Week 4: Framing, Limits of Arbitrage and Noise Traders
1. Framing and decision-making
This lecture links four topics that together explain why mispricing exists and can last: how the presentation of a choice changes behavior (framing), why rational traders cannot always correct prices (limits of arbitrage), the traders who create the mispricing (noise traders), how the industry turns these errors into products (smart beta), and how psychology affects the whole economy (behavioral macroeconomics).
According to the framing effect, the way a choice is presented (its frame) alters what people decide, even though the outcomes are exactly the same. Wording, the reference point, and whether something is cast as a gain or a loss all influence people.
In finance, framing affects the choice of investment products, risk tolerance, reactions to gains and losses, and saving decisions. The key sentence of the first slide: two economically equivalent options are not psychologically equivalent. A traditional economist would say only the outcomes and their probabilities matter; a behavioral economist adds that the description matters too.
2. The key papers on framing
Tversky & Kahneman (1981): "The Framing of Decisions and the Psychology of Choice"
This paper, which appeared in Science, is the landmark study that put the framing effect on the map. Its main point: people choose differently between problems that are economically identical, based on whether the problem is put in a gain frame or a loss frame. The best-known example is the Asian Disease Problem: if the results of public health programmes are phrased as lives saved (gain frame), most respondents go for the sure option; if those same results are phrased as lives lost (loss frame), most go for the risky one. In finance this is important because it alters how much risk investors take, because the presentation of portfolios and products shifts behavior, and because framing underlies many behavioral anomalies.
Kahneman & Tversky (1979): Prospect Theory
"Prospect Theory: An Analysis of Decision under Risk", published in Econometrica, provides the theory behind framing. Its key elements:
- Reference dependence: investors evaluate outcomes as gains or losses relative to a reference point (for example the purchase price), not as final levels of wealth.
- Loss aversion: losses "hurt" roughly twice as much as equivalent gains please.
- Risk attitudes: people are risk-averse in the domain of gains and risk-seeking in the domain of losses.
How this links to framing: the frame determines whether people experience an outcome as a gain or as a loss. Shift the reference point and risk tolerance shifts with it.
A standard form of the value function is v(x) = xα for gains (x ≥ 0) and v(x) = −λ(−x)α for losses (x < 0). Here x is the gain or loss relative to the reference point, α (about 0.88) makes the curve concave for gains and convex for losses (diminishing sensitivity), and λ (about 2.25) is the loss aversion coefficient.
- Gain of 100: v(100) = 1000.88 ≈ 57.5
- Loss of 100: v(−100) = −2.25 × 1000.88 ≈ −129.5
The loss of 100 weighs about 2.25 times as much as the gain of 100: this is "losses hurt about twice as much". A 50/50 bet of +100 or −100 has value 0.5 × 57.5 + 0.5 × (−129.5) = −36, so the investor rejects it even though its expected monetary value is zero.
Benartzi & Thaler (1995): Myopic Loss Aversion and narrow framing
"Myopic Loss Aversion and the Equity Premium Puzzle", in the Quarterly Journal of Economics, applies framing to investing. Investors evaluate their portfolio too frequently (narrow framing in time). Because stock prices go down on many individual days and months, frequent evaluation means they observe many short-term losses, which trigger loss aversion. The result is underinvestment in equities in the long run. This explains the equity premium puzzle: historically, stocks have earned much more than safe bonds, more than standard models of risk aversion can justify. If investors feel the frequent small losses intensely, they demand a large premium to hold stocks. The paper shows that framing the investment horizon changes risk-taking and explains why presenting returns daily or annually changes trading behavior.
