The document summarizes a study that tests the Capital Asset Pricing Model (CAPM) using two portfolios constructed from stocks on the Helsinki stock exchange. Daily return data from 2014-2015 on four large stocks was used to create an equal-weighted and value-weighted portfolio. The CAPM was tested to see if it could accurately price the returns of the two portfolios. The study found that the CAPM could precisely price the value-weighted portfolio but not the equal-weighted portfolio, suggesting some limitation of the CAPM in pricing assets.
An Empirical Investigation Of The Arbitrage Pricing TheoryAkhil Goyal
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.
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.
1) The document discusses risk-return analysis and the efficient frontier. It introduces the Capital Market Line (CML), which shows superior portfolio combinations when investing in both risky and risk-free assets.
2) The CML is tangent to the efficient frontier at the market portfolio, which offers the highest Sharpe Ratio. The Sharpe Ratio represents excess return per unit of risk.
3) With access to risk-free borrowing and lending, investors are no longer confined to the efficient frontier, but can choose portfolios along the CML based on their individual risk preferences.
This document analyzes the validity of the Capital Asset Pricing Model (CAPM) using data from the Karachi Stock Exchange (KSE) from 2011-2014. It finds that CAPM does not fully hold for the KSE. While expected and actual returns were slightly different for some stocks in some years, indicating CAPM may be applicable, there were large differences for many observations. Overall, CAPM did not accurately convey results for the KSE. The document reviews previous literature on CAPM which also found it does not always hold and may be more accurate for some stocks and time periods. The methodology used beta calculations to estimate expected returns for 30 KSE stocks which were then compared to actual returns.
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.
The Markowitz model generates an efficient frontier of optimal portfolios that maximize return for a given level of risk. The Capital Asset Pricing Model (CAPM) builds on this by deriving the security market line (SML) which plots the expected return of individual securities based on their beta coefficient in relation to the market portfolio. The capital market line (CML) extends the efficient frontier by including a risk-free asset, demonstrating how investors can optimize the trade-off between risk and return through borrowing and lending at the risk-free rate.
Does the capital assets pricing model (capm) predicts stock market returns in...Alexander Decker
This document examines whether the Capital Asset Pricing Model (CAPM) can predict stock returns in Ghana using data from selected stocks on the Ghana Stock Exchange from 2006-2010. The results found no statistically significant relationship between actual and predicted returns, indicating CAPM with constant beta cannot explain differences in returns. It was also found that some stocks were on average undervalued while one was overvalued over the period studied. The conclusion is that the standard CAPM model cannot statistically explain the observed differences in actual and estimated returns of the selected Ghanaian stocks.
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.
An Empirical Investigation Of The Arbitrage Pricing TheoryAkhil Goyal
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.
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.
1) The document discusses risk-return analysis and the efficient frontier. It introduces the Capital Market Line (CML), which shows superior portfolio combinations when investing in both risky and risk-free assets.
2) The CML is tangent to the efficient frontier at the market portfolio, which offers the highest Sharpe Ratio. The Sharpe Ratio represents excess return per unit of risk.
3) With access to risk-free borrowing and lending, investors are no longer confined to the efficient frontier, but can choose portfolios along the CML based on their individual risk preferences.
This document analyzes the validity of the Capital Asset Pricing Model (CAPM) using data from the Karachi Stock Exchange (KSE) from 2011-2014. It finds that CAPM does not fully hold for the KSE. While expected and actual returns were slightly different for some stocks in some years, indicating CAPM may be applicable, there were large differences for many observations. Overall, CAPM did not accurately convey results for the KSE. The document reviews previous literature on CAPM which also found it does not always hold and may be more accurate for some stocks and time periods. The methodology used beta calculations to estimate expected returns for 30 KSE stocks which were then compared to actual returns.
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.
The Markowitz model generates an efficient frontier of optimal portfolios that maximize return for a given level of risk. The Capital Asset Pricing Model (CAPM) builds on this by deriving the security market line (SML) which plots the expected return of individual securities based on their beta coefficient in relation to the market portfolio. The capital market line (CML) extends the efficient frontier by including a risk-free asset, demonstrating how investors can optimize the trade-off between risk and return through borrowing and lending at the risk-free rate.
Does the capital assets pricing model (capm) predicts stock market returns in...Alexander Decker
This document examines whether the Capital Asset Pricing Model (CAPM) can predict stock returns in Ghana using data from selected stocks on the Ghana Stock Exchange from 2006-2010. The results found no statistically significant relationship between actual and predicted returns, indicating CAPM with constant beta cannot explain differences in returns. It was also found that some stocks were on average undervalued while one was overvalued over the period studied. The conclusion is that the standard CAPM model cannot statistically explain the observed differences in actual and estimated returns of the selected Ghanaian stocks.
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.
Relationship Between Global Stosk Indices and Optimal Allocation for a Global...eurosigdoc acm
This document presents research analyzing the relationship between global stock indices and optimal allocation for a global equity portfolio. It introduces the topic, reviews literature on international diversification, outlines hypotheses about returns and correlations between indices, and describes the methodology including statistical tests and portfolio construction using random weights in Python. Key results include descriptive statistics on the indices, correlation analysis, and statistical tests showing differences in returns, variances, and correlations between index pairs. The document concludes with limitations and implications for optimal portfolios across global markets.
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.
This study analyzes the abilities of investors in Spanish domestic equity funds from January 1999 to December 2006. It finds:
1) New money/investors underperform old money/investors over 3-month and 12-month periods based on excess returns and alphas from single-factor, 3-factor, and 4-factor models.
