...Assumptions of Portfolio Theory • Investors are rational. • Investors are basically risk averse. • Investors wants to maximize the returns from his/her investments for a given level of risk. • Investor portfolio includes all of his/her assets and liabilities. • The relationship between the returns of assets in the portfolio is important since the returns from these investments interact with each other. Risk Aversion • Portfolio Theory assumes investors are basically risk averse. • Risk aversion means an investor, given a choice between two assets with equal rates of return, will select the asset with the lower level of risk. • Does not imply everybody is risk averse. • Most investors when committing large sums of money in developing an investment portfolio are risk averse. • This means investors expect a positive relationship between expected return and expected risk. Definition of Risk • Risk is the uncertainty of future outcomes. • Probability of an adverse outcome. Markowitz Portfolio Theory • Developed by Harry Markowitz in the 1950s. • Won a Nobel Prize for his work. • Basic portfolio model derived the expected rate of return for a portfolio of assets and an expected risk measure. Markowitz Portfolio Theory • He used variance of the rate of return as a measure of portfolio risk under a reasonable set of assumptions. • He also derived the formula for computing variance of a portfolio. Assumptions of Markowitz Model • Investors consider each investment...
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...Modern Portfolio Theory in the Modern Economy: MPT During the Credit Crisis 0f 2008 Abstract There are various theories of risk and return as it pertains to measuring and predicting investment return in a portfolio- one of the oldest and most prominent being Modern Portfolio Theory .An example of a hypothetical portfolio utilizing the principles of MPT invested during the credit crisis of late 2008/early 2009 will be utilized in part. In direct application, does Modern Portfolio theory hold strong during a major financial crisis? Past research will be compared to present the mechanics and applications of MPT order to answer the questions poised and to create hypothetical portfolios based on past fund performance during the time period of 2007 -2010. It is expected that a portfolio using MPT would not have performed significantly better than any other less diversified investment. Contents Introduction……………………………………..........................................................................4-7 Credit Crisis Thesis Statement Modern Portfolio Defined Prior Research Prediction Method…………………………………………………….........................................................8-9 Parameters/ Source of Portfolios Results……………………………………………………......................................................10-19 A. Application/ graphs Conclusion…………………………………………...............………………………............19-20 Restatement of Thesis Discussion of Results Limitations Recommendation References……………………………………………………………………...
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...fundamentals of the modern portfolio theory In the first paragraph we show the crucial differences between the modern portfolio theory and pre-Markowitz one, summarize the mathematical framework of the MPT and critically evaluate the core assumptions building the MPT. This paragraph is devoted to the second stage of the portfolio selection process assuming that all input parameters of the model are true. 2.1 Definition of the modern portfolio theory Harry Markowitz is highly regarded as a pioneer in theoretical justification of investor’s behavior and development of optimization model for portfolio selection process. In 1990, Markowitz shared a Nobel Prize for his contributions to financial economics and corporate...
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...The Development of Modern Finance "A Short History of Value" David Roubaud & Jean-Charles Bagneris 10/2011 The Main Steps of the Theory Building • Portfolio Selection (Markowitz, 1952) • CAPM (Sharpe, 1963) • Financing and Dividend Decisions Neutrality (Modigliani et Miller, 1958, 1961,1963) • Efficient Markets (Fama, 1965, 1970) • Options Pricing Theory (Black & Scholes, 1973, Myers, 1977) • Agency Theory (Jensen, Meckling, 1976) • Efficient Markets II (Fama, 1991) • Behavioural Finance (Kahneman & Tversky, 1979, Shiller, 1981, 2000) Portfolio Selection • Investors are rationals and risk averse • Diversification lowers specific risk • Any portfolio is a combination of the market portfolio and the riskless asset The CAPM Capital Asset Pricing Model • Systematic risk of an asset is measured by its beta coefficient • The model calibrates the risk-return relationship • Simple, elegant and linear model => big success • Low explaining power (strong assumptions) • Alternative models are difficult to use 1 The Development of Modern Finance 2 Financial Markets Efficiency "At any given point in time, assets prices on financial markets account for all available information." • Strong assumptions on: – markets organization – investors behaviour • One consequence of EMH is Random Walk Hypothesis • Assumptions are not always true: 3 forms of efficiency (strong, semi-strong, weak) The irrelevance of financing and dividends decisions In a world without taxes and with perfect financial markets...