3. The classic framing example in an investment setting
The lecture translates the Asian Disease Problem into a portfolio crisis. Your portfolio is worth €100,000 and the market is in crisis. Your advisor offers two "rescue" programmes.
| Group A: gain frame | Group B: loss frame | |
|---|---|---|
| Programme 1 (certain) | €50,000 will be saved for sure | Certain loss of €50,000 |
| Programme 2 (risky) | 50% chance €100,000 is saved, 50% chance €0 is saved | 50% chance €100,000 is lost, 50% chance nothing is lost |
| Typical majority choice | Programme 1 (certainty in gains) | Programme 2 (risk-taking in losses) |
The two problems are economically equivalent: in both, programme 1 leaves you with €50,000 for sure, and programme 2 gives a 50/50 chance of ending with €100,000 or €0. The expected value is €50,000 in every case. Yet in the gain frame most people are risk averse, and in the loss frame most become risk seeking.
Use v(x) with α = 0.88 and λ = 2.25, in thousands of euros.
- Gain frame. Programme 1: v(50) = 500.88 ≈ 31.3. Programme 2: 0.5 × v(100) = 0.5 × 57.5 ≈ 28.8. The sure gain wins (31.3 > 28.8), because the curve is concave for gains.
- Loss frame. Programme 1: v(−50) = −2.25 × 31.3 ≈ −70.4. Programme 2: 0.5 × v(−100) = 0.5 × (−129.5) ≈ −64.7. The gamble wins (−64.7 > −70.4), because the curve is convex for losses.
The only thing that changed is the reference point: "saved" counts from €0, "lost" counts from €100,000.
How this links to prospect theory: a concave value function for gains leads to risk aversion, a convex value function for losses leads to risk seeking, and the frame determines on which side of the curve an outcome lands. The slide concludes that the frame alters not just the choice but the attitude toward risk as well.
4. Framing in investment practice
Capital-protected products
Frame A: "after 5 years, 90% of your capital is guaranteed." Frame B: "after 5 years you face a sure loss of as much as 10%." Each describes the very same product (at worst you lose 10%), yet frame A suggests safety while frame B suggests a loss. Unsurprisingly, banks go with frame A.
Presentation of fund performance
"The fund earned +30% over 5 years" versus "Average annual return of 5.4% per year with significant drawdowns." These are the same numbers: (1.30)1/5 − 1 ≈ 5.4% per year. The first frame creates excitement because a big cumulative number looks impressive; the second creates caution because it shows a modest yearly figure and mentions losses along the way.
Risk disclosure
"A loss above 20% has only a 5% probability" compared with "in 1 of every 20 cases your loss can exceed 20%." Here too 5% = 1/20. Studies of risk communication find that frequencies ("1 in 20") come across as more concrete and more frightening than percentages, so people tend to take less risk under the second frame.
Narrow vs broad framing
| Narrow framing | Broad framing |
|---|---|
| Each investment is viewed separately, like a separate lottery | Decisions are made at the level of total wealth and a long horizon |
| Overreaction to short-term losses | Short-term fluctuations carry less psychological weight |
| Typical example: checking the portfolio every day | Typical example: reviewing the pension portfolio once a year |
The link to myopic loss aversion: frequent evaluation plus loss aversion leads investors to avoid investments that are risky but profitable, such as equities.
Take a simplified stock that returns +20% or −10% each year with equal probability, and a loss-averse investor with λ = 2.25 (for simplicity a linear value function, α = 1).
- Evaluated every year: value = 0.5 × 20 + 0.5 × (−2.25 × 10) = 10 − 11.25 = −1.25. Negative, so the investor avoids the stock.
- Evaluated every two years: outcomes are 1.2 × 1.2 = +44% (probability 0.25), 1.2 × 0.9 = +8% (probability 0.5) and 0.9 × 0.9 = −19% (probability 0.25). Value = 0.25 × 44 + 0.5 × 8 + 0.25 × (−2.25 × 19) = 11 + 4 − 10.7 = +4.3. Positive, so the same investor now holds the stock.
Nothing about the stock changed, only how often its result is "counted". This is the mechanism of Benartzi & Thaler (1995).
