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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  2r0  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
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