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Behavioral Finance

Chapter 2 Asset Pricing, Market Efficiency

and Agency Relationships

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The Pricing of Risk

The expected utility theory : maximizing the expected utility across possible states of the world. This is not a manageable task

– A financial asset may have potentially innumerable possible future outcomes

Asset pricing theory : to quantify the trade-off b/w risk and return.

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Risk and return

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Portfolio risk and return

What is the risk of a portfolio? – NOT simple average risk of the assets in the

portfolio Diversification:

– by combining assets in a portfolio, investors can eliminate some variability

– Statistical measures of how random variables are related are covariance and correlation

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Portfolio risk and return

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Portfolio risk and return

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𝑆𝑆𝑝𝑝2 = 𝑤𝑤𝑖𝑖2𝑆𝑆𝑖𝑖2 + 𝑤𝑤𝑗𝑗2𝑆𝑆𝑗𝑗2 + 2𝑤𝑤𝑖𝑖𝑤𝑤𝑗𝑗𝜌𝜌�𝑖𝑖,𝑗𝑗𝑠𝑠𝑖𝑖𝑠𝑠𝑗𝑗 The lower are correlations the lower is the risk of a portfolio!

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Optimal portfolio Example

– Suppose there are only two stocks, High Tech Corp. and Low Tech Corp., and a risk-free asset (U.S. Treasury bills). You are considering investing in a portfolio of the two stocks. Suppose you put 40% of your funds in High Tech and 60% in Low Tech. What is the expected return of the portfolio and the standard deviation, respectively?

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Optimal portfolio

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Expected Return S.D. of Returns

High Tech (HT) 15% 30%

Low Tech (LT) 8% 10%

Risk-free Asset (RF) 4% 0%

Corr. b/w HT & LT -0.1

Corr. b/w LT & RF 0

Corr. b/w HT & RF 0

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Optimal portfolio

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Expected Return S.D. of Returns

High Tech (HT) 15% 30%

Low Tech (LT) 8% 10%

Risk-free Asset (RF) 4% 0%

Corr. b/w HT & LT -0.1

Corr. b/w LT & RF 0

Corr. b/w HT & RF 0

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Two-security example

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The lower the correlation b/w the two stocks, the greater the curvature

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Efficient frontier(set)

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Efficient frontier: set of portfolios that maximize expected return for a given level of risk

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Measuring Portfolio Risk

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Number of Securities

Portf

olio

sta

ndar

d de

viat

ion

Market risk

Uniquerisk

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Exercise Q1: Suppose you invest 60% of your portfolio

in Wal-Mart and 40% in IBM. The expected dollar return on your Wal-Mart stock is 10% and on IBM is 15%. Calculate the expected return for the portfolio and the standard deviation of it. The standard deviation of their annualized daily returns are 19.8% and 29.7%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.

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Exercise Q2: What would be the general Formula for

portfolio risk w/ n stocks?

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Markowitz Portfolio Theory

Borrowing and Lending – Suppose borrow or lend money at some risk-

free rate of interest – Lending money in Treasury bills: line from S to

rf

– Borrowing money at rf and investing them as well as your own money in portfolio S

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Efficient Frontier

Standard Deviation

Expected Return (%)

Lending or Borrowing at the risk free rate (rf) allows us to exist outside the efficient frontier

rf

S

T

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Markowitz Portfolio Theory

Example: – Portfolio S: E[R]=15%, SD[R]=16% vs. Treasury

bills: rf =5%, SD=0

– Lend halfway b/w two r=1/2*15+1/2*5=10%, SD=8%

– Borrow at the Treasury bill rate an amount equal to your initial wealth, and invest everything in portfolio S you have twice your own money invested in S, but you have to pay interest on the loan: r=2*15-1*5=25%, SD=2*16-0=32%

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Markowitz Portfolio Theory Sharpe ratio

– The efficient portfolio at the tangency point is better than all the others

– It offers the highest ratio of risk premium to standard deviation

– Measures risk-adjusted performance

Investors’ job into two stages: 1) a risky portfolio S 2) risk-free loan(borrowing or lending)

p

fp rrσ−

==deviation Standard

premiumRisk ratio Sharpe

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Capital Asset Pricing Model (CAPM)

CAPM is an equilibrium model: – all investors have the same efficient frontier

(holding the market portfolio) Only risk related to market movements is

priced by market. – This is because all other risk can be diversified

away. Beta is measure of nondiversifiable risk for a

security.

