...Testing the CAPM Karl B. Diether Fisher College of Business Karl B. Diether (Fisher College of Business) Testing the CAPM 1 / 29 Testing the CAPM: Background CAPM is a model It is useful because it tells us what expected returns should be. We want test whether it is a good model. Remember, whenever we test a model we are jointly testing market efficiency. Testable Implication of the CAPM The market portfolio is the tangency portfolio: E (ri ) = rf + βiM [E (rM ) − rf ], where βiM = cov(ri , rM ) σ 2 (rM ) Karl B. Diether (Fisher College of Business) Testing the CAPM 2 / 29 Testing the CAPM: The Approach Average Return vs CAPM Prediction The most common approach is two compare historical average returns to the CAPM’s prediction. We compute the CAPM’s estimated prediction by estimating beta (β), the market premium (E (rM ) − rf ), and the risk free rate (rf ). We want the estimated prediction error (called α): ˆ αi = ¯i − CAPM Prediction ˆ r ˆ r = ¯i − ¯f − βim (¯M − ¯f ) r r r The CAPM and α ˆ α will not always be zero even if the CAPM is true. Why? ˆ What can we say about prediction error if the CAPM holds? Karl B. Diether (Fisher College of Business) Testing the CAPM 3 / 29 A Good Strategy? Stock tip: Invest in mid-cap stocks. It is a good strategy because everyone ignores mid-cap stocks. Investor want blue chips, or they want to invest in small start-up companies with growth opportunities. Therefore, mid-cap stocks tend to be undervalued...
Words: 2169 - Pages: 9
...Finance: The Capital Asset Pricing Model (CAPM) Prof. Alex Shapiro Lecture Notes 9 The Capital Asset Pricing Model (CAPM) I. II. III. IV. V. VI. Readings and Suggested Practice Problems Introduction: from Assumptions to Implications The Market Portfolio Assumptions Underlying the CAPM Portfolio Choice in the CAPM World The Risk-Return Tradeoff for Individual Stocks VII. The CML and SML VIII. “Overpricing”/“Underpricing” and the SML IX. X. Uses of CAPM in Corporate Finance Additional Readings Equilibrium Process, Supply Equals Demand, Market Price of Risk, Cross-Section of Expected Returns, Risk Adjusted Expected Returns, Net Present Value and Cost of Equity Capital. Buzz Words: 1 Foundations of Finance: The Capital Asset Pricing Model (CAPM) I. Readings and Suggested Practice Problems BKM, Chapter 9, Sections 2-4. Suggested Problems, Chapter 9: 2, 4, 5, 13, 14, 15 Web: Visit www.morningstar.com, select a fund (e.g., Vanguard 500 Index VFINX), click on Risk Measures, and in the Modern Portfolio Theory Statistics section, view the beta. II. Introduction: from Assumptions to Implications A. Economic Equilibrium 1. Equilibrium analysis (unlike index models) Assume economic behavior of individuals. Then, draw conclusions about overall market prices, quantities, returns. 2. The CAPM is based on equilibrium analysis Problems: – – There are many “dubious” assumptions. The main implication of the CAPM concerns expected returns, which can’t be...
Words: 1605 - Pages: 7
... 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...
Words: 1961 - Pages: 8
...Cost of Capital at Ameritrade 1 Objective j • This case provides the opportunity for you to p estimate the cost of capital. • To develop an understanding of how capital market data and the CAPM can be used to estimate the required rate of return for real investments 2 Background g • Ameritrade: formed in 1971, IPO in March , pioneer in the deep-discount p 1997, a p brokerage sector. – Helped create the deep discount market – The first to offer many new services that changed th way i di id l i h d the individual investors managed t d their portfolios. 3 • Ameritrade’s strategy: to grow its customer , q base, which required substantial investments in technology and advertising. • Needed an estimate of the project’s risk. risk 4 Q Question • How risky are these cash flows? • How are they related to the stock market? 5 To-do’s • Determining what firms can be considered comparable when estimating the cost of capital • Calculating returns from stock prices g q y • Estimating CAPM equity and asset betas from capital market data g g • Understanding the effect of leverage on equity betas g pp p • Evaluating how appropriate the estimated cost of capital is for different types of real investments 6 The Discount Brokerage Business g • What are the primary sources of revenue? – Transaction revenues • Brokerage commissions • Clearing fees • Payment for order flow – Interest revenues • Margin lending to customers • Interest on investment of...
Words: 1602 - Pages: 7
...2 Name _________________________________ Formulas Two risky assets E(Rp) = w1 R1 + w2 R2 σp2 = w12 σ12 + w22 σ22 + 2w1w2 ρ12 σ1σ2 ; note to find σp, take square root of σp2 One risk-free and One Risky Asset E(Rp ) = Rf + σp[(Rm-Rf)/σ2] E(Rp) = w1 Rf + w2 Rm w1 + w2 = 1 where w1 is % in risk-free asset and w2 is % in risky asset. σp = w2 σ2 CAPM: E(Rp) = rf + β(Rm-rf) σi2 = Σ[Ri - E(Ri)]2/(n-1) σi,m = Σ{[Ri - E(Ri)][Rm - E(Rm)]}/n-1 β = (ρi,m * σi)/σm or β = σi,m / σm2 ρim = σim/σiσm ρ2 or r-square = Explained Var./Total Var. = (βi2 * σm2)/σi2 Multiple Choice Use the following for the next 3 questions You are looking at two risky assets, the expected returns, standard deviations, and correlation between the two assets are given below: E(RA) = 7%, Standard deviation = 12%. E(RB) = 12%, Standard deviation = 18%. Correlation between the two assets is 1.0. 1. If you put 50% of your wealth in asset A and the other 50% in asset B, what is the expected return of your portfolio? A. 18% B. 9.5% C. 10.5% D. 5.4% 2. If you put 50% of your wealth in asset A and the other 50% in asset B, what is the standard deviation of your portfolio? A. Greater than 18% B. Greater than 12% but less than 18% C. Less than 12% 3. All else equal, if the correlation between the two assets became slightly negative, A. the standard deviation of the portfolio would be zero. B. the standard deviation of the portfolio would be unaffected. C. the standard...
