WEEK 8 - CAPM

Question 1

How do we calculate the required return on the share of a company?

Answer 1

Ri + Rf +RP

Where:
Ri is the required return on share of company i

Rf is the risk-free rate

RP is the risk premium

Question 2

How do we find the Risk Premium?

Answer 2

• Estimate the risk premium for the averagely risky share on the stock market (Using historical returns)
• Multiply this number by a risk adjustment factor for each individual share (RP = Rm-Rf)

Question 3

What are the Objections to looking at previous returns in finding the risk premium?

Answer 3

• Bold assumption that the extra returns received in the past reflect their required returns
• Investors in the past might’ve gotten lucky
• Don’t know how many years to look at
• Debate on using rate of return on Govt bonds or treasury bills in finding the risk-free

Question 4

What is the debate regarding finding the risk-free rate of return?

Answer 4

• Debate on using rate of return on Govt bonds or treasury bills in finding the risk-free rate of return.

Generally, use Bills in SR
Use treasury bills in LR (Gilts/Bonds)

Question 5

What is the generally accepted market premium rate?

Answer 5

3-5%

Question 6

How do we find the market premium?

Answer 6

Equity% - Rf

Question 7

What is the measure of risk on financial securities in the UK from 1900-2016?

Answer 7

Equities 20.0% St Dev.
Gilts 13.7% St Dev.
Treasury Bills 6.4% St Dev

Where St Dev is used as measurement of risk

Question 8

What does the Capital market line look like considering differing portfolios?

Answer 8

SEE GRAPH IN NOTES

Question 9

What does the Hypothetical Capital Market line look like?

Answer 9

SEE GRAPH IN NOTES

Question 10

How do we calculate the Expected Return?

Answer 10

E(Rp) = 𝜔𝐹Rf + 𝜔ME(Rm)

Where:
E - expectation operator,
𝑅𝑃 – return on portfolio P,
𝜔𝐹 – share of risk-free asset in portfolio,
𝑅𝐹 – return on the risk free asset,
𝜔𝑀 – share of market portfolio in portfolio,
𝑅𝑀 – return on the market portfolio

Question 11

What is the Capital Market Line calculation?

Answer 11

𝐸(𝑅𝑝 )=𝐸(𝑅𝐹 )+((𝐸(𝑅𝑀 )−𝑅𝐹))/𝜎𝑀 to the power of 𝜎𝑃

-How much extra return do I get if I increase risk by 1

SEE NOTES FOR BETTER VIEW

(SEE EXAMPLE IN NOTES)

Question 12

How do we identify if a share has a systematic or unsystematic risk?

Answer 12

SEE GRAPH IN NOTES

Question 13

What does the CAPM define Systematic risk as?

Answer 13

Beta

Where previously it was St Dev

Question 14

What does the Beta (β) measure?

Answer 14

Measures the Covariance between the returns on a particular share with the returns on the market as a whole

Question 15

What is one of the assumptions in the CAPM model?

Answer 15

All investors are assumed to hold the market portfolio

Question 16

What is the implication of this assumption to the CAPM model?

Answer 16

In the CAPM model, because all investors are assumed to
hold the market portfolio, an individual asset (e.g. a share) owned by an investor will have a risk that is defined as the amount of risk that it adds to the market portfolio

Question 17

What is the formula to calculate the Beta of an asset?

Answer 17

Bj = Cov (Ri,Rm)/ 𝜎2M (2 is to the power of)

Where:
- β= beta of asset, j; 
- Cov(Rj, RM ): Covariance of 
  Asset J with the market 
  portfolio  
𝜎2M: Variance of the market portfolio

Question 18

What does the beta explain?

Answer 18

β = 1 ⇒ A 1 per cent change in the market index return generally leads to a 1 per cent change in the return on a specific share.

0 < β < 1 ⇒ A 1 per cent change in the market index return generally leads to a less than 1 per cent change in the returns on a specific share.

β > 1 ⇒ A 1 per cent change in market index return generally leads to a greater return than 1 per cent on a specific company’s share.

Question 19

How do we calculate the Security Market line (SML)?

Answer 19

Rj = RF + β(RM − RF )

Where:
- Ri - Expected Return
- Rf - Risk free rate
- (Rm - Rf) - The average risk premium for a share
(Expected return on the market minus the risk free rate)

E.g.

For a share j with 𝛽=1.2
(𝑅𝐹=6% and 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚=5%):

Rj = 6% + 1.2(5% )=12%

Question 20

What does the Hypothetical Security Market line look like?

Answer 20

See graph in notes

Question 21

What cause a shift in the SML?

Answer 21

Changes to the risk free rate

Question 22

How do you calculate the expected return using the beta?

Answer 22

Ri + β (Rm - Rf)

Question 23

EXAMPLE OF CALCULATING THE SECURITY MARKET LINE

Answer 23

SEE IN NOTES

Question 24

How do we calculate the characteristic line?

Answer 24

Rj = α + βj × RM + e

Where:
Rj = rate of return on the jth share;
RM = rate of return on the market index portfolio;
α = regression line intercept; e = residual error about the regression line (in this simple case this has a value of zero because all the plot points are on a straight line);
βj = the beta of security j

Question 25

What is the slope of the characteristic line?

Answer 25

β = ∆Rj/ ∆Rm

Question 26

How do we calculate the regression line intercept?

Answer 26

α = (1- βj) Rf

Question 27

What does the characteristic line with no unsystematic risk look like?

Answer 27

SEE GRAPH IN NOTES

Question 28

What does the characteristic line with unsystematic risk look like?

Answer 28

SEE GRAPH IN NOTES

Question 29

What are the applications of CAPM?

Answer 29

Investment in the financial markets
-Portfolio selection
-Mispriced shares
-Measuring portfolio performance
Calculating the required rate of return on a firm's investment projects

Question 30

What are some accepted and controversial aspects of CAPM? (PART 1)

Answer 30

• Shareholders demand a higher return for riskier assets
• Risk-averters are wise to diversify
• The risk of securities (for example shares) has two elements: (a) unsystematic risk factors specific to firms which can be diversified away; and (b) systematic risk caused by risk factors common to all firms
• Investors will not be rewarded for bearing unsystematic risk

Question 31

What are some accepted and controversial aspects of CAPM? (PART 2)

Answer 31

• Different shares have different degrees of sensitivity to the systematic risk elements
• Systematic risk is measured by beta which, in practice, is
  calculated as the degree of co-movement of a security’s return with a market index return

-Beta, as calculated by examining past returns, is valid for decision making concerned about the future

Question 32

What are the technical problems with the CAPM?

Answer 32

• Measuring beta
• Ex ante theory with ex post testing
• The market portfolio is unobtainable
• One-period model
• Very few government securities are close to being risk free
• Unrealistic assumptions

Question 33

Why is measuring the beta a technical problem of the CAPM model?

Answer 33

not clear whether it is more appropriate to use daily, weekly or monthly data, or whether the observation period should be three, five or ten years.

Question 34

What are the unrealistic assumptions of the CAPM model?

Answer 34

• Investors are rational utility maximizers
• Information is freely available
• Investors can borrow and lend at the risk free-rate
• Capital markets are perfectly competitive and frictionless
• Securities are infinitely divisible

Question 35

Does the CAPM work in practise?

Answer 35

Not really,

Disparity between the Theoretical SML and the Early empirical SML

Question 36

What is Systematic Risk?

Answer 36

• Uncontrollable by an organisation

- Macro in nature

Question 37

What is Unsystematic Risk?

Answer 37

• Controllable by an organisation

- Micro by nature