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MTA 2007 Mid Winter Retreat Baskets A Practical Use of Common Trends Yngvi Hardarson MA, CMT

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Briefly on myself A founding Partner at Economic Consulting & Forecasting Ltd. in Reykjavik, Iceland since 1993 Specializing in Risk Management (FX) Economist by education University of Iceland cand. oecon. degree Queen’s University in Canada, MA degree emphasis on Econometrics, Monetary Economics Yrjö Jahnsson Foundation, Finland, Certificate Int. Trade MTA, CMT designation

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Askar Capital - Investment Bank Created on Jan. 1 2007 out of a merger between ECF and two other companies: - Aquila Venture Partners a private equity real estate investment co. - Sjova Finance a financing co. owned by Iceland’s largest insurance co.

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Potential Uses of Quantitative Analysis to the TA: 1. Analyze trading system performance - Potential performance. 2. Investigate impact of changing system parameters / Establish robustness of chosen parameters. 3. Make indicators and filters. 4. Datamine: To optimize system parameters and/or rule search. 5. Identify and manage risk in trading, e.g. money management and construct portfolio of trading strategies. 6. To manipulate (transform) the financial instrument to be traded. 7. To integrate technical analysis with fundamentals. There are more ways, e.g. bootstrap (or Monte Carlo) simulation and formal hypothesis testing. I will focus on 6 but involve 2, 3 and 5.

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Baskets What are they? A weighted combination of financial instruments. E.g.: Indices like S&P 500, Reuters-CRB, Dollar index, Custom Made (own) baskets. Why trade them? Cleaner market signals, i.e. zero-lag “noise” filter. Manage risk. “Redefine” the market being traded.

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Cleaner Signals on Basket Two stocks: NSM, SNDK Annualized Volatility of: NSM60% SNDK72% Basket57% NSM weighs 72% in basket

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Common Trends – Cointegration What is this? The Concept of Trend Accepted Among TA’s: “The Trend is Your Friend”. Statistics - 2 types of trend: - Deterministic - Stochastic We consider the stochastic version Source: Hamilton, JD, “ Time Series Analysis ”, Princeton University Press, NJ, 1994

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Stochastic Trend p t = p t-1 + + t A Random Walk (along Wall Street) with rift. Said to be Integrated of Order 1 (I1). Why? Rewrite as: p t - p t-1 = + t The 1 st difference of price. If p is a log (natural) of price then p t - p t-1 is percentage change. Price hardly I2 Would imply ever increasing price changes Not typical.

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Implications Cointegrated = Common Trends The prices must be cointegrated with common hidden factor Two cointegrated series: One Granger Causes Other Granger Causality implies a time lead. Employing “ differences ” only is WRONG. Differencing filters out important long term price information, i.e. the trend TA can benefit from this. (Bear with me).

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Cointegrated Markets - Example Causality based on so called Error Correction Mechanism (Sargan).

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Two methods for testing for cointegration Engle-Granger vs. Johansen Engle-Granger method simpler More than two variables then can ’ t identify which variable is dependent Engle-Granger method can be applied to Baskets (indices): “ Natural ” dependent variable Engle-Granger criterion is Minimum Variance Has an important Risk Management angle Normally have lots of data

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So... Let ’ s use this! First need a bit more bones to support the muscle Will work with PHLX Semiconductor Index (SOX). Why? It ’ s small & volatile

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The Truth - Almost the Whole Truth The “ Index ” is the Truth (the true model by construction) Let ’ s make OUR VERSION and then SKEW it Problem with the truth … “ It ’ s complicated ” - Index revisions - Calculation method - Many index components Solution: Our version - Calculate index history given current weights - Calculate based on geometric weighting - Could drop components but not needed

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Our Version Why? Know current weights Don ’ t know future weights We are simulating current state

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The Skewed Version – Misspecification Set chosen ’ s (weights) to ZERO Multiple Regression determines other ’ s Model estimated in natural logs

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Consequences of Intentional Misspecification Estimated weights not consistent Estimated weights unstable Potential shifts of projected var. Regression residual: - Residual t = ESOX t -ModelEst t - Autocorrelated - Heteroscedastic Stability of weights: Also depends on how much info contributed via remaining variables. Must monitor model closely

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Why this model? Estimate for different time periods. A moving 1001 day window. Figure on X-axis shows serial no. of day for ending period of regression. We want relatively stable weights indicating a ROBUST model

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ESOX Volatility and Residual SE Residual t = ESOX t -ModelFC t Model tracks closer when volatility low Volatility measured over 1001 days

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Investigate Residuals - Potential Shifts, etc. Estimate for period ending Jan. 3, 2006. (Obs. 1383) No visible shift or trend but drift of Weights and Residual SE indicates need for Model re-estimation and calibration. Note: Autocorrelation obvious. Complicates I1 test.

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Unwanted shift – What ’ s that? Estimation period Projection period

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Residual Employed as Indicator In this example buying Basket instead of SOX results in 4% outperformance on each trade less trading costs.

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Trade the Residual? Recall: Residual t = ESOX t -ModelFC t Thus: Buy long Model and Short SOX on Upper Trigger A market neutral strategy Then Reverse on Lower Trigger Residual Trends Sideways (by construction). Mean (zero) reversing Risk having to wait for it to come back to lower trigger

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Alternative Baskets? Recall: Model leaves out stocks Leave out other stocks. ESOX Vol. Residual SE

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References on Cointegration Hamilton, JD, Time Series Analysis, Princeton University Press, NJ, 1994 (Ch. 19) Alexander, C, Market Models, John Wiley & Sons, West Sussex, England, 2001 (Ch. 12) Davidson, R & MacKinnon, JG, Estimation and Inference in Econometrics, Oxford University Press, NY, 1993 (Ch. 20)

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