Behavioral Finance Flashcards

Rationality and Savage's Axioms Under Uncertainty

Standard economic theory defines rationality through Leonard Savage's axioms (1954), underpinning Subjective Expected Utility (SEU). Key axioms include completeness, transitivity, the Sure-Thing Principle (independence), and continuity. The essay posits that rigidly adhering to these axioms isn't always rational, particularly under deep uncertainty or ambiguity, as argued by Gilboa, Postlewaite, and Schmeidler (2009).

Savage’s theory ensures internal consistency, assuming decision-makers can identify a complete state space and assign meaningful subjective probabilities. However, this is often impossible in reality.

The Ellsberg Paradox

The Ellsberg Paradox (Ellsberg, 1961) demonstrates a violation of the Sure-Thing Principle. People prefer betting on outcomes with known probabilities over ambiguous ones, termed ambiguity aversion. SEU deems this irrational, but intuitively, it’s a rational response to limited knowledge.

Gilboa et al. (2009) argue external justification matters. Assigning precise probabilities where no meaningful information exists is epistemically dishonest. Remaining agnostic and rejecting completeness may be more rational. Rationality balances consistency and credibility.

Maxmin Expected Utility

Alternative models relax Savage’s axioms. Maxmin Expected Utility (Gilboa & Schmeidler, 1989) considers a set of possible priors and optimizes for the worst-case scenario. This model violates Savage’s completeness and the Sure-Thing Principle, but allows cautious decision-making under extreme uncertainty, such as in crisis management or policy planning.

Consider a health minister approving a vaccine with uncertain fatalities. Savage's framework requires assigning probabilities to all outcomes, but with insufficient data, this forces arbitrary numbers. A precautionary principle or maxmin approach may be more responsible.

In financial markets, assigning probabilities to a novel cryptocurrency's performance is speculative without price history or regulatory clarity. Waiting for information or hedging may be more prudent, violating completeness but aligning with real-world caution.

Critics argue abandoning axioms compromises rigor. However, as Slovic & Tversky (1974) show, people reject axioms due to discomfort with oversimplified assumptions. Starmer (2000) notes no single model captures all decision behavior under risk or ambiguity. Savage himself acknowledged his axioms were idealized.

Savage’s axioms are ill-equipped for profound ambiguity or informational emptiness. Clinging to them may result in fabricated beliefs. Gilboa et al. (2009) advocate for decisions that acknowledge the limits of knowledge, promoting justified, cautious, and flexible actions.

Behavioural Explanations of Stock Market Momentum and Reversal

Financial markets exhibit short-term momentum and long-term reversal, challenging the Efficient Market Hypothesis (EMH). Jegadeesh and Titman (1993) first documented these patterns. Traditional finance models struggle to explain this without ad hoc risk adjustments.

Behavioural finance offers explanations using psychological biases, including models by Daniel, Hirshleifer, and Subrahmanyam (1998), Barberis, Shleifer, and Vishny (1998), Grinblatt and Han (2005), and Hong and Stein (1999).

The DHS Model

The Daniel, Hirshleifer, and Subrahmanyam (DHS) model uses overconfidence and self-attribution bias. Overconfident investors overestimate their private information, while self-attribution leads them to credit successes and blame failures on bad luck. Investors underreact to public information but overreact to private signals. Public confirmation reinforces beliefs, causing prices to overshoot, generating momentum. Eventually, fundamentals reassert, leading to long-term reversal.

The BSV Model

Barberis, Shleifer, and Vishny (BSV) use representativeness and conservatism. Representativeness leads investors to overreact to confirming news, while conservatism leads them to underreact to conflicting information. Investors believe earnings follow mean-reverting or trending regimes and switch interpretations too slowly or eagerly. This biases expectations, predicting short-term momentum followed by long-term reversal due to incorrect regime beliefs and poor statistical inference.

The GH Model

Grinblatt and Han (2005) focus on the disposition effect and mental accounting. Investors sell winners too early and hold losers too long, framing gains and losses relative to a reference point from Prospect Theory (Kahneman and Tversky, 1979). This creates mispricing. Positive news prompts investors to sell winners, dampening price adjustment and causing underreaction. Over time, prices drift upward, generating momentum. The model implies reversal as prices eventually converge to intrinsic value.

