Market anomalies and limits to arbitrage - Momentum represen...

Learning Outcomes

This article explains key behavioral market anomalies and limits to arbitrage, including:

• defining momentum as a market anomaly and contrasting it with the predictions of the efficient market hypothesis;
• describing how representativeness bias shapes expectations, belief updating, and return-chasing behavior;
• analyzing how investor overreaction contributes to short-term momentum, long-term reversals, and pricing inefficiencies;
• identifying practical limits to arbitrage—such as short-sale constraints, implementation costs, and noise trader risk—that prevent rapid correction of mispricings;
• linking these behavioral mechanisms and frictions to the persistence of anomalies across markets and asset classes;
• evaluating the risk/return and portfolio-construction implications of trading on momentum and related anomalies;
• applying these concepts within CFA Level 3 exam-style scenarios, including qualitative explanations, item set interpretation, and calculation-based questions that rely on understanding behavioral finance foundations;
• distinguishing between risk-based and purely behavioral explanations for observed return patterns and articulating how exam questions may test these competing interpretations in CFA curriculum contexts.

CFA Level 3 Syllabus

For the CFA Level 3 exam, you are required to understand the behavioral foundations of persistent market anomalies, with a focus on the following syllabus points:

• explaining the emergence and persistence of market anomalies such as momentum in the context of the efficient market hypothesis (EMH);
• describing how cognitive biases, including representativeness and overreaction, influence investor behavior and security prices;
• discussing practical limits to arbitrage and the reasons anomalies can persist despite the actions of rational traders;
• analyzing the risk/return consequences for portfolios, including factor-based and active strategies that exploit momentum and reversals;
• evaluating how anomalies complicate asset-pricing models and the construction of benchmark-relative portfolios.

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. Which statement best describes the momentum anomaly in equity markets?
   1. Stock returns are independent over time, so past returns contain no information about future returns.
   2. Stocks with high past returns over medium horizons tend to continue outperforming, contrary to the weak-form EMH.
   3. Stocks with high past returns always revert immediately to their long-run mean.
   4. Momentum profits can be fully explained by differences in market beta.
2. An institutional investor allocates heavily to a “star” manager after observing three years of strong outperformance, assuming this short history is proof of skill and will continue indefinitely. Which bias best explains this behavior?
   1. Loss aversion
   2. Representativeness
   3. Overconfidence
   4. Anchoring
3. A contrarian manager buys stocks that have fallen sharply after bad news, expecting the initial price decline to be excessive and followed by a partial rebound. Which statement is most accurate?
   1. The manager is exploiting investor overreaction and expecting a subsequent reversal.
   2. The manager is exploiting underreaction and expecting further price declines.
   3. The manager is following a momentum strategy based on return continuation.
   4. The manager is arbitraging away risk-free profits with no implementation risk.
4. In the context of behavioral anomalies, “limits to arbitrage” most accurately refers to:
   1. Regulatory rules that prohibit short selling in all markets.
   2. Frictions and risks that prevent rational traders from fully and immediately eliminating mispricings.
   3. Accounting rules that restrict recognition of unrealized gains and losses.
   4. Investor risk aversion, which prevents investors from holding risky assets.

Introduction

Market anomalies are persistent patterns in returns that contradict the predictions of traditional finance models such as the CAPM and the efficient market hypothesis (EMH). Under the weak-form EMH, past price and return information should not help forecast future returns. Yet empirical evidence documents return continuation and reversals that are both economically and statistically significant.

This article focuses on three related ideas:

• momentum as a return anomaly;
• representativeness bias as a driver of extrapolative expectations and return-chasing;
• investor overreaction as a source of both short-term trends and long-term reversals.

These behavioral forces interact with real-world trading frictions—limits to arbitrage—to generate and sustain anomalies. The discussion connects directly to Level 3 portfolio management: managers may deliberately tilt portfolios toward momentum or contrarian (value/reversal) effects, must understand associated risks, and should be able to explain whether such strategies are consistent with a client’s investment policy statement (IPS).

Key Term: market anomaly
An observable pattern in financial returns that is inconsistent with standard asset pricing models and cannot be explained by risk alone.

