Trend-following strategies for tail-risk hedging and alpha generation

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1 Trend-following strategies for tail-risk hedging and alpha generation Artur Sepp FXCM Algo Summit 15 June 2018

2 Disclaimer I Trading forex/cfds on margin carries a high level of risk and may not be suitable for all investors as you could sustain losses in excess of deposits. Leverage can work against you. The products are intended for retail and professional clients. Due to the certain restrictions imposed by the local law and regulation, German resident retail client(s) could sustain a total loss of deposited funds but are not subject to subsequent payment obligations beyond the deposited funds. Be aware and fully understand all risks associated with the market and trading. Prior to trading any products, carefully consider your financial situation and experience level. Any opinions, news, research, analyses, prices, or other information is provided as general market commentary, and does not constitute investment advice. The market commentary has not been prepared in accordance with legal requirements designed to promote the independence of investment research, and it is therefore not subject to any prohibition on dealing ahead of dissemination FXCM will not accept liability for any loss or damage, including without limitation to, any loss of profit, which may arise directly or indirectly from use of or reliance on such information. 2

3 Disclaimer II The above speaker is neither an employee, agent nor representative of FXCM and is therefore acting independently. The opinions given are their own, constitute general market commentary, and do not constitute the opinion or advice of FXCM or any form of personal or investment advice. FXCM neither endorses nor guarantees offerings of third party speakers, nor is FXCM responsible for the content, veracity or opinions of third-party speakers, presenters or participants. 3

4 Disclaimer III All statements in this presentation are the author personal views and not those of Julius Baer This presentation does not constitute investment advice Past performance is not indicative of future results 4

5 Trend-Following Strategies Risk profile of quant strategies: Convexity and Skeweness of realized returns Trend-following strategies: crisis-alpha and the dependence on the autocorrelation A toy model to understand the impact of the autocorrelation Building trend-following system with illustrations using FX futures contracts 5

6 Two key Quant Strategies workacross major asset classes and long-term horizons (Ilmanen, CFM, AHL) Carry Trend-Following Target Current/forward spread For FX use the rate differential: buy/sell high/low yield currencies Advantages Simple, perform most of the time Drawbacks Limited upside with negative skeweness and convexity Target Expected price performance For FX: buy/sell outperforming/underperforming pairs Advantages Positive skeweness and convexity Drawbacks Underperformance in rangebound markets 6

7 Trend-Following Strategies trade in liquid exchangetraded futures contracts and OTC forwards Diversified across major asset classes: 1. Stock indices 2. Fixed-income 3. Commodities 4. FX A typical algo/systematic trend-following program trades in instruments Different time horizon: 1. Fast-paced trend-followers with short look-back periods 2. Slow-paced trend-followers with long look-back periods Biggest CTA hedge funds: Winton, AHL, Aspect... with total of about billion AUM Key benchmark index: SG Trend-following CTAs (NEIXCTAT Index) from year

8 Risk Profile of Quant Strategies is measured by the skeweness and convexity 8

9 The convexity profile of quant investment strategies to the S&P 500 index 25% 20% 15% 10% Monthly Returns on Hedge Fund strats (EurekaHedge) vs S&P500 Index '05-18 Short Vol HF index = Short Convexity y = -2.02x x Long Vol HF Index = Zero Convexity y = -0.02x x Tail Risk HF Index = Long Convexity y = 1.17x x SG Trend-following CTAs = Long Convexity y = 1.03x x % 0% -5% -10% -15% -20% X=Monthly Return on S&P500 Index -25% -30% -20% -10% 0% 10% 20% 30% Y=Monthly return of HF strategies 9

10 Skeweness profile of quant investment strategies Positive skeweness does not guarantee positive convexity for long volhfs Trend-followers have insignificant skeweness for returns measured on monthly scales Skewness of monthly returns on Quant Hedge Fund strategies: S&P500 TR index Short Vol HFs Relative Value Vol HFs Long Vol HFs Tail Risk HFs SG Trendfollowing CTAs 10

11 Trend-Following CTAs deliver long term performance with robust risk profile with crisis-alpha 3.0 NAV of 1$ Investment Short Vol HF index SG Trend-following CTAs S&P500 TR index Long Vol HF Index Tail Risk HF Index Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15 Jan-16 Jan-17 Jan-18 11