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...Review on Modern Portfolio theory Historical development and current state of theory: Modern Portfolio theory is developed by Markowitz (1952, 1959). Portfolio problem has been formulated as an option of the variance and mean of an asset portfolio. If investors concern on the return distributions for a single period, the mean and variance portfolio theory need to be developed to find the optimum portfolio. Then the investors need to find out the mean and the variance of return for each asset in the portfolio for that single period. Markowitz also has proved the fundamental theorem of mean variance theory, which are holding variance constant, maximize the expected return, as well as holding constant the expected return minimize variance. Based on these principles and individual risk return preferences, investors could choose their preferred portfolio and form the optimum efficient frontier. Issues in estimating the key inputs for portfolio theory There are two different models are used, which are index models and covariance estimates. The single-index model was developed and popularized by Sharpe (1967). However, multi-index model was developed to better explain the theory. Multi-index models can be used to provide inputs for a portfolio optimization technique; it also can be used to understand the sensitivity of the portfolio to various economic influences. If we make additional assumption that Capital Asset Pricing Model (CAPM) holds and ignore insight of Fama...
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...1. INTRODUCTION 1.1. INDUSTRY ALLOCATION The assets, combined in this portfolio, have been chosen from three different industries – banking, retail and drug manufacturing industry. Each industry has its own characteristics and distinguishes from one another, for the purpose of creating a diversified portfolio. Factors, affecting the banking sector and Barclays Bank (the chosen asset) are related to the current economic crisis, interest rates and the policy led by the government (either encouraging spending or saving). On the other hand the retail industry, represented by Marks and Spencer in this portfolio, is affected by the current economic climate in term of disposable and discretionary income. The final industry, drug manufacturing, which is most dependent on research and development, which incur high input costs and require a lot of testing (meaning the business process is time-consuming), is represented by GlaxoSmithKline. The three industries can be affected by completely different factors in nature. 1.2. PORTFOLIO CONSTRUCTION This portfolio was constructed by stocks, listed only on the London Stock Exchange (LSE), with no interaction with emerging markets. Although international diversification is not present, the unsystematic risk is lower due to the investment in already developed market (LSE), allowing enough liquidity and establishing fair price of the assets. The three companies (Barclays Bank, Marks and Spencer and GlaxoSmithKline) are all blue chips, with...
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...FINANCE PORTFOLIO ANALYSIS FINAL WORK DESCRIPTIVE ANALYSIS AND APPLICATION OF THE PORTFOLIO THEORY Abstract The main objective of the work is to construct, through application of the Portfolio theory, an efficient frontier which represents a set of portfolios with optimum risk-return ratio for ten companies from Mexican IPC. The sample used in this work is composed of the most representative companies in this index. A descriptive analysis of the behavior of the stocks included in this study is carried out using the binomial risk-return, which significantly contributes in selecting the most suitable stocks to be included in the portfolio. The work is concluded with finding an optimal portfolio for a risk adverse investor. The main conclusions from study are the poor performance of the construction sector, which holds the lowest returns, the highest risk and negative performance ratios, and the usefulness of the theory of portfolios to get a set of portfolios with higher returns and lower risk than the general Mexican IPC index that represents the market. The importance of diversification of assets is also noted. Keywords: Portfolio theory, Efficient Frontier, Risk-Return, Minimum Variance, Portfolio Contents 1. Introduction 6 1.1 Introduction 6 1.2 Goals 7 1.3 Methodology 7 1.4 Structure 9 2. Theoretical Framework 11 2.1 Risk and Return 11 2.1.1 Portfolio’s Expected Return 12 2.1.2 Portfolio Risk (Standard Deviation) 13 2.2 Diversification...
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...Economics Financial Theory Ben McClure Contact | Author Bio Advertisement No matter how much we diversify our investments, it's impossible to get rid of all the risk. As investors, we deserve a rate of return that compensates us for taking on risk. The capital asset pricing model (CAPM) helps us to calculate investment risk and what return on investment we should expect. Here we look at the formula behind the model, the evidence for and against the accuracy of CAPM, and what CAPM means to the average investor. Birth of a Model The capital asset pricing model was the work of financial economist (and, later, Nobel laureate in economics) William Sharpe, set out in his 1970 book "Portfolio Theory And Capital Markets." His model starts with the idea that individual investment contains two types of risk: Systematic Risk - These are market risks that cannot be diversified away. Interest rates, recessions and wars are examples of systematic risks. Unsystematic Risk - Also known as "specific risk," this risk is specific to individual stocks and can be diversified away as the investor increases the number of stocks in his or her portfolio. In more technical terms, it represents the component of a stock's return that is not correlated with general market moves. Modern portfolio theory shows that specific risk can be removed through diversification. The trouble is that diversification still doesn't solve the problem of systematic risk; even a portfolio of all the shares...
