Abstract The idea of an Efficient Market first came from the French mathematician Louis Bachelier in 1900: « The theory of speculation ». Bachelier argued that there is no useful information in past stock prices that can help predicting future prices and proposed a theory for financial options’ valuation based on Fourier’s law and Brownian’s motions (time series). Bachelier’s work get popular in the 60s during the computer’s era. In 1965, Eugene Fama published a dissertation arguing for the random walk hypothesis (Stock market’s prices evolve randomly: prices cannot be predicted using past data). In 1970, Fama published a review of the theory and empirical evidences The EMH (Efficient Market Hypothesis): Financial markets are efficient at processing information. Consequently, the prices of securities is a correct representation of all information available at any time. Weak: Not possible to earn superior profits (risk adjusted) based on the knowledge of past prices and returns. Semi-strong: Not possible to earn superior profits using all information publicly available. Strong: Not possible to earn superior profit using all publicly and inside information. The CAPM describes the relationship between market risks and expected return for a security i (also called cost of equity), E(Re_i): Re_i = Rf – Bi(Rm – Rf) With: Rf = Risk free rate (typically government bond rate) Rm = Expected return for the whole market Bi = The volatility risk of the security i compared to the whole market (Rm – Rf) is consequently the market risk premium According to the EMH, for a well-diversified portfolio, expected returns can only reflect those of the market as a whole. Consequently, in the CAPM formula, It would involves that for a diversified-enough portfolio: β = 1 so Re = Rm Investors want to value companies before making investment decisions. A typical way to do so is to use the Discounted Cash Flow (DCF) method: See also: Prospect theory, disposition effect, heuristic, framing, mental accounting, Home bias, representativeness, conservatism, availability, greater fool theory, self attribution theory, anchoring, ambiguity aversion, winner's curse, managerial miscalibration and misconception, Equity premium puzzle, market anomalies, excess volatility, Bubbles, herding, limited liabilities, Fama French three 3 factors model.

1. Arthur MEUNIER – arthur.meunier@cpe.fr
https://www.linkedin.com/in/meunierarthur
An overview of
Behavioral Finance
January 2018

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Introduction: History
The idea of an Efficient Market first came from the
French mathematician Louis Bachelier in 1900:
« The theory of speculation ».
Bachelier argued that there is no useful information in past stock prices
that can help predicting future prices and proposed a theory for financial options’
valuation based on Fourier’s law and Brownian’s motions (time series).
1945: Hayek claimed that markets were the
most effective way of aggregating pieces of information
dispersed among individuals within a society.
Bachelier’s work get popular in the 60s during the computer’s era.
In 1965, Eugene Fama published a dissertation arguing for the random walk
hypothesis (Stock market’s prices evolve randomly:
prices cannot be predicted using past data).

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EMH: Efficient Market Hypothesis
In 1970, Fama published a review of the theory and empirical evidences:
The EMH (Efficient Market Hypothesis): Financial markets are efficient at
processing information. Consequently, the prices of securities is a correct
representation of all information available at any time.
Hypothesis:
1- Price is always = fundamental value because all agents are rational.
2- If some agents trade randomly: their trades cancel each other.
3- Arbitrage is unlimited and efficient:
cancelled arbitrage situations at all time.

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3 Forms of Market Efficiency
Weak:
Not possible to earn superior profits (risk adjusted) based on the
knowledge of past prices and returns.
Semi-strong:
Not possible to earn superior profits using all information
publicly available.
Strong:
Not possible to earn superior profit using all publicly and inside
information.

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Implications: Asset pricing
The CAPM describes the relationship between market risks and expected return for
a security i (also called cost of equity), Rei:
Rei = Rf – 𝛽𝑖(Rm – Rf)
With:
Rf = Risk free rate (typically government bond rate)
Rm = Expected return for the whole market
𝛽𝑖 = The volatility risk of the security i compared to the whole market
(Rm – Rf) is consequently the market risk premium
According to the EMH, for a well-diversified portfolio, expected returns can only
reflect those of the market as a whole. Consequently, in the CAPM formula, It
would involves that for a diversified-enough portfolio:
β = 1 so 𝐑𝐞𝐢 = Rm