2) However, portfolios weighted by actual inflows perform similarly to or outperform old money portfolios, suggesting evidence of "smart money". In contrast, outflow portfolios generally underperform.
3) Positive flow portfolios, whether weighted by money or investors, exhibit higher excess returns and alphas than negative flow portfolios over 12-month periods, and these
Investment management chapter 4.2 the capital asset pricing modelHeng Leangpheng
The document summarizes the key aspects of the Capital Asset Pricing Model (CAPM). It outlines the three main assumptions of CAPM: 1) investors can trade securities without costs, 2) investors only hold efficient portfolios, 3) investors have homogeneous expectations. It then explains how given these assumptions, the market portfolio of all risky securities becomes the efficient portfolio. It defines beta and shows how an asset's expected return is determined based on the market risk premium and its beta. Examples are provided to illustrate how to calculate betas and expected returns for individual stocks and portfolios using CAPM.
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.
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.
Asset Pricing and Portfolio Theory
I have presented a unique analysis which showcases the concepts of Aggregate & Aggregate lending and the numerical aspects of CAPM theory
This study examines the relationship between stock returns and fundamental variables in Japan from 1971 to 1988. It finds significant relationships between returns and book-to-market ratio, cash flow yield, and earnings yield. Book-to-market and cash flow yield had the most positive impact on returns, while earnings yield sometimes had a negative impact. The results provide evidence that fundamental variables can predict returns in the Japanese market.
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.
The Capital Asset Pricing Model (CAPM) was developed in the 1960s as a way to determine the expected return of an asset based on its risk. CAPM assumes that investors will be compensated only based on an asset's systematic or non-diversifiable risk as measured by its beta. The model builds on Markowitz's portfolio theory and introduces the security market line, which plots the expected return of an asset against its beta. According to CAPM, the expected return of an asset is equal to the risk-free rate plus a risk premium that is proportional to the asset's beta.
This document provides an overview of an upcoming presentation on asset pricing models. The presentation will cover capital market theory, the capital market line, security market line, capital asset pricing model, and diversification. It will discuss the assumptions and formulas for the capital market line and security market line. The capital market line shows expected returns based on portfolio risk, while the security market line shows expected individual asset returns based on systematic risk. The capital asset pricing model uses the concept of beta to calculate the expected return of an asset based on its risk relative to the market.
The document discusses the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT). It outlines the key assumptions and results of CAPM, including that all investors hold the market portfolio and the security market line relates individual security risk premiums to market risk premiums through beta. It also discusses limitations of CAPM and how multifactor models like Fama-French can better describe returns. Finally, it explains how APT allows for arbitrage opportunities if mispriced portfolios exist and its relationship to CAPM.
CAPM: Introduction & Teaching Issues - Richard DiamondRichard Diamond
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.
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.
Coursework- Soton (Single Index Model and CAPM)Ece Akbulut
This document provides an introduction to portfolio management and the single-index model (SIM) and capital asset pricing model (CAPM). It first describes SIM and tests it on eight companies, analyzing the results. It finds SIM reduces the workload of estimating variables but oversimplifies risk. The document then introduces CAPM, tests it on the same companies, and analyzes the results and merits and demerits of CAPM. It concludes by discussing the sensitivity of the models to sector characteristics.
The document discusses Sharpe's single index model for portfolio optimization. It relates individual security returns to a single market index and uses a characteristic line equation to define the relationship between security returns and market returns. The model simplifies earlier approaches by using a single market index rather than complex matrices but has practical limitations in compiling expected returns and covariances of securities.
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.
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.
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.
Testing and extending the capital asset pricing modelGabriel Koh
This paper attempts to prove whether the conventional Capital Asset Pricing Model (CAPM) holds with respect to a set of asset returns. Starting with the Fama-Macbeth cross-sectional regression, we prove through the significance of pricing errors that the CAPM does not hold. Hence, we expand the original CAPM by including risk factors and factor-mimicking portfolios built on firm-specific characteristics and test for their significance in the model. Ultimately, by adding significant factors, we find that the model helps to better explain asset returns, but does still not entirely capture pricing errors.
Relationship Between Global Stosk Indices and Optimal Allocation for a Global...eurosigdoc acm
This document presents research analyzing the relationship between global stock indices and optimal allocation for a global equity portfolio. It introduces the topic, reviews literature on international diversification, outlines hypotheses about returns and correlations between indices, and describes the methodology including statistical tests and portfolio construction using random weights in Python. Key results include descriptive statistics on the indices, correlation analysis, and statistical tests showing differences in returns, variances, and correlations between index pairs. The document concludes with limitations and implications for optimal portfolios across global markets.
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.
This study analyzes the abilities of investors in Spanish domestic equity funds from January 1999 to December 2006. It finds:
1) New money/investors underperform old money/investors over 3-month and 12-month periods based on excess returns and alphas from single-factor, 3-factor, and 4-factor models.
2) However, portfolios weighted by actual inflows perform similarly to or outperform old money portfolios, suggesting evidence of "smart money". In contrast, outflow portfolios generally underperform.