Why framing matters for the limits of arbitrage
Investors "trapped" by framing:
- hold losing positions because realising the loss is psychologically painful (the disposition effect);
- purchase "guaranteed" products since the framing makes them seem safe, even when they offer low expected returns;
- react to the wording of news, for example "crash" versus "correction".
This connects to the rest of the lecture. Noise traders are influenced by frames, not only by fundamentals. Arbitrageurs face constraints and cannot always correct the resulting mispricing. As a result, anomalies and bubbles are created and persist.
5. The limits of arbitrage
Arbitrage is buying an asset that is too cheap and selling (shorting) an equivalent asset that is too expensive, to profit when the prices converge. The limits of arbitrage are the risks and costs that prevent arbitrageurs from fully correcting mispricing.
The EMH reasoning: whenever mispricing appears, arbitrageurs trade on it and the price moves back to fundamental value. Behavioral finance replies that real-world arbitrage is risky, uncertain and costly, which allows mispricing to last a long time. The limits come from three main sources: fundamental risk, noise trader risk, and implementation costs and constraints. When arbitrageurs are unable to fix the error, it stays. That is why behavioral finance rests on two pillars: biased investors cause mispricing, and limits of arbitrage allow it to persist.
1. Fundamental risk
An arbitrageur may find a mispriced security that has no perfect substitute. To hedge, he uses a similar but not identical security. If bad news then hits the hedge security (or good news the shorted one), he suffers an unexpected loss.
Example: pairs trading. Over the long run Coca-Cola and Pepsi trade at roughly the same P/E ratio, about 10. Should Coke's P/E climb to 20 while Pepsi's remains 10, a sensible trade is to buy Pepsi and short Coke, betting that both will move back to 10.
Assume earnings stay constant, so prices move in proportion to P/E. The arbitrageur buys €1,000 of Pepsi (P/E 10) and shorts €1,000 of Coke (P/E 20).
- Convergence to 10 and 10: Coke's price halves, so the short gains €500; Pepsi is unchanged. Profit €500.
- Divergence to 30 and 5: Coke rises 50%, so the short loses €500; Pepsi halves, so the long loses €500. Loss €1,000, the entire position. If it was financed with borrowed money, the arbitrageur is ruined before convergence ever happens.
The slide ends with Keynes's well-known warning: markets may stay irrational for longer than you are able to stay solvent.
2. Noise trader risk (Shleifer & Vishny, 1997)
Noise traders are investors driven by emotion, rumours and irrationality. The risk they create for arbitrageurs: mispricing may get worse before it corrects. If noise traders keep buying an overpriced asset, the price moves even further from fundamentals. The arbitrageur must then either commit more capital or face forced liquidation (lenders or fund investors pull money exactly when the trade is most attractive), which the slide calls the "Original Sin" of arbitrage. Shleifer & Vishny's insight is that arbitrage is done by professionals using other people's money, who are judged on short-term results, so they cannot wait indefinitely.
Example: MF Global (2011). MF Global, a derivatives broker, bought European government bonds at a discount that it regarded as guaranteed by the European stability fund (ESF on the slide). It used these bonds as collateral for new loans to buy even more bonds: in theory, the perfect arbitrage. But noise traders pushed bond spreads wider during the euro crisis, the collateral lost value, margin calls followed, and the leveraged structure collapsed. MF Global went bankrupt in 2011.
3. Implementation costs and constraints
- Short-sale constraints: you cannot always borrow a stock to short it, or borrowing is expensive.
- Transaction costs and bid-ask spreads: every trade costs money, which can eat a small mispricing.
- Margin requirements: leveraged positions require collateral that must be topped up if prices move against you.
- Lack of liquidity: large positions cannot be built or closed without moving the price.
- Funding liquidity risk: lenders may withdraw financing at the worst moment.
Conclusion: knowing that a mispricing is there does not mean you are able to profit from it.
6. The Law of One Price and its violations
Two economically equivalent goods or securities should have the same price: PA = PB. Arbitrageurs are supposed to enforce this by buying the cheap one and selling the expensive one.
