# Prospect Theory in Action: How Loss Aversion Shapes Online Trading

Cite as: Gorak, R. (2026). Prospect Theory in Action: How Loss Aversion Shapes Online Trading. Tradicted. https://www.tradicted.com/research/yang-yu-liu-prospect-2014/
Paper: Yang-Yu Liu, Jose C. Nacher, Tomoshiro Ochiai, Mauro Martino, Yaniv Altshuler — *Prospect Theory for Online Financial Trading*
Published in: arXiv Working Paper (2014)
Original: https://arxiv.org/abs/1402.6393

Key finding: Among 28.5 million trades (Jun 2010–Oct 2012), mirror trades won about 83% of the time, the only type with positive average ROI (≈0.03%).

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Prospect theory holds that people are risk-averse toward gains but risk-seeking toward losses, a pattern known as the reflection effect. In "Prospect Theory for Online Financial Trading," Liu et al. (2014) studied an online social trading platform for foreign exchanges and commodities. The dataset covers over 28.5 million trades by 81.3 thousand traders, June 2010 to October 2012. Mirror trades won positive returns about 83% of the time, the highest share of any trade type, but averaged only 0.03% ROI.

## What the Study Found

All three trade types showed a win rate above 50%, with mirror trades highest at about 83%. Only mirror trades averaged positive ROI, at about 0.03%, while single and copy trades did not. Mirror trades' winning positions earned just about 0.177% ROI, lower than single and copy trades' winning positions. Mirror trades' losing positions lost about 0.9% ROI on average, worse than single and copy trades' losing positions. Losing traders made up 85.2% of all traders, versus 14.7% who were net winners.

## Methodology

The data come from an online social trading platform for foreign exchanges and commodities trading, where traders can copy or mirror others' trades. The sample includes over 28.5 million trades placed by 81.3 thousand traders using real money. Trades were recorded from June 2010 to October 2012, a period of about 28 months. The study compares single, copy, and mirror trades, and separates traders into winning and losing groups by final net profit.

## Key Statistics

| Metric | Finding | Context |
|---|---|---|
| Win rate, mirror trades | ≈83% | Highest among single, copy, and mirror trades |
| Average ROI, mirror trades | ≈0.03% | Only trade type with positive average ROI |
| Average ROI, winning mirror positions | ≈0.177% | Lower than single and copy trades' winning positions |
| Average ROI, losing mirror positions | ≈-0.9% | Higher negative ROI than single and copy trades' losing positions |
| Winning vs. losing traders | 14.7% vs. 85.2% | Share of traders with net profit vs. net loss |
| Risk-reward ratio threshold | r* = 4 | Above this, winning traders dominate the P(r) distribution |
| Win-loss duration ratio threshold | s* = 100 | Above this, winning traders dominate the P(s) distribution |
| Win-loss ROI ratio threshold | u* = 2 | Above this, winning traders dominate the P(u) distribution |
| Risk-reward ratio formula | r := ⟨p+⟩ / ⟨\|p−\|⟩ | Average profit of winning trades over average loss of losing trades, per trader |

## Why This Matters

Behavioral metrics like the risk-reward and win-loss ROI ratios can flag potential winning traders before raw performance data would. Traders who copy or follow others based on short-term performance may be copying decisions driven by loss aversion rather than skill. For online social trading platforms, adjusting for these behavioral patterns could improve how gurus or trade leaders are selected. Reducing the emotional impact of the reflection effect may help individual traders avoid the outsized losses common among losing traders. The asymmetry appears in trade-level data before it appears in intuition. A [trading journal](/trading-journal/) keeps the entries needed to check for it.

## FAQ

### What is the reflection effect in prospect theory?

Liu et al. (2014) found reflection-effect evidence across over 28.5 million trades. Traders held losing positions far longer than similarly sized winning positions. The pattern reflects risk-aversion for gains and risk-seeking for losses, prospect theory's core prediction. Losing traders made up 85.2% of the sample overall.

### What percentage of online traders end up losing money?

85.2% of traders in this study ended with a net loss, versus 14.7% with a net profit. Losing traders typically had risk-reward, win-loss duration, and win-loss ROI ratios all below 1. Loss aversion and the reflection effect, both part of prospect theory, could explain this pattern.

### What trading metrics best predict which traders will end up winning?

Three characteristic values, r* = 4, s* = 100, and u* = 2, separate winning from losing traders with high probability. The values come from the risk-reward ratio, win-loss holding time ratio, and win-loss ROI ratio. Winning percentage alone was a poor predictor, since losers dominated up to w* = 0.95.

### How does mirror trading performance compare with single and copy trading?

About 83% of mirror trades were profitable, the highest win rate among single, copy, and mirror trades. Mirror trade was also the only type with a positive average ROI, at about 0.03%. Its winning positions earned only about 0.177% ROI, while losing positions lost about 0.9% ROI on average.

## Source

Liu, Y.-Y., Nacher, J. C., Ochiai, T., Martino, M., & Altshuler, Y. (2014). Prospect Theory for Online Financial Trading. arXiv Working Paper.

[Read the full paper →](https://arxiv.org/abs/1402.6393)