3) Positive flow portfolios, whether weighted by money or investors, exhibit higher excess returns and alphas than negative flow portfolios over 12-month periods, and these
Investment management chapter 4.2 the capital asset pricing modelHeng Leangpheng
The document summarizes the key aspects of the Capital Asset Pricing Model (CAPM). It outlines the three main assumptions of CAPM: 1) investors can trade securities without costs, 2) investors only hold efficient portfolios, 3) investors have homogeneous expectations. It then explains how given these assumptions, the market portfolio of all risky securities becomes the efficient portfolio. It defines beta and shows how an asset's expected return is determined based on the market risk premium and its beta. Examples are provided to illustrate how to calculate betas and expected returns for individual stocks and portfolios using CAPM.
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.
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.
Asset Pricing and Portfolio Theory
I have presented a unique analysis which showcases the concepts of Aggregate & Aggregate lending and the numerical aspects of CAPM theory
This study examines the relationship between stock returns and fundamental variables in Japan from 1971 to 1988. It finds significant relationships between returns and book-to-market ratio, cash flow yield, and earnings yield. Book-to-market and cash flow yield had the most positive impact on returns, while earnings yield sometimes had a negative impact. The results provide evidence that fundamental variables can predict returns in the Japanese market.
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.
The Capital Asset Pricing Model (CAPM) was developed in the 1960s as a way to determine the expected return of an asset based on its risk. CAPM assumes that investors will be compensated only based on an asset's systematic or non-diversifiable risk as measured by its beta. The model builds on Markowitz's portfolio theory and introduces the security market line, which plots the expected return of an asset against its beta. According to CAPM, the expected return of an asset is equal to the risk-free rate plus a risk premium that is proportional to the asset's beta.
This document provides an overview of an upcoming presentation on asset pricing models. The presentation will cover capital market theory, the capital market line, security market line, capital asset pricing model, and diversification. It will discuss the assumptions and formulas for the capital market line and security market line. The capital market line shows expected returns based on portfolio risk, while the security market line shows expected individual asset returns based on systematic risk. The capital asset pricing model uses the concept of beta to calculate the expected return of an asset based on its risk relative to the market.
The document discusses the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT). It outlines the key assumptions and results of CAPM, including that all investors hold the market portfolio and the security market line relates individual security risk premiums to market risk premiums through beta. It also discusses limitations of CAPM and how multifactor models like Fama-French can better describe returns. Finally, it explains how APT allows for arbitrage opportunities if mispriced portfolios exist and its relationship to CAPM.
CAPM: Introduction & Teaching Issues - Richard DiamondRichard Diamond
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.
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.
Coursework- Soton (Single Index Model and CAPM)Ece Akbulut
This document provides an introduction to portfolio management and the single-index model (SIM) and capital asset pricing model (CAPM). It first describes SIM and tests it on eight companies, analyzing the results. It finds SIM reduces the workload of estimating variables but oversimplifies risk. The document then introduces CAPM, tests it on the same companies, and analyzes the results and merits and demerits of CAPM. It concludes by discussing the sensitivity of the models to sector characteristics.
The document discusses Sharpe's single index model for portfolio optimization. It relates individual security returns to a single market index and uses a characteristic line equation to define the relationship between security returns and market returns. The model simplifies earlier approaches by using a single market index rather than complex matrices but has practical limitations in compiling expected returns and covariances of securities.
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.
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.
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.
Testing and extending the capital asset pricing modelGabriel Koh
This paper attempts to prove whether the conventional Capital Asset Pricing Model (CAPM) holds with respect to a set of asset returns. Starting with the Fama-Macbeth cross-sectional regression, we prove through the significance of pricing errors that the CAPM does not hold. Hence, we expand the original CAPM by including risk factors and factor-mimicking portfolios built on firm-specific characteristics and test for their significance in the model. Ultimately, by adding significant factors, we find that the model helps to better explain asset returns, but does still not entirely capture pricing errors.
Black littleman portfolio optimizationHoang Nguyen
This document provides an overview and application of the Black-Litterman portfolio optimization model. It summarizes the key steps of the Black-Litterman model, which combines an investor's subjective views on expected returns with an implied equilibrium to determine optimal portfolio weights. The document then applies the Black-Litterman model to 10 stocks from the Ho Chi Minh City stock exchange in Vietnam over a one-year period. It finds that Black-Litterman portfolios achieved significantly better return-to-risk performance than the traditional mean-variance approach.
The document summarizes a study that uses the Capital Asset Pricing Model (CAPM) to analyze the risk and returns of 5 stocks from 2013-2015. It calculates daily returns, beta, alpha, and the correlation of individual stock returns with market returns. The results show most stocks had a slight negative excess return and negative Sharpe ratio, indicating average risk-adjusted performance. Betas were all statistically significant, with GE closest to the market. R-squared values ranged from 20-48%, explaining some but not all variation in returns. The analysis supports that CAPM provides useful but imperfect insights into the relationship between a stock's risk and return.
This document summarizes the Capital Asset Pricing Model (CAPM). It begins by outlining the key assumptions and logic behind the CAPM. The CAPM builds on Harry Markowitz's portfolio choice model by adding assumptions of a risk-free rate and market clearing prices. This implies that the market portfolio must be mean-variance efficient. The CAPM then predicts that an asset's expected return is determined by its beta, or non-diversifiable risk relative to the market. However, the document notes that empirical tests have found the CAPM performs poorly in validating these predictions. It concludes that while theoretical or implementation issues may be to blame, the CAPM's failure in empirical tests means its applications are generally invalid.
