Market anomalies and limits to arbitrage - Investor sentimen...

Learning Outcomes

This article examines market anomalies and limits to arbitrage in the context of investor sentiment and liquidity effects, including:

• Explaining how investor sentiment waves, behavioral biases, and narrative-driven trading can push prices away from fundamental value, and why such mispricing can persist even in relatively liquid markets.
• Distinguishing and illustrating key limits to arbitrage—fundamental risk, noise trader risk, implementation costs, short-sale constraints, and redemption or funding risk—and relating them to common exam-style cases.
• Analyzing how liquidity risk, bid–ask spreads, market depth, and trading capacity shape arbitrage effectiveness across equities, fixed income, and alternative asset classes.
• Evaluating how institutional investor flows, benchmark mandates, liquidity requirements, and funding fragility interact with sentiment and liquidity to amplify or dampen anomalies through time.
• Linking prominent anomalies (e.g., momentum, value, closed-end fund discounts, liquidity premia, and speculative bubbles) to specific market frictions and behavioral drivers emphasized in the CFA Level 3 curriculum.
• Applying these concepts to portfolio construction, risk management, and manager evaluation, including how to judge the exploitability of a perceived mispricing given mandate, horizon, funding, and risk constraints.
• Interpreting qualitative vignettes and basic quantitative evidence in exam questions to determine whether observed return patterns reflect genuine anomalies, risk compensation, or liquidity and implementation effects.

CFA Level 3 Syllabus

For the CFA Level 3 exam, you are required to understand market anomalies and the limits to arbitrage, with a focus on the following syllabus points:

• Recognizing the role of investor sentiment in driving prices away from fundamental value.
• Discussing how behavioral factors and institutional constraints can lead to market characteristics inconsistent with traditional finance.
• Describing the main limits to arbitrage and how these limits impede the correction of mispricings.
• Analyzing the impact of liquidity risk, trading costs, and short-sale constraints on arbitrage strategies.
• Assessing how investor flows, liquidity mandates, and funding conditions increase or dampen anomalies.
• Integrating these concepts into portfolio construction, risk management, and client communication.

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. A portfolio manager believes a group of small-cap “story” stocks is significantly overvalued based on fundamentals. Shorting them is expensive and risky, and her clients judge performance quarterly. Which combination of forces most directly explains why the mispricing may persist?
   1. Low fundamental risk and high market liquidity
   2. High noise trader risk and high redemption risk
   3. Low implementation costs and low short-sale constraints
   4. High diversification benefits and low funding risk
2. An arbitrageur considers buying an off-the-run corporate bond that appears underpriced relative to an on-the-run issue with similar credit quality and duration. Which factor is most likely to prevent this apparent arbitrage from being fully exploited?
   1. High bid–ask spreads and limited secondary market depth in the off-the-run bond
   2. The inability to estimate default probabilities for the issuer
   3. The requirement to hold the bond to maturity in all institutional mandates
   4. The fact that yield curve shifts are always parallel
3. A hedge fund implements a long–short strategy to exploit a perceived valuation gap between a closed-end fund trading at a deep discount to NAV and its portfolio. Which limit to arbitrage is most likely to reduce the attractiveness of this trade?
   1. The existence of market-neutral ETFs
   2. Difficulty and cost of shorting all portfolio holdings in the correct weights
   3. The ability to perfectly hedge fundamental risk with index futures
   4. The guaranteed narrowing of the discount within a fixed horizon
4. In the context of portfolio construction, which statement best links investor sentiment, liquidity, and anomaly strength?
   1. Anomalies are strongest in large, liquid stocks because arbitrageurs can trade them cheaply.
   2. Mispricing is typically independent of investor flows and liquidity conditions.
   3. Anomalies tend to be more pronounced in illiquid, difficult-to-value securities when sentiment is extreme.
   4. Investor sentiment mainly affects government bonds, not equities or alternative assets.

Introduction

Conventional finance, based on the efficient markets hypothesis, assumes that asset prices fully and quickly reflect all available information because rational, profit-seeking traders eliminate mispricing through arbitrage. In such a world, any deviation from fundamental value would be small, short-lived, and easily exploited.

