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1) Arbitrage Pricing Theory (APT) is an equilibrium factor model that states a security's expected return is determined by its sensitivity to various macroeconomic factors. 2) APT assumes capital markets are perfectly competitive and investors prefer more wealth to less. The price-generating process can be modeled as a multi-factor model. 3) According to APT, if the risk-return relationship is non-linear, arbitrage opportunities exist as risk-free portfolios can be constructed with positive expected returns. Attempts to arbitrage will force the relationship between risk and return to become linear.
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12 apt
The document discusses the Arbitrage Pricing Theory (APT), which is an equilibrium factor model of security returns. APT assumes capital markets are perfectly competitive, investors prefer more wealth, and the price-generating process follows a multi-factor model. APT states that no arbitrage opportunities exist if expected returns are a linear function of various macroeconomic factors. Attempts to arbitrage will force a linear relationship between risk and return.
Investment management chapter 5 the arbitrage pricing theory
The document discusses factor risk models and the arbitrage pricing theory (APT). It provides examples of the single index model (SIM) and multiple index model (MIM), showing how an asset's expected return is determined by systematic factors like inflation, GDP growth, and exchange rates, as well as an asset-specific error term. The APT states that in efficient markets with no arbitrage opportunities, the expected return is linearly related to factor sensitivities or betas. Tests provide some support that risk factors beyond the market affect returns as the APT predicts.
An Empirical Investigation Of The Arbitrage Pricing Theory
The study empirically tests the Arbitrage Pricing Theory (APT) developed by Ross in 1976 using daily stock return data from 1962-1972. It finds:
1) Factor analysis identifies 5 factors that explain stock returns within industry groups, supporting the APT.
2) Cross-sectional regressions show factor loadings can explain expected stock returns, as the APT predicts.
3) Adding total return variance to the regressions does not eliminate the explanatory power of factor loadings, supporting the APT over alternatives.
4) Tests across industry groups find no evidence factor structures differ, as the APT assumes consistent factors across stocks.
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The document discusses the arbitrage pricing theory (APT), which relates a security's expected return to multiple common risk factors. It provides examples of how the APT can be used to model returns based on factors like inflation, GDP growth, and exchange rates. The APT assumes perfect capital markets, homogeneous investor expectations, and allows short selling and arbitrage opportunities. It implies a linear relationship between expected returns and factor sensitivities similar to the capital asset pricing model. Empirical tests provide some support for the APT but also have limitations.
Financial Management: Capital Asset Pricing Model (CAPM)
Capital Asset Pricing Model (CAPM) was introduced in 1964 as an extension of the Modern Portfolio Theory which seeks to explore the diverse ways by which investors can construct investment portfolios through means that can possibly minimize risk levels and at the same time ensure maximization of returns.
Capital Asset Pricing Model - CAPM
It shows the relationship between expected return and systematic risk of individual asset or securities or portfolios
Capital asset pricing model
The Fama-French model predicts a lower required return for this stock compared to the CAPM. This is because the Fama-French model accounts for additional factors beyond just market risk.
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The document discusses the Capital Asset Pricing Model (CAPM). It defines systematic and unsystematic risk, the beta coefficient as a measure of systematic risk, and outlines the key assumptions and formula of CAPM. The Security Market Line (SML) graphs the relationship between risk and return predicted by CAPM. Some limitations of CAPM are that it assumes variance captures all risk and homogeneous investor expectations. Alternatives to CAPM discussed include Consumption CAPM, Intertemporal CAPM, and Arbitrage Pricing Theory.
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12 apt
The document discusses the Arbitrage Pricing Theory (APT), which is an equilibrium factor model of security returns. APT assumes capital markets are perfectly competitive, investors prefer more wealth, and the price-generating process follows a multi-factor model. APT states that no arbitrage opportunities exist if expected returns are a linear function of various macroeconomic factors. Attempts to arbitrage will force a linear relationship between risk and return.
Investment management chapter 5 the arbitrage pricing theory
The document discusses factor risk models and the arbitrage pricing theory (APT). It provides examples of the single index model (SIM) and multiple index model (MIM), showing how an asset's expected return is determined by systematic factors like inflation, GDP growth, and exchange rates, as well as an asset-specific error term. The APT states that in efficient markets with no arbitrage opportunities, the expected return is linearly related to factor sensitivities or betas. Tests provide some support that risk factors beyond the market affect returns as the APT predicts.