In practice PA can differ significantly from PB, and the anomaly can persist for months or years, because of noise traders, limits of arbitrage and market segmentation (different investor groups trading the two assets in different markets). The LOP is the cleanest test of market efficiency, because there is no doubt about fundamental value: it is the same asset.
Royal Dutch / Shell
Royal Dutch (traded mainly in the Netherlands and the US) and Shell Transport (traded mainly in the UK) were two listed companies that together owned one combined business. Royal Dutch was entitled to 60% of the cash flows and Shell to 40%. If the market priced them correctly, the total value of Royal Dutch should be 60/40 = 1.5 times that of Shell:
Theoretical price relation: PRD = 1.5 × PShell (with prices expressed for equivalent units of the two companies).
What happened: Royal Dutch traded for years at a premium of up to 20% over this parity. Arbitrageurs bought Shell and shorted Royal Dutch, yet the gap lasted for years and the opportunity costs were huge. It is a textbook example of "impossible arbitrage".
Suppose Shell trades at €40 per equivalent unit. The parity value of Royal Dutch is 1.5 × €40 = €60. With a 20% premium, Royal Dutch trades at €60 × 1.20 = €72. An arbitrageur shorts Royal Dutch at €72 and buys 1.5 units of Shell for €60, locking in €12 if the gap closes. But if noise traders push the premium to 30% (Royal Dutch at €78 with Shell unchanged), the position shows a loss of €6 and needs more margin, and there is no date at which convergence is guaranteed.
The closed-end fund puzzle: DXYZ
A closed-end fund issues a fixed number of shares that trade on the stock exchange, and investors cannot redeem them at the fund's net asset value (NAV), the value of the assets per share. So the share price can drift away from NAV, as a premium or discount. On March 26 (2024), DXYZ (Destiny Tech100), a fund holding stakes in private technology companies, was listed on the NYSE.
| Item | Value | Premium to NAV |
|---|---|---|
| Net asset value (NAV) | $4.84 | (benchmark) |
| First-day price | $9 | 9 / 4.84 − 1 ≈ 86% |
| Price within two weeks | $105 | 105 / 4.84 − 1 ≈ 2,069%, more than 2,000% (about 21 times NAV) |
The 86% premium on the first day could perhaps be justified by the difficulty of valuing private stakes. The more than 2,000% premium is the largest ever observed in a US closed-end fund over the last century.
What led to the DXYZ phenomenon?
- Retail investor attraction: excitement about SpaceX, OpenAI and private tech, a narrative that went viral. DXYZ was one of the few ways for small investors to "own" these companies.
- Valuation difficulty: the underlying holdings are private equity stakes with no real market for price discovery.
- Inability to arbitrage: you cannot buy the NAV (the private stakes) and easily short DXYZ. This is a structural constraint of closed-end funds: there is no redemption mechanism that forces the price back to NAV.
The slide's formula: good narrative + retail mania + arbitrage limits = violation of the LOP.
If the market fails at the "easy ones"...
Lamont & Thaler (2002) label the mispricing of closed-end funds a "no-brainer failure": no valuation model is required to see that a share backed by $4.84 in assets should not trade at $105. The key question: if the market fails to grasp that $4.84 ≠ $105, what other things is it pricing wrong? Takeaways: hype and stories can dominate markets, the LOP is broken often, noise traders can "beat" arbitrage, and investors ought to distrust viral narratives. DXYZ serves as a case study of all the ways a market can go wrong, and of the reason behavioral finance is necessary.
7. Noise traders and why limits of arbitrage matter
Noise traders react to news, tweets and hype, are driven by emotion (fear and greed), and affect short-term prices. Their implications: they increase volatility, create bubbles and crashes, and alter the path of arbitrageurs by forcing them into liquidation when mispricing widens.
