9.3: CAPM and Market Risk

Question 1

What is the Capital Market Line (CML)?

Answer 1

The Capital Market Line (CML) represents the expected return of an efficient portfolio given its risk, as measured by standard deviation.

It applies only to efficient portfolios and not individual securities.

Question 2

What is unique (non-systematic) risk?

Answer 2

Unique (non-systematic) risk, also known as diversifiable risk, is the risk specific to an individual security or a small group of securities that can be eliminated through diversification.

Question 3

What is market (systematic) risk?

Answer 3

Market (systematic) risk, also known as non-diversifiable risk, is the inherent risk that affects the entire market and cannot be eliminated through diversification.

It is related to factors such as economic, political, and social changes.

Question 4

Explain the relationship between portfolio risk and diversification as shown in Figure 9.7.

Answer 4

Figure 9.7 illustrates that the average risk of a one-stock portfolio is high, but as the number of securities increases, unique risk is diversified away, and only market risk remains. This relationship shows the importance of diversification in reducing total risk.

Question 5

What is the key insight of the Capital Asset Pricing Model (CAPM) regarding risk?

Answer 5

The key insight of CAPM is that investors should not be compensated for unique (diversifiable) risk because it can be eliminated through diversification.

Market risk is the only risk for which investors are compensated.

Question 6

What is beta (β)?

Answer 6

Beta (β) is a measure of market risk or performance volatility that indicates the extent to which a security’s return moves with the return of the overall market.

It is calculated as the covariance between the investment and the market, divided by the variance of the market.

Question 7

What is the characteristic line?

Answer 7

The characteristic line is a line of best fit through the returns on an individual security plotted on the vertical axis, relative to the market returns plotted on the horizontal axis.

The slope of this line is the security’s beta (β) coefficient.

Question 8

How is beta (β) estimated?

Answer 8

Beta (β) is estimated by plotting the returns on an individual security against market returns and fitting a line through the observations. This involves regression analysis to determine the line’s slope, which is the security’s beta coefficient.

Question 9

What does a beta (β) of 1 indicate?

Answer 9

A beta (β) of 1 indicates that the security’s returns move with the market returns, meaning it has the same volatility as the market.

Question 10

What does a beta (β) greater than 1 indicate?

Answer 10

A beta (β) greater than 1 indicates that the security is more volatile than the market, meaning it is more aggressive or risky.

Question 11

What does a beta (β) less than 1 indicate?

Answer 11

A beta (β) less than 1 indicates that the security is less volatile than the market, meaning it is less risky or more defensive.

Question 12

How do you calculate the beta (β) of a security?

Answer 12

β_i = COV_{i,M} / σ²M = ρ{i,M}σ_i / σ_M

Where:
- β_i = Beta of security
- COV_{i,M} = Covariance of the security’s return with market return
- σ²M = Variance of the market return
- ρ{i,M} = Correlation coefficient between security and market
- σ_i = Standard deviation of the security’s return
- σ_M = Standard deviation of the market return

Question 13

What is an example of estimating beta (β)?

Answer 13

Example: Stock X has a standard deviation of 20% and a correlation coefficient of 0.8 with market returns, which have a standard deviation of 15%. The beta for stock X is calculated as:

β_X = ρ_{X,M}σ_X / σ_M = (0.8 × 20) / 15 = 1.07

Solution: Stock X’s beta is greater than 1, indicating it is more volatile than the market.

Question 14

What does a higher beta indicate about a company’s stock?

Answer 14

A higher beta indicates that a company’s stock is more volatile compared to the market, meaning it is more sensitive to market movements and considered riskier.

Question 15

How do betas vary across different industries?

Answer 15

Betas vary greatly across industries due to different risk profiles.

Even within the same industry, betas can differ based on factors like financial risk and company size.

Question 16

How do betas change over time, according to Table 9.1?

Answer 16

Betas can change significantly over time. For example, in Table 9.1, bank betas increased from 0.62 to 0.99 between 2014 and 2019, showing a higher correlation with market movements.

Question 17

How do you calculate the portfolio beta for an n-security portfolio?

Answer 17

The portfolio beta is a weighted average of the betas for individual securities:

β_p = w_1β_1 + w_2β_2 + … + w_nβ_n

Where:
- β_p = Portfolio beta
- w_n = Weight of each security in the portfolio
- β_n = Beta of each security

Question 18

What does a beta of zero signify for a security?

Answer 18

A beta of zero indicates that the security’s return is uncorrelated with the market, meaning all its return variability is diversifiable by holding a well-diversified portfolio.

