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

RESULTS Wealth evolution: 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 getting which checks whether the short positions make money.

RISK ADJUSTMENT SHARPE RATIO in terms of annualized means and volatilities JENSEN’S ALPHA

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 Let the mean outcome be The null hypothesis is:

COMPUTE and from using the stationary bootstrap of Politis and Romano(1994) a collection of other performance vectors can be computed whose quantiles provide critical values for

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