This document analyzes Sharpe's ratio as a measure of investment fund performance. It discusses Sharpe's ratio in the context of portfolio theory and as an approximation of a utility index. The document proposes some modifications to Sharpe's ratio to avoid inconsistent assessments and better approximate a utility index. It establishes six postulates regarding utility theory in the presence of risk to provide a conceptual framework. The document notes two cases where Sharpe's ratio may not function properly and proposes an alternative variation to address situations where expected return is less than the risk-free rate of return. It applies the various performance measures to a sample of Spanish investment funds.
Impact of capital asset pricing model (capm) on pakistanAlexander Decker
This document summarizes a research study that applied the Capital Asset Pricing Model (CAPM) to stocks traded on the Karachi Stock Exchange in Pakistan from 2003 to 2007. The study found that CAPM was able to estimate stock returns in the Pakistani market and showed the existence of a risk premium as the only factor affecting stock returns. The study used monthly return data from 5 portfolios sorted by size and book-to-market ratios. Regression analysis found the intercept was insignificant while the risk premium was significant, showing CAPM estimates stock returns accurately in this market. However, the study notes CAPM has limitations and future research could test different models or variations to further analyze factors affecting stock returns.
Questions and Answers At Least 75 Words each.Please answer th.docxmakdul
Questions and Answers: At Least 75 Words each.
Please answer the following questions.
1. What are the differences and similarities between samples and populations?
2. What are the measures of Central Tendency assumptions?
3. What are measures of Dispersion used for and what are the assumptions for each?
4. Define collaboration and how you will apply it in Statistics? (100 Words)
The Capital Asset Pricing Model:
Theory and Evidence
Eugene F. Fama and Kenneth R. French
T he capital asset pricing model (CAPM) of William Sharpe (1964) and JohnLintner (1965) marks the birth of asset pricing theory (resulting in aNobel Prize for Sharpe in 1990). Four decades later, the CAPM is still
widely used in applications, such as estimating the cost of capital for firms and
evaluating the performance of managed portfolios. It is the centerpiece of MBA
investment courses. Indeed, it is often the only asset pricing model taught in these
courses.1
The attraction of the CAPM is that it offers powerful and intuitively pleasing
predictions about how to measure risk and the relation between expected return
and risk. Unfortunately, the empirical record of the model is poor—poor enough
to invalidate the way it is used in applications. The CAPM’s empirical problems may
reflect theoretical failings, the result of many simplifying assumptions. But they may
also be caused by difficulties in implementing valid tests of the model. For example,
the CAPM says that the risk of a stock should be measured relative to a compre-
hensive “market portfolio” that in principle can include not just traded financial
assets, but also consumer durables, real estate and human capital. Even if we take
a narrow view of the model and limit its purview to traded financial assets, is it
1 Although every asset pricing model is a capital asset pricing model, the finance profession reserves the
acronym CAPM for the specific model of Sharpe (1964), Lintner (1965) and Black (1972) discussed
here. Thus, throughout the paper we refer to the Sharpe-Lintner-Black model as the CAPM.
y Eugene F. Fama is Robert R. McCormick Distinguished Service Professor of Finance,
Graduate School of Business, University of Chicago, Chicago, Illinois. Kenneth R. French is
Carl E. and Catherine M. Heidt Professor of Finance, Tuck School of Business, Dartmouth
College, Hanover, New Hampshire. Their e-mail addresses are �[email protected]
edu� and �[email protected]�, respectively.
Journal of Economic Perspectives—Volume 18, Number 3—Summer 2004 —Pages 25– 46
legitimate to limit further the market portfolio to U.S. common stocks (a typical
choice), or should the market be expanded to include bonds, and other financial
assets, perhaps around the world? In the end, we argue that whether the model’s
problems reflect weaknesses in the theory or in its empirical implementation, the
failure of the CAPM in empirical tests implies that most applications of the model
are invalid.
We begin by outlining the logic of t ...
This document summarizes the capital asset pricing model (CAPM). It begins by outlining the logic and key assumptions of the CAPM, including that all investors hold the same market portfolio which must lie on the efficient frontier. It then states that the CAPM predicts the expected return of an asset is determined by its beta, or non-diversifiable risk relative to the market. However, the document notes that empirical tests have found the CAPM performs poorly in applications. It concludes the CAPM's failings indicate applications based on the model are invalid, challenging researchers to develop alternative models.
This research paper summarizes a study conducted to test the empirical validity of the Capital Asset Pricing Model (CAPM) in the Indian stock market context. Researchers tested three hypotheses: 1) the intercept alpha is equal to zero, 2) there is a positive relationship between portfolio returns and betas, and 3) market capitalization explains cross-sectional returns. Daily return data from 66 BSE Sensex companies from 1995 to 2005 was analyzed using time series and cross-sectional regressions. The results showed that alpha is not significantly different from zero, supporting CAPM theory when using value-weighted portfolios. However, beta was not as expected by CAPM when using equally-weighted portfolios. Market capitalization also did not
L2 flash cards portfolio management - SS 18analystbuddy
Mean-variance analysis is used to identify optimal portfolios based on expected returns, variances, and covariances of asset returns. The minimum-variance frontier shows the efficient combinations of expected return and risk. The efficient frontier begins with the global minimum-variance portfolio and provides the maximum expected return for a given level of variance. The capital market line describes combinations of the risk-free asset and market portfolio. The capital asset pricing model expresses expected returns as a linear function of systematic risk measured by beta.
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Capital asset pricing_model
1. CAPITAL ASSET PRICING MODEL (CAPM).
AN EMPIRICAL TEST OF PORTFOLIO PRICING.
