This document discusses portfolio selection and the basic problem faced by investors of determining which risky securities to include in their portfolio given uncertain outcomes. It covers Harry Markowitz's approach to solving this problem by focusing on an investor's initial wealth, holding period, terminal wealth, and preference for diversification. Key aspects covered include calculating portfolio expected returns and risk, indifference curves, and the risk preferences of different types of investors including risk-averse, risk-neutral, and risk-seeking.
The Capital Asset Pricing Model (CAPM) uses beta to measure the non-diversifiable risk of a security and determine its expected return. CAPM assumes investors want to maximize returns and only consider systematic risk. It models expected return as the risk-free rate plus a risk premium based on the security's beta. The Security Market Line graphs this relationship between beta and expected return. Some researchers like Fama and French have expanded CAPM with additional size and value factors.
This document defines risk and return in investments. Return is the expected profit from an investment based on current information, while risk refers to the chance of losing some or all of the original investment. Generally, investments with higher risk like equity shares have higher expected returns around 10%, while lower risk debt instruments average 3-4% returns. However, equity shares also experience more volatile short-term returns. The relationship between risk and return is such that higher risk investments offer higher potential returns. Diversifying investments across a portfolio can help reduce overall risk.
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.
1. Portfolio management is a process of optimizing investment funds through activities like security analysis, portfolio construction, selection, revision and evaluation.
2. It involves choosing securities to create portfolios that balance risk and expected return. The optimal portfolio lies on the efficient frontier which shows maximum return for each risk level.
3. Risk is measured by variability of returns. The CAPM model relates expected return and systematic risk measured by beta for efficient portfolios on the SML and all 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 efficient market hypothesis proposes that security prices reflect all available information. It comes in three forms: weak (only past prices), semi-strong (all public information) and strong (all information). Evidence supports weak and semi-strong forms, showing prices adjust to new public information. The hypothesis implies that fundamental analysis and technical analysis may not identify mispriced securities. It also provides support for low-cost index funds. While influential, the hypothesis makes assumptions and some strategies have achieved above-average returns.
The document discusses the Capital Asset Pricing Model (CAPM). It explains that CAPM provides a framework to determine the required rate of return on an asset based on its relationship to risk. It also discusses the model's assumptions and how beta is used to measure non-diversifiable risk. Further, it shows how CAPM is used to estimate the cost of equity capital and determine an investment's intrinsic value.
The Capital Asset Pricing Model (CAPM) uses beta to measure the non-diversifiable risk of a security and determine its expected return. CAPM assumes investors want to maximize returns and only consider systematic risk. It models expected return as the risk-free rate plus a risk premium based on the security's beta. The Security Market Line graphs this relationship between beta and expected return. Some researchers like Fama and French have expanded CAPM with additional size and value factors.
This document defines risk and return in investments. Return is the expected profit from an investment based on current information, while risk refers to the chance of losing some or all of the original investment. Generally, investments with higher risk like equity shares have higher expected returns around 10%, while lower risk debt instruments average 3-4% returns. However, equity shares also experience more volatile short-term returns. The relationship between risk and return is such that higher risk investments offer higher potential returns. Diversifying investments across a portfolio can help reduce overall risk.
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.
1. Portfolio management is a process of optimizing investment funds through activities like security analysis, portfolio construction, selection, revision and evaluation.
2. It involves choosing securities to create portfolios that balance risk and expected return. The optimal portfolio lies on the efficient frontier which shows maximum return for each risk level.
3. Risk is measured by variability of returns. The CAPM model relates expected return and systematic risk measured by beta for efficient portfolios on the SML and all 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 efficient market hypothesis proposes that security prices reflect all available information. It comes in three forms: weak (only past prices), semi-strong (all public information) and strong (all information). Evidence supports weak and semi-strong forms, showing prices adjust to new public information. The hypothesis implies that fundamental analysis and technical analysis may not identify mispriced securities. It also provides support for low-cost index funds. While influential, the hypothesis makes assumptions and some strategies have achieved above-average returns.
The document discusses the Capital Asset Pricing Model (CAPM). It explains that CAPM provides a framework to determine the required rate of return on an asset based on its relationship to risk. It also discusses the model's assumptions and how beta is used to measure non-diversifiable risk. Further, it shows how CAPM is used to estimate the cost of equity capital and determine an investment's intrinsic value.
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.
A bond is a debt security where the issuer owes the holder a debt and is obliged to repay the principal and interest at maturity. Bonds have features like nominal value, coupon rate, maturity date, and call/put options. There are various types of bonds like fixed rate, floating rate, zero coupon bonds, and municipal bonds. Bond portfolio strategies include passive buy and hold strategies, active strategies like sector substitution, and semi-active strategies like immunization and duration matching to reduce interest rate risk. Bonds are evaluated based on the issuer's financial strength and past earnings, while valuation considers the present value of future cash flows and yield to maturity is the single discount rate that equals the current price.
1) Total risk of a security is composed of systematic risk, which stems from external market factors, and unsystematic risk, which is specific to a company.
2) Diversifying a portfolio by holding many securities with returns that are not perfectly positively correlated can reduce total risk through lowering unsystematic risk exposure.
3) The degree of risk reduction from diversification depends on the correlation between the returns of the securities in the portfolio. Perfectly negatively correlated securities eliminate risk, while perfectly positively correlated securities do not allow for risk reduction through diversification.