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...Judge the Risk by Portfolio When the investors put their money into the stock market, it means that they must take the risk of the stock market, because risk is one of the natural qualities of the stock market. One company easy to get a poor performance and its stocks will go down. Therefore, there will be no way to complete avoid risk, but judge it. In finance, risk is best judged in a portfolio context. Because the possibility that many companies gets serious performances, and their stock price go down at the same time is lower than for only one company. This essay will discuss that why the portfolio context is the best way to judge the risk in the finance market. The first part will introduce the basic theories for portfolios. The methods of measuring risks and value of the portfolio will be explained in the second part to demonstrate that why it is better select portfolios. The third part will give the example of family groupings on performance of portfolio selection in the Hong Kong stock market. The conclusion will be given at the end of the essay. Firstly, the theory of portfolio and the five suppositions of portfolio selection need to be explained before the following discussion of the value of portfolios. The article ‘Portfolio Selection’, which was issued on Journal of Finance in 1952 and the book ‘Portfolio Selection: Efficient Diversification of Investments’ which was published in 1959 was known as the opening if the modern portfolio theory. The author of these...
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...The Portfolio Theory also known as Modern Portfolio Theory was first developed by Harry Markowitz. He had introduced the theory in his paper ‘Portfolio Selection’ which was published in the Journal of Finance in 1952. In 1990, he along with Merton Miller and William Sharpe won the Nobel Prize in Economic Sciences for the Theory. The theory suggests a hypothesis on the basis of which, expected return on a portfolio for a given amount of portfolio risk is attempted to be maximized or alternately the risk on a given level of expected return is attempted to be minimized. This is done so by choosing the quantities of various securities cautiously taking mainly into consideration the way in which the price of each security changes in comparison to that of every other security in the portfolio, rather than choosing securities individually. In other words, the theory uses mathematical models to construct an ideal portfolio for an investor that gives maximum return depending on his risk appetite by taking into consideration the relationship between risk and return. According to the theory, each security has its own risks and that a portfolio of diverse securities shall be of lower risk than a single security portfolio. Simply put, the theory emphasizes on the importance of diversifying to reduce risk. Early on, investors stressed on individually picking high yielding stocks to earn maximum profits. So if one particular industry was offering good returns; an investor would have landed...
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...Efficient portfolio & Stock market efficiency Prepared by: Ahmed Mohamed Ahmed Zaki Nofal Submitted to: Dr.Tarek el Domiaty Modern portfolio theory Modern portfolio theory (MPT) is a theory of finance which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. Although MPT is widely used in practice in the financial industry and several of its creators won a Nobel memorial prize[1] for the theory, in recent years the basic assumptions of MPT have been widely challenged by fields such as behavioral economics. MPT is a mathematical formulation of the concept of diversification in investing, with the aim of selecting a collection of investment assets that has collectively lower risk than any individual asset. That this is possible can be seen intuitively because different types of assets often change in value in opposite ways. For example, to the extent prices in the stock market move differently from prices in the bond market, a collection of both types of assets can in theory face lower overall risk than either individually. But diversification lowers risk even if assets' returns are not negatively correlated—indeed, even if they are positively correlated More technically, MPT models an asset's return as a normally distributed function (or more generally as an elliptically distributed random...
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...Harry Markowitz, who’s earlier work, introduced the theory of modern portfolio and diversification. Along with Markowitz (1952), he began the theory of the model in 1956 when he was trying to find a dissertation topic. He built on Markowitz’s suggestions and set out his developed theory in his book “Portfolio Theory and Capital Markets.” (1970). This essay will try to outline the Capital Asset Pricing Model, explain the theory behind the model and outlay its uses. This will be done by using legal texts, journals and other resources. It is never possible to get rid of all the risk when investing and the actual return on an investment may differ from what the investor expects. For that reason investors always look for a rate of return that will repay them for their risk taking. The Capital Asset Pricing Model (CAPM) is a model that relates risk and return, helping investors calculate the risk of the investment and the return on the investment that should be expected. Haim Levy and Thierry Post (2005, p883) define the model as an “equilibrium asset-pricing model that predicts a linear relationship between expected return and beta.” It would be assumed that if an investor has decided to invest in a number of companies, the risk of the portfolio would be the average risk of each of the investments. However, the portfolio risk is in fact smaller therefore; the overall risk can be reduced by diversifying the investments in a portfolio. This is done by investing in a variety of investments...