Hanken School of Economics
Department of Finance and Statistics
Research Methods in Finance
Supervisor: Johan Knif and David Gonzalez
Authors: Ernest Owusu Boakye &
Abdullah Jobayed
Date: October 7, 2015
2. HANKEN SCHOOL OF ECONOMICS
Department of: Finance and Statistics Type of work:
Term paper
Authors:
Ernest Owusu Boakye
Abdullah Jobayed (
Date: 06.10.2015
Abstract:
Capital Asset Pricing Model, widely known as CAPM model, is an equilibrium model
used in asset pricing to test whether the expected return of assets or portfolios are in
line with market return. In this paper, the authors tested the CAPM model with two
portfolios to determine whether the CAPM can exactly price them. The authors
designed two portfolios, which are equal weighted and value weighted, using OMX
Helsinki 25 index as the market portfolio and the average of Euribor 1 Week discount
rate as risk free return. 415 observations were monitored in order to avoid statistical
errors.
The authors found that CAPM can exactly price the value weighted portfolios but not
the equal weighted portfolio. Even though the test found mispricing of the portfolio, it
has shown some aspects or scenarios which can help in further study.
Keywords: Capital asset pricing model (CAPM), OMX Helsinki 25, Equal Weighted
Portfolio, Value Weighted Portfolio.
3. CONTENTS
1 INTRODUCTION ......................................................................................................2
2 METHODOLOGY .....................................................................................................3
3 DATA COLLECTION...............................................................................................5
4 ANALYSIS ..................................................................................................................7
5 FINDINGS.................................................................................................................10
6 CONCLUSION .........................................................................................................15
REFERENCES ..............................................................................................................16
APPENDIX 1 AVERAGE DAILY RETURN, VALUE & EQUAL WEIGHT
PORTFOLIO AND EURIBOR DISCOUNT RATE.............................................17
4. 2
INTRODUCTION
Background of the Study.
Modeling expected returns in financial asset, such as stocks, had yield some anomalies
in empirical finance research in past decade. Previous studies have proved that some of
these anomalies can be explained in risk and return framework. Some Models that were
useful to explain these anomalies include Capital Asset Pricing Model (CAPM). The
CAPM was developed independently by three researchers (Treynor 1962; Sharpe 1964;
Lintner 1965). In their various study, the researchers tried to explain how returns on
financial asset can be related to their corresponding risk factors. The assumption is that
assets such as stock returns are proportional and linear related to their risk, which is
commonly expressed as security market line in finance theory (Markowitz 1959). That
is, for an investor to invest in the market, the investor should be compensated for taking
more risk with higher returns. Hence their works marked the foundation of asset pricing
theory in finance. Other studies such as Fama-French three factor model by Fama and
French (2004) used the CAPM model as a benchmark to model three factors Asset
Pricing to further explain the systematic risk component part in the CAPM with respect
to returns.
Problem of the Study
Many studies have been done in this field of asset pricing (Markowitz 1959; Jansen
1968; Kent et al, 2001; Fama and French, 2004; Choudhary and Choudhary, 2010 and
others). Jansen (1968) in his work introduces a variable Alpha (ᾳ) to the CAPM as a
performance measure of a portfolio mostly referred to as the market CAPM model.
Portfolio or fund managers use Jansen’s alpha as a benchmark to measure their portfolio
performance against the market. Measuring portfolio performance with Jansen’s alpha
evaluated by the intercept α is actively applied in corporate financial management
(Cuthbertson and Nitzsche 2004:175). Some of these studies have shown that the one
factor CAPM cannot be sufficient or adequate to price financial asset or explain the risk
and return framework in theoretical and empirical finance. Studies have compared
CAPM to other models and made various conclusions. As a result of that, previous
5. 3
studies have further model alternatives that capture more than one factor to explain the
systematic risk component part of the CAPM namely Fama and French (2004) three
factor model, the four factor model, the Arbitrage Pricing Model (APT) model and
others. However in all previous studies, the CAPM have been referred as the basis for
the modeling.
Purpose of the Study
This paper evaluate the validity of the Capital Asset Pricing Model (CAPM) under the
assumption that the CAPM model can price portfolios or determine the required rate of
return for an investor in financial market.
Objective of the Study.
To examine whether the Capital Asset Pricing Model (CAPM) can price assets or
portfolios in financial Market.
Study Question.
Can the Capital Asset Pricing Model (CAPM) exactly price assets or portfolio in
financial market?
METHODOLOGY
As previously stated, to test the CAPM model, the authors intend to introduce the
theoretical Capital Asset Pricing Model (CAPM) and the market Capital Asset Pricing
Model to test the pricing of the portfolios created using equal and value weight. The
portfolio will be created using random criteria for the selection of stocks from the
Finnish stock market. These stocks will be grouped into two portfolios by value (value
weighted portfolio) and equal weight (equal weighted portfolio) under the principle of
portfolio building. The number of stocks to be included in the portfolio will be limited
to four stocks due to time limitation; however it could be improved in further study. The
Helsinki OMX 25 as a market index and the Euribor risk free rate will be used as an
input variables to model the pricing of the portfolios using CAPM, under the hypothesis
that the CAPM can exactly price our portfolio from 0 to 10% significance level.