The Sharpe model provides a simpler approach to portfolio optimization compared to the Markowitz model. It assumes the return of individual securities is linearly related to a single market index. This allows estimation of systematic and unsystematic risk for individual stocks based on their beta coefficient. An optimal portfolio is constructed by selecting stocks with the highest excess returns over the risk-free rate relative to their beta, up to the cutoff point where this ratio begins declining. The percentage invested in each stock is based on its beta and unsystematic risk. This results in a portfolio with the highest expected return for a given level of risk.
Portfolio revision, securities, New securities, existing securities, purchases and sales of securities, maximizing the return, minimizing the risk, Transaction cost, Taxes, Statutory stipulations, Intrinsic difficulty, commission and brokerage, push up transaction costs, reducing the gains, constraint, Taxes, capital gains, long-term capital, lower rate, Frequent sales, short-term capital gains, investment companies, constraints, established, objectives, skill, resources and time, substantial adjustments, mispriced, excess returns, heterogeneous expectations, better estimates, generate excess returns, market efficiency, little incentive, predetermined rules, changes in the securities market, Performance measurement, Performance evaluation, superior or inferior, small investors, better performance, prompt liquidity, comparative performance, purchase and sale of securities.
This document discusses various concepts related to investment returns and risk. It begins by defining return as income received plus capital gains. It then discusses the components of return including yield and capital gains. It provides a formula to calculate total return. The document then discusses various types of risk including market risk, liquidity risk, and foreign exchange risk. It also covers sensitivity analysis using range and standard deviation. Finally, it discusses portfolio returns and risks, and introduces the Capital Asset Pricing Model to relate expected returns to market risk.
CAPM was developed in 1960 as an extension of Markowitz's portfolio theory. It derives the relationship between expected return and risk of individual securities. CAPM assumes investment decisions are based on risk-return assessments and that markets are efficient. It allows investors to combine risky and risk-free assets on the efficient frontier to maximize return for a given level of risk. The model is used to price individual securities based on their beta and expected market return.
A portfolio is a combination of various investment products like bonds, shares, securities, and mutual funds. Portfolio revision involves changing the mix of securities in an existing portfolio by adding or removing assets. This is done to maximize returns and minimize risks. Reasons for portfolio revision include having additional funds to invest, changes in financial goals, or market fluctuations. There are active and passive portfolio revision strategies, with active strategies involving more frequent changes and passive only changing according to predetermined rules. The roles of a portfolio manager include designing customized investment plans, keeping up to date on the market, guiding clients impartially, and regularly communicating with clients.
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.
Arbitrage pricing theory & Efficient market hypothesisHari Ram
Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset's returns can be predicted using the linear relationship between the asset's expected return and a number of macroeconomic variables that capture systematic risk.
This document provides an overview of the Capital Asset Pricing Model (CAPM). It was developed by Sharpe and Linter based on Markowitz's portfolio theory. CAPM assumes investors will create a portfolio using risky assets and risk-free assets, such as treasury bills. It can be used to analyze the risk and return of individual securities. The model relates the expected return of securities to market risk using the security market line formula.
This document discusses dividend policy and the various theories around it. It defines dividends and discusses Walter's model and Gordon's model, which propose that dividend policy affects firm value. It also covers the irrelevance theories of Modigliani-Miller and the traditional approach, which argue that dividend policy does not impact value. The document provides formulas for the different models and discusses their assumptions and criticisms.
The document summarizes the evolution of modern portfolio theory from its origins in Harry Markowitz's mean-variance model to subsequent developments like the Sharpe single-index model and CAPM. It discusses how Markowitz showed investors could maximize returns for a given risk level by holding efficient portfolios on the efficient frontier. The Sharpe model reduced the inputs needed for portfolio risk estimation by correlating assets to a market index rather than each other. CAPM then defined the market portfolio as the efficient portfolio and allowed a risk-free asset, changing the shape of the efficient frontier.
Fundamental analysis involves analyzing macroeconomic conditions, industries, and individual companies. At the macroeconomic level, factors like GDP growth, inflation, interest rates, and fiscal/monetary policies are examined. Industry analysis evaluates the attractiveness of industries based on their growth stage, competitive environment, and sensitivity to economic cycles. Finally, company analysis assesses the financial statements, management quality, and competitive positioning of specific firms. Together, this three-tiered fundamental analysis helps investors evaluate investment opportunities.
Yield to maturity (YTM) is the total expected return an investor will receive if a bond is held until its maturity date. YTM is calculated as the internal rate of return and includes all expected cash flows such as coupon payments and principal repayment. It provides a measure of return for fixed-income investments if held to maturity. Calculating YTM involves terms such as face value, present value, coupon rate, interest rate, discount/premium, and time to maturity.
1) Portfolio construction involves blending different asset classes like stocks, bonds, and cash to obtain returns while minimizing risk through diversification.
2) There are two main approaches - the traditional approach selects securities to meet an investor's needs, while the Markowitz efficient frontier approach constructs portfolios that maximize expected return for a given level of risk.
3) The Markowitz model helps investors reduce risk by choosing securities whose returns do not move together, identifying the efficient frontier of portfolio options, and allowing investors to select the portfolio with the highest return for a given risk level.
This document provides an introduction to investment terminology and concepts. It defines key terms like finance, investment, investor, and differentiates investment from speculation and gambling. It also outlines the major participants in the financial system including households, businesses, governments, banks, insurers, pension funds, and mutual funds. Finally, it describes different types of financial securities and markets.
