This chapter introduces modern portfolio theory in a simpli. The expected value is often referred to as the mean, or the average, of a distribution. Training on mean variance portfolio theory concepts for ct 8 financial economics by vamsidhar ambatipudi. We call the ratio r x 1 x 0 the return on the asset. Mean meanvariance analvariance analysis portfolio theory portfolio theory p f li f i ffi i f i portfolio frontier, efficient frontier, capm capm intuition 3.
We begin with the meanvariance analysis of markowitz 1952 when there is no riskfree asset and then move on to the case where there is a riskfree asset available. This is consistent with expected utility theory only under limited conditions, but these. The market portfolio is efficient since it is on the efficient frontier. By noel amenc, veronique le sourd portfolio theory and performance analysis by noel amenc, veronique le sourd for many years asset management was considered to be a marginal activity, but today, it is central to the development of financial industry throughout the world. Unsystematic risk portfolio risk sr usr total risk 5 10 15 20 number of shares. However, assets with high return usually correlate with high risk. With regard to measuring risk and reward, a number of assumptions are set forth for the remainder of the course. Second, an investor will want to minimize the risk of the portfolio. Meanvariance portfolio analysis and the capital asset. Mean variance analysis uses variance as the single measure of risk. Meanvariance analysis modern portfolio theory identifies two aspects of the investment problem. The theory of portfolio selection presented in thisentry,oftenreferredtoasmeanvarianceportfolio analysis or simply meanvariance analysis, isanormativetheory. The measure of risk by variance would place equal weight on the upside deviations and downside. As an indication of the limitations of mean variance optimization, this portfolio is identified as the least risky.
Meanvariance analvsis and the diversification of risk leigh j. Suppose we purchase an asset for x 0 dollars on one date and then later sell it for x 1 dollars. The fundamental goal of portfolio theory is to optimally allocate your investments between different assets. Meanvarianceskewnesskurtosis portfolio optimization with return and liquidity xiaoxin w. Modern portfolio theory identifies two aspects of the investment problem. Let v1 and v2 be the dollar amount invested in asset 1 and 2, respectively. The median and the mode are other measures of location.
Pdf the analysis on the portfolio theory and the capital asset pricing model doubtfully comply with shariah. Meanvariance analysis and the diversification of risk casualty. This book evaluates the origins of modern portfolio theory mpt as a guide for further study. The purpose of the present book, originally published in 1987, is to present a comprehensive and accessible account of the general meanvariance portfolio analysis, and to illustrate its usefulness in the practice of portfolio management and the theory of capital markets. Portfolio return rates an investment instrument that can be bought and sold is often called an asset.
The expected return and risk measured by the variance are the two main characteristics of a portfolio. Its key insight is that an assets risk and return should not be assessed by itself, but by how it contributes to a portfolios overall risk and return. In the markowitz meanvariance portfolio theory, one models the rate of returns on assets as. There is no inevitable connection between the validity of the expected utility maxim and the validity of portfolio analysis based on, say, expected return and. Modern portfolio theory mpt, or meanvariance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk, defined as variance. The analysis on the portfolio theory and the capital asset pricing model doubtfully comply with shariah. Meanvariance analysis is the theoretical foundation of modern portfolio theory established by professor harry markowitz and much of the material covered in this module traces its roots concept.
This linear relationship does not hold in an ex post setting when monthly or quarterly returns are used. The meanvariance, or riskreturn, approach to portfolio analysis is based upon the premise that the investor in allocating his wealth between different assets takes into account, not only the returns expected from alternative portfolio combinations, but also the risk attached to each such holding. All individual optimal portfolios are located on the halfline originating at point 0. The legacy of modern portfolio theory it is illegal to. Markowitzs meanvariance theory with method using modern approach to risk measure mean. Thus, as per the modern portfolio theory, expected returns, the variance of these returns and covariance of the returns of the securities within the portfolio are to be considered for the choice of a portfolio. A portfolio is said to be efficient, if it is expected to yield the highest return possible for the lowest risk or a given level of risk. Active management is based on the mathematics and principles of risk and return from basic meanvariance portfolio theory, but with a focus on. It is an investment theory based on the idea that riskaverse investors can. Given a choice of a 10 percent return versus a 5 percent return with the same degree of. In meanvariance analysis, only the first two moments are considered in the port folio model. Beardsley1, brian field2 and mingqing xiao3 abstract in this paper, we extend markowitz portfolio theory by incorporating the mean, variance, skewness, and kurtosis of both return and liquidity into an investors objective function. Mean variance optimization mvo is a quantitative tool that will allow you to make this allocation by considering the tradeoff between risk and return.