An Empirical Investigation Of The Arbitrage Pricing Theory
The study empirically tests the Arbitrage Pricing Theory (APT) developed by Ross in 1976 using daily stock return data from 1962-1972. It finds:
1) Factor analysis identifies 5 factors that explain stock returns within industry groups, supporting the APT.
2) Cross-sectional regressions show factor loadings can explain expected stock returns, as the APT predicts.
3) Adding total return variance to the regressions does not eliminate the explanatory power of factor loadings, supporting the APT over alternatives.
4) Tests across industry groups find no evidence factor structures differ, as the APT assumes consistent factors across stocks.
L Pch11
The document discusses the arbitrage pricing theory (APT), which relates a security's expected return to multiple common risk factors. It provides examples of how the APT can be used to model returns based on factors like inflation, GDP growth, and exchange rates. The APT assumes perfect capital markets, homogeneous investor expectations, and allows short selling and arbitrage opportunities. It implies a linear relationship between expected returns and factor sensitivities similar to the capital asset pricing model. Empirical tests provide some support for the APT but also have limitations.
Financial Management: Capital Asset Pricing Model (CAPM)
Capital Asset Pricing Model (CAPM) was introduced in 1964 as an extension of the Modern Portfolio Theory which seeks to explore the diverse ways by which investors can construct investment portfolios through means that can possibly minimize risk levels and at the same time ensure maximization of returns.
Capital Asset Pricing Model - CAPM
It shows the relationship between expected return and systematic risk of individual asset or securities or portfolios
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The Fama-French model predicts a lower required return for this stock compared to the CAPM. This is because the Fama-French model accounts for additional factors beyond just market risk.
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The document discusses the Capital Asset Pricing Model (CAPM). It defines systematic and unsystematic risk, the beta coefficient as a measure of systematic risk, and outlines the key assumptions and formula of CAPM. The Security Market Line (SML) graphs the relationship between risk and return predicted by CAPM. Some limitations of CAPM are that it assumes variance captures all risk and homogeneous investor expectations. Alternatives to CAPM discussed include Consumption CAPM, Intertemporal CAPM, and Arbitrage Pricing Theory.
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This document provides an overview of the Capital Asset Pricing Model (CAPM). It outlines the key assumptions of CAPM, including that investors aim to maximize returns based on risk. It describes how the capital market reaches equilibrium when there is no incentive to trade. It also defines concepts like the capital market line, securities market line, beta, and the CAPM formula. Examples are provided to demonstrate how to calculate expected returns using CAPM. The document concludes by discussing empirical testing of CAPM and common findings that its assumptions do not always hold in practice.
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The Arbitrage Pricing Theory (APT) provides an alternative to the Capital Asset Pricing Model (CAPM) for estimating expected returns. The APT assumes returns are generated by multiple systematic risk factors rather than a single market factor. It allows for assets to be mispriced and does not require assumptions of a market portfolio or homogeneous expectations. Under the APT, the expected return of an asset is equal to the risk-free rate plus the product of each risk factor's premium and the asset's sensitivity to that factor.
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The document provides an introduction to the Capital Asset Pricing Model (CAPM) by explaining its development, statistical workings, and applications in financial management. It also discusses pedagogical issues in presenting CAPM to undergraduate students, emphasizing the need for step-by-step explanations and demonstrating the practical inputs and outputs of the model.
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The document provides an overview of the Capital Asset Pricing Model (CAPM). It defines key terms like the capital allocation line, capital market line, security market line, beta, and expected return. The capital allocation line shows the risk-return tradeoff for efficient portfolios. The capital market line depicts the risk-return relationship for efficient portfolios available to investors. The security market line is a graphic representation of CAPM that describes the market price of risk. CAPM holds that the expected return of an asset is determined by its beta, or non-diversifiable risk. It assumes investors will hold an efficient portfolio consisting of a risk-free asset and the market portfolio.
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CAPM was developed in 1960 as an extension of Markowitz's portfolio theory. It derives the relationship between expected return and risk of individual securities. CAPM assumes investment decisions are based on risk-return assessments and that markets are efficient. It allows investors to combine risky and risk-free assets on the efficient frontier to maximize return for a given level of risk. The model is used to price individual securities based on their beta and expected market return.
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The chapter discusses the Capital Asset Pricing Model (CAPM). It introduces the efficient frontier and capital market line. The CAPM hypothesizes that the expected return of an asset is determined by its sensitivity to non-diversifiable risk, as represented by beta. All rational investors will hold the market portfolio and use leverage/borrowing according to their risk tolerance. The CAPM is used to determine the required rate of return for assets and their cost of equity.