12 CTA Smile: trend-followers deliver in both bear 1y Sharpe on the SG Trend d-following CTAs and bull markets Trend-Following CTA Smile: 1y trailing Sharpe ratio on SG Trend-following CTAs vs 1y Sharpe on the S&P 500 index y = 0.14x x R² = y Sharpe on the S&P 500 index 12

13 5.0% 4.0% 3.0% 2.0% 1.0% 0.0% -1.0% -2.0% -3.0% The risk profile of Trend-following CTAs is regime-dependent: positive skeweness in bear markets and zero skeweness in bull markets Average Quarterly Returns on SG Trend-following CTAs conditional on quantiles of returns on S&P 500 index: % All Sample: -35%<SP500<35% Bear Market 4.6% 0-25%Q: -35%<S&P500<-1% -1.8% 25-50%Q: - 1%<S&P500<2% -0.6% 50-75%Q: 2%<S&P500<6% Strong Bull Market 3.8% %Q: 6%<S&P500<35% Average Quarterly Return 5% 4% 3% 2% 1% 0% -1% -2% Average quarterly return vs skeweness on SG Trend-following CTAs conditional on quantiles of returns on the S&P 500 index: %Q: 6%<S&P500<35% Strong Bull Market 0-25%Q: - 35%<S&P500<-1% Bear Market 50-75%Q: 2%<S&P500<6% All Sample: - 35%<SP500<35% 25-50%Q: - 1%<S&P500<2% -3% Skeweness of Quarterly Returns 13

14 Trend-followers deliver in markets with strong autocorrelation / conditional predictability 14

15 Toy model helps understand the impact of autocorrelation on trend-following strategy Probability of Up Probability of Market Dynamics Move Down Move Symmetric Random Walk P + =1/2 P _ =1/2 Biased Up Drift P + =2/3 P _ =1/3 P Auto-Correlated Walk + =2/3 if R n-1 =+1 P _ =1 - P P + + =1/3 if R n-1 =-1 = +1, = + 1, = Market Expected Annual Volatility Sharpe Dynamics Return Symmetric Walk Biased Up Drift Auto-Correlated 0 Walk = =1 15

16 Illustrative path of simulated market returns Simulated Market Running Returns (using same randoms) Symmetric Random Walk Biased Up Drift Auto-Correlated Walk N

17 Toy model with three types of traders Trader type Position at End of Day W n Noise Trader +1, = 0.5 = 1, = 0.5 Long-Only Investor = 1 Trend-Follower = +1 = +1 1 = 1 252!" = 1 =1 17

18 Illustrative path of simulated equity curve for Symmetric Random Walk 40 Simulated Equity Curve for Symmetric Random Walk Noise Trader Long-Only Investor Trend-Follower N 18

19 Illustrative path of simulated equity curve for Biased Up Drift 90 Simulated Equity Curve for Biased Up Drift Noise Trader Long-Only Investor Trend-Follower N

20 Illustrative path of simulated equity curve for Auto-Correlated Walk 100 Simulated Equity Curve for Auto-Correlated Walk Noise Trader Long-Only Investor Trend-Follower N

21 Simulated Sharpe ratios using 100K paths: Auto-correlation is key for the performance of a trend-following strategy independently of overall drift Trend-follower performs under the two dynamics: 1. Strong performance in the auto-correlated random walk 2. Positive performance in the walk with the biased up drift but smaller than the performance of the Long-only investor Market/Trader Symmetric Random Walk Noise Trader Long-Only Investor Trend- Follower Biased Up Drift Auto-Correlated Walk

22 Construction of a Trend-Following System Time series transformation and normalization to variables with (about) unit standard deviation Smoothing and forecast of the normalized time series Mapping the signal into the position size Sizing the trade using volatility targeting Allocation in a portfolio of instruments and signals 22

23 FX Data Set using SCF continuous futures API using Quandl.com 7 USD FX futures contracts: EUR, GBP, JPY, AUD, CAD, NZD, CHF Free sample data from January 2005 to December 2014 Front month futures contracts with backwards ratio adjusted prices, roll on the first of month End-of-day price data with open/high/low/close 23