This presentation is an overview of Capital Structure Theories.
Dr. Soheli Ghose ( Ph.D (University of Calcutta), M.Phil, M.Com, M.B.A., NET (JRF), B. Ed).
Assistant Professor, Department of Commerce,St. Xavier's College, Kolkata.
Guest Faculty, M.B.A. Finance, University of Calcutta, Kolkata
This chapter discusses the relationship between risk and return for both individual assets and portfolios of assets. It defines risk as the chance of financial loss and explains that higher risk assets generally provide higher expected returns. The chapter covers measuring the expected return, standard deviation, and coefficient of variation of individual assets. It then explains how forming a portfolio of assets can reduce overall risk through diversification. The chapter discusses how the correlation between asset returns impacts the risk reduction from diversification. It also addresses how adding more assets to a portfolio continues to reduce non-market or unique risk.
The document discusses risk and return in investments. It defines key concepts such as realized and expected return, ex-ante and ex-post returns, sources and measurements of risk including standard deviation and coefficient of variation. It also discusses the risk-return tradeoff and how higher risk investments require higher potential returns to compensate for additional risk.
This module discusses key concepts related to investment avenues and portfolio management. It covers mutual funds, investor lifecycles, personal finance, international investing, and portfolio management of funds in banks, insurance companies and pension funds. It also provides an introduction to portfolio management, including the meaning of portfolio management, portfolio analysis, portfolio objectives, and the portfolio management process.
The document presents information on the Markowitz portfolio-optimization model. It discusses how the model provides tools for identifying portfolios that offer the highest returns for a given level of risk. It also notes that combining assets with low positive or negative correlations allows investors to reduce portfolio risk below the average risk of individual assets. The document then examines the security market line, efficient frontier, types of risk, and provides an example calculation of expected returns and risks for individual securities and a combined portfolio.
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.
A bond is a debt security where the issuer owes the holder a debt and is obliged to repay the principal and interest at maturity. Bonds have features like nominal value, coupon rate, maturity date, and call/put options. There are various types of bonds like fixed rate, floating rate, zero coupon bonds, and municipal bonds. Bond portfolio strategies include passive buy and hold strategies, active strategies like sector substitution, and semi-active strategies like immunization and duration matching to reduce interest rate risk. Bonds are evaluated based on the issuer's financial strength and past earnings, while valuation considers the present value of future cash flows and yield to maturity is the single discount rate that equals the current price.
1) Total risk of a security is composed of systematic risk, which stems from external market factors, and unsystematic risk, which is specific to a company.
2) Diversifying a portfolio by holding many securities with returns that are not perfectly positively correlated can reduce total risk through lowering unsystematic risk exposure.
3) The degree of risk reduction from diversification depends on the correlation between the returns of the securities in the portfolio. Perfectly negatively correlated securities eliminate risk, while perfectly positively correlated securities do not allow for risk reduction through diversification.
The Sharpe model provides a simpler approach to portfolio optimization compared to the Markowitz model. It assumes the return of individual securities is linearly related to a single market index. This allows estimation of systematic and unsystematic risk for individual stocks based on their beta coefficient. An optimal portfolio is constructed by selecting stocks with the highest excess returns over the risk-free rate relative to their beta, up to the cutoff point where this ratio begins declining. The percentage invested in each stock is based on its beta and unsystematic risk. This results in a portfolio with the highest expected return for a given level of risk.
Portfolio revision, securities, New securities, existing securities, purchases and sales of securities, maximizing the return, minimizing the risk, Transaction cost, Taxes, Statutory stipulations, Intrinsic difficulty, commission and brokerage, push up transaction costs, reducing the gains, constraint, Taxes, capital gains, long-term capital, lower rate, Frequent sales, short-term capital gains, investment companies, constraints, established, objectives, skill, resources and time, substantial adjustments, mispriced, excess returns, heterogeneous expectations, better estimates, generate excess returns, market efficiency, little incentive, predetermined rules, changes in the securities market, Performance measurement, Performance evaluation, superior or inferior, small investors, better performance, prompt liquidity, comparative performance, purchase and sale of securities.
This document discusses various concepts related to investment returns and risk. It begins by defining return as income received plus capital gains. It then discusses the components of return including yield and capital gains. It provides a formula to calculate total return. The document then discusses various types of risk including market risk, liquidity risk, and foreign exchange risk. It also covers sensitivity analysis using range and standard deviation. Finally, it discusses portfolio returns and risks, and introduces the Capital Asset Pricing Model to relate expected returns to market risk.
CAPM was developed in 1960 as an extension of Markowitz's portfolio theory. It derives the relationship between expected return and risk of individual securities. CAPM assumes investment decisions are based on risk-return assessments and that markets are efficient. It allows investors to combine risky and risk-free assets on the efficient frontier to maximize return for a given level of risk. The model is used to price individual securities based on their beta and expected market return.
A portfolio is a combination of various investment products like bonds, shares, securities, and mutual funds. Portfolio revision involves changing the mix of securities in an existing portfolio by adding or removing assets. This is done to maximize returns and minimize risks. Reasons for portfolio revision include having additional funds to invest, changes in financial goals, or market fluctuations. There are active and passive portfolio revision strategies, with active strategies involving more frequent changes and passive only changing according to predetermined rules. The roles of a portfolio manager include designing customized investment plans, keeping up to date on the market, guiding clients impartially, and regularly communicating with clients.
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.