Real-world markets do not completely fit this description. Empirical research documents persistent “anomalies” – predictable patterns in returns that are difficult to reconcile with standard risk–return models. Some anomalies appear related to risk factors, but many are closely tied to investor sentiment and are strongest where arbitrage is hardest.

Key Term: market anomaly
A pattern or regularity in asset prices that appears inconsistent with market efficiency and cannot be fully explained by standard risk–return models.

Understanding why mispricing arises, why it can persist, and how it eventually gets resolved is central at Level 3. For portfolio managers, the key is not just to recognize anomalies, but to identify the frictions and behavioral forces that limit arbitrage, especially when making active tilts or assessing client expectations about “inefficiencies.”

Two broad drivers explain why anomalies can endure:

• The influence of aggregate investor sentiment, particularly for assets that are hard to value or attract speculative attention.
• Significant limits to arbitrage, especially where liquidity is poor, trading costs are high, short selling is constrained, or funding and redemption risks are material.

These drivers are mutually supporting. Sentiment often pushes prices furthest away from fundamentals precisely in market segments where arbitrage is most constrained.

Key Term: investor sentiment
The propensity of investors to trade or hold views that are not fully justified by rational, fundamental analysis, often reflecting moods, narratives, or heuristics.

Key Term: limits to arbitrage
Practical frictions and risks that prevent rational investors from fully exploiting and correcting mispricings in financial markets.

The following sections develop these ideas and link them to specific anomalies such as momentum, closed-end fund discounts, and speculative bubbles, with emphasis on how they affect real-world portfolio decisions.

Investor Sentiment and Asset Pricing

Investor sentiment captures systematic deviations from rational valuation. Rather than focusing purely on discounted cash flows, investors may be driven by:

• Representativeness and availability: extrapolating recent trends or highly salient events.
• Overconfidence and self-attribution: overestimating their own skill and underweighting risk.
• Herding and social proof: following others because “everyone else is buying.”
• Framing and mental shortcuts: reacting differently to the same information based on how it is presented.

When optimistic sentiment dominates, investors bid up the prices of “glamour” stocks: fast-growing firms, narrative-driven sectors (e.g., new technologies), or companies that have recently outperformed. Pessimistic sentiment has the opposite effect on complex, opaque, or unpopular assets, such as distressed debt or out-of-favor value stocks.

In both cases, sentiment-driven demand can push prices away from fundamentals and create anomalies:

• Short-term momentum: continued outperformance of recent winners and underperformance of recent losers.
• Long-term reversals: eventual underperformance of previously favored glamour stocks and recovery of unloved value stocks.
• Bubbles and crashes: extreme overvaluation followed by sharp corrections.

Sentiment tends to be strongest in:

• New, difficult-to-value industries (e.g., emerging technologies, biotech).
• Small-cap or illiquid stocks where information is sparse and trade sizes are small.
• Assets with compelling narratives that attract media attention and retail participation.

Sentiment is often measured indirectly: survey data, retail trading volumes, IPO activity, fund flows, valuation ratios, or option-implied skew can all proxy for optimism or pessimism.

What keeps mispricing from being instantly arbitraged away is not the absence of rational investors, but the risks and costs they face in opposing sentiment. To see this, we need to unpack the main limits to arbitrage.

Limits to Arbitrage

In textbook finance, arbitrage is riskless: buy the underpriced asset, short the overpriced one, lock in a profit. In reality, arbitrage is usually risky, capital-intensive, and vulnerable to the behavior of others. Several limits are especially important for Level 3.

Key Term: fundamental risk
The risk that new fundamental information, unrelated to initial mispricing, moves a security’s value against the arbitrageur before prices converge to fair value.

Key Term: implementation costs
The explicit and implicit costs of executing and maintaining a trade, including commissions, bid–ask spreads, market impact, search costs, and financing costs.

Key Term: short-sale constraints
Legal, institutional, or economic frictions that limit the ability to establish or maintain short positions, including bans, borrowing costs, and recall risk.

Key Term: noise trader risk
The risk faced by arbitrageurs that irrational or sentiment-driven investors will move prices further away from fundamental value before correction occurs.

Fundamental risk

Even if a security is mispriced today, its true value is uncertain and can change. A “cheap” stock may become cheaper because bad news arrives, not because the market is irrational. Arbitrageurs cannot perfectly hedge security-specific or model risk; at best, they hedge broad market and factor exposures.

