Disposition Effect

Disposition Effect

The disposition effect (Shefrin & Statman 1985; Odean 1998) is the systematic tendency of individual investors to sell winning stocks too readily and hold losing stocks too long, where “winning” and “losing” are defined relative to the original purchase price. The classic test compares the Proportion of Gains Realized
$PGR=\frac{\text{Realized Gains}}{\text{Realized Gains}+\text{Paper Gains}}$
to the Proportion of Losses Realized
$PLR=\frac{\text{Realized Losses}}{\text{Realized Losses}+\text{Paper Losses}}.$
The disposition effect is the prediction that $PGR>PLR$. Both ratios are normalized so that an investor with no preference between winners and losers would have $PGR=PLR$ regardless of how many of each she owns.

Odean (1998). Using a unique dataset of $10,000$ accounts at a U.S. discount brokerage from $1987$–$1993$, Odean computes $PGR=0.148$ and $PLR=0.098$ for the entire year — a difference of $0.050$ with a $t$-statistic of $-35$. The disposition effect is therefore $50\%$ larger for gains than for losses, statistically overwhelming, and economically large. The pattern reverses in December ($PGR=0.108$, $PLR=0.128$) when tax-loss selling becomes attractive, confirming that the year-round effect is not tax-driven — if it were, $PLR$ should always exceed $PGR$ (selling losers is tax-efficient at any time).

Robustness. The pattern survives every standard challenge: it appears in both halves of the sample period, in both frequent and infrequent traders, after restricting to entire-position sales (ruling out portfolio rebalancing as the cause), and across other countries and asset classes. Past winners do not subsequently underperform past losers in the relevant horizon (the data sit in the 1–12 month momentum zone), so the disposition effect is return-decreasing: investors hold the stocks that subsequently keep losing and sell the ones that keep winning.

Cognitive sources. The leading explanations are reference-dependent preferences — the purchase price serves as a reference point and gains and losses are evaluated against it via prospect theory’s S-shaped value function — and realization utility (Barberis & Xiong, 2012), which holds that investors derive a burst of utility at the moment a gain is realized and a burst of disutility at the moment a loss is realized. Both stories generate $PGR>PLR$ as a prediction. Hartzmark (2015) extends the picture by showing that selling propensity has a V-shaped relationship with returns since purchase: investors sell both their best and worst performers more eagerly than middling positions, suggesting that simple winner-vs-loser categorization understates the underlying behavior.

Intuition

A rational investor with no transaction costs and no information on the stock should be indifferent between selling a winner and selling a loser of the same dollar amount — both convert risky equity into riskless cash. With taxes, the rational investor prefers to sell losers, because realized losses offset capital gains and lower the tax bill. With private information, she sells whichever stock she expects to underperform going forward, regardless of whether it is currently above or below her purchase price. None of these rational considerations justifies a systematic preference for selling winners.

The disposition effect appears anyway because the purchase price functions as a reference point in the investor’s mind. A stock above the purchase price is a “win” she wants to lock in. A stock below the purchase price is a “loss” she wants to avoid acknowledging — selling would convert paper losses into realized losses, which feel psychologically much worse. The asymmetry comes from prospect theory’s loss aversion (losses hurt about twice as much as equivalent gains feel good) combined with risk-seeking in losses (the convex part of the value function below the reference point makes investors want to “gamble for resurrection” by holding losers and hoping they recover). Realization utility tells essentially the same story but locates the bias at the moment of selling rather than the moment of holding: the act of selling a winner produces a discrete burst of utility that the investor wants to consume.

Properties

(Definition Through PGR and PLR) The standardized measures eliminate composition effects.

A naive test would count “winners sold” and “losers sold” but this confounds the disposition effect with how many winners and losers the investor owns. The Odean ratios fix this: $PGR$ is the fraction of opportunities to sell winners that the investor takes, and $PLR$ is the fraction of opportunities to sell losers. An investor who is indifferent between winners and losers will have $PGR=PLR$ regardless of how many of each are in her portfolio. The disposition effect is the empirical fact that across thousands of investors, $PGR$ is reliably larger than $PLR$ by a wide margin.

(Tax-Loss Selling Goes the Other Way) Pure rational tax motives predict $PLR>PGR$.

Selling losers reduces taxable capital gains; selling winners increases them. A purely tax-motivated investor should therefore sell losers preferentially, especially in December when the tax year ends. The Odean data show that PGR and PLR do swap signs in December ($PGR=0.108$, $PLR=0.128$), confirming that tax considerations are operative at year-end. But the fact that $PGR>PLR$ for the other eleven months proves that taxes cannot be the explanation — if they were, $PLR>PGR$ should hold year-round, only more strongly in December. The disposition effect is therefore robust against the rational benchmark, not consistent with it.

(Robust Across Subsamples) The effect appears in every cut of the data.