Arbitrage pricing theory & Efficient market hypothesisHari Ram
Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset's returns can be predicted using the linear relationship between the asset's expected return and a number of macroeconomic variables that capture systematic risk.
This document provides an overview of the Capital Asset Pricing Model (CAPM). It was developed by Sharpe and Linter based on Markowitz's portfolio theory. CAPM assumes investors will create a portfolio using risky assets and risk-free assets, such as treasury bills. It can be used to analyze the risk and return of individual securities. The model relates the expected return of securities to market risk using the security market line formula.
This document discusses dividend policy and the various theories around it. It defines dividends and discusses Walter's model and Gordon's model, which propose that dividend policy affects firm value. It also covers the irrelevance theories of Modigliani-Miller and the traditional approach, which argue that dividend policy does not impact value. The document provides formulas for the different models and discusses their assumptions and criticisms.
The document summarizes the evolution of modern portfolio theory from its origins in Harry Markowitz's mean-variance model to subsequent developments like the Sharpe single-index model and CAPM. It discusses how Markowitz showed investors could maximize returns for a given risk level by holding efficient portfolios on the efficient frontier. The Sharpe model reduced the inputs needed for portfolio risk estimation by correlating assets to a market index rather than each other. CAPM then defined the market portfolio as the efficient portfolio and allowed a risk-free asset, changing the shape of the efficient frontier.
Fundamental analysis involves analyzing macroeconomic conditions, industries, and individual companies. At the macroeconomic level, factors like GDP growth, inflation, interest rates, and fiscal/monetary policies are examined. Industry analysis evaluates the attractiveness of industries based on their growth stage, competitive environment, and sensitivity to economic cycles. Finally, company analysis assesses the financial statements, management quality, and competitive positioning of specific firms. Together, this three-tiered fundamental analysis helps investors evaluate investment opportunities.
Yield to maturity (YTM) is the total expected return an investor will receive if a bond is held until its maturity date. YTM is calculated as the internal rate of return and includes all expected cash flows such as coupon payments and principal repayment. It provides a measure of return for fixed-income investments if held to maturity. Calculating YTM involves terms such as face value, present value, coupon rate, interest rate, discount/premium, and time to maturity.
1) Portfolio construction involves blending different asset classes like stocks, bonds, and cash to obtain returns while minimizing risk through diversification.
2) There are two main approaches - the traditional approach selects securities to meet an investor's needs, while the Markowitz efficient frontier approach constructs portfolios that maximize expected return for a given level of risk.
3) The Markowitz model helps investors reduce risk by choosing securities whose returns do not move together, identifying the efficient frontier of portfolio options, and allowing investors to select the portfolio with the highest return for a given risk level.
This document provides an introduction to investment terminology and concepts. It defines key terms like finance, investment, investor, and differentiates investment from speculation and gambling. It also outlines the major participants in the financial system including households, businesses, governments, banks, insurers, pension funds, and mutual funds. Finally, it describes different types of financial securities and markets.
This presentation is an overview of Capital Structure Theories.
Dr. Soheli Ghose ( Ph.D (University of Calcutta), M.Phil, M.Com, M.B.A., NET (JRF), B. Ed).
Assistant Professor, Department of Commerce,St. Xavier's College, Kolkata.
Guest Faculty, M.B.A. Finance, University of Calcutta, Kolkata
This chapter discusses the relationship between risk and return for both individual assets and portfolios of assets. It defines risk as the chance of financial loss and explains that higher risk assets generally provide higher expected returns. The chapter covers measuring the expected return, standard deviation, and coefficient of variation of individual assets. It then explains how forming a portfolio of assets can reduce overall risk through diversification. The chapter discusses how the correlation between asset returns impacts the risk reduction from diversification. It also addresses how adding more assets to a portfolio continues to reduce non-market or unique risk.
The document discusses risk and return in investments. It defines key concepts such as realized and expected return, ex-ante and ex-post returns, sources and measurements of risk including standard deviation and coefficient of variation. It also discusses the risk-return tradeoff and how higher risk investments require higher potential returns to compensate for additional risk.
This module discusses key concepts related to investment avenues and portfolio management. It covers mutual funds, investor lifecycles, personal finance, international investing, and portfolio management of funds in banks, insurance companies and pension funds. It also provides an introduction to portfolio management, including the meaning of portfolio management, portfolio analysis, portfolio objectives, and the portfolio management process.
The document presents information on the Markowitz portfolio-optimization model. It discusses how the model provides tools for identifying portfolios that offer the highest returns for a given level of risk. It also notes that combining assets with low positive or negative correlations allows investors to reduce portfolio risk below the average risk of individual assets. The document then examines the security market line, efficient frontier, types of risk, and provides an example calculation of expected returns and risks for individual securities and a combined portfolio.
The document summarizes the Markowitz model for building optimal investment portfolios. It discusses key aspects of the model such as diversification to reduce risk, defining the efficient frontier of portfolios with maximum return for a given level of risk, and including both risky and risk-free assets as well as leverage to construct portfolios. The model provides a framework for investors to analyze risk and return tradeoffs across different portfolio combinations.
1. The document discusses portfolio selection using the Markowitz model.
2. The Markowitz model aims to find the optimal portfolio, which provides the highest return and lowest risk. It does this by analyzing different combinations of securities to identify efficient portfolios.
3. The document provides details on the tools and steps used in the Markowitz model for portfolio selection, including analyzing expected returns, variance, standard deviation, and coefficients of correlation between securities.