The key logical point: if limits of arbitrage did not exist, anomalies would not exist, because any mispricing would be traded away immediately. Limits of arbitrage therefore help explain:
- bubbles (dot-com, housing, crypto);
- anomalies (momentum, reversal, seasonality);
- post-earnings announcement drift (PEAD) and underreaction;
- ETF premiums and discounts relative to NAV.
The transition question: how are these anomalies transformed into investment strategies? That leads to smart beta and behavioral funds.
8. Smart beta
These strategies mix a passive element (systematic and rules-based, similar to an index) with an active element (capturing anomalies or factors). Rather than weighting stocks by market capitalisation as the S&P 500 does, they weight them by factors like value, momentum, size or low volatility, in the hope of beating the benchmark on a risk-adjusted basis. They sit between passive indexing and active management.
Foundational papers
- Arnott, Hsu & Moore (2005), "Fundamental Indexation", Financial Analysts Journal. Introduced fundamental indexing. Market-cap indices automatically hold more of stocks that have become overvalued (a stock whose price doubles gets double the weight). Indices weighted by fundamentals such as sales, cash flow or book value delivered higher returns.
- Fama & French (1992, 1993), Journal of Financial Economics. Value and size factors explain the cross-section of returns better than the CAPM. The foundation of all factor investing.
- Carhart (1997), Journal of Finance. Adds momentum, creating the four-factor model, which most smart beta ETFs follow.
Two firms each have sales of €10 billion. Firm A has a market cap of €300 billion (investors are euphoric), firm B €100 billion. A cap-weighted index holds 300/400 = 75% in A and 25% in B. A sales-weighted index holds 50% in each. If A is overvalued and its price later falls back, the cap-weighted index loses more. This is Arnott, Hsu & Moore's argument that cap weighting systematically overweights overvalued stocks.
Why smart beta exists: CAPM vs reality
The CAPM says that only market risk is rewarded. The slide writes it as E[Ri] = βi · (Rm − Rf), which is the expected excess return of stock i (its return above the risk-free rate). In full: E[Ri] = Rf + βi(E[Rm] − Rf), where Rf is the risk-free rate, Rm the market return and βi the sensitivity of the stock to the market. Example: Rf = 2%, E[Rm] = 8%, β = 1.2 gives 2% + 1.2 × 6% = 9.2%.
Yet the evidence shows that value stocks beat growth stocks, small caps beat large caps, momentum shows up in every market, and low-volatility stocks combine lower risk and higher returns. Some factors therefore explain returns better than the CAPM does, and smart beta funds harvest them in a systematic way. The Fama-French and Carhart models include these factors:
Ri − Rf = αi + βi(Rm − Rf) + siSMB + hiHML + miUMD + εi
SMB (small minus big) is the return of small firms minus large firms, HML (high minus low) the return of high book-to-market (value) minus low book-to-market (growth) firms, and UMD (up minus down) the return of past winners minus past losers. The loadings s, h and m measure exposure to each factor, and α is the return left unexplained. Without UMD it is the Fama-French three-factor model; with UMD it is Carhart's four-factor model.
Behavioral foundations of the factors
| Factor | Strategy | Behavioral explanation on the slides | Evidence on the slides |
|---|---|---|---|
| Value | Buy cheap stocks (low P/E, P/B, EV/EBITDA) | Overreaction to negative news (De Bondt & Thaler); representativeness, so investors avoid "ugly" companies; disposition effect delays correction | Over horizons of several decades value outperforms growth; evidence from many countries (Fama & French 1992, 1993) |
| Momentum | Buy winners, sell losers based on months t−12 to t−1 | Underreaction to news and earnings (Barberis, Shleifer & Vishny); herding by institutions; confirmation bias and representativeness | Among the most robust effects, found in over 40 countries |
| Size | Buy small caps | Attention bias and liquidity premium | Small caps outperform large caps |
| Low volatility / low beta | Buy low-risk stocks | Preference for lottery-like stocks (Kumar, 2009); excessive optimism; leverage constraints lead to overpricing of high-beta stocks | Low-vol premium exists in all developed markets |
| Quality | Buy profitable, stable firms | Mispricing due to noisy accounting signals | Quality Minus Junk premium (Asness, Frazzini & Pedersen 2018) |
The common message: factors exist because investors make systematic mistakes. Factors are not magic; they are behavioral mistakes that repeat.
