Finance Research Repository
Academic papers on trading, investing, and investor behavior.
Curated by Robert Gorak · 54 papers · Last updated June 2026
The Black-Scholes Formula: Pricing Options with Five Observable Inputs
Fischer Black and Myron Scholes · 1973
The value of a European call option is w(x,t) = xN(d1) - ce^(r(t-t*))N(d2), a formula depending on only 5 observable inputs and independent of the expected return on the underlying stock.
Market Overreaction: Why Prior Losers Outperform Prior Winners
Werner F. M. De Bondt and Richard Thaler · 1985
Over the last half-century, loser portfolios of 35 NYSE stocks outperform the market by 19.6% thirty-six months after portfolio formation, while winner portfolios earn about 5.0% below the market, yielding a return spread of 24.6% (t-statistic: 2.20) in favor of prior losers.
The Carhart Four-Factor Model: Why Mutual Fund Persistence Is Not Skill
Mark M. Carhart · 1997
Buying last year's top-decile mutual funds and selling last year's bottom-decile funds yields 8 percent per year; 4.6 percent is explained by size, book-to-market, and one-year momentum factor exposures, 0.7 percent by expense ratios, and 1 percent by transaction costs.
The Efficient Market Hypothesis: Fama's Foundational Framework
Eugene F. Fama · 1970
In 89 out of 115 mutual funds studied by Jensen over 1955–1964, net ten-year returns averaged -14.6% below the market line, indicating professional fund managers do not possess information unavailable to the market.
The Cross-Section of Expected Returns: Size and Value Beat Beta
Eugene F. Fama and Kenneth R. French · 1992
Highest BE/ME stocks returned 1.83% per month vs. 0.30% for lowest BE/ME stocks — a 1.53% monthly spread — while market beta showed no reliable relation to average returns over 1963-1990.
The Fama-French Three-Factor Model: Size, Value, and Market Risk
Eugene F. Fama and Kenneth R. French · 1993
A three-factor model adding SMB and HML to the market factor raises R² for 25 size- and BE/ME-sorted stock portfolios from 0.61–0.70 to 0.94–0.97, explaining the cross-section of average returns on NYSE, Amex, and NASDAQ stocks from July 1963 to December 1991.
Momentum Investing: How Buying Winners and Selling Losers Beats the Market
Narasimhan Jegadeesh and Sheridan Titman · 1993
The 6-month/6-month relative strength strategy realizes a compounded excess return of 12.01% per year on average over the 1965 to 1989 period.
Prospect Theory: How Losses Loom Larger Than Gains
Daniel Kahneman and Amos Tversky · 1979
82% of subjects preferred a certain 2,400 over a three-outcome gamble (2,500 at .33, 2,400 at .66, 0 at .01) in Problem 1, while 83% reversed that preference in the structurally equivalent Problem 2 — a direct violation of expected utility theory.
Mean-Variance Optimization: Markowitz's Framework for Portfolio Construction
Harry Markowitz · 1952
The E-V rule implies investors should hold diversified portfolios on the efficient frontier — minimizing variance for a given expected return or maximizing return for a given variance.
The Capital Asset Pricing Model: Sharpe's Theory of Risk and Return
William F. Sharpe · 1964
In equilibrium, expected asset returns are linearly related to their systematic risk (beta), with assets that move with the market promising higher returns than those unaffected by economic activity.
Excess Volatility: Why Stock Prices Are Too Volatile to Be Rational
Robert J. Shiller · 1981
Actual S&P stock price volatility (σ(p) = 50.12, 1871–1979) exceeds the ex post rational price volatility (σ(p*) = 8.968) by a factor of more than five, violating the efficient markets inequality σ(p) ≤ σ(p*).
Mental Accounting: How Sunk Costs and Self-Control Shape Spending
Richard H. Thaler · 1980
WTP and WTA for a 0.001 disease risk diverged by an order of magnitude or more: $200 (WTP) versus $10,000 (WTA), illustrating the endowment effect whereby owned goods are systematically overvalued relative to equivalent unowned goods.
Mental Accounting: How People Categorize Money and Spending
Richard H. Thaler · 1985
Median willingness to pay for an identical beer was $2.65 from a fancy resort hotel versus $1.50 from a run-down grocery store, demonstrating that transaction utility — perceived deal fairness relative to a reference price — affects demand independently of product value.
Three Heuristics That Distort Probability Judgment
Amos Tversky and Daniel Kahneman · 1974
Anchoring caused subjects given a starting point of 10 to estimate 25 percent African countries in the UN, while those given 65 estimated 45 percent — a 20-point spread from an arbitrary number.