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...Premium และคำนวณ Standard Deviationเพื่อนำไปคำนวณหา Sharpe Ratio ที่มีอัตราส่วนที่สูงที่สุด ซึ่งอธิบายถึงผลตอบแทนที่ถูกปรับด้วยความเสี่ยง ที่ดีที่สุด เมื่อได้ทำการวิเคราะห์และคำนวณ Sharpe Ratio แล้ว พบว่า หุ้นที่เหมาะสมที่จะทำการลงทุนเพิ่ม ได้แก่ Pioneer Gypsum โดยลงทุนในสัดส่วน 4% จึงทำให้การลงทุนในตลาดเป็น 96% เนื่องจากเป็นสัดส่วนที่ทำให้ Sharpe Ratio มีค่าสูงที่สุด คือ 0.4702 ซึ่งถือได้ว่าเป็นการกระจายการลงทุนที่ทำให้ความเสี่ยงลดลง ซึ่งสอดคล้องกับทฤษฎี Modern Portfolio Theory ของ Harry M. Markowitz (1952) ที่กล่าวไว้ว่า “Don’t put all your eggs in one basket” สรุปรายละเอียดของ Mini-Case : John & Marsha on Portfolio Selection John ทำหน้าที่บริหาร Portfolio ซึ่งมีมูลค่า 125 ล้านดอลลาร์ของนักลงทุนอยู่ เขาปรึกษากับ Marsha เกี่ยวกับปัญหาของการบริหารจัดการหุ้นใน Portfolio ของเขา โดย John คิดว่าที่ผ่านมาผลตอบแทนจาก portfolio ที่เขาดูแลอยู่นั้นมักจะใกล้เคียงกับอัตราผลตอบแทนของตลาดและอิงจากกราฟ S&P 500 market index ที่จัดทำขึ้น เขาจึงรู้สึกว่าการบริหารของเขาอ้างอิงแต่กับตัวเลขของตลาดมากเกินไป เขาอยากจะบริหารจัดการ portfolio เสียใหม่ให้มีความเป็นตัวของตัวเองมากขึ้น และได้รับผลตอบแทนที่สูงขึ้นกว่าอัตราผลตอบแทนของตลาด เพื่อทำให้การทำงานของเขามีประโยชน์ต่อลูกค้ามากขึ้น โดยเขาเลือกบริษัทที่ราคาตลาดของหุ้นต่ำกว่ามูลค่าที่ประเมินได้ (Undervalued) และที่ราคาตลาดของหุ้นสูงกว่ามูลค่าหุ้นที่ประเมินได้ (Overvalued) ามาส่วนหนึ่ง โดยบริษัทที่เขาคาดว่าน่าจะมีมูลค่า Undervalued และสมควรซื้อมากคือบริษัท Pioneer Gypsum และหุ้นของ Global mining นั้น Overvalued จึงไม่สมควรซื้อโดยข้อมูลต่างๆของทั้ง2บริษัทที่เขาหามาได้มีค่าตามตารางนี้ ...
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... CAPM Yasmeen Iman Snow Deforest Thompson Gary Oha CAPM Contents Overview of CAPM 1 Advantages and Limitations 3 Breakthroughs and Setbacks 4 Works Cited 6 Overview of CAPM The CAPM was introduced by Jack Treynor , William F. Sharpe , John Lintner and Jan Mossin in 1964, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory (Fama & French, 1982). Sharpe, Markowitz and Merton Miller jointly received the 1990 Nobel Memorial Prize in Economics for this contribution to the field of financial economics. Fischer Black developed another version of CAPM, called Black CAPM or zero-beta CAPM that does not assume the existence of a riskless asset. This version was more robust against empirical testing and was influential in the widespread adoption of the CAPM (Fama & French, 1982). CAPM has become very attractive as a tool that measures risk to possible in relation to expected return, although it is still widely used for estimating the cost of capital for firms and evaluating the performance of managed portfolios. While CAPM is accepted academically, there is empirical evidence suggesting that the model is not as profound as it may have first appeared to be. CAPM’s empirical fallings arise theoretically from many over simplified assumptions made by the model. This has made it difficult to implement valid test for this model (Kristina Zucchi, 2015). For example according to the CAPM model the risk...
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... • Financial intermediaries • Primary market, secondary market • Oder details • Market, limit, stop loss (stop sell) and stop buy orders • Bid ask spread, commission • Buying on margin and leverage, margin call • Short sale, margin, margin call • Unique, firm-specific diversifiable, nonsystematic risk • Market risk, beta, systematic, nondiversifiable risk • Modern portfolio theory • leverage • Minimum variance frontier, efficient frontier, global minimum variance portfolio, • Riskless asset, risky asset, optimal risky portfolio • Capital allocation line • Sharpe ratio Problems • See lecture slides and homework for clarification • Buying on margin • Short selling • NAV • Front end load, Back end load, Operating expenses, 12b-1 charges – marketing and distribution costs • Mutual fund rate of returns over several years • Types of returns – holding period, average (equal), compounded (time), dollar weighted, scenario • Stock risk – standard deviation • Portfolio returns, standard deviation and variance...
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