6. 4
The theoretical CAPM is stated as: the Expected return on a portfolio equals risk free
rate plus systematic risk (beta) times the risk premium on the market return over the risk
free rate
E(Ri) = Rf + βE(Rm – Rf) ≈ E(Rp-Rf)= βE(Rm – Rf) (1)
Where:
E(Rp) - Expected Return on a Portfolio (Required Rate of Return for Investor)
Rf - Riskless return on the market
Rm - Market Return
β - the Beta (the market volatility) calculated by:
The market model of the CAPM which integrate Jansen’s alpha as:
E(Rp-Rf) = ᾳ + βE(Rm – Rf)+ɛt (2)
Where:
E(Rp) - Expected Return on a Portfolio (Required Rate of Return for Investor)
Rf - Riskless return on the market
Rm - Market Return
β - The Beta (the market volatility or exposure to the portfolios) calculated by:
ᾳ - Measures mispricing (0 = no mispricing, otherwise mispricing)
ɛt - Residual Component under assumption that ɛt~ iid(0, δ
2
)
The market CAPM will be used to model the pricing of portfolios using regression
E(Rp-Rf) = ᾳ + βE(Rm – Rf)+ɛt (3)
β=
β=
7. 5
The theory will be tested under the Hypothesis that:
H0: E(Rp)=Rf + βE(Rm – Rf) (4)
CAPM estimated exactly the price of the portfolio and no systematic mispricing.
H1: E(Rp) ≠ Rf + βE(Rm – Rf) (5)
CAPM estimated over/under estimated the price of the portfolio and there were
systematic mispricing.
Under statistical assumption (0 < P- value < 0.10). as our significance level.
Where:
Ho = Null Hypothesis
H1 = Alternative Hypothesis.
DATA COLLECTION
Secondary data was collected to analyze this study due to the level of confidence and
accuracy from the financial market. The data was extracted from Helsinki stock
exchange which is part of the OMX group. Due to time limitation, the data collected
was limited to a period of 1 year 8 months from 03.01.2014 to 31.08.2015 given 415
observations. This is a sample data from four large companies listed on the exchange.
In order to conduct the test on the CAPM model, the authors imported daily average
stock price for individual stocks i.e. Elisa OYJ, Nokia OYJ, Sampo OYJ and Kone OYJ
for the time period of 03.01.2014 to 31.08.2015. These four companies were randomly
selected from Helsinki OMX 25 index to build the portfolio Value Weighted and the
Equal Weighted Portfolios. The Helsinki OMX25 index is a market index portfolio of
the most traded stocks on the finish stock market, categorized as large capitalization
stocks. From 415 daily average price of each stock, the authors calculated the daily
returns using log returns method, for each company for the same time period. Daily
closing price of the market (Helsinki OMX 25) index was also extracted for the same
period. Additionally, this paper used Euribor 1 week current rates as the risk free rate.
8. 6
The returns where calculated as:
Ri = ln(Pt/Pt-1) or (6)
Ri = ln(Pt) – In(Pt-1) (7)
Where:
Ri - Return of the stock
Pt - Current Price
Pt-1 - Previous Price.
The Portfolio was calculated as:
E(Rp) = ∑wiRi (8)
Where: The weight of the stock in the portfolio is multiplied by the return and sum to
form expected return on a portfolio
E(Rp) - Expected Portfolio return
Wi -Weight of the stock in the Portfolio
Ri - Daily return of the stock.
Average of one week Euribor rate was calculated using arithmetic mean method:
ẋ= (x1+x2……xn)/n-1 (9)
Value weight of a portfolio was calculated as:
Wi = mkti Cap/ Tcap. p (10)
Where:
Wi - Weight of the stock in the portfolio
mkti Cap - Market capitalization of a stock
Tcap. p. - Total Market Capitalization of the portfolio
9. 7
DATA ANALYSIS
Econometric software EViews and Microsoft Excel were used to analysis the data to
check for standards in empirical finance research such as descriptive statistics,
normality and regression outputs. The authors used excel to calculate and organized the
data for easy analysis in EViews. The results of the returns calculated using excel can be
found in Appendix.
Figure 1. Descriptive Statistics
ELSIA_OYJ EW_PORTFO... KONE_OYJ NOKIA_OYJ OMXH_25 SAMPO_A_O... VW_PORTFO...
Mean 0.104623 0.038904 0.017072 -0.012187 0.023506 0.046108 0.024564
Median 0.174125 0.074576 0.061576 0.000000 0.054869 0.086543 0.061198
Maximum 5.105028 3.699670 7.599276 7.611449 4.228915 3.340840 3.523872
Minimum -7.547004 -5.717911 -5.515814 -11.25127 -5.368657 -6.730883 -5.960839
Std. Dev. 1.263715 1.037867 1.357146 1.832891 1.127453 1.031524 1.097574
Skewness -0.796417 -0.332325 -0.036005 -0.499484 -0.227509 -1.120266 -0.447477
Kurtosis 10.27764 5.937528 6.201939 8.230021 4.505118 10.06566 5.833242
Jarque-Bera 959.7076 156.8498 177.3710 490.2369 42.75231 950.0650 152.6544
Probability 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
Sum 43.41850 16.14510 7.084697 -5.057747 9.754938 19.13494 10.19425
Sum Sq. Dev. 661.1481 445.9477 762.5237 1390.829 526.2565 440.5131 498.7329
Observations 415 415 415 415 415 415 415
Figure1. 1Represents the Descriptive Statistics for individual returns, the portfolio and the market
OMX 25
Table 1.
