MTA 2007 Mid Winter Retreat

BasketsA Practical Use of Common Trends

Yngvi Hardarson MA, CMT

Briefly on myself

A founding Partner at Economic Consulting & Forecasting Ltd. in Reykjavik, Iceland since 1993Specializing in Risk Management (FX)

Economist by educationUniversity of Iceland cand. oecon. degreeQueen’s University in Canada, MA degree emphasis on Econometrics, Monetary EconomicsYrjö Jahnsson Foundation, Finland, Certificate Int.

Trade

MTA, CMT designation

Askar Capital - Investment Bank

Created on Jan. 1 2007 out of a mergerbetween 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.

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) simulationand formal hypothesis testing.

I will focus on 6 but involve 2, 3 and 5.

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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SNDK(right axis)NSM

(left axis)

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3540Minimum Volatility Basket

Cleaner Signals on BasketTwo stocks:NSM, SNDK

AnnualizedVolatility of:NSM 60%SNDK 72%Basket 57%

NSM weighs72% in basket

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”, PrincetonUniversity Press, NJ, 1994

Stochastic Trend

pt = pt-1 + + t

A Random Walk (along Wall Street) with rift.Said to be Integrated of Order 1 (I1).

Why? Rewrite as:pt - pt-1 = + t The 1st difference of price.

If p is a log (natural) of price then pt - pt-1 is percentage change.

Price hardly I2Would imply ever increasing price changesNot typical.

Implications

Cointegrated = Common Trends

The prices must be cointegrated with common hidden factor

Two cointegrated series: One Granger Causes OtherGranger Causality implies a time lead.

Employing “differences” only is WRONG.Differencing filters out important long termprice information, i.e. the trend

TA can benefit from this. (Bear with me).

Cointegrated Markets - Example

Causality based on so called Error Correction Mechanism (Sargan).

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AEX

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DAX

Alexander 2001: "There is clear indication of a cointegrationvector... The results indicate a strong positive causality fromthe DAX to the other two markets."

Two methods for testing for cointegration

Engle-Granger vs. Johansen

Engle-Granger method simplerMore than two variables then can’tidentify which variable is dependent

Engle-Granger method can be applied toBaskets (indices): “Natural” dependent variable

Engle-Granger criterion is Minimum VarianceHas an important Risk Management angle

Normally have lots of data

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

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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SOX

ESOX

Our Version

lnexp19

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itiit PESOX

Why?Know current weights

Don’t know future weightsWe are simulating current state

The Skewed Version – Misspecification

Set chosen ’s (weights) to ZEROMultiple Regression determines other ’s

Model estimated in natural logs

Consequences of Intentional Misspecification

Estimated weights not consistentEstimated weights unstablePotential shifts of projected var.

Regression residual:- Residualt = ESOXt-ModelEstt

- Autocorrelated- Heteroscedastic

Stability of weights:Also depends on how much infocontributed via remaining variables.

Must monitor model closely

True ModelStock weight approximationALTR 4.23%AMAT 3.97% 26.36%AMD 4.40%BRCM 6.93% 12.83%IFX 2.97%INTC 4.37%KLAC 10.69% 18.74%LLTC 6.50% 22.67%MRVL 4.10%MU 3.00%MXIM 6.58%NSM 4.82% 12.25%NVLS 7.41%SNDK 9.10% 7.15%STM 3.98%TER 3.25%TSM 2.35%TXN 6.21%XLNX 5.14%Total 100.00% 100.00%

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

ESOX Volatility and Residual SE

Residualt = ESOXt-ModelFCt

Model tracks closer when volatility lowVolatility measured over 1001 days

Residual Standard Error and Daily ESOX Volatility

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Residual SE

ESOX Vol.

Date showing ending period of 1001 day moving regression window

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.

Unwanted shift – What’s that?

Estimation period

Projection period

2003 A M J J A S O N D 2004 A M J J A S O N D 2005 A M J J A S O N D 2006 A M J J A S O N D 2007

-4-3-2-1012345Residual (%) Residual from projection (%)

Upper trigger calibrated at 1.5

Lower trigger calibrated at -2.5

Buy Basket on first touch of upper triggerSell Basket on first touch of lower trigger

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ESOX

ESOX Basket

Residual Employed as Indicator

In this example buying Basket instead of SOXresults in 4% outperformance on each tradeless trading costs.

Trade the Residual?

Recall: Residualt = ESOXt-ModelFCt

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) reversingRisk having to wait for it to come back to lower trigger

2003 A M J J A S O N D 2004 A M J J A S O N D 2005 A M J J A S O N D 2006 A M J J A S O N D 2007

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5Residual (%) Residual from projection (%)

Upper trigger calibrated at 1.5

Lower trigger calibrated at -2.5

Buy Basket on first touch of upper triggerSell Basket on first touch of lower trigger

Alternative Baskets?

Recall: Model leaves out stocksLeave out other stocks.

True Model 1 Model 2Stock weight approximation approximationALTR 4.23%AMAT 3.97% 26.36%AMD 4.40% 6.23%BRCM 6.93% 12.83%IFX 2.97% 10.12%INTC 4.37%KLAC 10.69% 18.74%LLTC 6.50% 22.67% 13.61%MRVL 4.10% 12.88%MU 3.00%MXIM 6.58%NSM 4.82% 12.25% 18.04%NVLS 7.41% 23.30%SNDK 9.10% 7.15%STM 3.98%TER 3.25% 15.81%TSM 2.35%TXN 6.21%XLNX 5.14%Total 100.00% 100.00% 100.00%

ESOX Vol.Residual SE

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References on Cointegration

Hamilton, JD, Time Series Analysis, PrincetonUniversity Press, NJ, 1994 (Ch. 19)

Alexander, C, Market Models, John Wiley & Sons,West Sussex, England, 2001 (Ch. 12)

Davidson, R & MacKinnon, JG, Estimation andInference in Econometrics, Oxford UniversityPress, NY, 1993 (Ch. 20)