The HS Model

Hong and Stein (1999) offer a market microstructure explanation using newswatchers and momentum traders. Newswatchers receive private information but ignore price data; momentum traders respond to price trends. Prices initially underreact, giving momentum traders profit opportunities. Momentum traders exaggerate trends, causing prices to overshoot, setting the stage for long-term reversal. This relies on limited information processing and slow diffusion.

Comparison of Models

DHS and BSV use representative agent models. GH assumes heterogeneous investors. HS focuses on market interaction effects. DHS predicts stronger momentum in hard-to-value stocks. HS predicts momentum in stocks with low analyst coverage, supported by Hong, Lim, and Stein (2000).

DHS’s prediction that momentum is stronger after market gains is backed by studies, including Ji (2008). BSV’s assumptions about regime belief shifts offer a narrative. GH’s reliance on the disposition effect is supported by studies like Frazzini (2006) and Goetzmann and Massa (2008). HS’s predictions about analyst coverage and firm size have been corroborated.

Behavioural finance offers explanations for momentum and reversal. DHS focuses on biased learning, BSV on statistical misjudgment, GH on emotional attachment to gains and losses, and HS on bounded information processing.

Overconfidence in Financial Decision-Making

Overconfidence is a pervasive bias where individuals overestimate their knowledge, information precision, or ability to control outcomes. It manifests as overprecision and overplacement. In finance, it leads to excessive risk-taking and suboptimal trading.

Individual investors: Overconfidence drives excessive trading. Odean (1998) found overconfident investors trade more, reducing returns due to transaction costs. Barber and Odean (2000) showed high-turnover investors underperform low-turnover investors. Barber and Odean (2001) found that men traded 45% more than women and earned lower returns due to higher overconfidence.

Portfolios: Gervais and Odean (2001) modeled how trading success increases overconfidence, leading to aggressive risk-taking. Self-attribution bias creates a positive feedback loop, resulting in undiversified portfolios and vulnerability to market shocks.

Corporate finance: Overconfident managers overestimate investment returns, underestimate risks, and fund projects rational analysis rejects. Roll’s (1986) Hubris Hypothesis posits M&As are driven by executive overconfidence. Malmendier and Tate (2005) found overconfident CEOs are more likely to engage in value-destroying mergers financed with internal cash. Overconfident CEOs believe their stock is undervalued, leading to overinvestment. Heaton (2002) argued overconfident managers favour debt over equity, increasing financial fragility.

Baker and Wurgler (2013) articulate the managerial bias view, where executives act on distorted beliefs, leading to systematic errors in capital allocation. The PSA–DaimlerChrysler merger exemplifies executive overconfidence, resulting in post-merger write-downs.

Overconfidence leads to underperformance, misallocated capital, and value destruction. Solutions include governance mechanisms and debiasing strategies.

Behavioural Portfolio Theory and Mental Accounting

Traditional portfolio theory, formalized by Markowitz (1952), assumes rational investors maximize expected utility through risk-return trade-offs. Investors hold fully diversified portfolios based on total wealth and consistent risk attitudes. Behavioural Portfolio Theory (BPT) by Shefrin and Statman (2000) and mental accounting by Thaler (1980) offer a more realistic view.

BPT suggests investors build layered portfolios corresponding to different goals: a safety layer for preserving wealth and an aspiration layer for high returns. This mirrors Maslow’s hierarchy of needs, formalized by De Brouwer (2008) as Maslowian Portfolio Theory (MaPT).

Prospect Theory (Kahneman and Tversky, 1979) demonstrates individuals evaluate outcomes relative to a reference point, exhibit loss aversion, and are risk-averse in gains but risk-seeking in losses. BPT integrates these insights by modeling investor preferences as piecewise functions over gains and losses.

Mental accounting (Thaler, 1980) suggests investors compartmentalize wealth into separate “accounts” with different rules, failing to consider overall risk and return. For example, an investor might hold a risky position while keeping a large cash reserve.

Barclays Wealth’s Financial Personality Assessment (FPA) segments assets into Personal Holdings, Investment Portfolio, and Business/Opportunistic Holdings, mirroring BPT.

Grinblatt and Han (2005) show how the disposition effect arises when investors mentally account for individual stock positions based on purchase prices. Frydman et al. (2011) use neuroeconomic data to show selling at a gain activates reward centers.