This reading covers a number of key concepts and principles associated with active portfolio management. Meanvarianceskewnesskurtosis portfolio optimization. Based on the pioneering work of harry markowitz and john tobin we learn how anybody with todays software and a reasonable financial education can model risky investment portfolios. Investors prefer high to low return and low to high risk. Harry markowitzs meanvariance model for portfolio choice posits a linear relationship between the return of a portfolio and the returns of its component securities. This video lecture introduces the portfolio as a combination of securities and offers guidelines for what constitutes a good portfolio. Financial economics i slide 057 asset portfolio a meanvariance dominates asset portfolio b if.
Meanvariance analysis in portfolio choice and capital. One key result of the above analysis is the two mutual fund theorem. Mean variance portfolio theory simply explained youtube. We describe in detail the interplay between objective and constraints in a number of singleperiod variants, including semivariance models. Modern portfolio theory mpt, which originated with harry markowitzs seminal paper portfolio selection in 1952, has stood the test of time and continues to be the intellectual foundation for realworld portfolio management. Markowitz theory of portfolio management financial economics. These functions are meant to be used for learning the basics of portfolio theory. Portfolio theory video lectures and slides finance. A through guide covering modern portfolio theory as well as the recent developments surrounding it.
Modern portfolio theory mpt, or meanvariance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. We can invest in two non dividend paying stocks amazon a and boeing b over the next month. Anormativetheoryisone that describes a standard or norm of behavior that investors should pursue in. Meanvariance portfolio analysis and the capital asset pricing model 1 introduction in this handout we develop a model that can be used to determine how a riskaverse investor can choose an optimal asset portfolio in this sense. Markowitz in the 1950s developed meanvariance analysis, the theory of combining risky assets so as to minimize the variance of return i. An investor is supposed to be riskaverse, hence heshe wants a small variance of the. Even harry markowitz, the father of modern portfolio theory, viewed downside risk as a better way to assess risk than the meanvariance framework that he ultimately proposed and that has since. Sample portfolios and the efficient frontier without a riskfree security. In practice an investor would like to have the highest return possible. Meanvariance optimization and the capm these lecture notes provide an introduction to meanvariance analysis and the capital asset pricing model capm.
Meanvariance analysis and the diversification of risk. The basic principle underlying modern portfolio theory is that for a given level of expected return, a rational investor would choose the portfolio with minimum variance from among the set of. First, an investor will want to maximize the expected rate of return on the portfolio. Diversification and portfolio risk p p the standard deviation sr. Meanvariance models in portfolio analysis 33 bothalgorithmsandhardware. A meanvariance analysis is the process of weighing risk variance against expected return. Then the theory will be illustrated by deriving the efficient frontier of a portfolio of stocks, treasury bonds, and treasury bills, as discussed in ibbotsons stocks. The hm model is also called meanvariance model due to the fact that it is based on expected returns mean and the standard deviation variance of the various portfolios. I struggled with this concept back at university and i hope this video clears up your understanding. Meanvariance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. Modern portfolio theory mpt is a theory on how riskaverse investors can construct portfolios to optimize or maximize expected return based on a given level of market risk, emphasizing that risk.
It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. The assumptions underlying the meanvariance analysis are summarized below. The basic principle underlying modern portfolio theory is that for a given level of expected return, a rational investor would choose the portfolio with minimum variance from among the set of all possible portfolios. Meanvariance analysis and the capm are certainly two of the bestknown and most often used tools of modern finance theory. Some problems with the markowitz meanvariance model. A frontier portfolio is one which displays minimum variance among all. Particular emphasis is laid on avoiding the penalization of overperformance. Meanvariance analysis the tenants of meanvariance analysis are rather simple.