Finance Chapter 7: CAPM and APT

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Questions and Answers

What drives the equilibrium risk premium of a market portfolio?

Past performance of securities

Market demand

Investor confidence

Risk of market and risk aversion of average investor (correct)

In the context of CAPM, what does the expected return-beta relationship suggest?

Higher beta implies lower expected returns

Beta is a constant value regardless of market conditions

Security risk premiums are proportional to beta (correct)

Expected returns are unrelated to market fluctuations

What does the Security Market Line (SML) represent in the context of CAPM?

The relationship between expected return and market volatility

Expected return-beta relationship of CAPM (correct)

Growth rates of the economy over time

The correlation between stocks and bonds

What is considered an abnormal rate of return on a security in CAPM?

Alpha, exceeding that predicted by the CAPM model Signup and view all the answers

How can the SML be used effectively by investors?

As a benchmark for fair returns on risky assets Signup and view all the answers

What happens to investor behavior when risk premiums fall?

Investors move funds to risk-free assets Signup and view all the answers

What is the formula indicated for expected returns in CAPM?

E(rD) = rf + βD [E(rM) - rf] Signup and view all the answers

What does the term 'hurdle rate' refer to in the applications of CAPM?

The minimum acceptable return on an investment Signup and view all the answers

What general impact does demand have on prices in the context of risk premiums?

It lowers expected returns and risk premiums Signup and view all the answers

What does the term $e_{it}$ represent in the Index Model equation?

Firm-specific effects Signup and view all the answers

According to the CAPM, what factor is directly related to the alpha of a security?

The predicted return by the CAPM model Signup and view all the answers

In the equation $r_{it} - r_{ft} = α_i + β_i (r_{Mt} - r_{ft}) + e_{it}$, what does $α_i$ signify?

Intercept of the security characteristic line Signup and view all the answers

What is the expected return equation in the Index Model?

$E(r_{it} - r_{ft}) = α_i + β_i [E(r_{Mt}) - r_{ft}]$ Signup and view all the answers

What does $R_G$ represent in the estimation of the Index Model?

Excess return of Google Signup and view all the answers

According to CAPM principles, what type of risk is most significant for investors?

Systematic risk Signup and view all the answers

What element does the Security Characteristic Line (SCL) plot against excess market return?

Security's expected excess return Signup and view all the answers

Why is CAPM considered untestable as a theory?

It relies on unrealistic assumptions Signup and view all the answers

What does the residual represent in the estimation of the Index Model for Google?

Actual return minus predicted return Signup and view all the answers

What is the role of diversification according to CAPM principles?

To minimize firm-specific risk only Signup and view all the answers

What does the term 'required rate' in the context of the Security Characteristic Line refer to?

Return needed to compensate for market risk Signup and view all the answers

What does the Capital Asset Pricing Model (CAPM) suggest about a security's required rate of return?

It relates to systematic risk measured by beta. Signup and view all the answers

According to CAPM, the risk premium on an individual asset is proportional to which of the following factors?

The risk premium on the market portfolio. Signup and view all the answers

What is implied by the mutual fund theorem in the context of CAPM?

Investors can achieve optimal portfolios through a single mutual fund. Signup and view all the answers

Why is the market portfolio considered to be on the efficient frontier?

It is considered the optimal risky portfolio. Signup and view all the answers

In CAPM, the relationship between risk premium and investor’s risk aversion indicates that:

Higher risk aversion corresponds to a higher risk premium. Signup and view all the answers

What aspect does beta measure in the context of a security within CAPM?

The systematic risk of the security in relation to market movements. Signup and view all the answers

If all investors choose to hold the market portfolio, what is the implication for market efficiency?

The market is expected to achieve efficiency through collective behavior. Signup and view all the answers

What role does variance play in calculating the risk premium on the market portfolio?

It directly influences the size of the risk premium. Signup and view all the answers

What is the main criticism of following an active investment strategy outlined in the CAPM framework?

Active management incurs higher costs without guaranteed outperformance. Signup and view all the answers

The efficient frontier illustrates which of the following?

The optimal risk-return combinations an investor can achieve. Signup and view all the answers

What does the formula $𝑅𝑖𝑡 = α𝑖 + β𝑖𝑀 𝑅𝑀𝑡 + β𝑖𝑇𝐵 𝑅𝑇𝐵𝑡 + 𝑒𝑖𝑡$ represent in multifactor models?

Predicted returns based on various systematic factors Signup and view all the answers

In the Fama-French Three-Factor Model, which of the following is NOT a factor used?

Inflation rate Signup and view all the answers

What does a higher adjusted R-square indicate in the context of multifactor models?

Better explanatory power of the model Signup and view all the answers

What is the main principle behind Arbitrage Pricing Theory (APT)?

Risk-return relationships stemming from no-arbitrage conditions Signup and view all the answers

What is the expected return formula for a well-diversified portfolio according to APT?

$E (rP ) = rf + βP (rM - rf )$ Signup and view all the answers

Which component represents nonsystematic risk in multifactor models?

Alpha (α) Signup and view all the answers

Which of the following statements about well-diversified portfolios is true?