Goal-based investing encourages identifying financial goals and building separate portfolios to match each goal’s risk tolerance.

Critics argue BPT lacks mathematical elegance. However, its psychological realism captures people’s relationship with money. Hybrid advisory models evaluate BPT structures using risk-return metrics.

BPT challenges classical portfolio theory by presenting a multidimensional view of investor goals and emotions. The future lies in blending classical rigour with behavioural realism.

The Adaptive Markets Hypothesis

The Efficient Market Hypothesis (EMH) has been challenged by empirical anomalies. Andrew Lo (2004, 2012) proposed the Adaptive Markets Hypothesis (AMH), blending behavioral and efficient views using evolutionary biology. AMH provides a flexible framework for understanding dynamic market behaviour.

The EMH posits markets reflect all information, but behavioural finance shows patterns inconsistent with efficiency. Lo’s Adaptive Markets Hypothesis rejects static assumptions in favour of a dynamic model. Markets evolve like ecosystems, where investment strategies compete, adapt, and fail. Investors use heuristics, learning and adjusting based on feedback. Risk premia are time-varying, reflecting shifts in behavior, sentiment, and institutional structure.

AMH acknowledges markets can be efficient in some contexts and inefficient in others. During stable periods, arbitrage eliminates opportunities. In crises, behavioral biases dominate. This aligns with empirical observations, such as the 2008 crisis and the meme stock phenomenon.

AMH explains why anomalies are not permanent. The momentum effect may diminish as more traders exploit it. AMH suggests anomalies are context-sensitive, not fixed violations of rationality.

AMH is compatible with behavioural models. Heuristics can be adaptive. However, critics note AMH is more descriptive than predictive and requires a rich institutional context.

AMH has practical relevance for asset managers and policymakers. For portfolio construction, it suggests dynamic risk premia. For regulators, it warns that interventions should consider evolutionary dynamics.

AMH bridges economics with cognitive psychology, neuroscience, complexity theory, and evolutionary biology. It is a natural extension of EMH.

Psychological Heuristics and Biases in Financial Decision-Making

Traditional finance assumes rational agents objectively process information. However, psychological research reveals real-world decision-makers rely on heuristics that can lead to biases. These challenge the EMH and rational choice theory. Influential heuristics include representativeness, availability, anchoring, framing, and affect.

Representativeness: Judging probabilities based on resemblance to a stereotype. In finance, this manifests as extrapolating past performance to predict future returns, underpinning the BSV model. Such behaviour contributes to anomalies like momentum and reversal.

Availability: Judging likelihood of events based on how easily examples come to mind. Recent or salient events skew risk perception, as Dale (2015) notes, distorting information processing. This explains volatility clustering and overreaction to news.

Anchoring: Relying heavily on initial values when making decisions. Furnham and Boo (2011) review evidence that investors anchor on irrelevant or round numbers. This creates price stickiness or psychological barriers, as Donaldson & Kim (1993) and Dowling et al. (2013) provide evidence. Anchoring contradicts the EMH.

Framing: Distorting decision-making by influencing how choices are presented. Kahneman and Tversky (1981) demonstrated people are risk-averse in gains and risk-seeking in losses. Druckman (2001) emphasizes expert decision-makers are not immune to framing.

Affect: Emotional reactions influencing decisions more than analysis. Slovic et al. (2005) showed people associate “good” investments with low risk and high returns, fuelling bubbles and irrational exuberance, as Shiller (2000) discussed.

These heuristics aggregate, generating price patterns defying rational models. Barberis and Thaler (2003) argue representativeness, availability, and framing explain asset pricing anomalies.

Critics argue the emphasis on heuristics can lead to post hoc rationalisation. However, Lo’s Adaptive Markets Hypothesis (2004) suggests heuristics can be adaptive. Biases are tools for bounded rational agents.

Behavioural asset managers exploit biases. Regulators incorporate behavioural nudges into financial products.

Persistence of Arbitrage Opportunities

The Efficient Market Hypothesis (EMH) suggests arbitrage quickly eliminates mispricing. However, mispricings persist. The presence of rational traders is insufficient to guarantee price efficiency.

Limits to arbitrage: Practical and psychological frictions restrict the ability of rational investors to correct mispricings. Arbitrage is risky, costly, and constrained by the institutional structure.

