We document strong persistence in the performance of trades of individual investors. The correlation of the risk-adjusted performance of an individual across sample periods is about 10 percent. Investors classified in the top performance decile in the first half of our sample subsequently outperform those in the bottom decile by about 8 percent per year. Strategies long in firms purchased by previously successful investors and short in firms purchased by previously unsuccessful investors earn abnormal returns of 5 basis points per day. These returns are not confined to small stocks nor to stocks in which the investors are likely to have inside information. Our results suggest that skillful individual investors exploit market inefficiencies to earn abnormal profits, above and beyond any profits available from well-known strategies based upon size, value, or momentum. The paper is available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=364000

1. Joshua Coval, David Hirshleifer, and Tyler Shumway
HBS, Ohio State, and Michigan
December 2001
Can Individual Investors Beat the Market?

2. Efficient Market Hypothesis
EMH has been tested and debated for decades.
In most tests econometricians back-test `reasonable’ strategies
These tests assume that econometrician knows what investors
knew
– (Econometrician can condition on the most promising strategies).
If a profit opportunity was found, these tests do not indicate
whether smart investors were exploiting at the time.
– Was the profit opportunity clear to someone based on information
available at the time?
information processing technology, data availability

3. Alternative Approach
EMH: traders can not consistently outperform or underperform
the market.
Can we find a set of traders that can consistently beat the market?
– If not, markets may satisfy a weaker notion of efficiency.
Daniel/Titman (1999)
– If so, strategies existed which can exploit return predictability.
Tests do not identify what those strategies are.
With timely access to transactions data, it further suggests that
mimicking portfolios can be constructed which beat the market.

4. Alternative Approach
This approach is attractive along a number of dimensions:
1. Vastly expands the set of strategies being (indirectly) tested.
2. Expands set of information on which trades are conditioned.
3. Only considers strategies that can be implemented in ‘real
time’ using information available at the time to participants.
4. Places little burden on econometrician to run many diverse
tests or to figure out how to adjust for datamining.
This approach resembles research examining persistence of
mutual fund performance.

5. Persistence in Mutual Fund Performance
Average pre-expense mutual fund performance is mixed.
– Carhart (1995), Daniel, Grinblatt, Titman, Wermers (1997), and
Chevalier and Ellison (1999), Wermers (2000)
– Whether there is persistent superior performance depends on whether
the momentum effect is viewed as superior performance or an ordinary
benchmark return.
Little evidence of persistence beyond that due to expenses and
due to momentum.
Mutual funds that beat market consistently are tough to identify:
- trading costs (i.e. market impact) are high.
- cannot deviate too far from benchmark portfolio.
- quarterly transactions data insufficient.

6. Individual Investors
Examining individual investor performance is
worthwhile:
– price impact is minimal.
– are free to consider any strategies/sectors they’d like.
On the other hand, as a group, we should be
skeptical of individual trader ability. Traders using a
discount brokerage have been shown to:
– trade too much (Barber and Odean, 2000)
– hold on to losers too long (Odean, 1998)
– underperform the market (Barber and Odean, 2000).

7. Individual Traders
We focus upon the subset of accounts that outperform the
market (Barber and Odean (2000) find that 25% of accounts
outperform market by more than 6% per year).
Are these investors lucky or smart?
– I.e. does their performance persist?
Lucky:
– Confirms EMH implication that the market is difficult to beat.
Focusing on transactions – and performance of trades during
subsequent period – maximizes our power to detect ability.

8. The Data
Large discount brokerage dataset.
Data from 1991-1996.
Information on holdings, transactions, and account
characteristics.
110,000 accounts.
Many accounts are small and trade infrequently.

9. A Simple Test of Performance Persistence
1. “Risk-adjust” all returns
- factor-based adjustment
- characteristic-based adjustment
2. Split sample in half
3. Retain only accounts with at least 25 transactions in
first half.
4. Examine correlation in mean returns, risk-return
ratios, and p-values across sample halves.

10. Return Horizon
Our tests typically focus on the returns earned on
positions during the week after the trade is placed.
To the extent that the trader’s alpha (i.e. informational
(dis)advantage) reverts towards zero, shorter horizons
deliver superior power.
Longer horizons require more of the sample to classify
traders – since our sample is only 6 years, longer
horizons leave us with little data for testing.
We do examine the impact of horizon on our tests.

11. Measuring Economic Significance
To maximize our power in classifying a trader’s ability, we also a
complementary image procedure:
1. Corresponding to each trade of each trader, we construct a
p-value – the CDF of the t-stat that his other trades have
zero risk-adjusted average returns.
2. We then sort trades into deciles according to p-values of
trader’s other trades.
3. Calculate average risk-adjusted returns for each decile.
Since this procedure uses ex-post data, it does not represent a
feasible trading strategy.
But if risk-adjusted returns of an account are independent, zero-
mean draws, portfolios should all have zero average returns.

12. Robustness Checks
Results are robust to:
Including all trades and sorting according to average
return instead of p-value results not driven by
frequent traders.
Removing smallest third of all CRSP stocks results
not limited to small firms or due to microstructure
effects.
Removing any trade in a stock that has been traded by
that account more than once results not driven by
trading on inside information.

13. A Trading Strategy
1. Sort accounts at beginning of each month into quintiles
according to p-value that returns from start of the sample
have positive mean.
2. Drop smallest third of all stocks.
3. Only include accounts with 25+ purchases.
4. Mimic purchases of top quintile; fade purchases of bottom
quintile; place trades on following day and sell a week later;
value-weight portfolios.
5. Adjust strategy’s returns for risk: regress on daily realizations
of Rm-Rf, Size, BM, and Momentum ‘factors.’

14. Trading Strategy Returns
One-day horizon returns are largest, one-month
horizon returns are negligible.
Although returns are strong – 5 basis point per day –
strategy involves lots of trading.
Only have 6-years of data; with a longer time series,
returns should improve as classification becomes
more accurate.

15. Conclusions
There appears to be strong performance persistence
among individual investors.
Information contained in individuals’ trades is
economically and statistically significant.
If traders at a discount brokerage can select stocks
this well, the market cannot be too efficient.
If people learn about ability by trading, ‘excessive’
trading may not be so irrational.