This chapter discusses risk and return in investments. It covers (1) how investments involve uncertainty and investors must focus on expected returns and consider risk, (2) the concepts of risk, return distributions and probabilities, (3) how expected value, variance and standard deviation are used to quantify risk, and (4) how a portfolio's risk is reduced through diversification.
This document discusses various topics related to equity valuation and stock markets, including the dividend discount model for valuing stocks, primary and secondary markets, common terminology such as market capitalization and P/E ratio, and different approaches to analyzing stocks like fundamental analysis and the efficient market hypothesis. Key valuation techniques introduced are the dividend discount model under different growth scenarios as well as valuing the present value of growth opportunities.
The document discusses an event study conducted by a financial analyst to test the semi-strong form of market efficiency. The analyst examined 4 companies that announced dividend increases and calculated the characteristic lines for each company based on weekly returns over the prior 6 years. Abnormal returns were then calculated for each company over the 4 weeks before and after the announcement date. The average abnormal returns and cumulative average abnormal returns were close to zero, supporting the semi-strong form hypothesis that the market incorporated the information of the dividend increases prior to the official announcement.
The document discusses various methods for valuing different types of securities. It covers the valuation of debentures, preference shares, and equity shares. For debentures and preference shares, the valuation models discount future interest and principal cash flows to arrive at a present value. For equity shares, the dividend capitalization approach discounts expected future dividends, while the earnings capitalization approach discounts future earnings. Growth must be considered for shares but not for debentures or preference shares that offer fixed cash flows.
The Markowitz Model assists investors in selecting efficient portfolios by analyzing possible combinations of securities. It helps reduce risk through diversification by choosing securities whose price movements are not perfectly correlated. The model determines the efficient set of portfolios and allows investors to select the optimal portfolio based on their preferred risk-return tradeoff. Markowitz introduced diversification and showed holding multiple lower-risk securities can reduce overall portfolio risk compared to a single higher-risk security. The model calculates expected returns, variances, and correlations between securities to determine the minimum risk portfolio for a given level of return.
1) Portfolio theory shows that risk and return are negatively correlated, and diversification across many assets reduces unsystematic risk. Only systematic risk cannot be eliminated through diversification.
2) The efficient frontier graphs the set of optimal portfolios that maximize return for a given level of risk. The capital market line depicts the combination of investments in the market portfolio and risk-free asset.
3) The Capital Asset Pricing Model derives the security market line relationship between risk and return, defining risk as an asset's beta coefficient measuring its volatility relative to the market.
Exploring the role of technology in support of the ecosystem approachIna Smith
This document discusses the role of technology in supporting the ecosystem approach to libraries and information services. It defines key terms like ecosystem and digital citizenship. It outlines South Africa's Library and Information Services Transformation Charter which aims to promote literacy, access to information, and a modern library system. The document argues that integrating libraries, information technologies, literacy and information literacy can drive economic growth and social development. It highlights challenges like uneven access to technologies and proposes solutions like ensuring broadband access in all libraries and updating library education.
New Media New Technology Workshop 2, theme 'Space', Spring Semester 2015, Media Technology MSc Leiden University. See https://sites.google.com/site/newmedianewtechnology2015/
This document identifies the top "lemoneighborhoods" or ideal locations for lemonade stand success in the US. It analyzes data from Century21.com on factors like temperature, population density, income and education for the top 10 hottest cities. Beverly Hills, Coral Gables and Austin scored highest based on their temperatures, families with kids, and other criteria like tree to hammock ratios. To test the findings, lemonade stands were set up in each area and all generated $32.50 in revenue over 2 hours, confirming the top lemoneighborhood selections. The document recommends using C21.com for related real estate and business research.
The document discusses various types of waste in schools and recommendations to reduce waste. It notes that schools should use recycling bins, turn off lights and computers when not in use, and install energy efficient systems. For food waste, it suggests giving students the right amount of food to reduce leftovers and having students bring lunches to reduce aluminum trash. The document also provides examples of recycling paper, plastic, metal and glass, and lists international organizations focused on environmental issues like the Earth Day and Earth Hour.
The document discusses various approaches to marketing and getting buy-in for an institutional repository from internal and external stakeholders. Internally, it recommends training librarians, hosting information sessions, creating newsletters and web content, and leveraging champions. Externally, it suggests engaging with harvesters, directories, and services to increase international exposure. Metrics and impact monitoring are also addressed. The overall aims are to promote awareness and use of the repository through effective communication and collaboration across the institution.
This document discusses Markowitz portfolio theory and the portfolio selection problem. It introduces the basic problem of determining which risky securities an investor should hold given uncertain outcomes. It describes Markowitz's approach which involves assuming an initial wealth, a holding period of one period, a terminal wealth, and diversifying across securities. It defines how to calculate the expected return and risk of a portfolio as a weighted average of the individual securities. It also discusses indifference curves and how they graphically represent combinations of risk and return that provide the same level of utility for the investor.
The document discusses key concepts for investment analysis and project selection, including:
1) Projects should yield a return greater than the minimum hurdle rate, which is higher for riskier projects. Returns should consider cash flows, timing, and side effects.
2) The optimal financing mix minimizes the hurdle rate and matches the assets financed.
3) If not enough high-returning investments exist, excess cash should be returned to stockholders.