Key Term: momentum
The tendency for securities that have performed well (poorly) in the recent past to continue performing well (poorly) over subsequent periods.

Key Term: representativeness bias
A cognitive error where investors judge the probability or value of an event based on how closely it matches a prototype, often leading to neglect of base rates and sample size.

Key Term: overreaction
A behavioral pattern where investors place excessive weight on recent or salient news, causing prices to deviate from fundamental values.

Key Term: limits to arbitrage
Real-world constraints that prevent rational traders from quickly correcting mispricings caused by irrational market participants.

Key Term: noise trader risk
The risk that irrational traders push prices further away from fundamental value in the short run, causing losses for arbitrageurs before prices eventually correct.

From a Level 3 view, the important skills are:

• diagnosing which bias is at work in a case vignette;
• explaining how that bias translates into systematic return patterns;
• assessing whether and how a manager should exploit or avoid those patterns in constructing client portfolios.

THE MOMENTUM ANOMALY

Momentum refers to the empirical finding that stocks with high past returns over short to intermediate horizons tend to earn higher future returns than those with poor past performance. In cross-sectional momentum, securities are sorted by past performance and high-return “winner” portfolios subsequently outperform low-return “loser” portfolios. In time-series momentum, an asset’s own past return sign predicts its future excess return.

Typical implementations:

• rank stocks on 6–12 months of past returns (often skipping the most recent month to avoid very short-term reversals);
• go long the top decile (winners) and short the bottom decile (losers);
• hold the long–short portfolio for 6–12 months.

A simple momentum factor return can be written as:

Empirically:

• the strongest effects are over 3–12 month horizons;
• momentum has been documented in many equity markets and also in other asset classes (currencies, commodities, bonds);
• even after controlling for standard risk factors, the anomaly remains large in many samples.

This finding is at odds with the weak-form EMH, which predicts that past returns should have no predictive power after accounting for risk.

Psychological Drivers

Momentum arises partly because of behavioral biases that affect how investors process and project information:

• Representativeness: Investors conclude that recent winners are fundamentally superior and expect trends to persist. A few strong quarters of earnings growth or price appreciation are judged “representative” of a permanently improved company, leading to return projection and buying pressure in recent winners.

• Overreaction and underreaction: Initially, some investors may underreact to new information (conservatism bias), so prices adjust slowly. As positive news accumulates and price trends emerge, other investors overreact—placing too much weight on recent information and price moves. Return-chasing behavior amplifies trends and contributes to momentum.

• Confirmation and herding: Investors selectively attend to news that confirms the existing trend and ignore disconfirming evidence (confirmation bias). Professional managers face career risk if they lag peers, which encourages herding into popular trades and reinforces momentum.

These behavioral dynamics can rationalize why momentum appears strongest over intermediate horizons: a phase of underreaction (prices drift toward fundamentals) followed by overreaction (prices overshoot).

Risk-Based Versus Behavioral Explanations

Some researchers argue that momentum profits compensate for exposure to hidden risk factors:

• winner stocks may be more sensitive to macroeconomic or liquidity shocks;
• momentum portfolios can experience large drawdowns, suggesting they are “riskier” in some dimensions.

However, purely risk-based explanations struggle to explain:

• why momentum often coincides with eventual long-term reversals (over 3–5 years);
• why the pattern is linked so tightly to investor trading flows and sentiment measures.

The CFA curriculum presents momentum as a leading example where behavioral and risk-based views coexist. In exam questions, you may be asked to:

• contrast these explanations for a manager’s momentum tilt; or
• assess whether momentum returns are likely to persist given changing competition and transaction costs.

Portfolio Implementation and Risks

In practice, momentum is often implemented as one style factor within a diversified, factor-based portfolio. Key features and risks include:

• High turnover: Momentum strategies require frequent rebalancing as the winner and loser sets change, leading to:

  • higher transaction costs;
  • greater tax drag in taxable portfolios.

• Tail risk and crash risk: The curriculum highlights that simple price momentum strategies have experienced extreme losses, notably in 2009 when sharp market rebounds caused prior losers to surge and prior winners to lag. A long–short momentum portfolio lost more than 50% over a three-month period in that episode.

