Excerpt

## Contents

CHAPTER ONE: INTRODUCTION

CHAPTER TWO: CAPM

THE MODERN PORTFOLIO THEORY

DIVERSIFICATION

SELECTION OF THE OPTIMAL PORTFOLIO

SELECTION OF THE OPTIMAL PORTFOLIO

OPTIMAL PORTFOLIO SELECTION AND THE RISK FREE ASSET

A RISK MEASURE FOR THE CML

THE CAPITAL ASSET PRICING MODEL: EXPECTED RETURN AND RISK

THE SECURITY MARKET LINE (SML)

THE MARKET BETA

CHAPTER FOUR: THREE FACTOR MODEL

CHAPTER FIVE: FOUR FACTOR MODEL

CHAPTER SIX: REWARD BETA MODEL

References

## CHAPTER ONE: INTRODUCTION

The term financial market is describing any marketplace where lenders those who have excess fund and borrowers those who need fund deficit are meet together for exchange of instruments such as equities, bonds, currencies and derivatives. The lender in the financial market are called as investors who buys financial instruments. The investors are invest their fund to maximize their wealth. In reality investors are unable to achieve their objectives at all due to poor performance of respective stock and the market conditions when they are investing in equities. The reason could be the assets may underpriced or overpriced when making investment decisions. If the investors are priced correctly for the asset by considering all relevant factors which are affecting the value, they can enjoy normal profit by appropriately pricing the asset in an efficient market. It has always been the challenge of explaining the decision process of the investors in the stock market. In this context, the behavior of investor has a close relationship with the investment decisions and the way of enriching.

The rate of return and its determinations are the major issues in Finance. The rate of return is one of fundamental criteria for allocation of resources and analysis of risk and return. Their importance can be observed in the field of corporate and personal finance when define the viability of an investment and making investment decisions. Stock returns is always be considered as the principal point when investors going to put their money in financial market. More profit have been involved in higher risk, and vice versa. Investors should take into account their decision to invest their money in accordance with their risk-taking abilities. Many theories and models have developed to guide investors in measuring their proper risk for a given level of return, which will help investors to take a decision easier. All such theories and models unable practiced in all times in different markets. Anomalies could occur in all different conditions of the market (Ramdy 2011).

There are number of research on existing models developed in different markets in times and to find out the best model with considering all factors which determines and explain the behavior of assets prices for accurately pricing the assets to perform ideal financial decision making in financial market. However studies has not been able to find a supreme model that incorporate everything that happens in the stock market before last six decades. Currently there are various branches have emerged from research to treat of modeling the behavior of the stocks such as the modern portfolio theory and the theory of behavioral finance. The modern portfolios theory include models that have delivered major adjustment and improvement in predicting behavior of stocks to the reality. Based on the modern portfolio theory subsequent researcher able to deliver the important theoretical framework.

There are extensive researches are conducted to develop portfolio strategies to make profit on investment decisions in stock markets in this modern financial era. Investors are adopting complicated technique and advanced approaches for modelling framework towards investment decision making strategy in recent years. Meanwhile introduction of rapid improvement of stock market with automation system and the feasibility of introducing large number of stock listing for trading have change the way of investment decisions towards the structure of stock portfolios. This trend of selecting stock portfolios substantially eliminates diversifiable risk and reduces the default risk (Memtsa 1999).

Investment strategy in financial market during the early stage were based on common sense which measures total risk and assumes that the stock with high risk yielding higher return than lover risk investments. This fundamental framework help to introduction of modern portfolio theories. The single factor and multi factor asset pricing models are developed based on the risk return tradeoff relationship. Using the asset pricing model investor can measure the amount of risk the stocks hold. Furthermore it can be measure the magnitudes of the expected return to be rewarded for bearing any specific amount of risk (Memtsa 1999).

The models for asset pricing have been developing and evolving for more than 50 years since the modern portfolio theory introduced by Markowitz (1959) which explained the risk return relationship. The theory given important contribution for the advancement of a model to determine expected rate of return of an asset. Markowitz states that, the expected return (average) and the variance or the standard deviation (risk) of return of a portfolio are the selection criteria of assets for the portfolio construction. These foundation can be used as a maximum as possible for the manner in which investors need to act. It is interesting to note that, while the model is based on an economic fact of "the Expected Utility ". The concept of utility here is based on the fact that different investors have different investment objectives and can be satisfied in different ways (BOAMAH 2012). According to his theory investors make decision by considering two parameters of probability distribution of various assets of the economy: the mean and the variance. The investors are risk averse, as such they are trying to find a portfolio, consisting risky assets that will maximize the portfolio expected return for a given level of portfolio risk (Jiang 2014). Generally investors are risk aversions. They prefer more return at less risk. To accept greater risk, they charge more for it in the form of higher expected return.

## CHAPTER TWO: CAPM

### THE MODERN PORTFOLIO THEORY

The mean variance analysis explained in modern portfolio theory was introduced by Harry Markowitz in 1952 published in the Journal of Finance titled as “Portfolio Selection”. This idea of mean - variance analysis become the foundation for many models in current portfolio and investment management. The simple principles introduced in his paper is consistently being incorporated with new findings even after half century has past (Focardi & Fabozzi 2004). The theory states that the expected return measured by mean and variance of return are the fundamental criteria for selection of stocks for portfolio formation. These two criteria can be used to possible hypothesis the behaviors and guides the investors to be act when making investment decisions (BOAMAH 2012). His key insight for selection of individual assets for portfolio formations depends on the tradeoff between expected return of individual asset and the contribution of such individual asset for portfolio risk rather than its own risk (Sandberg 2005).

