Comparative Analysis of Portfolio Management Models: Markowitz, CAPM, and Multi-Factor Models

This chapter discusses theoretical foundations and empirical evidence for the most prominent asset pricing theory: the Capital Asset Pricing Model (CAPM). It represents a pricing model for risky assets. The CAPM has been extended to the multi– factor model (MFM) and arbitrage pricing theory (APT). The motivation of the latter has been to overcome the problems associated with the market portfolio in the CAPM by introducing a multi–factor approach. The subsequent chapter is kept simple and refers to the CAPM only. In some additional remarks crucial assumptions regarding investors’ preferences and stock return distributions are relaxed. Currently the debate whether exact pricing restrictions in the MFM and APT imply the return to the “good old CAPM” is still going on. By introducing state dependent relationships as well as general nonlinearities in a CAPM model one can try to unify the different views but we will not elaborate on such extensions. A more extensive treatment of static and dynamic portfolio theories is given in Part VI of the book.

The capital asset pricing model (CAPM) model has always been the core theory of asset pricing and is widely used in the world as a finance tool in the securities market, but it is not fully effective for the economic market due to the current state of development in some countries. This paper compares and analyses the CAPM model and its improved and alternative models based on existing literature and statistical data. This paper first explains the CAPM model, analyses its formula, and then describes the disadvantages and shortcomings of the CAPM model. Then it gives examples of other replaceable models, first explains those models, then lists the advantages of these models compared with the CAPM model as well as some of their shortcomings, and finally concludes through the comparison of these models to the CAPM model that although the CAPM model may not be applicable to the market in many cases, it can be replaced by other models, and even then there is no one-size-fits-all model that can replace all the market models, and conclusions need to be made on a case-by-case basis.

Portfolio management plays a significant role in the world of finance and investing, offering benefits and contributions to both individual investors and institutions. Researchers use many mathematical models to make informed decisions about how to allocate and manage investments within a portfolio to optimize risk versus return trade-off based on the investors preference and constraints. This paper primarily employs the literature review methodology and comparative analysis methodology. Firstly, it collects, summarizes, and analyzes multiple papers on portfolio management models, including Markowiz Mean-Variance Model, Capital Market Line (CML), Arbitrage Pricing Theory (APT) and Capital Asset Pricing Model (CAPM) with the origin of the models, their key assumptions, components, and applications. Additionally, this paper also utilizes comparative analysis by comparing the similarities, differences, and respective downsides and benefits of the four main research models. Through this comparison, the paper investigates the relationships and application distinctions among the models. As a result, these models evolve and refine over time, with some building on others. CAPM extends the Markowitz Model by introducing the risk-free rate and market portfolio as benchmarks, simplifying the risk-return relationship, and introducing systematic risk. The Capital Market Line (CML), derived from CAPM, illustrates efficient portfolios made up of both market and risk-free assets and shows the risk-return trade-off. APT, a later model, can be seen as an extension of CAPM.

Equity Returns, Bankruptcy Risk and Asset Pricing Models

This study is done to analyze and compare the accuracy of Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT) Model in predicting stocks’ actual return. The purpose of the study is to find the discrepancy of accuracy of CAPM and APT models in predicting company stocks’ return registered in IDX-30 index from Indonesian Stock Exchange from January 2020-2022. The period is chosen because of the Covid-19 pandemic in Indonesia. The chosen stocks are the stocks which have positive return, never leave the index, never have any changes in stocks’ amount in major and minor evaluation, never do stock split, and have routine dividend payout along the study’s period. The result is there is a significant difference between CAPM and APT models in predicting the actual return based on the result from t-test independent samples. Observed from the Mean Absolute Deviation (MAD) of the two models, CAPM model MAD is smaller than those from APT model, thus CAPM is the more accurate model in calculating return form IDX-30 stocks from January 2020-2022.

Since William Sharpe introduced the Capital Asset Pricing Model (CAPM) in the 1960s, it has profoundly influenced asset pricing, portfolio management, and corporate financial decision-making. This work employs a comprehensive literature review methodology, utilizing comparative and inductive analysis to elucidate the primary research trajectories and developmental patterns of the CAPM. The Capital Asset Pricing Model (CAPM) was formulated on the foundation of Markowitz's portfolio theory and introduced by William Sharpe. It has since had extensions, including the APT model, the three-factor model, and the four-factor model, along with the latest use of machine learning techniques, aligning capital price more closely with actual market conditions. The research conclusion indicates that, firstly, although the CAPM has certain limitations, its theoretical simplicity and logical rigor make it an important asset pricing tool for investors. Secondly, multi-factor models have become a new path for the development of the CAPM, and further increasing factors can enhance the model's explanatory power. Finally, behavioral finance provides a new perspective for understanding the limitations of the CAPM.