At the end of December, rank stocks on their return from the previous January to November (months t−12 to t−1), skipping December because one-month returns tend to reverse. Suppose the top decile averaged +40% and the bottom decile −25%. You buy the top decile and short the bottom decile in equal amounts. If over the next month winners return +2.0% and losers +0.8%, the long-short momentum return is 2.0% − 0.8% = 1.2% for that month. Under underreaction, the news that moved the winners is still being absorbed, so they keep drifting up.
The low-volatility paradox
The CAPM predicts that higher beta means higher return. In the data, low-risk (low beta, low volatility) stocks have earned higher returns than risky stocks. The behavioral explanation: investors overinvest in high-volatility "lottery stocks" (cheap shares with a small chance of a huge gain), driven by excessive optimism, so these stocks are overpriced and earn low returns later. Investors who cannot borrow (leverage constraints) also buy high-beta stocks to get more market exposure, adding to their overpricing.
Smart beta ETFs and empirical evidence
The main smart beta ETFs include Momentum (MTUM), Value (VLUE), Quality (QUAL), Low Volatility (USMV, SPLV) and multi-factor funds such as LQDI and MSCI Multi-Factor. What they share: portfolios built by rules, low fees, a lot of transparency, "passive" execution combined with "active" selection. Smart beta ETFs are now the usual vehicle for putting behavioral anomalies into practice.
Key empirical papers:
- Frazzini & Pedersen (2014), "Betting Against Beta": a factor built on low beta, with a strong behavioral basis.
- Asness, Moskowitz & Pedersen (2013), "Value and Momentum Everywhere": the factors hold in every market: equities, bonds, currencies and commodities.
- Asness, Frazzini & Pedersen (2018), "Quality Minus Junk": high-quality stocks earn a systematic premium (the quality factor).
The slide's conclusion: smart beta = systematic behavioral alpha.
Critiques and challenges
- Factor cloning: plenty of smart beta products are just factor tilts in a different wrapper. Hsu & Kalesnik (2014): "Not all smart beta is smart."
- Data mining and the "factor zoo": more than 400 factors have been proposed, and many do not survive out-of-sample (in new data or time periods). If you test enough variables, some will look significant by chance.
- Crowding risk: value, low volatility and momentum are crowded trades. When many funds hold the same positions, they can all try to exit at once.
- Implementation costs: high turnover, especially for momentum, leads to slippage (the difference between the theoretical and the achieved trading price).
- Cyclicality of factors: the value premium disappeared in 2010 to 2020 and reappeared after the pandemic.
Smart beta offers no guarantee of beating the market, though it rests on solid theoretical and behavioral grounds. Observe that crowding and lengthy periods in which a factor fails to pay off are limits of arbitrage in their own right: a manager who lags for a decade will lose clients before the factor comes back.
Behavioral funds: Fuller & Thaler Asset Management
Richard Thaler (Nobel Prize 2017) and Russell Fuller were among the first behavioral portfolio managers. Their philosophy: mispricing caused by behavioral biases creates opportunities, with a focus on underreaction, anchoring and overconfidence. Products include the Behavioral Small-Cap fund, the Core Behavioral Fund and Behavioral International Equity. It is one of very few funds worldwide with a purely behavioral philosophy.
AQR: factor investing with behavioral foundations
AQR (Asness, Frazzini, Pedersen) is among the world's leading factor investors. Even though it is labelled "quant", the factors it uses are rooted in behavior: value, momentum, profitability, quality and defensive (low beta). The firm's core view: "The behavioral biases are persistent, the factors are persistent."