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Application of CAPM: Valuation
Investors want to value companies before making investment decisions.
A typical way to do so is to use the Discounted Cash Flow (DCF) method:
NPV = ෍
𝑡=0
𝑇
𝐶𝐹𝑡
(1 + 𝑟) 𝑡
With:
NPV = Net Present Value of the asset
𝐶𝐹𝑡 = Expected Cash Flow at time t
r = expected return of the investment (CAPM + WACC)
T is the time at which the expected cash flows tend to become 0 (Often taken = ∞)
(See Corporate Finance presentation for more details)

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Challenges of the EMH
We saw that according to the 3 hypothesis of the EMH, prices of securities on
the market are always reflecting a correct intrinsic value (NPV), eventually
corrected by the current information available.
However, these hypothesis seem difficult to hold in reality:
1- Fully rational investors:
Hard to sustain (read wrong information, follow patterns, misconceptions, trade
too much, follow fake news, biases etc...)
2- Irrational traders cancel each other:
Evidence not (momentum), tend to follow each others (noise trading).
Even pros (rational investors) are impacted.
3- Unlimited arbitrage:
Arbitrage is risky and consequently limited.
Mispricing, volatility and noise trading amplify it: no risk-free arbitrage

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Market anomalies
1. Small Firms tend to outperform
2. January Effect
(Taxes: Realize losses in December and reinvest in January)
3. Low PB Value
(Companies with low price to book ratios tend to outperform the market)
4. Neglected Stocks
(Small and less liquid stocks neglected by analysts once discovered by
investors tend to outperform)
5. Reversals
(Yesterday’s over performers become tomorrow’s underperformers)
6. Day of the week
(More movements on Fridays than on Mondays)

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Puzzles
Equity premium:
Market returns on securities are on average way higher
(~7% in average over the last 120 years) than those
for risk-free fixed income securities
(short-term T-bond ~1%).
Excessive volatility:
Stock prices are more volatiles than they should,
given that they are NPVs of DCF.
Bubbles:
Markets get sometimes too far out of
the fundamentals (deviations)

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Behavioral Finance
Aim to propose a behavioral approach besides conventional
economic theories in order to account for irrationallity,
observed market anomalies and puzzles.
Kanheman and Tversky are considered the fathers of
Behavioral Finance.
They started to collaborate in the early 70s and published
their « Prospect theory » in 1979.
The prospect theory won a Nobel Memorial Price in 2002
(Economic sciences)

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Prospect theory
• People make decisions based on the potential
value of loss and gains rather than the final
outcome, because of heuristics.
• Heuristics: Simple rules that people
often use to form judgments and make
decisions (mental shortcuts).
• The Prospect theory shows that people
are more risk averse in the gain domain
and risk seeking in the loss domain.
• Losses hurts more than gains feel good
(risk aversion).
V = expected utility (value) of the outcome for the
individual making decision.
v(𝑥𝑖) are the values assigned to the potential
outcomes (𝑥1, 𝑥2… 𝑥 𝑛).
𝜋(𝑝𝑖) the probability weighted function of the
respective probabilities (𝑝1, 𝑝2… 𝑝 𝑛) associated with
the potential outcomes (𝑥1, 𝑥2… 𝑥 𝑛).

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Other behavioral biases
Disposition effect:
Tendency for investors to sell assets that have increased in value,
while keeping assets that have dropped in value.
Framing:
Perception & memory are influenced by the context. People tend to
reach conclusions based on the 'framework' within which a situation
is introduced.
Mental accounting:
Individuals classify personal funds differently and therefore are
prone to irrational decision-making in their spending
and investment behavior.

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Other behavioral biases
Familiarity:
Associate familiar situation with lower risks (See Home biais).
Home bias:
Investing primarily in their country of residence or local companies
because it is familiar. lack of diversification.
Representativeness:
See patterns in random sequences:
Past history influence future prospects (momentum)
Conservatism:
Individuals are slow to change beliefs in face of new evidences.

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Other behavioral biases
Availability:
Mental shortcut that relies on immediate examples that come to a
given person's mind when evaluating a specific topic, concept,
method or decision. (planes are more dangerous than cars).
Greater fool theory:
Possible to make money by buying securities, whether or not they
are overvalued, by selling them for a profit at a later date. This is
because there will always be someone who is willing to pay a
higher price.
Self-attribution theory:
Tendency for investors to self-attribute success to their own talent
but blaming external factors for losses (as bad luck).

