Measurement of Risk 1.1 Risk 1.2 Capital Asset Pricing Model The estimation of systematic risk (or ‘beta’) is central to the implementation of the capital asset pricing model (CAPM) for researchers and practitioners. Markowitz (1952) argued that investors should be concerned with holding efficient portfolios‚ that is‚ a portfolio offering the highest expected return for each level of risk. Sharpe (1964) and Lintner (1965) took Markowitz’s work one step further to develop the CAPM to explain the
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1. Convert prices to total return (% change in the price) = (Pt – Pt-1) / Pt-1 2. Remove outliers – sort data and remove anything +/- 20% 3. Calculate historical average and historical risk X-BAR = Σx/n Calculate the sum of the total return and divide by the number of observations • Variance = σ2 = Σ(x – x bar) 2 / (n-1) Fix X-BAR‚ double click to apply to all dates‚ get the sum‚ divide by (n-1) Risk = σ = √σ = SQRT(Variance) = standard deviation 4. Average Matrix Excel Options
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Suggested Answers to Previous Semesters Exam Questions Question 4 (Semester 2‚ 2005) 96633337 Juan (a) Expected Portfolio Return and Risk Expected Return Risk Covariance = (0.002)(0.06)(0.09)=0.0000108 (b) Minimum Variance (Pendix Ltd) The minimum variance for this portfolio is 0.693‚ indicating that risk is minimized when 69.3 percent of the portfolio is invested in Pendix’s shares. A rational investor would not allow Pendix’s shares to
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Yang TABLE OF CONTENT Title Page……………………………………………………1 Content…………………………………………………...…2 Problem…………………………………………………...3-4 Answers…………………………………………………..5-7 Problem: The Financial advisor’s investment case: Inferior investment alternatives Although investing requires the individual to bear risk‚ the risk can be controlled through the construction of diversified portfolios and by excluding any portfolio that offers an inferior return for a given amount of risk. While this concept seems obvious
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CHAPTER 10 Return and Risk: The Capital Asset Pricing Model (CAPM) Multiple Choice Questions I. DEFINITIONS PORTFOLIOS a 1. A portfolio is: a. a group of assets‚ such as stocks and bonds‚ held as a collective unit by an investor. b. the expected return on a risky asset. c. the expected return on a collection of risky assets. d. the variance of returns for a risky asset. e. the standard deviation of returns for a collection of risky assets. Difficulty level: Easy PORTFOLIO WEIGHTS
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Risk and Return: Portfolio Theory and Asset Pricing Models Portfolio Theory Capital Asset Pricing Model (CAPM) Efficient frontier Capital Market Line (CML) Security Market Line (SML) Beta calculation Arbitrage pricing theory Fama-French 3-factor model Portfolio Theory • Suppose Asset A has an expected return of 10 percent and a standard deviation of 20 percent. Asset B has an expected return of 16 percent and a standard deviation of 40 percent. If the correlation between A and B is 0.6
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flows. (2)The riskiness of an asset may be measured on a stand-alone basis or in a portfolio context. An asset may be very risky if held by itself but may be much less risky when it is a part of a large portfolio. (3)In the context of a portfolio‚ the risk of an asset is divided into two parts: diversifiable risk (unsystematic risk) and market risk (systematic risk). Diversifiable risk arises from company-specific factors and hence can be washed away through diversification. Market risk stems from
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I. DEFINITIONS PORTFOLIOS 1. A portfolio is: a. a group of assets‚ such as stocks and bonds‚ held as a collective unit by an investor. b. the expected return on a risky asset. c. the expected return on a collection of risky assets. d. the variance of returns for a risky asset. e. the standard deviation of returns for a collection of risky assets. PORTFOLIO WEIGHTS 2. The percentage of a portfolio’s total value invested in a particular asset is called that
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Asset Pricing Model (CAPM) has been one of the most widely used techniques in the global investing community for calculating the required return of a risky asset. This project aims to test whether CAPM is a valid model for predicting the price/return of some selected companies listed on the S&P 500 Index. Also we investigate‚ whether there appear to be some deviations from the model and look for plausible reasons to explain these. For the purpose of the project‚ actual monthly returns of sample companies
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Nondiversifiable and Diversifiable Risk c) Because Diversifiable risk can be eliminated through portfolio diversification‚ the more relevant risk is the Nondiversifiable risk. This kind of risk can be attributed to market forces and factors that affect ALL the firms and cannot be eliminated through portfolio diversification. In this case‚ the nondiversifiable risk is about 6.00%. Notice that the area between the red curve and the green line (which represents the diversifiable risk) diminishes as it approaches
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