Week 3- CAPM

Question 1

What do rational investors do?

Answer 1

Eliminate all unsystematic risk

Question 2

What does the CAPM give us?

Answer 2

An exact linear relationship between risk and return

Question 3

Give the 5 assumptions that underlie the CAPM.

Answer 3

– 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

Question 4

Does the CML give us any information about an individual stock?

Answer 4

No

Question 5

What does the average (expected) return to the portfolio =?

Answer 5

(risk free return) + (price of risk) × (amount of risk)

Question 6

What are 2 reasons why the CML equation is incomplete?

Answer 6

• Only gives portfolio information, and gives no information about singular stocks
• The equation assumes a well-diversified portfolio, which it may not be

Question 7

What does the Security Market Line (SML) examine?

Answer 7

The SML examines the return to the ith security.

Question 8

What is the SML equation?

Answer 8

• (risk free return) + (Beta) × (risk premium)
• 𝑅bar𝑖 = 𝑅𝑓 + 𝛽𝑖(𝑅bar𝑚 − 𝑅𝑓)

Question 9

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

Answer 9

• 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.

Question 10

What is 𝛽 in the market portfolio? Why?

Answer 10

𝛽 is 1 in the market portfolio as m is the most efficient portfolio, so we can assume that it only contains systematic risk.

Question 11

How do we draw the SML?

Answer 11

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

Question 12

How can we define 𝛽?

Answer 12

The market risk of a security, ie how sensitive the security is to market changes

Question 13

How do we calculate 𝛽?

Answer 13

𝛽𝑖 = 𝜎𝑖𝑚/ ∑𝑛𝑖=1 𝑤𝑖𝜎𝑖𝑚 = 𝜎𝑖𝑚/𝜎2𝑚
where:
𝜎𝑖𝑚 = 𝜎𝑖𝜎𝑚p𝑚
Is the covariance between the stock return and the market return.

Question 14

What is the calculation of 𝛽 in simple terms?

Answer 14

The covariance between the stock return and the market return divided by the market variance

Question 15

What is the 𝛽 of an average stock?

Answer 15

1, as the market portfolio consists of all stocks by definition

Question 16

What is true about stocks with 𝛽 >1? What about those with 0< 𝛽<1

Answer 16

• 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.

Question 17

What is the beta for a portfolio?

Answer 17

The value weighted sum of the betas of the assets in the portfolio

Question 18

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?

Answer 18

30%, as it is 20% x 1.5

Question 19

Why do security betas determine portfolio risk?

Answer 19

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.

Question 20

How would we write the difference between the expected rate of return on the portfolio and the risk free asset?

Answer 20

E(RPp) = E(Rp) - Rf

Question 21

What does the CAPM say about the relationship between the expected risk premium and beta?

Answer 21

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.

Question 22

Is a negative beta realistic?

Answer 22

No

Question 23

Do inefficient portfolios lie on the CML?

Answer 23

NO

Question 24

Give 2 uses of the CAPM

Answer 24

• 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)

Question 25

What is the required return?

Answer 25

The required return is the rate of return one should expect or require for a specific risky asset using the CAPM

Question 26

What is the actual/estimated return?

Answer 26

The actual/estimated return is the actual rate of return that you anticipate using other information (not the CAPM).

Question 27

How do we compute the estimated rates of return for a stock?

Answer 27

By summing the expected capital gain and expected dividend yield.

Estimated return=
(𝑃𝑡+1−𝑃𝑡/𝑃𝑡) + (𝐷𝑡+1/𝑃𝑡)

Question 28

If in equilibrium, all assets and portfolios should plot on the SML, what is true about securities with estimated returns plotting below or under the SML?

Answer 28

• Any security with an estimated return that plots above the SML is underpriced
• Any security with an estimated return that plots below the SML is overpriced

Question 29

If a fund has done well in the past 5 years, why may it not be worth investing in/

Answer 29

• Past performance doesn’t indicate future performance
• What about the risk the fund has taken

Question 30

Is a high or low Sharpe Ratio desired?

Answer 30

High

Question 31

What is the Sharpe Ratio?

Answer 31

(Portfolio Return - Risk free rate)/ Standard Deviation/Risk of the portfolio