...

Max Drawdown