This means that expected arbitrage profit must compensate for both mispricing and residual risk. A simple way to represent this is:

where:

• $E[\Pi]$ = expected net profit from the trade
• $E[V_T]$ = expected fundamental value at horizon $T$
• $P_0$ = current market price
• $C_{\text{impl}}$ = present value of implementation costs

Arbitrageurs will act only if $E[\Pi]$ is sufficiently positive relative to the risk of adverse fundamental shocks. If fundamental risk is large or mispricing is small, the trade may not be attractive, allowing anomalies to persist.

Implementation costs

Implementation costs are particularly important in less liquid markets:

• Wide bid–ask spreads and low depth increase the round-trip cost of trading.
• OTC markets, such as many fixed-income sectors, involve search costs and less transparent pricing.
• Market impact from trading in size can erode expected profit.

In bonds, for example, bid–ask spreads and duration combine to create significant trading costs. The curriculum illustrates that a 10 bp bid–ask spread on a 15-year duration corporate bond implies roughly a 1.5% cost of moving in and out. An arbitrageur needs a much larger mispricing to justify such trades in illiquid securities.

Short-sale constraints

Profiting from overvaluation is often harder than from undervaluation. Short-sale constraints arise because:

• Some securities are hard or expensive to borrow (“specials” in securities lending).
• Lenders can recall shares, forcing shorts to close at unfavorable times.
• Regulations may temporarily ban short selling or impose rules such as uptick constraints.
• Many institutional investors (e.g., mutual funds) are long-only by mandate and cannot short individual stocks.

Short sellers also face asymmetric payoff profiles (limited upside, potentially unlimited downside) and reputational or relationship costs (e.g., reduced management access). These frictions mean that overpriced assets can remain overpriced for extended periods.

Noise trader risk

Noise trader risk reflects the danger that sentiment becomes more extreme before it reverses. An arbitrageur who shorts an overvalued stock risks:

• Further price increases driven by speculative buying or short squeezes.
• Margin calls and forced liquidation if interim losses trigger risk limits.
• Client redemptions if performance temporarily deteriorates.

Because arbitrage is typically performed with levered capital, mark-to-market losses can force unwinding well before convergence, turning a fundamentally sound idea into a realized loss.

Redemption and funding risk

Professional arbitrageurs manage external capital. Their investors often evaluate performance over relatively short horizons and may redeem after periods of underperformance.

Key Term: redemption (run) risk
The risk that investors in arbitrage funds withdraw capital during periods of underperformance or market stress, forcing managers to liquidate positions regardless of longer-term value.

Redemption risk is especially acute when many funds follow similar strategies. If a common trade moves against them, they may all try to exit simultaneously, depressing prices further and intensifying the anomaly—at least temporarily.

Funding risk (the possibility that banks reduce credit lines, increase margins, or withdraw financing) operates similarly. During crises, leverage becomes scarce and expensive just when arbitrage opportunities look most attractive, as seen in fixed-income arbitrage and convertible bond strategies around the global financial crisis.

Together, these limits mean that arbitrage is:

• Risky, not riskless.
• Capital- and liquidity-intensive.
• Often horizon-mismatched: mispricing may take longer to correct than investors’ patience.

Consequently, mispricings can be large and persistent, especially where liquidity is poor and sentiment is strong.

Liquidity and Arbitrage Effectiveness

Liquidity is central to understanding anomalies and limits to arbitrage.

Key Term: liquidity risk
The risk of being unable to transact a security in sufficient size or at a reasonable price due to limited market depth, wide spreads, or disrupted trading conditions.

In the fixed-income reading, a liquid security is one that can be “transacted quickly with little effect on the security’s price.” This definition highlights three dimensions:

• Tightness: narrow bid–ask spreads.
• Depth: ability to trade size without large price moves.
• Resiliency: speed with which prices revert after trades.

Illiquid assets impose costs on arbitrageurs:

• Higher expected trading costs (spreads, impact, search).
• Higher price volatility when trades occur, because small orders can move prices.
• Greater difficulty exiting under pressure, increasing the risk of fire-sale losses.

