1. When Do Stop-Loss Rules Stop Losses? Kathryn M. Kaminski and Andrew W. Lo TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A AA A A A AA March 31st, 2008

2. © 2008 Kaminski and LoPage 2 Motivation “You Will Lose Money: One of the hardest aspects of investing is losing money. But there isn't any way to avoid it. Stick around long enough, take enough positions, and you will lose money. Plus, there are multiple ways to lose. How you deal with loss is important.” "The best way to get rich is to not lose money." – Warren Buffet “If you can't accept losing, you can't win.” - Vince Lombardi

3. © 2008 Kaminski and LoPage 3 Motivation  What should I invest in?  How much should I invest?  When should I invest?  When should I get out?  How much should I lose before I get out?  How much should I gain before I get out?  When should I get back in?  Is getting in/out/in better than buy-and-hold?  Do stop-loss rules really stop losses?

4. © 2008 Kaminski and LoPage 4 Literature Review Key Points: 1.Investors use rules and heuristics for investing 2.Investors commonly stop in and out of investments discretely, and most do this infrequently 3.Investors are impacted asymmetrically and substantially by loss and large negative events 4.Industry professionals make use of stop-loss rules routinely

5. © 2008 Kaminski and LoPage 5 Talk Outline I.Performance Impact of Stop-Loss Rules  Random Walk Hypothesis  Momentum and Mean Reversion  Regime Switching II.Empirical Analysis of Stop-Loss Rules  Household Investors and Stop-loss  Equities and Long Term Government Bonds

6. © 2008 Kaminski and LoPage 6 A Framework for Analyzing Stop-Loss Arbitrary Portfolio Strategy with returns Assumptions: (A1) are stationary with a finite mean and variance (A2) the risk premium is positive

7. © 2008 Kaminski and LoPage 7 Basic Stop-Loss Strategies General Definition: A stop-loss strategy is a policy to close out a position after taking a certain threshold of losses and re-establish a position after another threshold of gains Stop-loss Threshold Re-Entry Threshold Observation Window Focus on Cumulative Returns Key Characteristics:

8. © 2008 Kaminski and LoPage 8 Simple Stop-Loss Policy Definition: A simple stop-loss policy for a portfolio strategy with is a dynamic binary asset- allocation rule between and a riskfree asset with returns, where is the proportion allocated to : return (S)return (P)riskfree

9. © 2008 Kaminski and LoPage 9 Connections with Behavioral Finance 1.Enable an investor to take a loss and avoid risk seeking behavior on the downside  Loss aversion, disposition effects, regret 2.“Snake-bite effect”

10. © 2008 Kaminski and LoPage 10 Observe a loss below the threshold over six months – Get out Insufficient recovery stay out Illustration:

11. © 2008 Kaminski and LoPage 11 Basic Stop-Loss Strategies Definition: The stopping premium is the difference in expected returns between the stop-loss policy and Stop-Loss StrategyPortfolio Strategy *** The sign of allows us to determine when stop- loss rules can actually stop losses

12. © 2008 Kaminski and LoPage 12 Basic Stop-Loss Strategies Since Difference in Conditional Expectations Probability of being Stopped-out

13. © 2008 Kaminski and LoPage 13 Basic Stop-Loss Strategies Definition: We define as the stopping Sharpe ratio difference and as the stopping volatility difference

14. © 2008 Kaminski and LoPage 14 The Random Walk Hypothesis  Stop-Loss Rules NEVER stop losses  Reduction in variance at an appropriate cost  Invalidates many common industry practices Forget non-linear market timing and stop-loss

15. © 2008 Kaminski and LoPage 15 As volatility increases less momentum is required before you should consider stop-loss For larger risk premium more momentum is required to consider using stop-loss policies **Using an AR(1) with (ρ,π,σ) and reasonable Momentum and Mean Reversion For mean reversion – stop-loss is clearly a bad idea >0

16. Regime Switching Models © 2008 Kaminski and LoPage 16 Performance of Stop-Loss Rules Accuracy in Predicting Regimes

17. © 2008 Kaminski and LoPage 17 When Do Stop-Loss Rules Stop Losses? Random walk – NO Mean Reversion – NO Momentum - YES –Need sufficient momentum effects Regime Switching - YES –Need sufficient conditional asymmetries and accuracy in predicting regimes Basic Stop-Loss Strategies Stop-loss rules can actually stop losses

18. © 2008 Kaminski and LoPage 18 Empirical Analysis Consider investors who switch purely between equities and long-term bonds Experiment –How do basic stop loss rules impact performance? –How does the choice of stopping threshold relate to portfolio performance? Robustness and sensitivity? –J={3,6,12,18} Months, ={4-14%} ={0-4%} Data –CRSP VW monthly returns 195001:200412 –Ibbotson’s monthly 10yr T-notes 195001:200412

19. © 2008 Kaminski and LoPage 19 Empirical Analysis Asset Ann. Mean Ann. SD 11 SkewKurt MinMedMax Ann. SR MDD (%) Equities12.514.42-0.34.7-21.61.316.80.5438.4 Long-Term Bonds6.29.060.66.4-9.80.315.20.1525.1 Short-Term Bonds4.80.8961.04.40.00.41.40.001.3 Summary statistics for the CRSP Value-Weighted Total Market Index, and Ibbotson Associates Long-Term and Short-Term Government Bond Indexes, from January 1950 to December 2004

20. © 2008 Kaminski and LoPage 20 J=3 J=6 J=12 J=18 Empirical Analysis

21. © 2008 Kaminski and LoPage 21 J=3 J=6 J=12 J=18 Empirical Analysis Robustly Positive For many window sizes ≈ 50-100 bps/month

22. © 2008 Kaminski and LoPage 22 Empirical Analysis Robust reductions in Volatility for window sizes

23. © 2008 Kaminski and LoPage 23 Conclusions: Empirical Study Stop-loss rules imply WHY and WHEN?  Asset Pricing –Conditional momentum – Conditional asymmetries  Behavioral Finance  “Flight-to-Safety”  Hope, Denial, and Desperation  Loss Aversion  Passivity and Attention  Temporary irrationality Exploits Nonlinear Dynamics of Asset Returns Exploits an Understanding of Hardwired Aspects of Human Behavior

24. © 2008 Kaminski and LoPage 24 Conclusions “If you can't accept losing, you can't win.” - Vince Lombardi  Dealing with loss is important  Stop-loss rules can actually stop losses

25. Thank you