Portfolio construction involves blending different asset classes like stocks, bonds, and cash to obtain the optimal risk-return tradeoff. Diversification across many assets reduces unsystematic risk. The traditional approach selects securities to meet an investor's needs, while the Markowitz model constructs portfolios on the efficient frontier with maximum return for a given risk. The Capital Market Line shows the combination of risky and risk-free assets that is optimal for an investor given their risk tolerance.
Japanese firms rely more heavily on bank financing and internal cash flows, while U.S. firms rely more on external financing through public debt and equity markets. This difference stems from Japan's main bank system where long-term relationships between firms and banks facilitate internal financing, compared to the U.S. where arm's-length capital markets play a larger role in corporate financing. As financial systems globalize, the differences in financing practices between countries have narrowed to some degree.
The document outlines the process of portfolio management over four parts. It discusses background principles like security analysis and portfolio construction. The portfolio manager's job begins with an investment policy statement setting objectives and constraints. The six steps of portfolio management are to learn principles, set objectives, formulate strategy, plan for revisions, evaluate performance, and protect the portfolio. Portfolio construction involves diversification, international investments, and analyzing stock and debt securities. Portfolio management requires maintenance and allows for passive or active approaches. Performance is evaluated based on return and risk. Portfolio protection tools and contemporary issues are also reviewed.
The document outlines the process of portfolio management over four parts. It discusses background principles like security analysis and portfolio construction. Portfolio management involves maintaining the portfolio over time through both passive and active strategies. Part four discusses protecting the portfolio through tools like futures and addressing contemporary issues. The overall document provides an introduction to portfolio management concepts, strategies, and responsibilities.
This document provides a summary of key concepts in corporate finance, including:
1) Sources of corporate funding and capital structure, capital expenditures, and tools used for allocating funds. Key goals are investing and financing.
2) Investing involves forgoing current consumption for future returns. Financing examines return ratios like ROCE, ROE, and ROIC from different perspectives.
3) Tools used in corporate finance include NPV, IRR, payback period, and leverage. Equity valuation methods include free cash flow, NPV, IRR, relative valuation, and payback period. Modern portfolio theory examines efficient diversification of risk.
This document provides an overview of mutual funds, including:
- Mutual funds pool money from investors and invest it in stocks, bonds, etc. on their behalf.
- Investors prefer mutual funds over directly investing in stocks because it reduces the time spent researching companies and allows for a more diversified, lower risk portfolio.
- Asset management companies (AMCs) professionally manage the investors' money in mutual funds and charge fees for their services.
- Mutual funds can be invested in either through a lump sum payment or systematic investment plan (SIP) which invests a fixed amount each month.
- The main types of mutual funds are open-ended and closed-ended funds, which differ based on whether
This document discusses key concepts in finance including present value, time value of money, risk management through diversification and insurance, asset valuation, and the efficient markets hypothesis. It defines present value as the current worth of a future cash flow given a discount rate. It also explains that individuals can reduce risk through insurance, diversifying investments, and accepting lower returns. Further, it describes the efficient markets hypothesis that asset prices reflect all public information and are difficult to predict beyond broad market changes.
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2. INTRODUCTION
• Portfolio is a collection of securities.
• With a given amount of wealth and
securities, an investor can design
innumerable portfolios.
• THE BASIC PROBLEM:
– given uncertain outcomes, what risky securities
should an investor own?
4/19/2012 Syed Karim Bux Shah 2
3. INTRODUCTION
• THE BASIC PROBLEM:
– The Harry Markowitz Approach
• assume an initial wealth
• a specific holding period (one period)
• a terminal wealth
• diversify
4/19/2012 Syed Karim Bux Shah 3
4. INTRODUCTION
• Initial and Terminal Wealth
• recall one period rate of return
we wb
rt
wb
where rt = the one period rate of return
wb = the beginning of period wealth
we= the end of period wealth
4/19/2012 Syed Karim Bux Shah 4
5. INITIAL AND TERMINAL WEALTH
• DETERMINING THE PORTFOLIO RATE
OF RETURN
– similar to calculating the return on a security
– FORMULA
w1 w0
rp
w0
4/19/2012 Syed Karim Bux Shah 5
6. INITIAL AND TERMINAL WEALTH
• DETERMINING THE PORTFOLIO RATE
OF RETURN
w1 w0
Formula: rp
w0
where w0 = the aggregate purchase
price at time t=0
w1 = aggregate market value at
time t=1
4/19/2012 Syed Karim Bux Shah 6
7. INITIAL AND TERMINAL WEALTH
• OR USING INITIAL AND TERMINAL
WEALTH
w1 1 rp w0
where
w0 =the initial wealth
w1 =the terminal wealth
4/19/2012 Syed Karim Bux Shah 7
8. THE MARKOWITZ APPROACH
• MARKOWITZ PORTFOLIO RETURN
– portfolio return (rp) is a random variable
– defined by the first and second moments of the
distribution
• expected return
• standard deviation
4/19/2012 Syed Karim Bux Shah 8
9. THE MARKOWITZ APPROACH
• MARKOWITZ PORTFOLIO RETURN
– defined by the first and second moments of the
distribution
• expected return (mean returns)
• standard deviation (dispersion of returns about
mean)
4/19/2012 Syed Karim Bux Shah 9
10. THE MARKOWITZ APPROACH
• MARKOWITZ PORTFOLIO RETURN
– First Assumption:
• Non-satiation: investor always prefers a higher rate of
portfolio return/higher terminal wealth.
