What do rational investors do?
Eliminate all unsystematic risk
What does the CAPM give us?
An exact linear relationship between risk and return
Give the 5 assumptions that underlie the CAPM.
– No transaction costs, that is no cost in buying or selling stocks
– Investors hold a diversified portfolio, eliminating all unsystematic risk.
– Absence of personal income tax
– Individuals cannot affect the price of a stock by their own buying and selling actions
– All decisions are taken solely in terms of expected values and the standard deviation of returns on their portfolios, that is individuals are only concerned with the return and risk of a portfolio
– Homogeneous expectations
Does the CML give us any information about an individual stock?
No
What does the average (expected) return to the portfolio =?
(risk free return) + (price of risk) × (amount of risk)
What are 2 reasons why the CML equation is incomplete?
- Only gives portfolio information, and gives no information about singular stocks
- The equation assumes a well-diversified portfolio, which it may not be
What does the Security Market Line (SML) examine?
The SML examines the return to the ith security.
What is the SML equation?
- (risk free return) + (Beta) × (risk premium)
- 𝑅bar𝑖 = 𝑅𝑓 + 𝛽𝑖(𝑅bar𝑚 − 𝑅𝑓)
In the equation - 𝑅bar𝑖 = 𝑅𝑓 + 𝛽𝑖(𝑅bar𝑚 − 𝑅𝑓)
What does 𝛽 represent? What about Rf or (𝑅bar𝑚 − 𝑅𝑓)?
These are the 3 factors affecting the return on a security
- Pure time value of money as measured by 𝑅𝑓.
- The reward for bearing systematic risk as measured by the risk premium (𝑅bar𝑚 − 𝑅𝑓)
- The amount of systematic risk as measured by 𝛽.
What is 𝛽 in the market portfolio? Why?
𝛽 is 1 in the market portfolio as m is the most efficient portfolio, so we can assume that it only contains systematic risk.
How do we draw the SML?
We need the returns 2 points, the risk free rate (at 𝛽=0) and m (at 𝛽=1), then it is just a straight line
How can we define 𝛽?
The market risk of a security, ie how sensitive the security is to market changes
How do we calculate 𝛽?
𝛽𝑖 = 𝜎𝑖𝑚/ ∑𝑛𝑖=1 𝑤𝑖𝜎𝑖𝑚 = 𝜎𝑖𝑚/𝜎2𝑚
where:
𝜎𝑖𝑚 = 𝜎𝑖𝜎𝑚p𝑚
Is the covariance between the stock return and the market return.
What is the calculation of 𝛽 in simple terms?
The covariance between the stock return and the market return divided by the market variance
What is the 𝛽 of an average stock?
1, as the market portfolio consists of all stocks by definition
What is true about stocks with 𝛽 >1? What about those with 0< 𝛽<1
- Stocks with β>1 are known as aggressive or volatile and amplify the overall movements of the market.
- Stocks with 0<β<1 tend to move in the same direction as the market, but not as far. Known as defensive.
What is the beta for a portfolio?
The value weighted sum of the betas of the assets in the portfolio
Say a portfolio with a large number of stocks with a beta of 1.5, and market risk was 20%, what is the risk/standard deviation of the portfolio?
30%, as it is 20% x 1.5
Why do security betas determine portfolio risk?
As they measure the sensitivity of individual securities to market movements. Total risk is dependent on the number of securities in the portfolio, and in a well-diversified portfolio, market risk accounts for most of the risk.
How would we write the difference between the expected rate of return on the portfolio and the risk free asset?
E(RPp) = E(Rp) - Rf
What does the CAPM say about the relationship between the expected risk premium and beta?
CAPM says that the expected risk premium varies in direct proportion to beta. If you want a higher return you must be prepared to bear greater risk.
Is a negative beta realistic?
No
Do inefficient portfolios lie on the CML?
NO
Give 2 uses of the CAPM
- Investment in financial markets (ie portfolio selection/mispriced shares)
- Calculating the required rate of return on a firm’s investment projects (the cost of capital)