This study is based on the rapid development of the investment world. Hence, most investors have limited abilities and strategies in investing, therefore it takes important methods and concepts to assess the level of profit from an investment with various existing risk factors. This study focuses on the comparison of the accuracy between the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT) methods in predicting stock returns of LQ 45 index companies for the 2016-2020 period. This study aimed to determine which method was more appropriate in predicting the company's stock returns. The accuracy of the CAPM and APT methods was measured by using the Mean Absolute Deviation (MAD). The Independent Sample T-test was used to determine whether there was a difference in accuracy between the CAPM and APT methods in predicting stock returns. The results of this study show that by using the calculation of the Mean Absolute Deviation, the APT method is more accurate than the CAPM method in predicting stock returns. The MAD APT value (0.000246) is smaller than the MAD CAPM value (0.003739) and based on data processing from the Independent Sample T-test shows that H0 is rejected, which means that there is a significant difference in accuracy between the CAPM and APT models particularly in predicting the company's stock return.

In this paper we provide a summary of the capital asset pricing model (CAPM) and point out how it might possibly be used as a tool for strategic planning by corporations that own a portfolio of businesses. We also point out some of the assumptions underlying the CAPM which must be satisfied if it is to be used for strategic planning. Next we include a critical appraisal of the CAPM as a strategic planning tool. Finally, we state the case for linking competitive strategy models, CAPM models, and business simulation models.

The Correlations and Volatilities of Stock Returns: The CAPM Beta and the Fama-French Factors

This thesis consists of three empirical studies on what drives stock market dynamics. The first empirical study explores the effect of crude oil price changes on the stock market returns of oil-exporting countries and oil-importing countries as well as those of a number of global stock indices. Using the Ordinary Least Squares (OLS) approach as well as the more robust Quantile Regression (QR) approach to explore the relationship between crude oil and stock market dynamics. The empirical findings suggest that the QR approach provides further insights compared to the OLS approach. For instance, the QR approach is able to identify specific quantiles where a significant relation exists. In particular crude oil price increases tend to have a negative impact on the stock market returns for some oil-exporting countries (such as Mexico, Iraq, Ecuador, and Venezuela) and a positive effect for other oil-exporting countries (such as Brazil and Algeria). However, the OLS approach suggests that these relationships are insignificant at the level of the mean. Overall, the empirical findings confirm that the QR approach can reveal more information about the relationship between crude oil price changes and stock market return across different quantiles of their distribution.The second study explores the extent to which implied volatility extracted from commodity markets and developed stock markets can predict the implied volatility of stock markets in BRICS countries. Using daily data from 2011 to 2016 and employing the newly developed Bayesian Graphical Vector Autoregressive (BGVAR) model of Ahelegbey et al. (2016) which does not suffer from over-parameterization and the identification problems associated with traditional VAR frameworks, this study finds that implied volatilities extracted from global and regional stock markets have a significant predictive power over the implied volatilities in BRICS stock markets. However, the predictive power of implied volatility from commodity markets are significant only in the case of South Africa.The third empirical study analyses the relationship between illiquidity and stock market returns in the G7 and BRICS countries. More specifically, this study explore the extent to which the Amihud (2002) illiquidity measure can improve the explanatory power of three commonly used asset pricing models, namely the Capital Asset Pricing Model (CAPM), the Fama-French three-factor model and the Carhart four-factor model. The empirical analysis is based on 15 years of monthly data on the returns of seven stock portfolios: 100 largest companies (Largest100), small value (S/V), small neutral (S/N), small growth (S/G) stocks, big value (B/V) stocks, big neutral (B/N) stocks, and big growth (B/G) stocks. The findings suggest that incorporating illiquidity as an additional factor results in a significant improvement in the explanatory power of these asset pricing models across several of the sample countries (8 countries in the case of the CAPM and Carhart four-factor model, and 6 countries in the case of the Fama-French three-factor model). For example, in the US adding illiquidity to the CAPM leads to an increase of the goodness of fit by 2.6% in the B/V portfolio, and for the Fama-French three-factor model the goodness of fit increases by up to 3% in all portfolios Moreover, the goodness of fit increases in all portfolios in the US by adding illiquidity to the Carhart four-factor model, with an up to 36% increase in the B/N portfolio.

This study re-evaluates the validity of the Capital Asset Pricing Model (CAPM) in the U.S. Consumer Discretionary sector over the turbulent 2015–2025 decade, a period marked by pandemics, inflationary surges, monetary tightening, and shifts in tariff policy. Adopting a two-pass regression framework with the Shanken (1992) correction to mitigate errors-in-variables bias, we analyze 20 representative S&P 500 firms across subsectors of the sector. Empirical results show the sector's average beta at 1.25, significant beta instability during structural shocks, and a flatter Security Market Line (SML) than CAPM's theoretical prediction. The market risk premium is positive but statistically insignificant after Shanken correction, and the low-beta anomaly is pronounced, with defensive stocks outperforming high-beta counterparts on a risk-adjusted basis. We find that non-market systematic factors—including tariff policy risk, interest rate duration, and operating leverage—undermine CAPM's explanatory power, alongside behavioral herding and speculative bubbles. Multifactor models (e.g., Fama-French Three-Factor) exhibit better performance but still struggle with tail-risk events. This research concludes that CAPM serves as a useful first-order risk approximation but is insufficient for the modern Consumer Discretionary sector. Dynamic, multifactor frameworks that incorporate policy and macroeconomic sensitivities are necessary for accurate asset pricing and investment decision-making in this volatile sector.

