CAES Workshop: Risk Management and Commodity Market Analysis

Transcription

1 CAES Workshop: Risk Management and Commodity Market Analysis ARE THE EUROPEAN CARBON MARKETS EFFICIENT? -- UPDATED Speaker: Peter Bell April 12, 2010 UBC Robson Square 1

2 Brief Thanks, Personal Promotion To the organizers and presenters: thank you! Dr Kees V. Kooten: thanks for getting me here Short term Goal: hold an ACCELERATE Internship in Fall 2010 related to finance and carbon credit offsets Long term goal: scientific-entrepreneurship and career in facilitation of internship projects 2

3 To Do List Achieve Markellos replication Statistics to asses predictive power of past prices Reject AR(1) Model, focus on Box-Ljung statistics Present profitability of basic trading strategies Extensions Consider markets for carbon other than in Markellos Reconsider AR(1) model after cleaning data and perform unit root tests Present visualizations for profitability of trading and consider new strategies Consider the case of periodic endowments 3

4 Project Overview: Replication and Extension Benefits of Replication Approach: Allows non-experts to access advanced topics Extends published results Paper to be replicated: Markellos and Daskalakis Are the European Carbon Markets Efficient Review of Futures Markets, Vol. 17, No. 2, pp ,

5 Presentation Schedule Schedule: 5 Minutes gone already 5 Minutes on Financial Time Series 10 Minutes on Trading Strategies 5 Minutes discussion (clarifications, topics) Goals: Replicate and extend Markellos statistical results Establish research in trading strategies for Carbon 5

6 Section 1 Time Series and Price Efficiency 6

7 Section 1 Statistical Approach Daily spot prices for several carbon exchanges: DJ CCX CER, DJ CCX EUR CER, BlueNext CER Others waiting in the wings Outliers: observations more than three standard deviations away from sample mean 7

8 Descriptive Statistics Daily Returns DJ CCX CER DJ CCX CER - X OUTLIERS DJ CCX EUR CER DJ CCX EUR CER - X OUTLIERS BLUENEXT CER BLUENEXT CER - X OUTLIERS Mean -0.05% 0.01% -0.09% -0.06% -0.13% -0.09% Median 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Mode 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Minimum % -7.63% % -7.68% % -7.75% Maximum 25.91% 8.19% 11.25% 7.30% 9.44% 7.24% Standard Deviation Skewness Kurtosis

9 Replication: Statistical Tests to Reject Random Walk Hypothesis Markellos main technique: Ljung-Box statistic to test serial autocorrelation Markellos secondary technique: Variance ratio to test unit variance Our statistical techniques: Replication of Ljung-Box tests We do not replicate variance ratio test We do consider unit root tests 9

10 Markellos Methodology Ljung-Box Markellos Results Achieves test statistics that reject null (of no serial autocorrelation) for all lags Inference is that AR(1) is insufficient lag and some longmemory model is better Results are uniform across European Powernext/ECX and Nord Pool exchanges My results All markets give same inference as Markellos When outliers are removed, the result is gone can no longer reject the null To study this further, unit root tests will determine if AR(1) is appropriate model 10

11 Impact of Outliers on Ljung-Box Results: p-values Lags ICE CFI ICE CFI - EX OUTLIERS 1 2% 91% 6 0% 27% 11 0% 56% 16 0% 80% 21 0% 58% Recall Markellos is based on European Markets: Intercontinental Exchange (ICE) & Carbon Financial Instruments (CFI) Question to Markellos: did you screen outliers? 11

12 Did the original paper screen outliers? Answer: No Excerpt from exchange: The purpose of the paper was to apply simple technical trading rules [based on] a trivial examination of autocorrelation and variance ratio tests From the series however we never really checked what will happen if we remove the outliers. The reason was that we wanted to base our inferences on the technical analysis results, meaning that even a predictability in lag 1 would have sufficed for actually going forward with it. Dr. Daskalakis Short version: No Quote makes an important point: statistics are used simply to motivate study of trading strategies 12

13 Ljung-Box Results: more p-values DJ CCX EUR CER - EX OUTLIERS Lag DJ CCX EUR CER DJ CCX CER 1 30% 58% 54% 71% 6 0% 15% 0% 0% 11 4% 42% 0% 3% 16 9% 63% 0% 6% 21 5% 24% 0% 10% DJ CCX CER - EX OUTLIERS For markets not considered by Markellos, we find the same results that he achieved; and the same foible Suggests that outlier observations cause the AR(1) to fail 13