• This leads to a conclusion “Given two portfolios with similar
risk, investor would prefer the portfolio with higher returns.
Preferable
Portfolio Portfolio Returns Risk
A 12% 10%
B 8% 10%
4/19/2012 Syed Karim Bux Shah 10
11. THE MARKOWITZ APPROACH
• MARKOWITZ PORTFOLIO RETURN
– Second Assumption
• Risk aversion: assume a risk-averse investor will choose a
portfolio with a smaller standard deviation
Portfolio Returns Risk
Preferable
A 12% 10%
Portfolio
B 12% 08%
• in other words, these investors when given a fair bet (odds
50:50) will not take the bet, i.e. $5 if head, and $-5 if tail. Note
expected return on this is 0=(5*0.5)+(-5*0.5).
4/19/2012 Syed Karim Bux Shah 11
12. THE MARKOWITZ APPROACH
• MARKOWITZ PORTFOLIO RETURN
– INVESTOR UTILITY
– DEFINITION: is the relative satisfaction derived by
the investor from the economic activity- work,
consumption, investment.
– It depends upon individual tastes and preferences-One
individual may not seek same satisfaction/utility from
same activity.
– It assumes rationality, i.e. people will seek to maximize
their utility
– Utility wealth function: shows relationship between
utility and wealth.
4/19/2012 Syed Karim Bux Shah 12
13. THE MARKOWITZ APPROACH
• MARGINAL UTILITY
– each investor has a unique utility-of-wealth
function
– incremental or marginal utility differs by
individual investor and depends upon the
amount of wealth one already possesses.
– Richer investor value marginal $ less than a
poor investor does.
4/19/2012 Syed Karim Bux Shah 13
14. THE MARKOWITZ APPROACH
• MARGINAL UTILITY
– Assumes
• diminishing characteristic: As one has more of
wealth, additional/marginal unit of wealth will add
positive utility but on decreasing rate i.e. utility
derived from marginal unit will keep on decreasing
with successive units.
• An investor with diminishing marginal utility is risk
averse and such an investor rate certain investment
higher than riskier one.
• nonsatiation
• Concave utility-of-wealth function
4/19/2012 Syed Karim Bux Shah 14
15. THE MARKOWITZ APPROACH
UTILITY OF WEALTH FUNCTION
Utility Risk
Utility of premium
Uc Wealth
Ur
Certainty
equivalent
Wealth
103 110
100 105
4/19/2012 Syed Karim Bux Shah 15
16. Conclusions
• Uc=Utility from certain investment
• Ur=Utility from risky investment
• Uc > Ur
• The amount of positive utility derived from an
additional $1 < the amount of negative utility
(disutility) resulted from loss of $1.
• Note: This is evident from the slope of utility
wealth function which is increasing on decreasing
rate. At any point on curve slope towards right is
lower than the slope to left (Concavity).
4/19/2012 Syed Karim Bux Shah 16
17. Understanding Certainty Equivalents and Risk Premiums
• Suppose you are given two options A and B for investing
$100.
A: that you will earn Rs.105 with certainty.
B: that you will earn either Rs.110 or nothing, probability
of both events is 50:50.
Note: Both options have same expected pay off i.e. Rs.105.
• Which option would you choose?
• Your decision depends upon your attitude to risk. You are:
Risk indifferent, if both options are equally attractive to
you.
Risk averse: if you choose option A, preferring safe $ to
risky $.
Risk taker: if you choose plan B.
4/19/2012 Syed Karim Bux Shah 17
18. Understanding Certainty Equivalents and Risk Premiums
• A risk averse investor will choose option B only if:
~ ceteris paribus, he receives lesser pay off in riskless investment e.g. Rs.101
~ ceteris paribus, he receives even higher pay off in risky investment (Option
B) e.g. Rs.120.
Note there must be an amount, where the investor regard both investments
equally. For example in the Option A, if instead of certain $105, you are
offered $103 and as a result you now regard both certain and risky investments
equal, i.e. you derive same level of expected utility from both options. We call
$103 Certainty Equivalent (CE). And the difference between expected
payoff and CE is called Risk Premium (RP), a compensation to investor for
additional risk taking.
The more risk averse you are the higher risk premium you demand and hence the
lower CE, you have.
Risk averse have positive RP, risk neutral have zero risk premium, and risk takers
have negative risk premium.
Expected payoff (EP)= Risk Premium (RP) + Certainty Equivalent (CE)
CE = EP-RP
RP = EP-CE
4/19/2012 Syed Karim Bux Shah 18
19. INDIFFERENCE CURVE ANALYSIS
• INDIFFERENCE CURVE ANALYSIS
– DEFINITION OF INDIFFERENCE CURVES:
• a graphical representation of a set of various risk
and expected return combinations that provide the
same level of utility
4/19/2012 Syed Karim Bux Shah 19
20. INDIFFERENCE CURVE ANALYSIS
• INDIFFERENCE CURVE ANALYSIS
– Features of Indifference Curves:
• no intersection by another curve
• “further northwest” is more desirable giving greater
utility
• investors possess infinite numbers of indifference
curves
• the slope of the curve is the marginal rate of
substitution which represents the nonsatiation and
risk averse Markowitz assumptions
4/19/2012 Syed Karim Bux Shah 20
21. Indifference Curves Analysis
Return further northwest
A risk averse investor will
A choose Portfolio A, which
offers highest returns, with
B C
relatively lower risk.
