Asset Pricing Models Flashcards
Diversification in Stock Portfolios
Firm-Specific Versus Systematic Risk
When many stocks are combined in a large portfolio, the firm-specific risks for each stock will average out and be diversified.
The systematic risk, however, will affect all firms and will not be diversified.
only compensated for systematic risk as it is unavoidable
No Arbitrage and the Risk Premium
What is the risk premium for diversifiable risk and whats the effect of this?
What is the risk premium of a security determined by? (2)
What is risk premium
- The risk premium for diversifiable risk is zero, so investors are not compensated for holding firm-specific risk.
- The risk premium of a security is determined by its systematic risk and does not depend on its diversifiable risk.
- risk premium is the extra return you expect to earn when you invest in something risky compared to a safer option.
The Capital Asset Pricing Model
What is it?
What does it link?
What is it used as a model for? (3)
- CAPM is a model developed by Sharpe, Lintner, Traynor (1960s) for predicting equilibrium return
- It links risk (systematic) and expected return
- It is used as a model for estimating required return on equity for a given level of systematic risk:
- Return that shareholders require
- An input to the cost of capital (cost of equity)
The Security Market Line
What is it?
According to…, …
There is a linear relationship between a stock’s beta and its expected return. The security market line (SML) is graphed as the line through the risk-free investment and the market.
– According to the CAPM, if the expected return and beta for individual securities are plotted, they should all fall along the SML.
Are there any shares or portfolios that can lie above the SML?
a. The SML plots all shares and portfolios
b. On average, expected risk return combinations must lie on the line
c. Nothing would plot consistently above (or below) the SML
Nothing would plot consistently above (or below) the SML
Formulas
The stock of XYZ Corporation has a beta of 0.65. If the riskfree rate of return is 3% and the expected market return is 9%, the expected return for XYZ is closest to:
**CML vs SML **
Graphical representation difference?
Measures…?
Graph defines…?
Y axis and X axis represent?
Extra
Capital Market Line(CML):
- graphical representation of CAPM which shows the relationship between the expected return on efficient
portfolio and their total risk. - measures the risk through standard deviation, or through a total risk factor.
- The graphs of Capital Market Line defines efficient portfolios.
- The Y axis of the CML represents the expected return and X axis represents the standard deviation or level of risk.
- Applies for efficient portfolios: combinations of the risk free asset and the market portfolio
Security Market Line(SML):
- the graphical representation of CAPM which shows the relationship between the required return on individual security as a function of systematic, non-diversifiable risk (compensation needed)
- measures the risk through beta, which helps to find the
security’s risk contribution for the portfolio. - The graphs of Security Market Line defines both efficient and non-efficient portfolios.
- The Y axis of the SML represents the level of required return on individual assets, and the X axis shows the level of risk represented by beta.
- gives the equilibrium relationship for any share or portfolio
The Security Market Line (cont’d)
What is the beta of a portfolio
Beta of a Portfolio
- The beta of a portfolio is the weighted average beta of the securities in the portfolio.
The CAPM in Practice
In practice, what is the SML used for?
rf is estimated from?
rm is based on?
What have market risk premiums over time tended to average at?
How is βε estimated?
In practice the SML is used to estimate the expected return on equity:
- rf is estimated from the return on Treasury Bills or government bonds
- rm is based on the return on a market index (such as FTSE100)
Market risk premiums over time have tended to average at around 6-7%
βε is estimated by regressing the company returns on the market return, called the Market Model
Examples of where CAPM is used (3)
- Companies use CAPM to determine the required return on equity. Graham and Harvey (2001) surveyed managers:
73% used CAPM
39% used average historical return
34% used CAPM plus some extra risk factors - Industry regulators use CAPM to determine the return on equity, which is an input in the determination of maximum price increases
- Analysts use CAPM to explore the risk/return relationship for stocks
Beta in Practice
- βE is based on _____________ _______________ and therefore can ___________ according to the _______________ _________ used, the ________________ of the ______, etc.