The final link: smart beta strategies exploit systematic behavioral weaknesses of investors, turn anomalies into return factors, and offer a structured, systematic form of "behavioral arbitrage". This connects theory and practice and shows how psychology affects security prices.
9. Behavioral macroeconomics: animal spirits
The psychological factors that shape economic behavior: confidence, emotion, narratives, fear and enthusiasm. The term goes back to Keynes. Behavioral macro studies how human psychology affects the real economy.
Why this is relevant: consumers do not decide in a purely rational way; companies invest when they "feel" confident; investors trade out of fear or excitement; and the public mood sways governments.
Behavioral macroeconomics bibliography
- Akerlof & Shiller (2009), Animal Spirits: the starting point of behavioral macro, covering confidence, narratives and money illusion.
- Shiller (2019), Narrative Economics: economic stories travel like epidemics and have real economic effects.
- Gennaioli, Shleifer & Vishny (2012, 2015), on neglected risks and memory in economic decisions: investors notice only the risks that stand out, and this leads to bubbles and crashes.
- De Grauwe (2011), on animal spirits in DSGE models: macroeconomic models that incorporate behavioral expectations.
- Bordalo, Gennaioli & Shleifer (2018), diagnostic expectations: a bias in forecasting that leads to overreaction to macroeconomic news.
The five categories of animal spirits
| Element | What it stands for |
|---|---|
| Stories (narratives) | When a story spreads virally, it helps explain bubbles and cycles |
| Money illusion | People reason in nominal rather than real terms |
| Confidence | The main psychological force behind economic decisions; when optimism is widespread the economy flourishes |
| Fairness | Because of what is perceived as fair, employers avoid cutting wages |
| Dishonesty / corruption | Fraud rises during recessions as a result of pressure and desperation |
Confidence as a macroeconomic lever
Consumers buy more when they feel safe, firms invest more when there is optimism, and banks lend more easily when markets are calm. Akerlof & Shiller argue that confidence can be a self-fulfilling prophecy: confidence ↑ ⇒ investment ↑ ⇒ GDP ↑. Higher GDP then justifies the original confidence. Confidence acts as an economic multiplier; the same chain works in reverse in a downturn.
Narratives: when stories move markets
According to Shiller's narrative economics (2017 to 2019), viral stories shape economies: stories alter expectations, expectations alter decisions, and decisions alter markets. Examples include "AI will change everything", "Housing never goes down" (2003 to 2007), "Crypto will replace money" and the "New Economy" of the dot-com bubble. Stories carry as much weight as fundamentals.
Money illusion
People respond to nominal changes rather than reasoning in real (inflation-adjusted) terms. Consequences: employees accept a higher nominal wage even when their real wage is unchanged; companies can lift prices without pushback from consumers; and the central bank (the Fed) influences the economy via inflation expectations. The chain: money illusion causes wage rigidity, and wage rigidity causes unemployment during recessions.
Case 1: inflation is 4% and your wage rises 2%. Your real wage changes by 1.02 / 1.04 − 1 ≈ −1.9%. Case 2: inflation is 0% and your wage is cut by 2%. Your real wage changes by −2%. Economically the two cases are almost the same, but most workers accept case 1 and protest against case 2. Because firms cannot easily cut nominal wages in a recession with low inflation, they lay off workers instead: wage rigidity creates unemployment.
Animal spirits and business cycles
Boom: confidence, credit expansion, investment, optimism, bubble. Bust: fear, deleveraging (paying down debt), falling prices, reduced consumption, recession. The behavioral macro view: cycles do not come only from external shocks, but from psychological shifts in confidence.
Example: the housing bubble (2002 to 2007)
The story everyone told was "house prices never fall". Households took on too much debt, banks relaxed their lending criteria (subprime mortgages), and investors bought homes out of FOMO (fear of missing out) to resell them quickly. Herding and overoptimism were the psychological drivers, and the narrative produced an actual economic bubble. Once the story "broke", the market crashed, which led into the 2008 financial crisis.
