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FINANCIAL ECONOMETRICS FALL 2000 Rob Engle OUTLINE • • • • DATA MOMENTS FORECASTING RETURNS EFFICIENT MARKET HYPOTHESIS FOR THE ECONOMETRICIAN • TRADING RULES • THE BOOTSTRAP SNOOPER DATA • PRICES - TRANSACTIONS OR QUOTES • RETURNS – – – – DIVIDENDS TOTAL AND EXCESS COMPOUNDING HORIZON • ANNUALIZATION MOMENTS • • • • Mean, Variance, Skewness, Kurtosis Conditional Versions of these Quantiles Densities ANNUALIZATION • • • • Annualize means Annualize volatilities (standard deviations) Annualize variances Annualize quantiles? FORECASTING RETURNS • • • • • SET UP IN EVIEWS BUILD SIMPLE MODELS BUILD ARMA MODELS CHECK AUTOCORRELOGRAM BUILD NON-LINEAR TIME SERIES MODELS ARE RETURNS FORECASTABLE? • EFFICIENT MARKET HYPOTHESIS ASSERTS NOT – weak form uses own past – semi-strong form uses public information – strong form uses private information • IF THE FUTURE COULD BE PREDICTED, THEN THE PRICE WOULD MOVE TODAY…... BUT • RISK PREMIA ARE PREDICTABLE • MEASUREMENT ERRORS MAKE ‘RETURNS’ PREDICTABLE – STALE PRICES – DISCRETENESS&BID ASK BOUNCE – PRICING ERRORS • DATA SNOOPING - HOW TO FOOL YOURSELF AS WELL AS YOUR INVESTORS TRADING RULES • COMPONENTS: Signal, Action, Result and Evaluation • SIGNAL: up or down prediction • ACTION: buy 1$ of asset with borrowed funds/ or sell 1$ of asset and invest funds pt pt SELL Wt Wt 1 (1 r0 ) BUY 1 r0 pt 1 pt 1 RESULTS • Wealth evolution: Wt Wt 1 rt r0 2BUY 1 • Actual wealth evolution will be lower due to transaction costs, execution delays and inferior prices RESULTS ABOVE A BENCHMARK • If the benchmark is the riskless asset, then the previous formula is correct. • If the benchmark is a buy and hold strategy, then we subtract rt r0 • getting Wt Wt 1 2r0 rt SELL • which checks whether the short positions make money. RISK ADJUSTMENT • SHARPE RATIO in terms of annualized means and volatilities SR r r0 • JENSEN’S ALPHA rt rm,t t DATA SNOOPING • Sullivan, Timmermann, and White(1999), “Data-Snooping, Technical Trading Rule Performance, and the Bootstrap”, Journal of Finance THE QUESTION: • Suppose many trading rules are used and the average profit above a benchmark is computed over a fixed sample period, • Suppose the efficient market hypothesis is true in the sense that no rule can beat the benchmark in expected value • Find an outperformance number which gives the 5% point for random outcomes. STATISTICS • Let the outcome for date t for all rules be given by ft 1 f ft • Let the mean outcome be n • The null hypothesis is: t H 0 : E ft 0 COMPUTE k 1,..., l Vl max n fk • and from using the stationary bootstrap of Politis and Romano(1994) a collection of other performance vectors can be computed n f *k ,i f k k 1,..., l Vl ,i max • whose quantiles provide critical values for Vl RESULTS • Technical trading rules significantly outperform for historical periods using the Dow. • This is true with Brock Lakonoshok and LeBaron rules or with more general rules • Result disappears in most recent decade