N= 4 COMPANIES
MKT CAP VALUE
WEIGHT
EQUAL WEIGHT
ELSIA 4,901,244,288.00 0.08 0.25
NOKIA 21,520,055,062.00 0.33 0.25
KONE 14,535,806,522.00 0.23 0.25
SAMPO A 23,553,420,000.00 0.37 0.25
TOTAL CAP 64,510,525,872.00 1.00 1
Table1: Represents portfolio weights and individual market capitalization (total number
of outstanding share times the share price).
10. 8
Normality Test
The assumption for normality test is a standard test for a distribution in empirical
finance. It is assumed that stock returns studied over time exhibit close to normal
distribution, seldom will a distribution exhibit a normal distribution empirically,
theoretical yes. That gives the researcher some confidence in the data to use for
modeling or prediction purpose. Statistical benchmarks to check this normality have
been developed and accepted in finance. The first and second moment’s i.e. mean and
standard deviations are mostly used to measure normality test. Other tests such as
skewness and kurtosis further gives the researcher the idea of extreme examples that
often may be considered statistically significant to consider in the distribution.
Assumption
Under efficient market hypothesis, stock returns over time are normally distributed with
Mean = 0, Standard deviation = 1
X~N (0, 1),
H0: μ = 0, δ = 1
H1: μ ≠ 0, δ ≠ 1
In finance perceptive, the mean represents expected return stated previously and the
standard deviation the risk. The authors tested the distribution to verify its conformity to
the standard normal distribution to be used in modeling. The econometric software
EViews was used to run the test and statistical measures such as the mean, standard
deviation, skewness, kurtosis are shown in figure 1 above, Three independent
distributions i.e. equal weight portfolio, value weight portfolio and the market portfolio
(OMX 25) distributions were tested separately and shown graphically below.
The authors tested for correlations between the distributions to verify the relationship
between them. The statistical benchmark to observe is 1 and – 1, which is interpreted as
perfectly positive correlation and perfectly negative correlation. Positive correlation
means the distributions move in the same direction and negative for opposite direction.
The test informs the researcher the pattern of the results.
11. 9
Figure 1: Normality test of equal weighted portfolio
Figure 2: Normality test of equal weighted portfolio
From the figures above, with 415 observations, both equal weighted and value
weighted portfolio distributions failed the normality test with mean and standard
deviation of 0.038904, 0.024564 and 1.037867, 1.097574 respectively. Both
observations are negatively skewed with kurtosis = 5. Hence we reject the null
hypothesis that our distribution is a normal distribution.
Figure 5: Normality test of Helsinki OMX 25 stock index
12. 10
Furthermore, the Helsinki OMXH 25 distribution with 415 observations also failed the
normality test with mean = 0.023506 and standard deviation = 1.127453, negatively
skewed with 4.5 kurtosis, however it is statistically significate to be included in the
model because it is very close to normal distribution.
Correlation test
Correlation is a statistical parameter that measures “the degree of linear association”
between parameters. Even though two correlated variable may be treated symmetrical
way, it doesn’t necessarily mean that changes in one variable would cause changes in
another variable. In this context, correlation coefficient shows a linear relationship
between two variables and relates the variables on an average scale in their movement
in perspective of one another (Brooks 2008: 28).
OMXH_25 EW_PORTFO...VW_PORTFO...
OMXH_25 1 0.821961930...0.817021706...
EW_PORTFO...0.821961930... 1 0.977212934...
VW_PORTFO...0.817021706...0.977212934... 1
The correlation coefficient test shows that, the equal and value weighted portfolio
distributions are positively correlated with the OMX 25 index. The correlation
coefficients are very high indicating that there will not be much diversification of risk
because the performance of the portfolio moves together with the market that is to
emphasize that if the market is doing well, it is a signal to us that the portfolio will also
be doing well likewise in bad times hence they will be exhibiting high betas. However,
this is not the main objective of the study but to be considered in further studies.
FINDINGS
For empirical interpretations of the findings, econometric software tool EViews was
used to running multiply one factor CAPM regression to ascertain the validity of the
model in pricing financial assets i.e. returns of portfolio. Ordinary Least Squares (OLS)
regression estimates will be used for interpretations.
13. 11
Test 1.
Assumption: daily risk free rate do not change significantly and will be excluded in the
model:
Figure 8: Simple regression analysis between Equal Weighted Portfolio and
Helsinki OMX 25 index
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 0.090619 Prob. F(1,413) 0.7635
Obs*R-squared 0.091037 Prob. Chi-Square(1) 0.7629
Scaled explained SS 0.241645 Prob. Chi-Square(1) 0.6230
From the result it shows that, there is no systematic mispricing in the model from the
constant c (alpha) of 0.021118 and a Prob. Value of 0.4678, which is statistically
insignificant. The OMXH 25 (beta) coefficient is 0.75665 below the benchmark of 1
meaning that no risk premium will be require investing in the index which is statistically
significant with prob. Value of 0.0000. The model explained 0.675621 of the variations
between the variables leaving about 0.32 unexplained with adjusted R square of
0.674836. Overall the model is statistically significate with prob. F- statistic of 0.000.
A test on heteroskedascity with Breusch-Pagan-Godfrey shows that, the constant
variance in the error component has not been violated with P. Value of the R squared
0.7629, giving the authors the confident that the estimates coefficients are reliable.