### DIVERSIFICATION

The return and risk are the important concepts in portfolio management theory and practices. The higher risk of an investment expects to have higher return. The risk of an investments is not measures what actually happening, but it measures of what is likely to be happen for investment. Markowitz, Harry (1952) Proposed that a well-diversified portfolios will gives highest level of return at given level of risk or provide minimum risk for given level of return. The individual assets combined into a set of portfolio, the expected returns of the portfolio return becomes the weighted average of the individual asset’s expected return. The weights are assigned based on the proportions of these assets held in the portfolio. However the risk of portfolio is not only depends on the weight of the respective individual asset’s risk. But also depends on the correlation between the assets includes in the portfolio (Sandberg 2005).

Markowitz (1952) provided theoretical justification for his theory of diversification which is derived from the statistical principle ‘Variance of the sample mean tends to zero when sample size tends to infinity. Though investors aware and understood this statistical norm of divarication by saying like “do not put all your eggs in one basket” (Francy 2014). Based on his principal Markowitz, Henry (1959) advocated that the investors should diversify their portfolios to being as risk adverse investor. Markowitz understood that through well Diversification and cast diversification in the framework of optimization, the risk-return trade-off of investments could be improved (Focardi & Fabozzi 2013).

Markowitz delivered an approach for portfolio diversification based on measure of weighs of individual assets to be invested and measure of risk and return relationship between such individual assets. The degree of the diversification benefit is depends on the degree of correlation of return of individual securities includes in the portfolio. Markowitz explained this concept of diversification benefit through the statistical notion of covariance, or correlation. The investors should select securities to construct well diversified portfolios. They should consider the correlation of return among the individual securities. In the sense that the investors may face poor performance on portfolio when they invested on portfolio of assets which returns are highly correlated each other. In this case if an individual asset perform badly, other stocks of the portfolio also trend perform in such manner due to higher return correlation. This kind of investment are not a very prudent strategy.

However in practice no assets which are perfectly correlated each other due to fact that different factors are affect their returns. As such when including more and more assets in the portfolio, the total risk trend to become less than the weighted average their risk. The reduction of risk is depends on the correlation between the assets selected in the portfolio. Investors can enjoy the greater benefit of diversification by selecting assets with lower correlation of returns between assets. As such investors can be hold well diversified portfolios by selecting assets which are not perfectly correlated, could eliminate the risk associated with the individual assets (Sandberg 2005).

#### SELECTION OF THE OPTIMAL PORTFOLIO

Under the assumption of risk averse and rational investors, Markowitz approach is based on the fact that the investors expects higher return from their investment portfolio and wanted to minimize risk of that return (Sandberg 2005). Therefore the investors make decisions based on the tradeoff between risk and return. The investors expects to be maximize their return for a certain level of risk, or minimize the risk for a certain level of return. The expected return measured in mean value and the risk is measured in variance. The optimization of portfolio return and risk is called mean variance optimization. Markowitz considered mean-variance on his work and use as the whole criteria for portfolio selection (BOAMAH 2012). Markowitz developed a mathematical model for portfolio selection using an efficient portfolio that maximize expected return for a certain level of variance or minimize variance for certain level of return (Salomons 2007).

Markowitz argued that investor should choose the portfolio for any level of expected return with minimum variances from set of possible portfolios that can be made. The set of possible portfolios called as feasible set. In the feasible set, the portfolios with minimum variance are called mean-varianceefficient portfolios. As such the efficient frontier is formed from the combination of mean-varianceefficient portfolios. Each portfolios constructed in the efficient frontier has highest expected return at certain level of risk or lowest risk for a given level of expected return than any portfolios below the efficient frontier. This benefit arises due to the diversification effect where correlation among return of assets are imperfect. Because the efficient frontier is constructed with portfolios of assets rather than individual assets. The end one point of efficient frontier represent the portfolio with highest expected return and another and point represents portfolios with lowest risk (Reilly & Brown 2011).

#### SELECTION OF THE OPTIMAL PORTFOLIO

Investors are normally risk averse and they are expect to have higher return at minimum risk. The risk averse investors tradeoff more risk to get more expected return. In other words they expects higher return for assuming high risk of investments (Sharifzadeh 2010). However in practice the risk attitude is varies among investors. Therefore selection of portfolio also varies among investors. They choice the portfolios in the efficient frontier based on the risk tolerance of the investors. Because Different portfolios have different risk return combinations in the efficient frontier. The selection process of optimal portfolio and behavior of investor can be explained by theory of choice, utility function, indifference curve and efficient frontier.

Individual solves the choice problems by selecting the one which gives maximum utility value in given set of constrains. The theory assumed that the decision making process of individuals based on optimization of utility function. The utility function can be express by indifference curves. For a given investor all points in an indifference curve gives same level of utility with different risk return combination. The indifference curves are parallel for an individual and different for each individual according to the risk return combination. The indifference curve has higher utility than the indifference curve below it and lower utility than above curve in it.

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- Quote paper
- Mohamed Ismail Mohamed Riyath (Author), 2015, An Overview of Asset Pricing Models, Munich, GRIN Verlag, https://www.grin.com/document/310573

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