• Sector and industry concentration: Simple momentum can inadvertently concentrate exposure in hot sectors (e.g., technology in a boom), increasing idiosyncratic risk. A sector-neutral implementation—ranking stocks relative to their sector and constructing long–short positions within each sector—tends to reduce unintended industry bets and downside risk.

• Capacity constraints: As assets under management grow, trading in illiquid names becomes more costly or impossible at scale, limiting the size of implementable momentum strategies.

Level 3 questions may ask whether a momentum tilt is appropriate for a given client, given:

• tolerance for short-term underperformance and drawdowns;
• constraints on turnover and costs;
• benchmark-relative risk limits (tracking error budgets).

Worked Example 1.1

A fund manager notices that technology stocks have outperformed for six months. She increases her portfolio allocation to the sector, expecting outperformance to continue. What behavioral bias is this and how might it influence portfolio risk?

Answer:
This is an example of representativeness bias, where the manager assumes recent sector performance is indicative of future outcomes without considering base rates, valuation, or mean reversion. By projecting a short performance history forward, she may take a concentrated sector position, increasing active risk and the likelihood of significant underperformance if the trend reverses or if tech-specific risks materialize.

Worked Example 1.2

A quantitative equity manager runs a global momentum strategy. Version A ranks all stocks on past 12‑month returns and goes long the top decile and short the bottom decile, regardless of sector. Version B performs the same ranking within each sector and constructs long–short portfolios that are sector neutral. Which version is likely to have lower downside risk, and why might that be important for an institutional client?

Answer:
Version B, the sector-neutral momentum strategy, is likely to have lower downside risk. By ranking and trading within sectors, it removes large, unintended sector bets and focuses on stock selection. This reduces the risk that a sharp reversal in a single popular sector will severely damage performance. For institutional clients with tracking-error limits or who are evaluated relative to sector-diversified benchmarks, sector-neutral momentum better aligns with risk budgets and may reduce the likelihood of extreme underperformance periods that could trigger client withdrawals or mandate termination.

REPRESENTATIVENESS BIAS IN INVESTMENT DECISION-MAKING

Representativeness bias causes investors to believe that a small set of recent data (such as a strong quarter or a short period of outperformance) indicates a permanent change in fundamentals. Rather than integrating long-term probabilities (base rates), investors classify information according to stereotypes or salient prototypes.

Typical manifestations include:

• projecting a few years of high earnings growth into the indefinite future, treating the company as a “growth stock” that deserves a permanently high valuation multiple;
• assuming a fund manager with a short streak of outperformance must be highly skilled, ignoring that many managers underperform after becoming “stars”;
• inferring that a country or sector experiencing a boom is permanently transformed and will continue to deliver superior returns.

Mechanically, representativeness involves:

• base-rate neglect: underweighting or ignoring the long-run frequency of outcomes (e.g., how often star managers persist) in favor of vivid, recent performance;
• insensitivity to sample size: treating a small sample (a few periods of strong data) as if it were statistically reliable.

This bias explains return-chasing behaviors and the tendency to overvalue recent winners while undervaluing laggards. It helps fuel momentum, as investors buy securities whose recent behavior matches the “good investment” prototype.

Consequences for portfolios can include:

• Style and sector crowding: Overweighting recent winners (e.g., high-growth tech, private equity) and underweighting “boring” assets (e.g., value stocks, government bonds), leading to poor diversification and vulnerability to regime changes.

• Performance-chasing in manager selection: Firing underperforming managers and hiring recently outperforming ones, often at exactly the wrong time. The empirical evidence shows that such performance-chasing frequently destroys value after fees.

• Overpaying for glamour stocks: Paying high multiples for companies with exciting narratives and recent success while avoiding out-of-favor value stocks, setting up future long-term reversals.

Representativeness is a cognitive error, so it can be moderated through education and process discipline:

• use long-run statistics (e.g., persistence of manager alpha, historical sector cycles) when forming expectations;
• require minimum sample sizes and robust performance attribution before classifying a manager as “skilled” or a strategy as “broken”;
• embed checklists in the investment process that explicitly ask whether base rates are being ignored and whether the sample is large enough.