They minimize nonsystematic risk substantially. Signup and view all the answers

In the context of the APT, what does an arbitrage portfolio entail?

A portfolio with a positive return and zero-net-investment Signup and view all the answers

What characteristic distinguishes the multifactor model equation $𝑟𝐺 − 𝑟𝑓 = α𝐺 + β𝑀 𝑟𝑀 − 𝑟𝑓 + β𝐻𝑀𝐿 𝑟𝐻𝑀𝐿 + β𝑆𝑀𝐵 𝑟𝑆𝑀𝐵 + 𝑒𝐺$?

It captures both market and specific factors Signup and view all the answers

What does the variable $eta_{iT B}$ represent in the multifactor model equations?

Sensitivity to bond market returns Signup and view all the answers

Study Notes

Chapter 7: CAPM and APT

This chapter covers the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT).
CAPM describes the relationship between a security's required rate of return and its systematic risk (beta).
APT describes risk-return relationships from no-arbitrage considerations in large capital markets.

7.1 The Capital Asset Pricing Model

Capital Asset Pricing Model (CAPM): A security's required rate of return is related to its systematic risk, measured by beta.
Market Portfolio (M): Each security is held in proportion to its market value.
Hypothetical Equilibrium: All investors choose to hold the market portfolio.
The market portfolio is on the efficient frontier, representing the optimal risky portfolio.
Risk premium on the market portfolio is proportional to the variance of the market portfolio and investor risk aversion.
Risk premium on individual assets is proportional to the risk premium on the market portfolio and proportional to the beta coefficient of the security on the market portfolio.
The Security Market Line (SML) represents the expected return-beta relationship of CAPM.
SML graphs individual asset risk premiums as a function of asset risk.
- Alpha represents abnormal rate of return on security in excess of what's predicted by CAPM.
Passive Strategy is Efficient: All investors desire the same portfolio of risky assets and can be satisfied with a single mutual fund composed of that portfolio.
If passive strategy is costless and efficient, why follow active strategy?
If no-one does security analysis, what brings about efficiency of market portfolio?
Risk Premium of Market Portfolio: Demand drives prices and lowers expected rate of return/risk premiums. When premiums fall, investors move funds into risk-free assets. The equilibrium risk premium of the market portfolio is proportional to the risk of market and risk aversion of average investor.
Expected Returns on Individual Securities: Expected return-beta relationship. Implication of CAPM: security risk premiums (expected excess returns) will be proportional to beta. E(ri) = rf+ beta (E(rm)-rf)
The Security Market Line (SML) represents the expected return-beta relationship of CAPM.

7.2 CAPM and Index Models

Index Model, Realized Returns, Mean-Beta Equation: rit - rft = ai + Bi(rmt -rft) + eit
rit: Holding Period Return
i: Asset
t: Period
ai: Intercept of the security characteristic line.
β₁: Slope of the security characteristic line.
rm: Index return
eit: Firm-specific effects
Estimation Index Model: RGt = αG + βGRMt + eGt ; RG = rg – rf, residual = actual return – predicted return
Security Characteristic Line (SCL): Plot of security's expected excess return over risk-free rate as a function of excess return on market. Required rate = Risk-free rate + Beta x Expected excess return of index.

7.3 CAPM and the Real World

CAPM is false based on validity of its assumptions but is a useful predictor of expected returns.
It is untestable as a theory. However, its principles are still valid.
Investors should diversify.
Systematic risk is the risk that matters.
A well-diversified risky portfolio is suitable for a wide range of investors.

7.4 Multifactor Models and CAPM

Multifactor models: Models of security returns that respond to several systematic factors.
Two-index portfolio in realized returns: Rit = ai + BiMRMt + BiTBRTBt + eit
Two-factor SML: E(ri) = rf + βim [E(rm) – rf] + BiTв[E(rтв) – rf]
Fama-French Three-Factor Model: rG – rf = ag + βM(rm – rf) + βHMLHML + βSMB SMB + eG
Estimation results: Three aspects of successful specification: Higher adjusted R-squared, Lower residual SD, Smaller value of alpha. Tabulated estimates are available.

7.5 Arbitrage Pricing Theory

Arbitrage: Relative mispricing creates riskless profit.
Arbitrage Pricing Theory (APT): Risk-return relationships from no-arbitrage considerations in large capital markets.
Well-diversified portfolio: Nonsystematic risk is negligible.
Arbitrage portfolio: Positive return, zero-net-investment, and risk-free portfolio.
Calculating APT: rp = rf + Bp(rm – rf) + ep where Bp is the sensitivity to the market portfolio and ep is the firm-specific risk.
- Returns on well-diversified portfolio: E(rp) = rf + βp[E(rm)-rf]
Multifactor Generalization of APT and CAPM: Factor portfolio, Well-diversified portfolio constructed to have beta of 1.0 on one factor and zero on any other factor, Two-factor Model for APT: R₁ = α₁ + β₁₁RM1 + β₁₂RM2 + e₁.

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Description

This chapter explores key financial concepts: the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT). Understand how CAPM relates a security's return to its systematic risk and how APT analyzes risk-return relationships in capital markets. Dive into the implications of the market portfolio and risk premiums.