Efficient market hypothesis - I

Table of Contents

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

Always use the information set to evaluate EMH related questions.

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)