14 Section 1 Conclusion: Foundational for trading strategies Mixed results We achieve same results as Markellos with other carbon markets and longer time periods than the original work We show this result is sensitive to outlier observations Unifying Result: Phillip Peron unit root test First difference of log prices gives p-value =0.001 (smallest possible) under null that underlying data comes from zero drift unit root process We can reject the unit root model Past prices are predictive: begin search for arbitrage! 14

15 Section 2 Technical Trading Rules 15

16 Trading Strategies - Introduction Given predictability of prices, autocorrelation filters should exist that give profitable trading Not deterministic arbitrage, but statistical profit Is it possible to exploit the predictability? Novel visualizations for profitability and risk Rephrasing: Are the returns to a trading strategy less-random than the spot market? 16

17 Markellos Trading Strategies Moving Average Cross Calculate fast and slow filter of price Where fast filter > slow filter, hold long position; vice versa Trading Range Bound When price goes above recent high, go long; vice versa Random Walk When last price change was positive, go long; vice versa Buy and Hold Hold long position throughout the sample period All Markellos strategies assume portfolio is fully invested each day, long or short for the entire day 17

18 Our Trading Strategies Moving Average Cross Direction of position: Long or Short each day, based on signals Signals derived from ranking of Moving Average filters Two MA filters considered, each specified by one argument (lag) Lags are generally not equal, one is fast and one slow As before, go long when the fast filter is above the slow one We focus exclusively on Moving Average cross because it is an autoregressive strategy; can it exploit predictive power of prices? Extend Markellos and others by considering a variant where position size is related to signal strength; good results 18

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20 Trading Strategy Criteria Markellos criteria: Cumulative Return Average Daily Return Number of Buy (Sell) Signals Proportion of Winning Trades Profitability Index (winning trades / total trades) Standard deviation of returns Coefficient of variation (average daily return / std.dev) Sharpe Ratio (abnormal returns / std.dev) 20

21 Trading Strategy Criteria Our criteria: Prepared: the same as Markellos Presented: Cumulative return and standard deviation We focus on the MA Strategy so that we can vary the two specification parameters to generate a visual surface for each criteria and filter type Results: Variable size rules are best for exploiting prices 21

22 Next, Visuals For DJ CCX EUR CER 22

23 Profit Surface for Fixed Size MA Rank 23

24 Profit Surface for Fixed Size MA Rank 24

25 Comment Differences in Z-axis of prior graphs suggest we are comparing apples and oranges (or cows and corn?) But this difference can be overcome Key insight: striking difference represents fundamental difference between the two strategies; the variable size strategy is better at exploiting predictive power of prices 25

26 Risk Surfaces This surface is also from a variable size strategy with a equal weight moving average filter This surface represents standard deviation of trading returns Strange, in my opinion 26

27 Psuedo-code for Trading Strategy Surface Arguments: timeseries, int1, int2 Procedure: Loop over int1, int2 in (1,500) For each stage, run trading strategy Use int1, int2 to specify MA Filter Output: overall profit table, variance of profit table Plot function by int1, int2 (heat map or surface); Note: Symmetric by coding Code available on request 27

28 Pause When position size is a function of signal strength, profitability is more regular! Intuitive? 28

29 Comparison of Surfaces to Markellos We do match the magnitude and sign of Markellos published results Markellos results are one point on our surface Comment: local regression and other filters were used but generally results were the same 29

30 To Do: Create equity curves (time series of cumulative profits for strategy) and compare curve randomness amongst strategies Introduce fancy filters: local regression, golay smoothing, updating AR model every time period Use strategies on simulated prices Enter SDE 30

31 Paper Conclusions Markellos replication success Foible with outliers Trading strategy profitability surfaces Particular to Moving Average cross Framework for comparing strategies 31

32 Takeaway Results Carbon prices do not pass random-walk tests Past prices have predictive power Markets are not efficient Trading strategies are not created equal When position size is related to signal strength, we find increased regularity in strategy returns Anyone hiring in the Carbon Markets? 32

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34 Appendix GRAPHICS AND THOUGHTS 34

35 Conversation for Coffee If you periodically received endowments of credits, how best could you distribute them? Ideas? Contact us: 35

36 Repetition of graphs from Presentation Return surface under variable size rule Return surface under fixed size rule 36

37 Variable Size using BlueNext CER spot prices Profitability surface Risk Surface 37

38 Variable Size using DJ-CCX CER spot prices Profitability surface Risk Surface 38

39 Fully invested strategy using BlueNext CER spot prices Profitability surface Risk Surface 39

40 Fully invested strategy using DJ-CCX CER spot prices Profitability surface Risk Surface 40

41 Profit Surface for Variable Size MA Rank 41