Exam Warning

Misidentifying the base rate when estimating future returns can lead to overestimating the success probability of “hot” managers or stocks. In exam cases, look for:

• short performance histories being treated as conclusive evidence of skill;
• ignored references to long-term averages or failure rates;
• language that labels investments as “obvious winners” based on a small number of observations.

Such cues typically point to representativeness rather than to sound statistical reasoning.

Worked Example 1.3

A committee is reviewing two equity managers. Manager X has outperformed the benchmark by 3% per year for the past three years. Manager Y has a 10‑year record with modest outperformance of 0.5% per year and a more defensive style. The committee recommends replacing Y with X, arguing that “X clearly has more skill, as shown by recent results.” Which bias is most evident, and what are the potential implications?

Answer:
The committee is displaying representativeness bias by treating three years of strong results as representative of Manager X’s true skill and implicitly ignoring the longer base-rate evidence that few managers sustain such outperformance. They also undervalue Manager Y’s longer track record and defensive characteristics. The portfolio may become tilted toward a recently popular style, with higher active risk and a greater chance that subsequent mean reversion in styles leads to disappointing relative performance.

OVERREACTION AND LIMITS TO ARBITRAGE

When investors overreact, prices move excessively in response to current information, deviating from their fundamental value. Overreaction is closely linked to representativeness: investors project recent news too far into the future and interpret it as evidence of a new regime.

Overreaction can generate both:

• short-term momentum: Prices continue in the direction of recent news as investors chase trends and latecomers pile into winning trades.
• long-term reversals: Eventually, when expectations prove too optimistic or pessimistic, prices correct, and past winners underperform while past losers outperform.

Contrarian and deep-value investors aim to exploit these long-term reversals, while momentum investors exploit the intermediate-horizon trend.

Key Term: overreaction
Occurs when investors place too much weight on new or salient news, leading to exaggerated price movements and potential asset mispricings.

From a portfolio view, understanding overreaction helps in:

• timing rebalancing or contrarian tilts (e.g., adding to value stocks after a sharp sell-off);
• assessing whether a manager’s tilt toward distressed assets or past losers is justified by fundamentals or is simply premature risk-taking.

Limits to Arbitrage

Although overreaction and representativeness create mispricings, these mispricings are not automatically arbitraged away. Limits to arbitrage explain why behavioral anomalies can persist.

Key Term: limits to arbitrage
Real-world frictions—such as transaction costs, institutional constraints, and the risk of further divergence—that reduce or delay the effectiveness of rational trading strategies.

Key limits include:

• Short-sale constraints:

  • Regulatory restrictions or internal policies may ban or limit short selling.
  • Securities may be difficult or expensive to borrow; lenders can recall shares, forcing premature closure of short positions.
  • Short squeezes can inflict large losses on arbitrageurs, deterring aggressive shorting of overvalued securities.

• Implementation costs:

  • High bid–ask spreads, market impact, and commissions particularly in small-cap or illiquid stocks restrict trade size and frequency.
  • High turnover strategies such as momentum have larger cost drag, which can erode expected alpha, especially in real-world implementations versus academic backtests.

• Noise trader risk (horizon risk):

  • Prices can move further away from fundamentals before correcting as noise traders continue to trade on sentiment.
  • Arbitrageurs with finite capital and performance evaluation horizons may suffer interim losses, trigger risk limits, or face client redemptions, forcing trade liquidation before mispricing resolves.

• Model and fundamental risk:

  • True fundamental value is uncertain; arbitrageurs might be wrong in their assessment of mispricing.
  • Unexpected news can permanently change fundamentals in the direction arbitrageurs had bet against.

• Institutional and career risk:

  • Managers are evaluated relative to benchmarks and peers. Positions that deviate significantly from consensus (e.g., heavy shorting of popular winners) increase tracking error and the risk of near-term underperformance.
  • Fear of losing mandates or bonuses discourages managers from exploiting mispricings aggressively, especially when doing so requires going against prevailing market sentiment.

Key Term: noise trader risk
The risk that irrational trades will cause prices to diverge further from fundamental value in the short run, exposing arbitrageurs to losses and client withdrawals before prices mean revert.