The Liquidity Premium: How Bid-Ask Spreads Drive Stock Returns
Yakov Amihud and Haim Mendelson · 1986
A 1% increase in the bid-ask spread was associated with a 0.211% increase in monthly risk-adjusted excess return on NYSE stocks from 1961 to 1980.
Attention-Driven Buying: Why Retail Investors Chase High-Visibility Stocks
Brad M. Barber and Terrance Odean · 2008
Individual investors at a large discount brokerage had a buy-sell imbalance of −18.15% for stocks in the lowest abnormal-volume decile, rising 29.5 percentage points to approximately +11% for stocks in the highest-volume 5%, across 78,000 households from January 1991 to November 1996.
Most Day Traders Lose Money: Evidence from Taiwan's Stock Exchange
Brad M. Barber and Yi-Tsung Lee and Yu-Jane Liu and Terrance Odean · 2004
More than eight out of ten day traders lost money in the typical six-month period on the Taiwan Stock Exchange from 1995 through 1999.
Individual Investors Lose 3.8 Percentage Points Annually to Active Trading
Brad M. Barber and Yi-Tsung Lee and Yu-Jane Liu and Terrance Odean · 2009
The aggregate portfolio of individual investors on the Taiwan Stock Exchange suffered an annual performance penalty of 3.8 percentage points from 1995 to 1999, equivalent to 2.2% of Taiwan's GDP, with virtually all losses traceable to aggressive orders.
How Individual Investors Trade: Overtrading and Underperformance
Brad M. Barber and Terrance Odean · 2013
The most active 20% of individual investors earned 11.4% annually net of costs versus 18.5% for the least active 20%—a 7 percentage-point gap—in 78,000 US brokerage accounts over 1991–1996.
Day Traders Lose Money and Keep Trading: Evidence from Taiwan
Brad M. Barber and Yi-Tsung Lee and Yu-Jane Liu and Terrance Odean and Ke Zhang · 2020
Day traders on the Taiwan Stock Exchange lost an average of 23.9 basis points per day net of fees across all 15 years from 1992 to 2006, with nearly three-quarters of day trading volume generated by traders with a history of losses.
Men Trade 45% More Than Women and Earn Less for It
Brad M. Barber and Terrance Odean · 2001
Men traded 45 percent more than women from February 1991 through January 1997, reducing their net returns by 2.65 percentage points per year versus 1.72 percentage points for women.
Overtrading Destroys Returns: Why the Most Active Individual Investors Earn the Least
Brad M. Barber and Terrance Odean · 2000
Of 66,465 households at a large discount broker from 1991 to 1996, those in the highest turnover quintile (monthly turnover >8.8%) earned a net annualized geometric mean return of 11.4 percent, while the lowest turnover quintile earned 18.5 percent and the market returned 17.9 percent.
Deliberate Practice Stabilizes Working Memory in the Brain
Arash Bellafard and Ghazal Namvar and Jonathan C. Kao and Alipasha Vaziri and Peyman Golshani · 2024
Volumetric imaging of up to 73,307 secondary motor cortex (M2) neurons in mice showed that late-delay working-memory decoding accuracy was significantly higher on days 6-10 of expert performance than on days 1-5 (P < 0.0001), showing representations stabilize only after sustained practice.
Why Overconfidence Survives: The Evolutionary Case for Entrepreneurs
Antonio E. Bernardo and Ivo Welch · 2001
In a group of 500 individuals with signal precision p = 0.51, the expected group benefit of the first overconfident entrepreneur is approximately 114 times larger than the expected cost to that individual.
Black-Litterman Model: Why Combining Market Equilibrium with Investor Views Fixes Portfolio Optimization
Fischer Black and Robert Litterman · 1992
With currency hedging, a globally diversified bonds-and-equities portfolio earned a 5.61% expected excess return versus 4.76% for a domestic-only portfolio at a constant 10.7% risk, an 85 basis-point gain, over January 1975-August 1991.
Do Moving Averages Predict Stock Returns? 90 Years of Dow Jones Evidence Says Yes
William Brock and Josef Lakonishok and Blake LeBaron · 1992
Buy signals from the variable-length moving average rule earned an average daily return of 0.042 percent (about 12 percent annualized) versus -0.025 percent (about -7 percent annualized) for sell signals over the 1897-1986 Dow Jones sample.
Quitting Your Job to Day Trade? 97% of Persistent Traders Still Lose Money
Fernando Chagué and Rodrigo De-Losso and Bruno Giovannetti · 2020
97% of the 1,551 individuals who persisted in day trading mini-Ibovespa futures for more than 300 days (Brazil) lost money net of fees.