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This document provides an overview of the Capital Asset Pricing Model (CAPM). It begins by explaining that CAPM helps determine the fair price of assets by comparing the fair price to the market price. It then lists the key assumptions of CAPM, including that investors can borrow/lend at the risk-free rate and there are no taxes or transaction costs. The document goes on to define terms like the market portfolio return, market risk premium, individual risk premium, and the security market line. It also discusses how to calculate beta through regression analysis and how beta represents the systematic risk of an asset. In the end, it notes some of the limitations of CAPM and possibilities for relaxing its assumptions.
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The Capital Asset Pricing Model (CAPM) uses beta to measure the non-diversifiable risk of a security and determine its expected return. CAPM assumes investors want to maximize returns and only consider systematic risk. It models expected return as the risk-free rate plus a risk premium based on the security's beta. The Security Market Line graphs this relationship between beta and expected return. Some researchers like Fama and French have expanded CAPM with additional size and value factors.
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The Capital Asset Pricing Model (CAPM) describes how investors should price assets based on their risk levels. It assumes investors only consider risk and return, have homogeneous expectations, and can borrow and lend at the risk-free rate. The Capital Market Line plots expected returns against risk and identifies efficient investments. The Security Market Line is the graphical representation of CAPM, showing the expected return of individual assets based on their beta in relation to the market. Assets priced correctly will lie on the SML, while under- or over-valued assets will lie above or below it.
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1. The document discusses risk on portfolios and individual securities, as well as measures of risk like average absolute deviation and standard deviation.
2. It then explains the Capital Asset Pricing Model (CAPM), which relates expected return and systematic risk for assets. CAPM was developed by William Sharpe and considers both systematic and unsystematic risk factors.
3. The key elements of CAPM are outlined, including the capital market line, security market line, beta as a measure of individual asset risk compared to the market portfolio, and the CAPM formula.
capital asset pricing model
In finance, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset.
3. sharpe index model
The document discusses the Sharpe index model for portfolio management. [1] It presents an equation that divides a stock's expected return into two parts: return due to market movements and return independent of the market. [2] Beta indicates a stock's sensitivity to market changes and can be used to estimate systematic and unsystematic risk. [3] The variance of a portfolio is calculated based on the systematic risk and unsystematic risk of the stocks within it.
5.capital asset pricing model
The document discusses several assumptions of portfolio theory models including CAPM and APT. It assumes investors have homogeneous expectations, are risk averse utility maximizers, and operate in a environment of perfect competition with no transaction costs. The key aspects of CAPM discussed are the efficient frontier and relationship between risk and return. APT relaxes some CAPM assumptions and focuses on factor sensitivities driving returns rather than just beta. Arbitrage pricing looks for riskless profit opportunities by making small adjustments to portfolio weights.
Capital Asset Pricing Model
Capital Asset Pricing Model (CAPM)
A model that describes the relationship between risk and expected return. The general idea behind CAPM is that investors need to be compensated in two ways: time value of money & risk. The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is calculated by taking a risk gauge (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf).
Financial Mgt. - Capital Asset Pricing Model
This document presents an overview of the Capital Asset Pricing Model (CAPM). It discusses the key assumptions of CAPM, including that investors hold diversified portfolios and can borrow/lend at the risk-free rate. CAPM represents the relationship between required return and systematic risk using the formula: Ke = Rf + β(Rm - Rf). It also discusses the different degrees of market efficiency, advantages of CAPM in considering only systematic risk, and disadvantages such as its assumptions. The conclusion states that while criticisms exist, CAPM remains a useful model and stands up well to criticism.
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CAPM model that describes the relationship between risk and expected return and that is used in the pricing of risky securities.
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The document summarizes a presentation on the Capital Asset Pricing Model (CAPM). It includes an introduction to CAPM, objectives to understand the relationship between risk and return and validate the CAPM model through literature review. Research questions on whether risk and return are related and if CAPM is valid. The methodology section describes using Markowitz's model, the three-factor model, and regression analysis. While some studies have found issues, the conclusion is that CAPM remains the best option for measuring expected returns though could be improved. Recommendations include using daily data for betas and carefully selecting risk-free rates and market returns.
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The Markowitz model generates an efficient frontier of optimal portfolios based on expected return and risk. The Capital Asset Pricing Model (CAPM) further develops this by incorporating a risk-free asset, creating the Capital Market Line (CML). The CML represents equilibrium pricing relationships between expected return and risk for all efficient portfolios. According to CAPM, the expected return of any security or portfolio is equal to the risk-free rate plus a risk premium proportional to the security's systematic risk relative to the market.