It is already well established that neither the bias inherent in, nor the extent to which a multifactor specification of the Capital Asset Pricing Model (CAPM) prices behaviors (priors), as opposed to rationality (risk preferences) is decipherable from the output of any such model. Hitherto, empirical structures that facilitate either inference have been lacking. This study’s formal theory directly spans an empirical structure which nests inferences in respect of the bias inherent in a CAPM in inferences in respect of the extent to which the same CAPM prices risk preferences, as opposed to priors that are systemically realized (‘systemic priors’) within populations of agents. The resulting empirical evidence in respect of the Fama and French three factor model is unequivocal, namely that it solely prices systemic priors, not agents’ risk preferences, a finding that is consistent with the suspicion, in prior studies, that the market betas that are generated by the model are so high, it is unlikely they evince rational pricing. Contrarily, conditional on the presence, in markets, of non-globally risk averse agents, a multifactor CAPM which incorporates the market portfolio and market skewness factors prices agents’ risk preferences and systemic priors and outperforms all other candidate models.

Purpose- The purpose of this study is to construct a portfolio based on downside beta as a measure of downside risk. The analysis uses data from all listed companies on the Pakistan Stock Exchange (PSE) over the period from January 2000 to December 2021. Study Design/Methodology/Approach - The study employs a rolling window approach with 36 consecutive months to estimate downside beta values for portfolios ranked from lowest to highest downside beta. Portfolio returns are evaluated using the Generalized Method of Moments (GMM) in conjunction with the Capital Asset Pricing Model (CAPM) and the Fama-French three- and five-factor models. A six-month Treasury bill rate is used as the risk-free rate. Findings- The study reveals a significant spread between the downside beta values of the constructed portfolios, confirming that downside risk can be effectively captured through this approach. The hypothesis of equal mean downside beta across the portfolios is rejected, indicating that portfolios based on downside beta exhibit different risk-adjusted returns. Furthermore, the rejection of the alpha equal to zero hypothesis suggests that these risk-adjusted returns are statistically significant. However, the study finds that lower partial moments do not fully explain the variation in downside risk. Practical Implications- These findings are particularly relevant for investors focused on managing downside risk. The study offers alternative methods for constructing portfolios that account for downside risk, which could enhance risk management strategies. However, the reliance on historical data from the PSE may limit the generalizability of these findings to other markets. Originality/Novelty - This study contributes to the literature by constructing portfolios grounded in downside beta as a measure of downside risk, offering a novel approach to portfolio formation and risk-adjusted return evaluation. It highlights the importance of incorporating downside risk in portfolio management and presents an innovative application of downside beta within the context of emerging markets.

Capital asset pricing model (CAPM) has become a fundamental tool in finance for assessing the cost of capital, risk management, portfolio diversification and other financial assets. It is generally believed that the market risks of the assets, often denoted by a beta coefficient, should change over time. In this paper, we model time-varying market betas in CAPM by a smooth transition regime switching CAPM with heteroscedasticity, which provides flexible nonlinear representation of market betas as well as flexible asymmetry and clustering in volatility. We also employ the quantile regression to investigate the nonlinear behavior in the market betas and volatility under various market conditions represented by different quantile levels. Parameter estimation is done by a Bayesian approach. Finally, we analyze some Dow Jones Industrial stocks to demonstrate our proposed models. The model selection method shows that the proposed smooth transition quantile CAPM-GARCH model is strongly preferred over a sharp threshold transition and a symmetric CAPM-GARCH model.

Students considering a masters in Finance Engineering or Artificial Intelligence in Finance are usually required to have an undergraduate background in science, technology, engineering, or mathematics (STEM). STEM students have a good capacity in mathematics and science, but they may not have studied financial theory. To facilitate the classroom teaching of the Capital Asset Pricing Model (CAPM) for STEM students, this paper seeks to expound on the essence of the theory starting at a two-asset framework. Adopting the concepts proposed by Merton (1972), this paper accomplishes the derivation by virtue of basic mathematical tools such as linear algebra, geometry, and statistics except for calculus. We show that the major aspects of Merton’s derivation of the CAPM for a universe of N assets may also be obtained in a two-asset world. Through the methods of this article, students will learn the in-depth theory of CAPM and its hands-on empirical tool. For example, students will realize that even if investors specify different threshold rewards, their different CAPMs will yield identical pricing for assets and portfolios.