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Anchoring:
Use of irrelevant information as reference point, such as the
purchase price of a security for estimating another financial
instrument’s price (of an unknown value).
Ambiguity aversion:
(also known as uncertainty aversion) is a preference for known
risks over unknown risks.
Momentum:
Speed at which the price is changing in the same direction (sell
low and buy lower or buy high and sell higher).
Reversal:
Change in the price trend = correction
Other behavioral biases

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Overconfidence & Mispricing
Winner’s curse in M&A:
Overpayment during a bet because overconfidence and sentiment.
Tendency for the winning bid in an auction to exceed the
intrinsic value or true worth of an item.
Because of incomplete information, emotions or any other
number of factors regarding the item being auctioned,
bidders can have a difficulties determining the item's real
intrinsic value.
As a result, the largest overestimation of an item's value
ends up winning the auction.

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Overconfidence & Mispricing
Managerial miscalibration and misconception:
CFO/CEO are overconfidents regarding their company.
Often think their company is underpriced and are reluctant
to pay in shares for acquisitions.
Tend to overestimate returns of their investment projects.
Overinvest when internal cash is available.
Do not accept bid if too far from 52week high.
(Malmendier and Tate, 2005)

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How Behavioral Finance explains puzzles
Equity premium:
“Why is the equity premium so large or why is anyone willing to hold bonds?”
Explained by Prospect theory (loss aversion) and trading relativity:
Diversified portfolios are overall less risky on long term than on short term
because of volatility. Long term strategies dominate and involve to hold and
reevaluate only periodically.
Benartzi and Thaler (1995)
Suggest investors overestimate equity risk because of “mental accounting”
bias used to evaluate the outcomes of investment decisions.
McQueen and Vorlink (2004)
Investors who are away from their customary level of wealth do not only
become more or less risk averse, but also more sensitive to news.

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How Behavioral Finance explains puzzles
Excessive volatility:
Market movements are often not explained by new information (50
biggest market moves of last 50 years was against NYT explanation).
Investors often think (wrongly) than changes are permanents rather
than transitory (exceptional revenues, increase in dividends,
substantial growth...).
Consequently they overreact and once they figure things out, trade in
the opposite direction (momentum and reversals) .
High returns are followed by low returns (and vice versa):
Disposition effect
Hold for the overall market.

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How Behavioral Finance explains puzzles
Bubbles indicators (Shiller):
1- Abnormally high trading volumes
2- Abnormally High P/E ratios
(Means investors expect important growth in the future: Is it
realistic?)
3- Investor’s sentiment:
Over-optimism/ overconfidence
4- Short-selling risks:
Overvaluation is more common because trading
against it is riskier.

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How Behavior Finance explains puzzles
Behavioral models of Bubbles:
1- Herding effect
Fund managers follow the herd because betting against it is very costly as
clients may give their funds to another fund manager.
Reputation’s penalties are more severe if wrong when everyone is right
than rewards are if right when everybody is wrong.
2- Limited liabilities:
Fund managers do not play with their own money: benefit from a rising
bubble but don't suffer in the same proportions when the bubble burst.
3- Perverse incentives:
Analysts tend to give good reviews to companies they cover (otherwise no
job). Similar for rating agencies and accounting auditors who may
overlook questionable investments choices.

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Back to Asset pricing
3 Factors Model
Fama & French (1993)
Rei = Rf – 𝛽𝑖(Rm – Rf) + 𝑏𝑠𝑖.SMB + 𝑏𝑣𝑖.HML
2 new factors added: SMB & HML
SMB: Small [market capitalization] Minus Big (Excess returns of small caps over big caps)
HML: High (Market to Book ratio) Minus Low (Excess returns of value stocks over growth stocks)
bs and bv are their corresponding coefficients (obtained by linear regression)
β is analogue but not equal to CAPM β
Explains 90% of diversified portfolios returns versus 70% for CAPM, but
still have limitations.
Different other models have been proposed since, some accounting for
behavioral aspects but none is yet able to fully explain the market.

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Conclusion
Behavioral Finance tries to explain market anomalies
and to challenge the EMH.
Argue that the caracteristics of the market’s participants and the
information structure systematically impact
individual’s investment decisions.
It explores rationality and propose to study how the effect of
cognitive, psycological, emotional, social and cultural factors
may affect investment’s decision for individuals and institutions.
It allows to better understand the factors that may influence our own
decision making process as well as the market as a whole.