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The document summarizes the capital asset pricing model (CAPM) and reviews early empirical tests of the model. It begins by outlining the logic and key assumptions of the CAPM, including that the market portfolio must be mean-variance efficient. However, empirical tests found problems with the CAPM's predictions about the relationship between expected returns and market betas. Specifically, cross-sectional regressions did not find intercepts equal to the risk-free rate or slopes equal to the expected market premium. To address measurement error, later tests examined portfolios rather than individual assets. In general, the early empirical evidence revealed shortcomings in the CAPM's ability to explain returns.
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The document discusses the Capital Asset Pricing Model (CAPM) and some of its key assumptions and implications. It summarizes Sharpe's (1964) development of CAPM based on Markowitz portfolio theory. Sharpe's model shows how asset prices adjust to create a linear relationship between risk and expected return in equilibrium. However, later studies found some empirical issues with CAPM's assumptions around unlimited borrowing and lending. Black (1972) discusses how relaxing this assumption could change CAPM and better explain observed returns that did not perfectly fit the model.
Capital asset pricing Model (CAPM-Asif).pptx
The Capital Asset Pricing Model (CAPM) measures the relationship between the expected return and the risk of investing in security.
This model is used to analyze securities and price them given the expected rate of return and cost of capital involved.
Capital Asset pricing model- lec6
Capital asset pricing model, risk return, beta, variance, standard deviation, assumption of model, implication of the model
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This document provides an overview of the Capital Asset Pricing Model (CAPM). It outlines the key assumptions of CAPM, including that investors aim to maximize returns based on risk. It describes how the capital market reaches equilibrium when there is no incentive to trade. It also defines concepts like the capital market line, securities market line, beta, and the CAPM formula. Examples are provided to demonstrate how to calculate expected returns using CAPM. The document concludes by discussing empirical testing of CAPM and common findings that its assumptions do not always hold in practice.
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The Arbitrage Pricing Theory (APT) provides an alternative to the Capital Asset Pricing Model (CAPM) for estimating expected returns. The APT assumes returns are generated by multiple systematic risk factors rather than a single market factor. It allows for assets to be mispriced and does not require assumptions of a market portfolio or homogeneous expectations. Under the APT, the expected return of an asset is equal to the risk-free rate plus the product of each risk factor's premium and the asset's sensitivity to that factor.
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The document provides an introduction to the Capital Asset Pricing Model (CAPM) by explaining its development, statistical workings, and applications in financial management. It also discusses pedagogical issues in presenting CAPM to undergraduate students, emphasizing the need for step-by-step explanations and demonstrating the practical inputs and outputs of the model.
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The document provides an overview of the Capital Asset Pricing Model (CAPM). It defines key terms like the capital allocation line, capital market line, security market line, beta, and expected return. The capital allocation line shows the risk-return tradeoff for efficient portfolios. The capital market line depicts the risk-return relationship for efficient portfolios available to investors. The security market line is a graphic representation of CAPM that describes the market price of risk. CAPM holds that the expected return of an asset is determined by its beta, or non-diversifiable risk. It assumes investors will hold an efficient portfolio consisting of a risk-free asset and the market portfolio.
Capital Asset Pricing Model
CAPM was developed in 1960 as an extension of Markowitz's portfolio theory. It derives the relationship between expected return and risk of individual securities. CAPM assumes investment decisions are based on risk-return assessments and that markets are efficient. It allows investors to combine risky and risk-free assets on the efficient frontier to maximize return for a given level of risk. The model is used to price individual securities based on their beta and expected market return.
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The chapter discusses the Capital Asset Pricing Model (CAPM). It introduces the efficient frontier and capital market line. The CAPM hypothesizes that the expected return of an asset is determined by its sensitivity to non-diversifiable risk, as represented by beta. All rational investors will hold the market portfolio and use leverage/borrowing according to their risk tolerance. The CAPM is used to determine the required rate of return for assets and their cost of equity.
CAPITAL ASSET PRICING MODEL
This document provides an overview of the Capital Asset Pricing Model (CAPM). It begins by explaining that CAPM helps determine the fair price of assets by comparing the fair price to the market price. It then lists the key assumptions of CAPM, including that investors can borrow/lend at the risk-free rate and there are no taxes or transaction costs. The document goes on to define terms like the market portfolio return, market risk premium, individual risk premium, and the security market line. It also discusses how to calculate beta through regression analysis and how beta represents the systematic risk of an asset. In the end, it notes some of the limitations of CAPM and possibilities for relaxing its assumptions.