Risk
4/19/2012 Syed Karim Bux Shah 21
22. PORTFOLIO RETURN
• CALCULATING PORTFOLIO RETURN
– Expected returns
• Markowitz Approach focuses on terminal wealth
(W1), that is, the effect various portfolios have on
W1
• measured by expected returns and standard
deviation
4/19/2012 Syed Karim Bux Shah 22
24. PORTFOLIO RETURN
– Expected returns:
• Method Two:
N
rp X i ri
t 1
where rP = the expected return of the portfolio
Xi = the proportion of the portfolio’s initial
value invested in security i
ri = the expected return of security i
N = the number of securities in the
portfolio
4/19/2012 Syed Karim Bux Shah 24
25. Expected returns
• Portfolio expected return is a weighted
average of expected returns of its
constituents securities, i.e. each security
contributes to portfolio by its expected
return and its proportion in portfolio.
4/19/2012 Syed Karim Bux Shah 25
26. PORTFOLIO RISK
• CALCULATING PORTFOLIO RISK
– Portfolio Risk:
• DEFINITION: a measure that estimates the extent
to which the actual outcome is likely to diverge
from the expected outcome
4/19/2012 Syed Karim Bux Shah 26
27. PORTFOLIO RISK
• CALCULATING PORTFOLIO RISK
– Portfolio Risk:
1/ 2
N N
P Xi X j ij
i 1 j 1
where ij = the covariance of returns
between security i and security j
4/19/2012 Syed Karim Bux Shah 27
28. PORTFOLIO RISK
• CALCULATING PORTFOLIO RISK
– Portfolio Risk:
• COVARIANCE
– DEFINITION: a measure of the relationship between two
random variables
– possible values:
» positive: variables move together
» zero: no relationship
» negative: variables move in opposite directions
4/19/2012 Syed Karim Bux Shah 28
29. PORTFOLIO RISK
CORRELATION COEFFICIENT
– rescales covariance to a range of +1 to -1
Note: Covariance between two
ij ij i j securities i and j = correlation
between i and j x Standard deviation
of I x Standard deviation of j.
where
ρ i j = +1: denotes perfectly positive relationship
between i and j’s returns, implying that as returns
ij ij / i j
of i increase so does j’s.
ρ i j = -1: denotes perfectly negative relationship.
ρ i j = 0: indicate no identifiable relationship.
Note:
-1 ≤ ρ i j ≤ +1
4/19/2012 Syed Karim Bux Shah 29
31. Graphical representation of correlation
B’s return
B’s return
A’s return A’s return
a) Perfectively Positively b) Perfectively negatively
correlated returns correlated returns
4/19/2012 Syed Karim Bux Shah 31
32. Calculating Portfolio Risk
Exp: Given the following variance-covariance matrix for
three securities A, B, and C, as well as the percentage of
the portfolio for each security, calculate the portfolio’s risk
(standard deviation σp.
Variance-covariance Matrix
Security A Security B Security C
(50%) (30%) (20%)
Security A 459 -211 112
Security B -211 312 215
Security C 112 215 179
4/19/2012 Syed Karim Bux Shah 32
33. Calculating Portfolio Risk
1/ 2
N N
Solution: We know PF risk equals P Xi X j ij
i 1 j 1
(.5x.5x459) = (.5x.3x-211)= (.5x.2x112)=
114.75 -31.65 11.2
(.3x.5x-211)= (.3x.3x312)= (.3x.2x215)=
-31.65 28.08 12.9
(.2x.5x112)= (.2x.3x215)= (.2x.2x179)=
11.2 12.9 7.16
Note: This reduces to
((.5x.5x459) + (.3x.3x312) + (.2x.2x179) +
½ ½
2 (.5x.3x-211) + 2 (.5x.2x112) + 2 (.3x.2x215)) = (134.89) = 11.61%
4/19/2012 Syed Karim Bux Shah 33
34. Calculating Portfolio Risk
% of PF in each stock
Sec A 0.5
Variance-covariance Matrix Sec B 0.3
Sec A Sec B Sec C Sec C 0.2
Sec A 459 -211 112
Sec B -211 312 215
Sec C 112 215 179
Some important points about
Solution:
Variance-covariance Matrix:
114.75 -31.65 11.2
-31.65 28.08 12.9
11.2 12.9 7.16 1. It is Square Matrix, having N2
elements for N securities.
2. Variance appear on the
Portfolio Variance = 134.9 diagonal of matrix.
3. The matrix is symmetric.
Portfolio SD = 11.61 %
4/19/2012 Syed Karim Bux Shah 34
35. Risk-seeking Investor
• Risk seeking investor will prefer:
– a gamble when presented a choice.
– Large gambles over small gambles, because utility
gained from winning is greater for him than disutility
gained from loosing.
– on indifference curve position of Farthest northeast
• Risk seeking investors utility functions will be
convex and their indifference curves will be
negatively sloped.
4/19/2012 Syed Karim Bux Shah 35
36. Risk-neutral investors
Risk neutral investors:
• are indifferent to risk.
• Have horizontal indifference curves (IC).
• Will prefer farthest north position on IC.
Note that as risk-neutral
investor just for 1% additional
Return Preferable
A IC expected returns (from portfolio
15% B Portfolio A compared to B) is willing to
14% take 10% additional risk. Such
an investor consider the return
factor only, ignoring risk
altogether.
10% 20% Risk
4/19/2012 Syed Karim Bux Shah 36