Trading Rules and Market Efficiency Fin250f: Lecture 4.3 Fall 2005 Reading: Taylor, chapter 7

Outline  Moving average rules  Channel rules  Filter rules  Rule evaluation Statistical significance and risk Breakeven transaction costs  Monte-carlo and bootstrap tests

Moving Average Trading Rules (Simplest)

Multiple Averages

Bands

Channel Rule

Filter Rule  Buy period to sell Price falls by f fraction from recent price max  Sell period to buy Price rises by f fraction from recent price min

Rule Evaluation  Statistical significance  Breakeven transaction costs  Risk

Significance Test I: Buy-Sell

Significance Test II: Dynamic strategy, genmatrule.m

Probability of a Price Rise

Results From Equity Markets  Brock, Lakonishok, LeBaron(1992) Dow data (daily/100 years) Standard MA rules (5, 50, 150, 200 day) Stat sig predictability Volatility forecasts  Sullivan, Timmermann and White(1999), LeBaron(2000) Results drop in 90’s  Day and Wang(2002) Nonsynchronous prices

Global Equity Markets  Bessembinder and Chen(1995) Repeat results for Asia  Hudson, Dempsey, and Keasey(1996) Long range results form UK  Consistent predictability over many years, many countries  Predictability falling over time

FX Markets  Generally stronger predictability than equity markets Levich and Thomas(1993) LeBaron(1992)  Some connections with intervention LeBaron(1999)

Transaction Costs  Costs of trading: Important  Often assume proportional  Depends on strategy  First strategy: Simple (Long/short) futures Long in buy periods Short in sell periods

Transaction Costs: I. Simple long/short futures

Breakeven Transaction Costs: Simple long/short futures

Transaction Costs: Simple Equity Strategy  Equity strategy: Sell: Hold risk free Buy: Leverage position  Invest own $1, borrow additional $1  Designed to replicate risk on buy and hold

Transaction costs: Equity strategy

Breakeven Transaction Costs: Equity portfolio

Results  US equity(Dow): 0.22% for recent periods Smaller than most T-cost estimates  Older periods (up to 1%)  Currencies: large returns for 0.2% transaction levels (6-10%) (Sharpe ratios near 1)  All near zero beta

Recent Results  All trading rule returns falling in the 1990’s  Increased efficiency?  LeBaron(1999): FX interventions Removing intervention period removes most fx predictability Few US interventions in the 90’s

Evidence Summary  Generally large statistical significance  Marginal break even results Except FX  Big returns after T-costs  Good risk tradeoff  Careful: All results getting smaller over all recent periods!!!!

Bootstrap Tests  Brock, Lakonishok, and LeBaron(1999) Scrambled returns series  (Monte-carlo: simulated normal returns) Destroy patterns Evaluate rules on scrambled series Compare with original Matlab:  bsmarule.m

Extensions  Fancier rules Better positions Pattern recognition systems  Changing position sizes based on various signals  More advanced risk measures