The classic arbitrage argument assumes identical assets sell for the same price, mispricings can be exploited without cost, and rational arbitrageurs will step in. Shleifer and Vishny (1997) argue arbitrage is limited due to risks and costs. Horizon risk captures the idea that arbitrageurs must act within short timeframes. If prices don't correct quickly enough, arbitrageurs face redemptions. De Long et al. (1990) analyze how noise traders introduce noise trader risk—the possibility that mispricing will widen in the short run. Rational traders face the risk that sentiment-driven trading will increase their losses. Several empiricial examples illustrates this Logic.

Further constraint: short-selling restrictions. Shorting carries higher risk than taking long positions, discouraging arbitrage activity. As Shleifer (2000) notes, short-sale constraints make the correction of optimistic mispricing far slower.

Another relevant constraint is model risk, particularly with complex derivatives. Arbitrageurs may hesitate to exploit inefficiencies if they are unsure whether the mispricing is real. During the 2007–08 crisis many investors misunderstood the true risk embedding in morgage-backed securities.

Arbitrage is capital-intensive and relies on leverage which can be infeasible if margind requirements tighten.

The principal-agent relationship in asset management exacerbates arbitrage limits. Fund managers are judged quarterly. As noted in Baker and Wurgler (2013), even rational managers may behave irrationally. Behavioural finance reframes market inefficiencies not as errors to be exploited, but as structural features of the system. Inefficiencies persist because rational traders face frictions that limit their ability to act. Behavioural finance shows market forces are often muted or delayed.

The Disposition Effect and Realization Utility

Traditional financial theory states decisions should be based on future prospects, not past outcomes. Yet investors exhibit a disposition effect – selling winners too early and holding losers too long. Realization utility theory suggests investors gain psychological satisfaction from realizing a gain or loss. Together, these concepts challenge traditional asset pricing.

The disposition effect, first described by Shefrin and Statman (1985), proposes investors are reluctant to realize losses to avoid regret and eager to realize gains to experience pride. This violates loss realization neutrality. Traditional portfolio theory assumes investors maximize expected utility and rebalance. The disposition effect implies investors are path-dependent, making decisions based on historical purchase prices, central to Prospect Theory (Kahneman & Tversky, 1979). Investors are risk-averse in gains and risk-seeking in losses.

Empirical evidence supports the disposition effect. Odean (1998) demonstrated individual investors disproportionately sell winners and hold losers, resulting in lower returns. Barberis and Xiong (2009) formalized a Prospect Theory model.

Realization utility theory, introduced by Barberis and Xiong (2011), suggests investors derive utility from selling an asset at a gain. This generates emotional feedback. Frydman et al. (2011) showed that brain regions associated with reward processing were activated when participants sold assets at a profit. Investors can maximize psychological satisfaction instead of maximizing return. This all goes against the traditional theory.

Grinblatt and Han (2005) modeled how the disposition effect can lead to underreaction to news and short-term momentum. The dynamics have been observed across various markets and asset classes, indicating that the disposition effect is not merely anecdotal but systematic and influential. Institutional investors aren't immune to these effects.

Critics contend tax considerations may partially explain this behaviour. However, Odean (1998) controls for tax timing and finds strong behavioural effects. Also, realisation utility assumes investors derive pleasure from recognising gains, but this may vary across individuals and cultures, which could be a topic of further discussion.

The disposition effect challenges classical financial theory. Investors are influenced by emotional attachments to past outcomes, contradicting rational models.

Speculative Bubbles and Herding in Financial Markets

Speculative bubbles – asset prices deviating from fundamental values – challenge the Efficient Market Hypothesis (EMH). Behavioural finance highlights psychological biases, heuristics, and social dynamics such as herding. A speculative bubble is a market scenario in which asset prices rise rapidly and substantially beyond intrinsic value.

One psychological driver of bubbles is overconfidence. As shown in Daniel, Hirshleifer, and Subrahmanyam (1998), overconfident investors place weight on private beliefs. Confirmation bias also impacts them - and others.