24 Simulated Performance of FX Futures Data Set 80% 60% 40% 20% Performance of FX futures roll strategies: 2005 to 2015 GBP EUR JPY AUD CAD CHF NZD EqualWeight Sharpe SkeweneMaxDD GBP % EUR % JPY % AUD % CAD % CHF % NZD % EqualWeight % 0% -20% -40% 24

25 Normalized Time Series are obtained by normalizing returns by recent volatility $ %&'( = $ Volatility Normalized Time Series For GBP futures Daily Weekly Monthly -5 Mar-14 Apr-14 May-14 Jun-14 Jul-14 Aug-14 Sep-14 Oct-14 Nov-14 Dec-14 25

26 Volatility normalized returns have about unit standard deviation 1.15 Running standard deviation of the volatility normalized timeseries Daily Weekly Monthly

27 Volatility normalized returns have stationary distribution Value and Running Quantiles of Weekly Vol-Normalized Returns Weekly Value Median 1-Std Lower Quantile 1-Std Upper Quantile Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 27

28 Normalized time series are smoothed with Exponential Moving Average with set Half-Life 100% 80% Contribution % to Signal from recent data as function of Half-Life 98% 92% 96% 92% 84% 71% Last week contribution 85% Last month contribution 73% Last year contribution 60% 50% 50% 40% 20% 0% 35% 13% 25% 6% 2% 0% 0% 0% 8 months 4 months 2 months 1 month 2 weeks 1 week Signal Half-Life 28

29 Illustration of EMA with Half-life of 2 months for Volatility Normalized Returns of GBP futures 1 EMA of Vol-Normalized Returns with Half-Life of 2 months Value Median 1-Std Lower Quantile 1-Std Upper Quantile 0-1 Dec-05 Dec-06 Dec-07 Dec-08 Dec-09 Dec-10 Dec-11 Dec-12 Dec-13 Dec-14 29

30 EWA time series are normalized to generate raw signal with about unit standard deviation Raw Signal Using Half-life of 2 months Value Median 2 1-Std Lower Quantile 1-Std Upper Quantile Dec-05 Dec-06 Dec-07 Dec-08 Dec-09 Dec-10 Dec-11 Dec-12 Dec-13 Dec-14 30

31 Raw Signal is mapped into the position size bounded between -1 and 1 Signal Mapping Functions For Position Sizing 1.0 Binary CappedLinear NormalCDF Sigmoid2 Sigmoid Raw Signal 31

32 Illustration of Position Size Using EMA with Half-life of 2 months for GBP futures Time Series of Position Size for GBP futures contract Binary CappedLinear NormalCDF Sigmoid2 Sigmoid Dec-05 Dec-06 Dec-07 Dec-08 Dec-09 Dec-10 Dec-11 Dec-12 Dec-13 Dec-14 32

33 Volatility estimation and forecast applied for both returns normalization and volatility targeting 30% 25% Time Series of EWA volatility for GBP futures contract Value Median 1-Std Lower Quantile 1-Std Upper Quantile 20% 15% 10% 5% 0% Dec-05 Dec-06 Dec-07 Dec-08 Dec-09 Dec-10 Dec-11 Dec-12 Dec-13 Dec-1 33

34 Volatility Targeting is applied to scale notional size to set level of risk % )' = $ *+, '( $ 400% 350% 300% Time Series of Notional Size with 15% Volatility Target for GBP futures Value 1-Std Lower Quantile Median 1-Std Upper Quantile 250% 200% 150% 100% 50% 0% Dec-05 Dec-06 Dec-07 Dec-08 Dec-09 Dec-10 Dec-11 Dec-12 Dec-13 Dec- 34

35 Parameterisation of Trend-Following Strategy should account for performance and risk profile Period for returns computation (daily, weekly, monthly) Weak impact - the higher the transaction costs, the longer scale Half-life parameter for trend smoothing High impact: the smaller half-life, the more rapidly changing signal with strategy generating stronger convexity Mapping of signal into position Modest impact for properly normalized signal Volatility targeting Modest impact set by the risk appetite Portfolio Allocation Modest impact with typical equal weight allocations 35