Odean partitions his data by sub-period ($1987$–$1990$ vs. $1991$–$1993$), by trader type (frequent vs. infrequent), and by sale type (full vs. partial position). The disposition effect appears in every cut with $t$-statistics ranging from $-22$ to $-32$. It is not driven by a small number of unusual investors, by a single time period, or by portfolio-rebalancing strategies that would mechanically generate partial sales of winners. The behavior is a population-wide individual-investor phenomenon.

(Costs the Investor Money) Past winners outperform past losers at the relevant horizons.

If past winners and past losers had the same expected return, the disposition effect would be merely a curiosity — investors would be expressing a preference without losing money. But at the $1$–$12$ month horizon, past winners outperform past losers (the momentum anomaly), and the disposition-effect investor is therefore systematically selling the stocks she should keep and keeping the ones she should sell. Odean estimates that the average disposition-effect-driven trade reduces returns by roughly $3.4\%$ over the subsequent year. The bias is costly.

(Prospect-Theory Microfoundation) S-shaped value function generates $PGR>PLR$.

Under prospect theory, gains are evaluated on a concave value function and losses on a convex one, with the kink at the reference point. An investor holding a winner faces a concave choice — she is risk-averse in gains and prefers the certain gain (selling) to the uncertain continuation. An investor holding a loser faces a convex choice — she is risk-seeking in losses and prefers the uncertain continuation (holding) to the certain loss (selling). Both forces push toward $PGR>PLR$. The disposition effect is therefore one of the cleanest empirical confirmations of prospect-theory preferences in financial markets.

(Realization Utility) Selling itself produces utility, not just the resulting wealth change.

Barberis & Xiong (2012) propose that investors derive utility directly from the act of realizing gains and disutility from the act of realizing losses, separate from the lifetime-wealth implications. This generates the disposition effect even for risk-neutral investors, because the burst of utility from selling a winner is hedonically valuable regardless of consumption smoothing. Realization utility also rationalizes a behavior that pure prospect theory has trouble explaining: investors who close out a stock position immediately upon achieving a gain and use the proceeds to buy a similar stock, which is irrational under any wealth-based framework but trivially explained as harvesting a realization-utility “payoff.”

(V-Shaped Selling) Hartzmark (2015) finds investors also sell their worst losers eagerly.

Hartzmark (2015) refines the disposition picture by showing that within a portfolio, investors are more likely to sell both the best performer and the worst performer than they are to sell middling positions. The relationship between selling propensity and return-since-purchase is V-shaped, not monotonic. This complicates the standard “sell winners, hold losers” story: the worst losers do get sold, just not at the same rate as the worst winners. The result is consistent with a rank-based attention mechanism — investors notice the extremes of their portfolio and act on them — combined with a residual disposition effect for the marginal cases.

Examples

An Odean-style investor at year-end

An investor’s portfolio at the end of November contains $20$ stocks: $12$ are above their purchase price (gains) and $8$ are below (losses). During December she sells $3$ stocks. If she behaves randomly, $\mathbb{E}[\text{sold winners}]=3\cdot (12/20)=1.8$ and $\mathbb{E}[\text{sold losers}]=3\cdot (8/20)=1.2$. A pure tax-loss seller would sell $3$ losers and $0$ winners. A pure disposition-effect investor would sell $3$ winners and $0$ losers. The Odean-data investor in December actually splits about evenly with a slight tilt toward losers ($PLR>PGR$ in December), reflecting tax considerations. In the other months her behavior tilts the opposite way: she sells more winners than the random benchmark would predict, with $PGR\approx 1.5\times PLR$.

Computing PGR and PLR from a single trading day

Suppose an investor’s portfolio on a particular trading day contains $10$ positions, of which she sells $2$:

• Stock A: bought at $$50$, currently $$60$, sold today → realized gain.
• Stock B: bought at $$80$, currently $$70$, not sold → paper loss.
• Stock C: bought at $$30$, currently $$25$, sold today → realized loss.
• Stock D: bought at $$100$, currently $$120$, not sold → paper gain.
• Stocks E–J: $4$ paper gains (held), $2$ paper losses (held).

Tally: $1$ realized gain, $1$ realized loss, $1+4=5$ paper gains, $1+2=3$ paper losses.
$PGR=\frac{1}{1+5}=0.167,PLR=\frac{1}{1+3}=\mathrm{0.250.}$
For this single investor on this single day, $PLR>PGR$ — she happens to be acting against the disposition effect. Odean’s contribution is to compute these ratios across $10,000$ accounts and millions of trading-account-days, finding that the population average shows $PGR>PLR$ with overwhelming statistical confidence.

See Also

• 8.10. Behavioral Household Finance — parent hub.
• 8.5.1. Prospect Theory — the leading microfoundation via reference-dependent preferences and loss aversion.
• 8.5.2. Cumulative Prospect Theory — the refined formulation used in modern realization-utility models.
• 8.8. Momentum — the cross-sectional pattern that makes the disposition effect costly.