In many bond market sub-sectors, such as small corporate issues, municipal bonds, or structured products, liquidity is weak:

• They trade OTC with limited transparency.
• Many issues are small, thinly traded, and held by buy-and-hold investors.
• Dealers are less willing to commit capital, especially post-crisis.

Illiquidity is reflected in liquidity premia in yields.

Key Term: liquidity premium
The incremental expected return (or yield) investors demand for holding a less liquid security instead of an otherwise similar, more liquid security.

A familiar example is the yield difference between on-the-run and off-the-run government bonds of similar maturity: off-the-run bonds typically trade at slightly higher yields, compensating for lower liquidity.

For arbitrageurs, liquidity affects both the opportunity and the risk:

• Apparent mispricing in illiquid securities may simply reflect required liquidity premia, not true anomalies.
• Even when a security is genuinely mispriced, the cost and risk of trading it can outweigh expected profit.

During periods of market stress, liquidity often deteriorates sharply:

• Bid–ask spreads widen.
• Market depth evaporates.
• Dealers reduce inventories and cut risk exposures.

This “flight to liquidity” often strengthens anomalies:

• Illiquid value stocks, distressed debt, or complex structured products may sell off excessively as risk-averse investors rush into cash or government bonds.
• Leveraged arbitrageurs facing margin calls may be forced to liquidate precisely these positions at distressed prices, worsening mispricing.

A key observation for portfolio managers is that many documented anomalies are strongest:

• Among smaller, less liquid securities.
• In stressful or high-volatility periods.
• Where shorting is difficult or funding fragile.

This pattern is exactly what we would expect if limits to arbitrage and liquidity risk are central to anomaly persistence.

Worked Example 1.1

A hedge fund observes a group of biotech stocks trading at high valuations, far above estimated net present value. While fundamentals suggest overpricing, short-selling these stocks is costly and exposed to the risk that positive sentiment or news flow may drive prices even higher. If the fund’s clients withdraw capital after several months of losses, the hedge fund could be forced to liquidate its position at even greater loss, leaving the anomaly uncorrected in the short term.

Answer:
In this scenario, short-sale constraints (high borrow costs and recall risk), noise trader risk (sentiment pushing prices even higher), and redemption risk (clients redeeming after interim losses) combine to impede arbitrage. Fundamental risk is also present because the true value of future drug cash flows is uncertain. The overvaluation can persist because the arbitrageur is unable or unwilling to take a sufficiently large, long-horizon position and may be forced to close it prematurely, especially in a volatile, sentiment-driven sector.

Worked Example 1.2

A fixed-income arbitrageur notes that a 10-year off-the-run government bond yields 35 bps more than the current on-the-run bond of the same issuer and similar duration. Historical data suggest this spread is unusually wide. The fund considers a “liquidity arbitrage” trade: long the off-the-run bond, short the on-the-run bond in a duration-matched amount, using leverage to magnify the small spread.

Shortly after entering the trade with 10:1 leverage, a bout of market stress causes investors to rush into the most liquid securities. On-the-run bond yields fall, while off-the-run yields rise further as dealers cut inventories. The spread widens, generating large mark-to-market losses and margin calls. The fund is forced to liquidate at a loss, even though the manager continues to believe the spread will eventually normalize.

Answer:
The apparent mispricing reflects a combination of liquidity premia and transient stress. The arbitrageur faces liquidity risk (difficulty exiting off-the-run positions), funding risk (margin calls on the levered trade), and noise trader risk (flight-to-liquidity demand for on-the-run bonds). While the spread may ultimately revert, the manager’s horizon is constrained by financing and risk limits. This illustrates that even near–risk-neutral arbitrage strategies can be destabilized by liquidity shocks, and that illiquidity is a key limit to arbitrage in fixed-income markets.

Investor Flows and Arbitrage Constraints

Investor flows and institutional constraints often determine how much capital is available to exploit anomalies and how fragile that capital is.

Institutional flows and mandates

Different institutions face different constraints:

• Mutual funds and ETFs: daily liquidity; flows heavily influenced by recent performance and benchmark-relative results.
• Pension funds and insurers: regulatory capital requirements; limits on illiquid holdings; constraints on short selling and leverage.
• Hedge funds: varying lock-up periods, but often subject to quarterly or annual redemptions and lender-imposed leverage limits.