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CAPM relationship and beta

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CAPM equation CAPM equation: E(Ri) = Rf + βi * [E(Rm) – Rf] Notes: E(Rm) – Rf is market risk premium βi = σ(Ri , Rm)/σ 2(Rm)

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Market Efficiency

What is a function of financial markets? – Ideally, markets transfer funds from savers to

borrowers w/ good investment opportunities. W/ efficient capital markets,

– lenders are better off b/c they earn a higher risk-adjusted return

– borrowers are better off b/c they do not have to forgo profitable opportunities.

However, well-documented “mistakes” do occur: IT bubble and the global financial crisis

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Efficiency and information

Value vs. Price – Value is what a security should be worth based

on careful analysis. – Price is what the market says it is worth.

What is relationship between value and price if markets are efficient? – Older version of market efficiency: value and

price are always identical. – More subtle and realistic version: they can

sometimes differ a little. 26

1- 27 Operational definition of market efficiency

Financial markets are efficient if no one can consistently earn excess returns. Excess means…

– After risk is factored in – After all costs have been considered

What sort of costs? – Transaction costs – Information acquiring costs – Analysis costs – etc.

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What does market efficiency imply?

An asset’s price equals its expected fundamental value

E.g. stock price: 𝑝𝑝𝑡𝑡 = ∑ 𝐸𝐸𝑡𝑡(𝑑𝑑𝑡𝑡+𝑖𝑖)(1+𝛿𝛿)𝑖𝑖

∞𝑖𝑖=1

– discount rate reflects the stock’s risk – Information means items that are truly

unanticipated EMH suggests

– A manager cannot systematically generate returns above the expected, risk-adjusted return

– Excess return opportunities are unpredictable 28

1- 29 What should be true if markets are efficient?

Security prices should respond quickly and accurately to new information. Professional investors should not

outperform net of all fees. Simulated trading strategies should fail.

– possible strategies using historical data

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Joint hypothesis problem All tests of market efficiency have two

maintained hypotheses: – Markets are efficient. – A fair return on a security or portfolio is from a

particular model (in early tests usually CAPM). Rejection means:

– Markets are not efficient. – Method for calculating fair returns is faulty. – Or both.

But which? Joint hypothesis problem! – If a test rejects the EMH, is it b/c the EMH does not

hold, or b/c we did not properly measure excess returns? 31

1- 32 Market efficiency and available information

Weak Form Efficiency (historical prices and returns) – Market prices reflect all historical information

Semi-Strong Form Efficiency – Market prices reflect all publicly available

information Strong Form Efficiency

– Market prices reflect all information, both public and private

– If so, securities will be fairly priced and security returns will be unpredictable no one earns superior returns in such a market

1- 33 Market efficiency and available information

Weak Form Efficiency – To test it, measure the profitability

Semi-Strong Form Efficiency – To test it, measure how rapidly security prices

respond to different items of news, such as earnings or dividend announcements, news of a takeover, or macroeconomic information

Strong Form Efficiency – To test it, examine the recommendations for

professional security analysts and look for any outperformance of mutual funds or pension funds

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Exercise

Q3: Warren Buffett has been a very successful investor. In 2008 Luisa Kroll reported that Buffett topped Forbes Magazine’s list of the world’s richest people with a fortune estimated to be worth $62 billion (March 5, 2008, "The world's billionaires," Forbes). Does this invalidate the EMH?

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Agency Theory

Agency relationship exists – whenever someone (the principal) contracts with

someone else (the agent) – to take actions on behalf of the principal and

represent the principal’s interests. In an agency relationship, agent has authority

to make decisions for the principal. An agency problem arises when the agent’s

and principal’s incentives are not aligned.

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Agency costs

Agency costs are incurred – because managers’ incentives are not consistent

with maximizing value of firm. Direct vs. Indirect costs Direct costs:

– Any expenditures that benefit the manager but not the firm

– E.g.: need to monitor managers, including cost of hiring outside auditors

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Agency costs

Indirect costs: – Lost opportunities – E.g. Managers of a firm that is an acquisition

target may resist the takeover attempt because of concern about keeping their jobs, even if the shareholders would benefit from merger

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Tools to Mitigate Agency Problem

1. Legal and Regulatory requirements: SEC sets accounting and reporting standards for public companies

2. Compensation plans: incentive schemes producing big returns if shareholders gain but are valueless if they lose

3. Board of Directors: SOX requires that corporations place more independent directors on the board

4. Monitoring: monitored by security analysts, and by banks

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Tools to Mitigate Agency Problem

5. Takeovers: Companies that consistently fail to maximize value are natural targets for takeovers

6. Shareholder pressure: If shareholders believe that the corporation is underperforming and that the board of directors is not holding managers to task, they can attempt to elect representatives to the board to make their voices heard