7. Efficient market hypothesis  I
Table of Contents
A. Using Multifactor model
1. FamaFrench (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 booktomarket ratio historically explain stock returns.
MVSP = P x # of shares outstanding
Observation: Smaller firms have higher beta; morethan 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. FamaFrench (FF)  3 Factors model
$$E(r_G) = r_f + \beta_{G,M}(E(r_M)r_f) + \beta_{G, SMB}E(r_{SMB}) + \beta_{G, HML}E(r_{HML})$$

Market Index Excess Return: $E(r_M)r_f$; We only subtract the riskfree rate because

Small Minus Big (SMB) Index Excess Return: $E(r_{SMB})$
 Difference between the returns of small and big firms

High Minus Low (HML) Index Excess Return: $E(r_{HML})$
 Difference between the returns of high and low booktomarket 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

FamaFrench 3factor model is better than the singleindex CAPM at explaining stock returns because it includes important factors.

Singleindex CAPM fails to explain the returns on too many stocks
B. Random Walks and the Efficient Market Hypothesis
1. Efficient Market Hypothesis (EMH)

If markets are efficient:
 On average, investors cannot earn riskadjusted positive profits

If markets are not efficient:
 active strategies should eaarn riskadjusted positive profits and outperform passive strategies
2. Competition
 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
$$P_{i,t} = B_{i} \times P_{i,t1} + e_{i,t}$$
 $P_{i,t}$: 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

Weak Form: Prices reflect all past information (historical prices and trading data)
 if markets are weakform efficient, investors can never construct a strategy with positive riskadjusted returns using using historical price and trading data.

SemiStrong Form: Prices reflect all public information
 if markets are semistrongform efficient, investors can never construct a strategy with positive riskadjusted returns using growth forecasts, accounting statements, past price, volume data & earnings

Strong Form: Prices reflect all information: both public and private
 if markets are strongform efficient, investors can never construct a strategy with positive riskadjusted returns using any information (public or private)