Beyond individual psychology, herding behaviour plays a role in bubble dynamics. Herding occurs when investors mimic others. There are can be different informational and reputational reasons for this. Informationally, investors may infer that others possess knowledge. This leads to informational cascades (Bikhchandani, Hirshleifer & Welch, 1992). Reputationally, fund managers may herd to avoid standing out. Herding can amplify price movements and sustain bubbles by detaching behaviour from fundamentals.

Social media has accelerated herding mechanisms. . Also, bubbles persist due to limits to arbitrage. Empirical evidence supports behavioural explanations for bubbles.

Behavioural models simulate bubble dynamics. Critics contend with the bubble concept often being defined retrospectively and lacking predictive power. Heuristics like herding may help investors adapt. Understanding the behavioural underpinnings of bubbles is essential.

Standard economic theory rigorously defines rationality through Leonard Savage's axioms (1954), which underpin Subjective Expected Utility (SEU). These axioms encompass several crucial principles, including completeness, transitivity, the Sure-Thing Principle (independence), and continuity. The essay proposes that a rigid adherence to these axioms may not always be rational, particularly in scenarios involving deep uncertainty or ambiguity, as articulated by scholars such as Gilboa, Postlewaite, and Schmeidler (2009).

Savage’s framework ensures internal consistency and posits that decision-makers are capable of identifying a complete state space and assigning meaningful subjective probabilities to various outcomes. However, the practical execution of this assumption is often fraught with challenges, as identifying all potential outcomes and their associated probabilities can be virtually impossible in real-world situations.

The Ellsberg Paradox

The Ellsberg Paradox, presented by Ellsberg in 1961, illustrates a significant violation of the Sure-Thing Principle. In the paradox, people display a marked preference for betting on outcomes with known probabilities rather than on ambiguous outcomes, a behavior termed ambiguity aversion. Although SEU deems this preference irrational, it aligns with a more intuitive understanding of decision-making where individuals rationally respond to the limitations of their own knowledge.

Gilboa et al. (2009) emphasize the importance of external justification in understanding this phenomenon. They argue that the assignment of precise probabilities when no meaningful information exists can be considered epistemically dishonest, prompting a more agnostic approach that questions the completeness of information available to decision-makers. In this context, rationality must balance not only internal consistency but also external credibility, acknowledging the limits imposed by available knowledge.

Maxmin Expected Utility

Alternative decision-making models have been developed to circumvent the constraints imposed by Savage’s axioms. One noteworthy approach is the Maxmin Expected Utility model, introduced by Gilboa and Schmeidler in 1989. This model allows for the consideration of a set of possible priors and focuses on optimizing for the worst-case scenario. By doing so, it diverges from Savage’s axioms of completeness and the Sure-Thing Principle, facilitating cautious decision-making in situations characterized by extreme uncertainty—this is particularly useful in fields such as crisis management or policy planning.

For example, consider a health minister tasked with approving a vaccine amidst uncertain fatality rates. Savage's framework would necessitate the assignment of probabilities to all potential outcomes, but in the absence of sufficient data, this practice can result in arbitrary and potentially misleading numbers. In such scenarios, adopting a precautionary principle or a maxmin approach may yield more responsible decision-making, reflecting a better alignment with the realities of ambiguity.

In financial markets, when evaluating the potential performance of a novel cryptocurrency, assigning definitive probabilities is inherently speculative due to the lack of price history or regulatory clarity. Here, the prudent approach may involve awaiting more information or hedging investments, actions that may violate the traditional notion of completeness yet resonate more authentically with real-world decision-making practices.

Critics of the maxmin approach argue that abandoning foundational axioms like those of Savage could compromise the rigor of decision-making frameworks. Nonetheless, as evidenced by the work of Slovic & Tversky (1974), it is important to note that human decision-making often involves a rejection of overly simplified assumptions that traditional models rely upon. Starmer (2000) also highlights that no singular model can effectively capture all aspects of decision behavior when dealing with risk or ambiguity. Even Leonard Savage himself acknowledged that his axioms represent an idealized abstraction rather than the necessary conditions of real-world choices.

Savage’s axioms prove inadequate for addressing profound ambiguity or informational deficiency. Persisting with these axioms without regard to their limitations can lead to the formation of fabricated beliefs. Gilboa et al. (2009) advocate for decision-making processes that recognize the inherent limits of knowledge, thereby endorsing actions that are justified, cautious, and adaptable to the complexities inherent in uncertainty.