# 7. Efficient market hypothesis - I

## A. Using Multi-factor model

### 1. Fama-French (FF) 3 Factor Model

Fama and French 3 factor model is a standard model for analyzing stock returns. Built upon the observation that firm size and the book-to-market ratio historically explain stock returns.

MVSP = P x # of shares outstanding

Observation: Smaller firms have higher beta; more-than average returns.

• Conclusion: Smaller firms haver higher returns that what the CAPM would predict; This deviation is not captured by the CAPM. This missing factor was the FIRM SIZE.

$$\text{Book to Market Ratio} = \frac{\text{Book value of equity}}{\text{Market value of equity}}$$

### 2. Fama-French (FF) - 3 Factors model

$$E(r_G) = r_f + \beta_{G,M}(E(r_M)-r_f) + \beta_{G, SMB}E(r_{SMB}) + \beta_{G, HML}E(r_{HML})$$

1. Market Index Excess Return: $E(r_M)-r_f$; We only subtract the risk-free rate because

2. Small Minus Big (SMB) Index Excess Return: $E(r_{SMB})$

• Difference between the returns of small and big firms
3. High Minus Low (HML) Index Excess Return: $E(r_{HML})$

• Difference between the returns of high and low book-to-market firms

Kahoot! Q1: If the TRUE model of expected returns is the 10 Fama French 3 factor model:

$$E(r_G) = r_f + \beta_{G,M}(E(r_M)-r_f) + \beta_{G, SMB}E(r_{SMB}) + \beta_{G, HML}E(r_{HML})$$

An analyst instead estimates the CAPM index model:

$$E(r_i) = r_f + \alpha +\beta_{i}(E(r_M)-r_f)$$

What is the $\alpha$ if the analyst uses the CAPM model?

(2) Greater than 3%, less than 5%

### 3. Omitted Systematic Factors

"Index models that OMIT important systematic factors produces poor estimates of $E(r_i)$"
• Fama-French 3-factor model is better than the singleindex CAPM at explaining stock returns because it includes important factors.

• Single-index CAPM fails to explain the returns on too many stocks

## B. Random Walks and the Efficient Market Hypothesis

### 1. Efficient Market Hypothesis (EMH)

"EMH proposes that security prices accurately reflect all available information"
• If markets are efficient:

• On average, investors cannot earn risk-adjusted positive profits
• If markets are not efficient:

• active strategies should eaarn risk-adjusted positive profits and outperform passive strategies

### 2. Competition

"Investor competition causes stock prices to fully and accurately reflect relevant, available information very quickly"
• Once information becomes available, market participants quickly analyze it and trade on it.

Competition may not imply information efficiency when:

• Information is not available to all market participants

### 3. Random Walks

"Stock prices should exhibit a Random Walk if price changes are unpredictable and random"

$$P_{i,t} = B_{i} \times P_{i,t-1} + e_{i,t}$$

• $P_{i,t}$: Price of stock $i$ at time $t$
• $B_{i}$: $1+E(r_i)$
• $e_{i,t}$: Random change

Why is there a postive trend?

• Investors are risk averse average and they demand for positive risk premiums. They on average invest in stocks with positive risk premiums.
• Firms invest in postive NPV projects and grow on average
• Survivorship Bias. What about the firms performing poorly consistently? Kicked out

### 4. EMH: Three Forms

1. Weak Form: Prices reflect all past information (historical prices and trading data)

• if markets are weak-form efficient, investors can never construct a strategy with positive risk-adjusted returns using using historical price and trading data.
2. Semi-Strong Form: Prices reflect all public information

• if markets are semi-strong-form efficient, investors can never construct a strategy with positive risk-adjusted returns using growth forecasts, accounting statements, past price, volume data & earnings
3. Strong Form: Prices reflect all information: both public and private

• if markets are strong-form efficient, investors can never construct a strategy with positive risk-adjusted returns using any information (public or private)