Time, Dynamics, and Uncertainty

Notes and code only

Examples

• Multiperiod investment problems– Done

• Trading strategies

• Retirement

Dynamic Strategies

• Adjusting trading positions over time

• Examples– Market timing– Technical trading– Momentum

Trend Following Strategies

• Buy (long) when P(t)>MA(t)– MA(t) = moving average of past P’s

• Sell (short) otherwise

• Methods for testing– Statistical – Bootstrap

Simple Bootstrap Tests

• Random walk null hypothesis

• Moving average rule

• Single rule– No snooping correction

• trule1.m

• New data: (next slide)

jyfxbis.dat

• jyfxbis.dat– Date– Matlab date– $/Yen– Yen interest rate– $ interest rate

Wild Bootstrap

• Problem with random walk bootstrap– Volatility

• Allow persistent volatility, but destroy predictable components

• trule2.m

Data Snooping Adjustments

• Researcher has reported best result for many strategies

• Search over many strategies on the random walk and record distribution of “best” strategy

• Compare to actual “best”

• trule3.m