14. 12
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 0.090619 Prob. F(1,413) 0.7635
Obs*R-squared 0.091037 Prob. Chi-Square(1) 0.7629
Scaled explained SS 0.241645 Prob. Chi-Square(1) 0.6230
However, the model was tested under the assumption of no significant changes in the
daily risk free rate and that was not included in the model. Further test was done
incorporating the risk free rate and the result shows:
Figure 10: Simple regression analysis between Equal Weighted Portfolio and
Helsinki OMX 25 index
In this result, it was found that there were some significant systematic mispricing in the
model indicating a Constant (c) value of 0.056915 and a prob. value of 0.0534 under the
stated significance level. The systematic risk component OMXH 25 – Euribor risk free
(beta) coefficient did not change, is still statistically significant with prob. Value of
0.000 as well as the R squared and the Adjusted R squared. The model showed
homoscedasticity, meaning that the constant variance of the error component is upheld
and we can be confident in the estimates to be true representative of the variables.
15. 13
From this inference, we can reject the Null Hypothesis (H0) and accept the Alternative
Hypothesis (H1) that the CAPM estimated over/under estimated the price of the
portfolio and there were systematic mispricing for the equal weighted Portfolio.
Test 2.
The same procedure for the test 1 was implemented in test 2 for the value weighted
portfolio, under the same assumptions.
Dependent Variable: VW_PORTFOLIO
Method: Least Squares
Date: 10/01/15 Time: 21:17
Sample: 1/03/2014 8/31/2015
Included observations: 415
Variable Coefficient Std. Error t-Statistic Prob.
C 0.005869 0.031111 0.188637 0.8505
OMXH_25 0.795369 0.027621 28.79578 0.0000
R-squared 0.667524 Mean dependent var 0.024564
Adjusted R-squared 0.666719 S.D. dependent var 1.097574
S.E. of regression 0.633635 Akaike info criterion 1.930119
Sum squared resid 165.8165 Schwarz criterion 1.949532
Log likelihood -398.4997 Hannan-Quinn criter. 1.937796
F-statistic 829.1967 Durbin-Watson stat 2.246786
Prob(F-statistic) 0.000000
Figure 12: Simple regression analysis between Value Weighted Portfolio as constant
and Helsinki OMX 25 index
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 1.067564 Prob. F(1,413) 0.3021
Obs*R-squared 1.069968 Prob. Chi-Square(1) 0.3010
Scaled explained SS 2.912995 Prob. Chi-Square(1) 0.0879
From the above results, similar pattern was shown that there is no systematic mispricing
in the model from the constant c (alpha) of 0.00586 and with high Prob. Value of
0.8505 which is statistical insignificant under the stated significance level. The OMXH
16. 14
25 (beta) coefficient is + 0.79536 below the benchmark of 1, meaning no risk premium
will be required investing in the index, which is statistically significant with prob. Value
of 0.0000. The model explained 0.66758 of the variations between the variables leaving
about 0.32 unexplained with adjusted R square of 0.666719. Overall the model is
statistically significate with prob. F- statistic of 0.0000 and no heteroscedasticity in the
model hence we can be confident in the result.
Moreover, incorporating the Euribor risk free rate, the results have shown that:
Dependent Variable: VW_PORTFOLIO-EURIBOR_RATE
Method: Least Squares
Date: 10/01/15 Time: 21:44
Sample: 1/03/2014 8/31/2015
Included observations: 415
Variable Coefficient Std. Error t-Statistic Prob.
C 0.035970 0.031459 1.143392 0.2535
OMXH_25-EURIBOR_RAT... 0.795369 0.027621 28.79578 0.0000
R-squared 0.667524 Mean dependent var 0.171664
Adjusted R-squared 0.666719 S.D. dependent var 1.097574
S.E. of regression 0.633635 Akaike info criterion 1.930119
Sum squared resid 165.8165 Schwarz criterion 1.949532
Log likelihood -398.4997 Hannan-Quinn criter. 1.937796
F-statistic 829.1967 Durbin-Watson stat 2.246786
Prob(F-statistic) 0.000000
Figure 14: Regression analysis between Value Weighted Portfolio (c) excluding
Euribor Rate and Helsinki OMX 25 index.
Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic 1.067564 Prob. F(1,413) 0.3021
Obs*R-squared 1.069968 Prob. Chi-Square(1) 0.3010
Scaled explained SS 2.912995 Prob. Chi-Square(1) 0.0879
There is no statistically mispricing in the model, given a prob. Value of 0.2535 for the
constant coefficient of 0.03597 indicating no significance under the stated significance.
Beta coefficient of the value weighted portfolio minus the Euribor risk-free rate is
0.795369 at a prob. Value of 0.00000. R squared and the Adjusted R square gives an
indication that the model is a good model and statistically significant given the input
data. The model showed homoscedasticity ( there is no heteroscedasticity). Hence, we
17. 15
are confident that, the model estimated true coefficients with accurate P. values,
therefore we can accept the null hypothesis on this result that the CAPM could exactly
price the value weighted portfolio.
CONCLUSION
From the findings, it can be concluded that, the tested theoretical CAPM model which at
any point in time should hold in pricing financial asset or estimating returns could only
pass the test empirically on the value weighted portfolio and not on the equal weighted
portfolio. Testing financial theories empirically could yield a different result, however
that should not undermine the model as a good model to be used as a benchmark (Edwin
et al. 2003:309)
The approach under which this study was conducted may be different from the approach
other researchers may adopt, however the underline assumption is to test the validity of
CAPM in pricing the portfolios the authors have designed. The data size, portfolio stock
selection and designing were very limited due to time and the authors recognize that it
could impact on the result but alternatives or more diversified portfolios with very large
data set can be used to improve on this finding in the future.
18. 16
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