Capital Asset Pricing Model
The Capital Asset Pricing Model (CAPM) uses beta to measure the non-diversifiable risk of a security and determine its expected return. CAPM assumes investors want to maximize returns and only consider systematic risk. It models expected return as the risk-free rate plus a risk premium based on the security's beta. The Security Market Line graphs this relationship between beta and expected return. Some researchers like Fama and French have expanded CAPM with additional size and value factors.
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The Capital Asset Pricing Model (CAPM) describes how investors should price assets based on their risk levels. It assumes investors only consider risk and return, have homogeneous expectations, and can borrow and lend at the risk-free rate. The Capital Market Line plots expected returns against risk and identifies efficient investments. The Security Market Line is the graphical representation of CAPM, showing the expected return of individual assets based on their beta in relation to the market. Assets priced correctly will lie on the SML, while under- or over-valued assets will lie above or below it.
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1. The document discusses risk on portfolios and individual securities, as well as measures of risk like average absolute deviation and standard deviation.
2. It then explains the Capital Asset Pricing Model (CAPM), which relates expected return and systematic risk for assets. CAPM was developed by William Sharpe and considers both systematic and unsystematic risk factors.
3. The key elements of CAPM are outlined, including the capital market line, security market line, beta as a measure of individual asset risk compared to the market portfolio, and the CAPM formula.
capital asset pricing model
In finance, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset.
3. sharpe index model
The document discusses the Sharpe index model for portfolio management. [1] It presents an equation that divides a stock's expected return into two parts: return due to market movements and return independent of the market. [2] Beta indicates a stock's sensitivity to market changes and can be used to estimate systematic and unsystematic risk. [3] The variance of a portfolio is calculated based on the systematic risk and unsystematic risk of the stocks within it.
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The document discusses several assumptions of portfolio theory models including CAPM and APT. It assumes investors have homogeneous expectations, are risk averse utility maximizers, and operate in a environment of perfect competition with no transaction costs. The key aspects of CAPM discussed are the efficient frontier and relationship between risk and return. APT relaxes some CAPM assumptions and focuses on factor sensitivities driving returns rather than just beta. Arbitrage pricing looks for riskless profit opportunities by making small adjustments to portfolio weights.
Capital Asset Pricing Model
Capital Asset Pricing Model (CAPM)
A model that describes the relationship between risk and expected return. The general idea behind CAPM is that investors need to be compensated in two ways: time value of money & risk. The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is calculated by taking a risk gauge (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf).
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This document presents an overview of the Capital Asset Pricing Model (CAPM). It discusses the key assumptions of CAPM, including that investors hold diversified portfolios and can borrow/lend at the risk-free rate. CAPM represents the relationship between required return and systematic risk using the formula: Ke = Rf + β(Rm - Rf). It also discusses the different degrees of market efficiency, advantages of CAPM in considering only systematic risk, and disadvantages such as its assumptions. The conclusion states that while criticisms exist, CAPM remains a useful model and stands up well to criticism.
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The document summarizes a presentation on the Capital Asset Pricing Model (CAPM). It includes an introduction to CAPM, objectives to understand the relationship between risk and return and validate the CAPM model through literature review. Research questions on whether risk and return are related and if CAPM is valid. The methodology section describes using Markowitz's model, the three-factor model, and regression analysis. While some studies have found issues, the conclusion is that CAPM remains the best option for measuring expected returns though could be improved. Recommendations include using daily data for betas and carefully selecting risk-free rates and market returns.
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The Markowitz model generates an efficient frontier of optimal portfolios based on expected return and risk. The Capital Asset Pricing Model (CAPM) further develops this by incorporating a risk-free asset, creating the Capital Market Line (CML). The CML represents equilibrium pricing relationships between expected return and risk for all efficient portfolios. According to CAPM, the expected return of any security or portfolio is equal to the risk-free rate plus a risk premium proportional to the security's systematic risk relative to the market.
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The document summarizes the capital asset pricing model (CAPM) and reviews early empirical tests of the model. It begins by outlining the logic and key assumptions of the CAPM, including that the market portfolio must be mean-variance efficient. However, empirical tests found problems with the CAPM's predictions about the relationship between expected returns and market betas. Specifically, cross-sectional regressions did not find intercepts equal to the risk-free rate or slopes equal to the expected market premium. To address measurement error, later tests examined portfolios rather than individual assets. In general, the early empirical evidence revealed shortcomings in the CAPM's ability to explain returns.
