when do stop-loss rules stop losses? kathryn m. kaminski and andrew w. lo texpoint fonts used in...

When Do Stop-Loss Rules Stop Losses?

Kathryn M. Kaminski and Andrew W. Lo

March 31st, 2008

© 2008 Kaminski and Lo Page 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

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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?

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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

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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

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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

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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 ThresholdRe-Entry ThresholdObservation WindowFocus on Cumulative Returns

Key Characteristics:

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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

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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”

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Observe a loss below the threshold over six months – Get out

Insufficient recovery stay out

Illustration:

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Basic Stop-Loss Strategies

Definition: The stopping premium is the difference in expected returns between the stop-loss policy and

Stop-Loss Strategy Portfolio Strategy

*** The sign of allows us to determine when stop-loss rules can actually stop losses

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Basic Stop-Loss Strategies

Since

Difference in Conditional Expectations

Probability of being Stopped-out

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Basic Stop-Loss Strategies

Definition: We define as the stopping Sharpe ratio difference and as the stopping volatility difference

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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

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• 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

Regime Switching Models

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Performance of Stop-Loss

Rules

Accuracy in PredictingRegimes

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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

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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

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Empirical Analysis

Asset

Ann. Mean

Ann. SD 1 Skew Kurt Min Med Max Ann.

SRMDD

(%) (%) (%) (%) (%) (%) (%)

Equities 12.5 14.4 2 -0.3 4.7 -21.6

1.3 16.8 0.54 38.4

Long-Term Bonds 6.2 9.0 6 0.6 6.4 -9.8 0.3 15.2 0.15 25.1

Short-Term Bonds 4.8 0.8 96 1.0 4.4 0.0 0.4 1.4 0.00 1.3

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

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J=3 J=6 J=12 J=18

Empirical Analysis

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J=3 J=6 J=12 J=18

Empirical Analysis

Robustly PositiveFor many window sizes

≈ 50-100bps/month

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Empirical Analysis

Robust reductions in Volatility for window sizes

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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

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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

Thank you