Disposition Effect: How Investor Sophistication Reduces the Bias
Ravi Dhar and Ning Zhu · 2002
Individual-level disposition effect averaged 0.19, compared with a market-aggregate-level disposition effect of just 0.068, among 7,965 investors from January 1991 to November 1996.
Deliberate Practice: Why 7,400 Hours Separate Elite Performers from Amateurs
K. Anders Ericsson and Ralf Th. Krampe and Clemens Tesch-Römer · 1993
By age 18, the best violinists had accumulated an average of 7,410 hours of solitary practice, reliably more than the 5,301 hours accumulated by good violinists and the 3,420 hours accumulated by music teachers, F(1, 27) = 11.86, p < .01.
How the Three-Factor Model Explains Stock Market Anomalies
Eugene F. Fama and Kenneth R. French · 1996
The three-factor model leaves an average absolute intercept of just 0.093 percent per month on the 25 size-BE/ME portfolios, absorbing most CAPM anomalies over July 1963–December 1993.
Bitcoin Price Manipulation: How Two Trading Bots Fueled the 2013 Price Spike
Neil Gandal and JT Hamrick and Tyler Moore and Tali Oberman · 2018
The USD-BTC exchange rate rose by an average of four percent on days when suspicious trades took place at Mt. Gox in 2013, compared to a slight decline on days without suspicious activity.
Why Bid-Ask Spreads Exist: Adverse Selection and Informed Trading
Lawrence R. Glosten and Paul R. Milgrom · 1985
A positive bid-ask spread arises purely from adverse selection even when the specialist is risk-neutral, has zero transaction costs, and earns zero expected profit, with the equilibrium ask set to A_t = E[V|S_t, Z_t > A_t] and bid to B_t = E[V|S_t, Z_t < B_t].
Sensation Seeking and Overconfidence Drive Investor Trading Frequency
Mark Grinblatt and Matti Keloharju · 2009
Each additional speeding ticket raised the probability of trading by 4.7% and the number of trades by 9.8%, controlling for wealth, income, age, number of stocks owned, marital status, and occupation.
Momentum Profits: Why Winning Stocks Reverse Course After Five Years
Narasimhan Jegadeesh and Sheridan Titman · 2001
The cumulative momentum profit for winner-minus-loser portfolios rose to 11% by Month 12 but fell to just .79% by Month 60 over the 1965–1997 period.
Estimation Risk in Portfolios: How Bayes-Stein Shrinkage Improves Return Forecasts
Philippe Jorion · 1986
In risk-free equivalent return, Jorion (1986) found the gain of the Bayes-Stein estimator over the Bayes Diffuse Prior estimator ranges from 8 percent per annum (T = 25) to 2 percent per annum (T = 50) to 0.2 percent per annum (T = 200).
Why Investors Buy 'Lottery Stocks' (And Why They Underperform)
Alok Kumar · 2009
Individual investors allocate an average of 3.74% of their aggregate portfolio weight to lottery-type stocks, compared with 1.25% in the aggregate market portfolio and only 0.76% in the aggregate institutional portfolio, during the 1991-1996 sample period.
The Kyle Model: How Insider Trades Move Prices and Reveal Information
Albert S. Kyle · 1985
In the single auction one-half of the insider's private information is incorporated into prices (Σ₁ = ½Σ₀), and in the continuous limit all of it is, with the insider earning Σ₀^½·σ_u — exactly double the single-auction profit.
Stock Prices Don't Follow Random Walks: Evidence From 1,216 Weeks of Returns
Andrew W. Lo and A. Craig MacKinlay · 1987
Lo and MacKinlay (1987) found the equal-weighted CRSP NYSE-AMEX index had a weekly first-order autocorrelation of approximately 30 percent across 1,216 weekly observations from September 6, 1962 to December 26, 1985, rejecting the random walk hypothesis.
Technical Analysis Chart Patterns: What 35 Years of Stock Data Show
Andrew W. Lo and Harry Mamaysky and Jiang Wang · 2000
Lo, Mamaysky, and Wang (2000) found that all 10 technical chart patterns tested were statistically significant for Nasdaq stocks at the 5 percent level from 1962 to 1996, versus only 5 of 10 patterns for NYSE/AMEX stocks.
Fat Tails in Markets: Mandelbrot's Case Against the Bell Curve
Benoit Mandelbrot · 1963
Doubly logarithmic plots of cotton price changes (New York, 1900-1905, 1944-58, and 1880-1940) closely matched a stable Paretian distribution with an estimated exponent of 1.7, not the Gaussian curve.