Because of these limits, profitable anomalies can coexist with rational arbitrageurs. Even if arbitrage is eventually effective, the path of prices can be slow and painful, which is critical for understanding the real-world risk of strategies such as momentum and contrarian value.

Worked Example 1.4

A value hedge fund identifies an overheated growth stock with poor fundamentals. Due to inability to borrow shares and high transactions costs, it cannot short the stock in size. The stock price continues to rise before eventually collapsing. What prevented the arbitrage?

Answer:
Limits to arbitrage restricted the hedge fund’s ability to profit from the mispricing. Short-sale constraints and stock lending availability limited position size, while high trading costs further reduced the attractiveness of the trade. Noise trader risk was also significant: continued buying by optimistic investors pushed the price higher in the short run, exposing any early short positions to large mark-to-market losses. These frictions allowed the overvaluation to persist until fundamentals eventually reasserted themselves.

WHY ANOMALIES PERSIST

The persistence of anomalies like momentum and long-term reversals is best understood as the joint outcome of:

• Psychological biases:

  • representativeness and confirmation bias drive return projection and trend-chasing;
  • overreaction and herding magnify price swings;
  • conservatism and cognitive costs can delay incorporation of complex information, allowing slow-moving price drifts.

• Institutional frictions and limits to arbitrage:

  • short-sale constraints and funding frictions limit contrarian positions against popular overvalued assets;
  • transaction costs and capacity constraints reduce the net benefits of exploiting high-turnover anomalies;
  • benchmark-oriented evaluation and career concerns discourage large, contrarian, high-tracking-error trades.

Even in highly developed markets, these forces can keep prices misaligned with fundamentals for months or years. For Level 3 exam purposes, when asked why a documented anomaly has not disappeared despite awareness and arbitrage activity, it is rarely sufficient to mention “markets are inefficient.” Instead, integrate:

• the main behavioral bias;
• the key arbitrage limits relevant for that specific anomaly; and
• any risk-based rationale that might justify part of the return pattern.

Revision Tip

The CFA exam often tests the practical limits to arbitrage. When evaluating a strategy that appears to exploit mispricing (momentum, value, or contrarian), always consider:

• behavioral origins of the anomaly;
• market frictions and institutional constraints that may prevent rapid correction;
• whether the strategy’s returns could instead reflect compensation for bearing specific risks.

Summary

Momentum, representativeness, and overreaction illustrate how behavioral biases and real-world constraints combine to generate persistent return patterns that challenge classical market efficiency:

• Momentum captures intermediate-horizon return continuation, driven by trend-based expectations and trend-chasing, but is subject to high turnover and severe crash risk.
• Representativeness leads investors to overweight recent, salient information and underweight base rates, driving performance-chasing and crowding into recent winners.
• Overreaction creates excessive price swings and, over longer horizons, opportunities for contrarian and value strategies to capture reversals.
• Limits to arbitrage—short-sale constraints, implementation costs, noise trader risk, and institutional career concerns—prevent rational traders from fully and immediately correcting mispricings.

For Level 3 candidates, the core task is to integrate these ideas into portfolio decisions: determining when exploiting anomalies is consistent with a client’s objectives and constraints, assessing the risks of such strategies, and clearly articulating risk-based versus behavioral explanations in exam-style responses.

Key Point Checklist

This article has covered the following key knowledge points:

• Define momentum and explain why short- to medium-term return continuation contradicts the weak-form EMH.
• Describe representativeness bias, including base-rate neglect and sample-size insensitivity, and its impact on belief updating and portfolio risk.
• Explain how overreaction can generate both short-term momentum and long-term reversals, creating opportunities for momentum and contrarian strategies.
• Identify main limits to arbitrage—short-sale constraints, implementation costs, noise trader risk, and institutional frictions—that hinder correction of mispricings.
• Discuss risk-based versus behavioral explanations for momentum and reversals and how they affect the interpretation of factor-based strategies.
• Evaluate the implementation challenges and tail risks associated with momentum strategies, including sector concentration and high turnover.
• Apply these principles to CFA-style questions on behavioral anomalies, portfolio construction, and manager evaluation.

Key Terms and Concepts

• market anomaly
• momentum
• representativeness bias
• overreaction
• limits to arbitrage
• noise trader risk