These characteristics shape arbitrage capacity:

• Managers with daily redemption risk are reluctant to hold highly illiquid assets or positions that may underperform for long periods, even if expected long-run returns are attractive.
• Benchmark-sensitive managers may avoid aggressive bets against widely held, overvalued sectors because of career risk: underperforming peers in the short term can lead to client or board pressure.

These forces help explain why anomalies are often more pronounced:

• In securities outside major benchmarks (e.g., micro-caps, off-benchmark bonds).
• In illiquid segments that cannot absorb large institutional allocations.
• In strategies that require significant tracking error or leverage.

Liquidity mandates and funding fragility

Regulatory and internal risk constraints often require:

• Minimum holdings in highly liquid instruments (e.g., government bonds, cash).
• Limits on exposure to private markets or thinly traded securities.
• Stress tests that assume rapid liquidation under adverse scenarios.

These rules are sensible from a risk-management standpoint but may reduce the capital available to exploit slow-moving or illiquid anomalies (e.g., deep value in distressed credit, closed-end fund discounts, or certain merger arbitrage opportunities).

Funding fragility is heightened in crises:

• Banks and prime brokers may reduce credit lines to hedge funds, especially for complex or illiquid exposures such as structured credit or convertibles.
• Investors, reacting to recent losses (availability and loss-aversion biases), may overweight liquidity – reallocating from illiquid alternatives into cash or government securities, even if it means locking in losses.

Behavioral finance recognizes that recent traumatic experiences (e.g., the 2008 liquidity squeeze) can create a lasting availability bias, causing investors to overestimate the likelihood of extreme liquidity events and underweight illiquid but fundamentally attractive investments.

The net effect is procyclical arbitrage capacity:

• Capital and risk budgets are plentiful when anomalies are small and volatility is low.
• Capital evaporates when anomalies are largest and volatility is high.

This procyclicality is central to understanding the persistence and time variation of anomalies.

Examples of Persistent Market Anomalies Due to Arbitrage Limits

Several well-documented anomalies illustrate the interaction between sentiment, liquidity, and arbitrage constraints.

Momentum

Momentum refers to the tendency of recent winners to continue outperforming and recent losers to continue underperforming over horizons of roughly 3–12 months, even after adjusting for conventional risk factors.

A behavioral interpretation emphasizes:

• Underreaction to news: investors adjust slowly to fundamental information because of conservatism and anchoring.
• Herding and feedback trading: as prices rise, more investors chase past winners, inflating prices further.

Limits to arbitrage strengthen momentum:

• High turnover and trading costs, especially in smaller or less liquid stocks, erode arbitrage profits.
• Shorting recent losers (which would arbitrage negative momentum) is often expensive or constrained.
• Momentum can reverse abruptly (“momentum crashes”), particularly when markets shift from risk-on to risk-off regimes, exposing arbitrageurs to tail risk.

For Level 3, the key link is that momentum profits are often stronger:

• In illiquid, high-sentiment segments (small caps, glamour stocks).
• During periods of strong sentiment and low funding constraints.

Closed-end fund discount

Closed-end funds (CEFs) issue a fixed number of shares that trade on exchanges. Unlike open-end funds, they do not continuously issue or redeem at NAV.

Empirically:

• New CEFs often list at a premium to NAV, reflecting optimistic sentiment from retail investors.
• Over time, many drift to a discount, which can persist for years and varies across funds.

Why not arbitrage?

• Shorting the fund's portfolio holdings in exact proportion to the CEF is operationally difficult and costly.
• Shorting the CEF itself may be constrained.
• Liquidity in CEF shares is limited; large trades can have significant price impact.
• The timing of discount narrowing (e.g., via corporate actions like fund liquidation or conversion to open-end) is uncertain.

Therefore, even persistent, visible discounts can remain only partially exploited.

Bubbles and fad stocks

Speculative bubbles in sectors such as dot-coms, housing-related equities, or cryptocurrencies exhibit:

• Extremely high valuations unsupported by cash flows.
• Heavy retail participation and media attention.
• Narrative-driven sentiment (“new era” thinking).