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The document discusses the Capital Asset Pricing Model (CAPM) and some of its key assumptions and implications. It summarizes Sharpe's (1964) development of CAPM based on Markowitz portfolio theory. Sharpe's model shows how asset prices adjust to create a linear relationship between risk and expected return in equilibrium. However, later studies found some empirical issues with CAPM's assumptions around unlimited borrowing and lending. Black (1972) discusses how relaxing this assumption could change CAPM and better explain observed returns that did not perfectly fit the model.
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12 apt
- 2. 2 BackgroundBackground • Estimating expected return with the AssetEstimating expected return with the Asset Pricing Models of Modern FinancePricing Models of Modern Finance – CAPMCAPM • Strong assumption - strong predictionStrong assumption - strong prediction
- 3. Expected Return Risk (Return Variability) Market Index on Efficient Set Market Index A B C Market Beta Expected Return Corresponding Security Market Line xxx xxxx xxxx xx xx x x x xxx xx x
- 4. Market Index Expected Return Risk (Return Variability) Market Index Inside Efficient Set Corresponding Security Market Cloud Expected Return Market Beta
- 5. 5 FACTOR MODELS • ARBITRAGE PRICING THEORY (APT) – is an equilibrium factor model of security returns – Principle of Arbitrage • the earning of riskless profit by taking advantage of differentiated pricing for the same physical asset or security – Arbitrage Portfolio • requires no additional investor funds • no factor sensitivity • has positive expected returns – Example …
- 6. Curved Relationship Between Expected Return and Interest Rate BetaCurved Relationship Between Expected Return and Interest Rate Beta -15%-15% -5%-5% 5%5% 15%15% 25%25% 35%35% Expected ReturnExpected Return -3-3 -1-1 11 33 Interest Rate BetaInterest Rate Beta AA BB CC DD EE FF
- 7. • Two stocks A: E(r) = 4%; Interest-rate beta = -2.20 B: E(r) = 26%; Interest-rate beta = 1.83 Invest 54.54% in E and 45.46% in A Portfolio E(r) = .5454 * 26% + .4546 * 4% = 16% Portfolio beta = .5454 * 1.83 + .4546 * -2.20 = 0 With many combinations like this, you can create a risk-free portfolio with a 16% expected return. The Arbitrage Pricing TheoryThe Arbitrage Pricing Theory
- 8. The Arbitrage Pricing TheoryThe Arbitrage Pricing Theory • Two different stocks C: E(r) = 15%; Interest-rate beta = -1.00 D: E(r) = 25%; Interest-rate beta = 1.00 Invest 50.00% in E and 50.00% in A Portfolio E(r) = .5000 * 25% + .4546 * 15% = 20% Portfolio beta = .5000 * 1.00 + .5000 * -1.00 = 0 With many combinations like this, you can create a risk-free portfolio with a 20% expected return. Then sell-short the 16% and invest the proceeds in the 20% to arbitrage.
- 9. 9 • No-arbitrage condition for asset pricing If risk-return relationship is non-linear, you can arbitrage. Attempts to arbitrage will force linearity in relationship between risk and return. The Arbitrage Pricing TheoryThe Arbitrage Pricing Theory
- 10. APT Relationship Between Expected Return and Interest Rate BetaAPT Relationship Between Expected Return and Interest Rate Beta -15% -5% 5% 15% 25% 35% Expected ReturnExpected Return -3 -1 1 3 Interest Rate Beta A B C D E F
- 11. 11 FACTOR MODELS • ARBITRAGE PRICING THEORY (APT) – Three Major Assumptions: • capital markets are perfectly competitive • investors always prefer more to less wealth • price-generating process is a K factor model
- 12. 12 FACTOR MODELS • MULTIPLE-FACTOR MODELS – FORMULA ri = ai + bi1 F1 + bi2 F2 +. . . + biKF K+ ei where r is the return on security i b is the coefficient of the factor F is the factor
- 13. 13 FACTOR MODELS • SECURITY PRICING FORMULA: ri = λ0 + λ1 b1 + λ2 b2 +. . .+ λKbK where ri = rRF +(δ1−rRF )bi1 + (δ2− rRF)bi2+ . . . +(δ−rRF)biK
- 14. 14 FACTOR MODELS where r is the return on security i λ0 is the risk free rate b is the factor e is the error term
- 15. 15 FACTOR MODELS • hence – a stock’s expected return is equal to the risk free rate plus k risk premiums based on the stock’s sensitivities to the k factors