36 Simulated Performance of FX Futures TF Daily rebalancing using weekly trailing returns and the half-life of 2 months Capped linear map of the signal with volatility target of 15% Equal weight allocation 60% 50% 40% 30% 20% 10% 0% -10% -20% -30% Performance of FX Trend-Following Strategies: 2005 to 2015 GBP EUR JPY AUD CAD CHF NZD Trend Following EqualWeight Sharpe Vol MaxDD GBP % -28% EUR % -22% JPY % -27% AUD % -23% CAD % -32% CHF % -29% NZD % -26% EqualWeigh % -13% Skeweness Beta1 Convexity B GBP EUR JPY AUD CAD CHF NZD EqualWeigh

37 40% 35% 30% 25% 20% 15% 10% 5% 0% -5% -10% -15% FX Trend-following strategy delivers positive convexity and crisis-alpha with respect to Performance of FX Trend-following Strategy: 2005 to 2015 Trend Following EqualWeight delta-1 FX Basket Delta-1 Basket EqualWeight Monthly return on Trend-Follow wing Strategy 10% 5% 0% -5% Monthly returns on the trend-following strategy vs returns on delta-1 basket y = 7.07x x R² = % -10% -5% 0% 5% 10% Monthly Return on Delta-1 Equal Weight Basket 37

38 Impact of Half-life Parameter for trend smoothing: faster trends generate higher convexity Simulated Sharpe as function of Signal Half-Life week 2 weeks 1 month 2 months 4 months 8 months Simulated Skeweness as function of Half-Life week 2 weeks 1 month 2 months 4 months 8 months Simulated Convexity Beta as function of Half-Life week 2 weeks 1 month 2 months 4 months 8 months 38

39 Impact of Signal Mapping for Position Sizing: modest when not accounting for transaction costs Simulated Sharpe as function of Signal Mapping Simulated Skeweness as function of Signal Mapping Simulated Convexity Beta as function of Signal Mapping

40 In-sample Correlations for Delta-1 and Trend- Following Strategies: correlation for TF are reduced by 50% but still positive Delta-1 Correlations, Average = 0.44 GBP EUR JPY AUD CAD CHF NZD GBP EUR 0.7 JPY AUD CAD CHF NZD Trend-following Strategies Correlations, Average =0.25 GBP EUR JPY AUD CAD CHF NZD GBP EUR 0.5 JPY AUD CAD CHF NZD

41 PCA Loadings using Lasso regressions: the first principal component is not diversifiable Detect strategy significant betas to the statistical factors CFM paper (2016) for risk-based allocation using PCA: Agnostic Risk-Parity Delta-1 Lasso PCA Loadings R^2 PC1 PC2 PC3 PC4 PC5 PC6 PC7 GBP 96% EUR 93% JPY 95% AUD 96% CAD 95% CHF 95% NZD 97% Average Trend-following Lasso PCA Loadings R^2 PC1 PC2 PC3 PC4 PC5 PC6 PC7 GBP 95% EUR 93% JPY 96% AUD 95% CAD 95% CHF 94% NZD 95% Average

42 Improvements for the indicative trendfollowing strategy Signal generation and execution using intraday prices Dynamic estimation of the half-life parameter and auto-correlation regimes Time series normalization using advanced volatility models Time series smoothing and forecast using advanced econometric tools Portfolio allocation using factor exposures and optimization 42

43 Machine learning for volatility estimation reduces the dimensionality of strategy back-test Strategy design Volatility Model Parameters Strategy Parameters *Optimal 2-d set and execution Split 2-dimensional problem into two orthogonal 1-dimensional problems Volatility Model Parameters *Optimal 1-d set Strategy Parameters *Optimal 1-d set 43

44 Occam s razor and Minimum description length Select the answer that makes the fewest assumptions Look for a model that best predicts the data, out of several hypotheses Layered/conditional models have less sensitivity to error propagation Kolmogorov complexity and mutual information: the shortest program to produce BOTH Data AND Model = program to produce model + program to produce data given model + logarithmic term Leading terms Second order corrective term 44

45 References to Personal work 1. Trend-Following Strategies for Tail-Risk Hedging and Alpha Generation 2. Diversifying Cyclicality Risk of Quantitative Investment Strategies 3. Volatility Modelling and Trading 4. Machine Learning for Volatility Trading Research blog 45

Machine Learning for Volatility Trading

Machine Learning for Volatility Trading Artur Sepp artursepp@gmail.com 20 March 2018 EPFL Brown Bag Seminar in Finance Machine Learning for Volatility Trading Link between realized volatility and P&L of