Question 19

What effect does adding a security with a beta greater than 1 have on a portfolio?

Answer 19

Adding a security with a beta greater than 1 increases the portfolio’s beta, making it more sensitive to market movements and increasing the overall risk of the portfolio.

Question 20

Provide an example of estimating a portfolio beta.

Answer 20

Example: An investor has a portfolio with $10,000 in stock B (β = 1.2), $20,000 in stock C (β = 0.8), and $20,000 in stock D (β = 1.3). The portfolio beta is:

w_B = $10,000 / $50,000 = 0.20
w_C = $20,000 / $50,000 = 0.40
w_D = $20,000 / $50,000 = 0.40

β_p = (0.20)(1.2) + (0.40)(0.8) + (0.40)(1.3) = 1.08

Question 21

What is the Security Market Line (SML)?

Answer 21

The Security Market Line (SML) represents the trade-off between market risk and the required rate of return for any risky investment, whether an individual security or a portfolio.

It is derived from the Capital Market Line (CML) and is a key component of the CAPM.

Question 22

What is the formula for the Security Market Line (SML)?

Answer 22

k_i = RF + (ER_M - RF)β_i

Where:
- k_i = Required return on security or portfolio i
- RF = Risk-free rate
- ER_M = Expected return on the market
- β_i = Beta of security or portfolio i

Question 23

What does the slope of the SML indicate?

Answer 23

The slope of the SML indicates the market risk premium, which is the additional return expected from holding a risky market portfolio instead of risk-free assets. It reflects the expected return on the market minus the risk-free rate.

Question 24

What is the market risk premium?

Answer 24

The market risk premium is the expected return on the market minus the risk-free rate, reflecting the additional return investors require for taking on market risk.

Question 25

How does the SML relate to securities with different betas?

Answer 25

According to the SML, securities or portfolios with betas greater than 1 will have larger risk premiums and higher required rates of return.

Conversely, securities with betas less than 1 are less risky and have lower required rates of return.

Question 26

What are some difficulties in estimating required returns using the CAPM?

Answer 26

Estimating required returns with CAPM involves challenges, such as:
- Estimating accurate betas using historical data, which might not predict future market sensitivity.
- Estimating the expected market return, which can vary widely over time.

Question 27

What is a key lesson from using CAPM to estimate required returns?

Answer 27

While CAPM is useful for predicting average returns over the long run, one must consider that both beta and expected market returns can vary over time and might not reflect current market conditions.

Question 28

What does it mean for a security to be on the Security Market Line (SML)?

Answer 28

A security on the SML is correctly priced, meaning its expected return equals its required return according to its market risk (beta).

Question 29

What does it mean for a security to be above the Security Market Line (SML)?

Answer 29

A security above the SML is undervalued because its expected return is greater than its required return, given its beta.

Question 30

What does it mean for a security to be below the Security Market Line (SML)?

Answer 30

A security below the SML is overvalued because its expected return is less than its required return, given its beta.

Question 31

What is ‘alpha’ in the context of security valuation?

Answer 31

Alpha (α) measures the risk-adjusted excess return of a security or portfolio, indicating performance above or below the expected return predicted by its beta.

Question 32

How is alpha (α) calculated?

Answer 32

α_i = (R_i - RF) - [β_i(R_M - RF)]

Where:
- α_i = Alpha of security or portfolio i
- R_i = Actual return on security or portfolio i
- RF = Risk-free rate
- β_i = Beta of security or portfolio i
- R_M = Expected return on the market

Question 33

How is the CAPM used to estimate long-term discount rates?

Answer 33

The CAPM estimates the required return on equity using the risk-free rate (often long-term government bonds) and the market risk premium. It helps in discounting expected cash flows for investment decisions.

Question 34

What is the market risk premium used for estimating long-term discount rates?

Answer 34

The market risk premium is the difference between the expected market return and the risk-free rate, used to calculate the required return on equity.

Question 35

What is the process of estimating the required return on a firm’s common equity using CAPM?

Answer 35

The process involves calculating the expected return based on the risk-free rate, the beta of the firm’s stock, and the market risk premium, considering historical data and market conditions.

Question 36

What are some concept review questions related to the Security Market Line (SML)?

Answer 36

1. Why is beta a measure of market risk for a security?
2. If a security’s correlation with the market return increases, will its beta get larger or smaller?
3. What is a characteristic line, and why is it useful?
4. If the market risk premium increases, will securities become overvalued or undervalued?