The behavioral side of macroeconomics
| Traditional macro models (DSGE) | Behavioral macro |
|---|---|
| Representative agent (one "average" household stands for everyone) | Heterogeneous beliefs |
| Perfectly rational expectations | Expectation errors and inelastic expectations |
| Perfect information | Transmission of expectations from person to person |
DSGE is short for Dynamic Stochastic General Equilibrium, the kind of model central banks normally use. From a behavioral angle, the economy resembles a "psychological system" more than a machine.
Sentiment indicators
- Michigan Consumer Sentiment Index: survey of US households on their economic expectations.
- MOVE index: implied volatility of US Treasury bonds, the bond market's "fear gauge".
- VIX: implied volatility of S&P 500 options, known as the "fear index".
- Baker & Wurgler Sentiment Index: an investor sentiment measure built from market data such as IPO activity and closed-end fund discounts.
- Social media sentiment: FinTwit, Reddit.
Empirically: confidence leads consumption, pessimism causes a drop in investment, and sentiment affects swings of the business cycle.
10. Course synthesis: what did we learn in behavioral finance?
The lecture ends with a summary of the whole course. People are not fully rational: decisions are influenced by emotion, narrative and confidence, and micro-behaviors create macro-phenomena (animal spirits drive consumption, investment and housing; narratives drive bubbles, booms and busts; sentiment drives valuation and business cycles). Behavior is not "noise", it is a driving force of the economy. The five lessons:
- Markets do not move only due to fundamentals. Investors make systematic mistakes: overconfidence, framing, loss aversion, herding.
- Market anomalies have psychological roots. Momentum, reversal, seasonality, PEAD and bubbles are linked to biases and arbitrage limits.
- Mispricing is not always corrected by arbitrageurs. Shleifer & Vishny: noise trader risk, fundamental risk, constraints.
- Behavior becomes strategy. Smart beta, factor investing and behavioral funds: psychology creates predictable patterns.
- Macroeconomics is also behavioral. Animal spirits, narratives and confidence affect consumption, investment and cycles.
Closing message: finance is about human behavior as much as about numbers. Understand the psychology of the market and you understand the market.
- Persistence of closed-end fund or ETF premiums. Track premiums to NAV for funds holding hard-to-value assets (such as DXYZ) and test whether premiums rise with retail attention (Google Trends, Reddit mentions) and how slowly they close. Base it on Lamont & Thaler (2002) and Shleifer & Vishny (1997).
- Do smart beta factors still work after they become ETFs? Compare value, momentum and low-volatility returns before and after the launch of VLUE, MTUM and USMV using Kenneth French data library factor returns, and discuss crowding and the factor zoo.
- Framing in fund marketing. Run a small survey experiment among students: present the same fund as "+30% over 5 years" or "5.4% per year with drawdowns", or the same product as "90% capital guarantee" versus "loss of up to 10%", and measure willingness to invest (Tversky & Kahneman 1981, Benartzi & Thaler 1995).
- Sentiment and the business cycle. Test whether the Michigan Consumer Sentiment Index or the Baker & Wurgler index predicts consumption growth or stock returns, in the spirit of Akerlof & Shiller (2009).
- Framing changes choices between economically identical options: gain frames make people risk averse, loss frames risk seeking, as prospect theory predicts.
- Narrow framing plus loss aversion (myopic loss aversion) makes investors underinvest in equities and helps explain the equity premium puzzle.
- Arbitrage is limited by fundamental risk, noise trader risk and implementation costs; mispricing can widen before it closes.
- Royal Dutch/Shell (up to 20% premium) and DXYZ (more than 2,000% above NAV) show the Law of One Price failing even in "no-brainer" cases.
- Smart beta turns behavioral anomalies (value, momentum, size, low volatility, quality) into rules-based products, but faces factor cloning, data mining, crowding, costs and cyclicality.
- Animal spirits (confidence, fairness, corruption, money illusion, stories) carry behavioral finance into macroeconomics and business cycles.