Arbitrage is inhibited because:

• Shorting is risky and sometimes impossible (no liquid derivatives, hard-to-borrow shares).
• Noise trader risk is extreme: prices can become even more detached from fundamentals.
• Fundamental risk is high: new technologies have uncertain payoff distributions.

From a portfolio standpoint, recognizing bubble dynamics is important for risk control. However, timing bubble peaks is very difficult, and limits to arbitrage explain why many rational investors choose simply to avoid participation rather than aggressively shorting.

Worked Example 1.3

A global equity manager notices that a particular emerging market sector ETF has attracted large inflows from retail investors after a strong 12-month run. The ETF holds a concentrated portfolio of small, illiquid stocks that have become very expensive on traditional valuation metrics. The manager considers underweighting the sector relative to the benchmark but hesitates to short the ETF or the constituent stocks.

Which factors should the manager consider when deciding whether and how to act on this perceived anomaly?

Answer:
The manager must balance potential long-run alpha against limits to arbitrage:

• Investor sentiment: heavy retail inflows and media attention suggest optimism may be unsustainable, but may persist longer than expected (noise trader risk).
• Liquidity risk: constituent small-cap stocks are illiquid; shorting them directly (or via ETF arbitrage) could be costly and difficult to unwind, especially in a sell-off.
• Short-sale constraints: borrowing costs and recall risk may be high for popular ETF or small-cap shorts.
• Benchmark and career risk: aggressively shorting a hot sector could cause near-term underperformance relative to the benchmark if the rally extends, affecting client perceptions.
• Implementation options: a modest underweight (rather than outright short) may align better with liquidity constraints and the manager’s mandate, while still reducing exposure to a likely overvalued segment. Overall, limits to arbitrage and institutional constraints might justify only a cautious tilt rather than a full arbitrage trade, illustrating how sentiment, liquidity, and mandate design interact in practice.

Summary

Persistent market anomalies are better understood as the outcome of an ongoing contest between sentiment-driven investors and constrained arbitrageurs, rather than as evidence that markets are entirely irrational or that easy arbitrage profits abound.

Investor sentiment, shaped by behavioral biases such as overconfidence, representativeness, and availability, can drive prices away from fundamentals, especially in hard-to-value, illiquid, or attention-grabbing assets. Limits to arbitrage—including fundamental risk, implementation costs, short-sale constraints, noise trader risk, and redemption or funding risk—make it risky and sometimes infeasible for rational investors to fully exploit and correct mispricings.

Liquidity plays a central role:

• Illiquid securities embed liquidity premia and have higher trading costs.
• During stress, liquidity dries up, increasing mispricing and constraining arbitrage capacity.
• Many anomalies are strongest precisely where liquidity is poorest and sentiment most volatile.

Institutional investor flows, mandates, and risk management frameworks further shape arbitrage effectiveness. Daily redemption risk, benchmark constraints, and regulatory liquidity requirements often reduce the ability of large pools of capital to exploit anomalies, particularly those involving illiquid or complex instruments.

For Level 3 candidates, the key is to apply these concepts to portfolio construction and risk management: recognizing where anomalies are more likely to exist, understanding why they might or might not be exploitable for a given mandate, and communicating realistically with clients about the opportunities and risks involved.

Key Point Checklist

This article has covered the following key knowledge points:

• Defined market anomalies and explained how they challenge strict forms of market efficiency.
• Described investor sentiment and its role in driving prices away from fundamental value.
• Identified and explained major limits to arbitrage: fundamental risk, implementation costs, short-sale constraints, noise trader risk, and redemption/funding risk.
• Analyzed how liquidity risk and liquidity premia affect arbitrage effectiveness, especially in fixed-income and small-cap equity markets.
• Discussed how institutional flows, liquidity mandates, and funding fragility interact with sentiment to increase or dampen mispricing.
• Illustrated these concepts through examples such as momentum, closed-end fund discounts, liquidity arbitrage in bonds, and speculative bubbles.
• Emphasized how to link specific anomalies to key frictions and behavioral drivers in exam-style, portfolio-focused scenarios.

Key Terms and Concepts

• market anomaly
• investor sentiment
• limits to arbitrage
• fundamental risk
• implementation costs
• short-sale constraints
• noise trader risk
• redemption (run) risk
• liquidity risk
• liquidity premium