- Usually we would use _ ________ of __ _____________ (e.g. ______ ________ _____)
- Assume that __ is ____________
Try to do without gap fill
- βE is based on empirical observation and therefore can change according to the estimation period used, the frequency of the data, etc.
- Usually we would use a range of βE estimates (e.g. high and low)
- Assume that βE is stationary
Is the CAPM a satisfactory model for risk and return?
3 criticisms? (2,2,1)
Criticism 1:
- Return is related to β but the slope of the line is flatter than CAPM would predict – e.g. evidence for 1931-1961 in the USA (Black, 1993)
- Defenders of CAPM say it’s concerned with expected returns whereas we observe only actual returns which contain a lot of ‘noise’ or surprise elements
Criticism 2:
- It’s impossible to test as the market portfolio should contain all risky investments, including stocks, bonds, commodities, real estate, paintings, human capital…
- Market indices (used as a proxy) only contain a sample of common stocks.
Criticism 3:
- Return is related to other measures
The Arbitrage Pricing Theory Model (APT)
How did it come along?
Main points (3,2,2)
Criticism (3+4)
Formula
It arose out of dissatisfaction with the CAPM, particularly over the inability to specify the market portfolio (which should be all risky assets, whether traded or not).
- Main Points:
- The APT model doesn‘t ask which portfolios are efficient
- It assumes that each stock’s return depends partly on:
- economic influences or factors; and
- ‘noise’ – events that are unique to the company.
- For any share, there are two sources of risk:
- risk from the macroeconomic factors (not eliminated)
- risk from events that are unique to the company (diversified away)
- APT criticism
- The theory doesn‘t say what the factors are.
- Statistical analysis must be performed to try to judge what they might be.
- Different research studies have for example identified the following possibilities:
- GDP,
- inflation,
- exchange rates,
- market and size.
APT Model
What does the risk premium on a share depend on?
What happens if the sensitivity (b) to each factor is zero?
What should a portfolio constructed with zero sensitivity to each factor earn?
What does the APT model assume about arbitrage opportunities?
What does the risk premium on a share depend on
- It depends on the risk premium associated with each factor and the share’s sensitivity to those factors.
What happens if the sensitivity (b) to each factor is zero?
- The risk premium is zero.
What should a portfolio constructed with zero sensitivity to each factor earn?
- It should earn the risk-free rate of interest. If not, there are arbitrage opportunities.
What does the APT model assume about arbitrage opportunities?
- It assumes that such opportunities are eliminated.
Comparison of CAPM and APT
1 similarity, 2 differences
Similarity:
- Expected return depends upon risk stemming from economy wide influences is not affected by unique risk
Differences:
- There is only one determinant factor for return in CAPM (return on market)
- APT model can have any number of factors, and they are not specified in advance. Statistical analysis must be done to try to work out what these factors might be.
Fama-French Three-Factor Model
What did they find?
Describe all parts of the formula (3)
3 factors
Fama and French (1995) found that shares of small firms and those with high book to market ratios have provided above average returns. These could be important factors that are left out of the CAPM.
b is the sensitivity to the factor – which will vary between companies
rRP is the risk premium on the factor – which is constant across companies (but not necessarily across time)
Fama and French developed a three-factor version of the APT with a good fit
Factor 1:
- The return on the market index minus the risk-free return
Factor 2:
- The return on a portfolio of “small” stocks minus the return on a portfolio of “large” stocks
Factor 3:
- The return on a portfolio of “value” stocks minus the return on a portfolio of “growth” stocks
What can we say about the Fama-French model? (3)
- It’s not widely used in practice to estimate the cost of equity because it requires three betas and three risk premiums.
- The three betas are not as easy to predict or interpret as the CAPM beta.
- It can, however, be used to measure the performance of mutual funds, pension funds, and other professionally managed portfolios.