The Disposition Effect: Why Investors Sell Winners Too Soon and Hold Losers Too Long
Terrance Odean · 1998
Investors realized gains at a 14.8% rate versus 9.8% for losses across 10,000 U.S. brokerage accounts from 1987 to 1993, making a winning stock more than 50% more likely to be sold on any given day than a losing stock.
Overtrading and Poor Stock Selection Reduce Individual Investor Returns
Terrance Odean · 1999
Over a one-year horizon, the securities purchased by discount brokerage investors underperformed those they sold by 3.31 percent (January 1987–December 1993), even before accounting for round-trip trading costs of approximately 5.9 percent.
The Disposition Effect: Why Investors Sell Winners Too Early and Hold Losers Too Long
Hersh Shefrin and Meir Statman · 1985
In Broker/Dealer mutual funds (January 1961–December 1981), the mean redemption ratio was 0.93 in capital-gains months versus 0.74 in capital-losses months (t = 1.69, significant at the 0.05 level), consistent with investors selling winners too early.
Financial FOMO: How Fear of Missing Out Drives Trading and Problem Gambling
Frank Song · 2022
Higher financial FOMO (F-FOMO) scores were significantly associated with stock market trading participation among 285 college students (t(284) = 0.08136, p = 0.006732).
Investor Overconfidence and Trading Volume: How Past Returns Fuel Overtrading
Meir Statman and Steven Thorley and Keith Vorkink · 2003
A one standard deviation market return shock produced an 8.6% increase in NYSE/AMEX market turnover the following month, accumulating to a 30% increase over six months (Statman, Thorley, and Vorkink, 2003).
Support and Resistance Levels: A Limited-Attention Theory of Technical Trading
Keisuke Teeple · 2020
A 1,000,000-period simulation with spacing ε = 100 and transaction cost τ = 2 produces a symmetric, single-peaked ergodic price density satisfying the formal support-and-resistance condition Covmod(E[pt+1|p] − p, p) < 0 (Teeple, 2020).
The Kelly Criterion: How to Size Bets for Maximum Long-Term Growth
Edward O. Thorp · 2006
Thorp (2006) reports that a Kelly-managed convertible-hedging investment partnership compounded at approximately 20 percent annually for about 28.5 years, from November 3, 1969 through May 1998, turning $10,000 into $18 million tax-exempt.
Prospect Theory in Action: How Loss Aversion Shapes Online Trading
Yang-Yu Liu, Jose C. Nacher, Tomoshiro Ochiai, Mauro Martino, Yaniv Altshuler · 2014
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%).
Individual Investors Lose 3.8% a Year From Trading: Evidence From Taiwan
Brad M. Barber and Yi-Tsung Lee and Yu-Jane Liu and Terrance Odean · 2009
The aggregate portfolio of individual investors in Taiwan suffered an annual performance penalty of 3.8 percentage points from 1995 to 1999, while institutions earned an annual performance boost of 1.5 percentage points.
The Martingale Betting System: What the Math Says About the Risk of Ruin
Peter Pflaumer · 2019
After 10,000 simulated martingale rounds (20,529 coups) on a simple chance in European roulette (p=19/37), the expected total profit is E(W) = -3,056.27 and the probability of a positive profit is only 18.28 percent.
Do Candlestick Chart Patterns Predict Stock Returns? Evidence from Thailand
Piyapas Tharavanij, Vasan Siraprapasiri and Kittichai Rajchamaha · 2017
The highest statistically significant candlestick pattern return was 0.71% (Opening White Marubozu, 10-day holding period, MYR exit strategy), while most patterns tested on Thailand's SET50 index from 2006 to 2016 showed no significant predictive power.
Correlated Betting Streaks and Risk of Ruin: A Martingale Analysis
Vladimir Pozdnyakov · 2025
For a fair-coin game betting on HH against TH, the ruin probability formula α = (B - 1/2)/(A + B) gives α = .25 when A = B = 1.
The Framing Effect: How Wording Alone Flips Preference From 72% to 22%
Amos Tversky and Daniel Kahneman · 1981
Tversky and Kahneman (1981) found that framing an identical outcome as lives saved led 72 percent of respondents to choose the certain option, while framing it as lives lost led only 22 percent to choose the same certain option.
Memory Bias in Trading: Why Investors Recall Better Returns Than They Earned
Daniel J. Walters and Philip M. Fernbach · 2021
Overconfidence fell from 9.2% among investors relying on memory of past returns to 5.8% among those who looked up their actual returns, t(364) = 2.91, P = 0.004 (n = 366, 2018 trades).