Words: 1937 - Pages: 8
...pricing model (CAPM) is a very useful model and it is used widely in the industry even though it is based on very strong assumptions. Discuss in the light of recent developments in the area.’ MN 3365 Strategic Finance Table of Contents Introduction Concept of CAPM Assumptions of CAPM . Other Suggested Models Disadvantages of CAPM Advantages of CAPM Problems in applying CAPM Conclusion Bibliography / References INTRODUCTION This essay will highlight the use of Capital asset pricing model ( CAPM ) to be considered as a pricing theory model for assets . CAPM model helps investors to analyse the risk and what expectation to keep from an investment (Banz , 1981) . There are two types of risk associated with CAPM known as systematic and unsystematic risk . The systematic risks are market risk which cannot be diversified such as fluctuations in interest rates and recession in the economy .Unsystematic risk are risks associated with an individual stock , it occurs when an investor increases the number of stocks on his portfolio. The unsystematic risk cannot be diversified as it is related an individual stock irrespective to the general market . (Amihud and Lev, 1981). The CAPM was introduced independently by Jack Trenor (1961 , 1962) , Jan Mossin (1996) and William F . Sharpe (1964) , it is basically an uplifment of the existing work of Harry Markowitz on modern portfolio therory as well as diversification which was given a name as CAPM (Investopedia...
Words: 1863 - Pages: 8
...1. What is the WACC and why is it important to estimate a firm’s cost of capital? Do you agree with Joanna Cohen’s WACC calculation? Why or why not? Answer: The cost of capital refers to the maximum rate of return a firm must earn on its investment so that the market value of company's equity shares will not drop. This is a consonance with the overall firm's objective of wealth maximization. WACC is a calculation of a firm's cost of capital in which each category of capital is proportionately weighted. All capital sources - common stock, preferred stock, bonds and any other long-term debt - are included in a WACC calculation. All else equal, the WACC of a firm increases as the beta and rate of return on equity increases, as an increase in WACC notes a decrease in valuation and a higher risk. The WACC of a firm is a very important both to the stock market for stock valuation purposes and to the company's management for capital budgeting purposes. In an analysis of a potential investment by the company, investment projects that have an expected return that is greater than the company's WACC will generate additional free cash flow and will create positive net present value for stock owners. Thus, since the WACC is the minimum rate of return required by capital providers, the managers in the company should invest in the projects which generate returns in excess of WACC. We do not agree with Joanna Cohen’s calculation regarding the WACC from 3 aspects: 1) When Joanna Cohen...
Words: 1480 - Pages: 6
...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 in the stock market can't eliminate that risk. Therefore, when calculating a deserved return, systematic risk is what plagues investors most. CAPM, therefore, evolved as a way to measure this systematic risk. (To...
Words: 1195 - Pages: 5
...Questions • What is the WACC and why is it important to estimate a firm’s cost of capital? What does it represent? Is the WACC set by investors or by managers? • Do you agree with Joanna Cohen’s WACC calculation? Why or why not? If you do not agree with Cohen’s analysis, calculate your own WACC for Nike and be prepared to justify your assumptions. What mistakes did Joanna Cohen make in her analysis? Which method is best for calculating the cost of equity? • Calculate the costs of equity using CAPM, the dividend discount model, and the earnings capitalization ratio. What are the advantages and disadvantages of each method? • What should Kimi Ford recommend regarding an investment in Nike? 2 1 13/3/2013 Background • Kimi Ford needs to decide on investing in Nike, Inc. • To do so, Kimi Ford needs to derive fair value of Nike stock to compare with current market share price • Kimi Ford tasked Cohen to compute Nike’s Cost of Capital 3 Scope 1. Review of Cohen’s Analysis 2. Nike’s Cost of Equity 3. Valuation Methods and Selection a. Market Approach b. Income Approach 4. Choice of Valuation Method 5. Risk Assessment a. Sensitivity Analysis b. Scenario Analysis 6. Investment Recommendation 4 2 13/3/2013 Cohen’s Analysis Issues Opinion Single or Multiple Cost of Capital Appropriate to use Single Cost of Capital as business segments in Nike subject to same risk factors Methodology for Appropriate to use WACC calculating...
Words: 1203 - Pages: 5
...Markowitz, Single Index, CAPM, and APT, have one single goal that is accomplished by using them. This goal is to make a portfolio, or individual securities, as efficient and well performing as possible by finding the optimal weights, highest return, and lowest risk. The Harry Markowitz model of 1952, or the mean-variance model, was one of the earliest models created to compare and contrast securities outcomes. This model uses the weights, standard deviation, and covariance for each security, creating a weighted covariance matrix, therefore forecasting a very accurate estimate of what return and risk the securities or portfolio would give. The Single-Index model, introduced by William Sharpe in 1963, is a simplified variation of the Markowitz model. Using the same premise of estimating in order to forecast optimal portfolios and securities, the single-index model instead uses beta and alpha substitutes for the standard deviation and covariance portions. Beta, measures the volatility of the portfolio or security comparatively to the market as a whole, i.e. the sensitivity to the market, and alpha, measures risk-adjusted performance (comparative to the appropriate benchmarks). These two combined simplify the process of the Markowitz model, while still gaining a result of the optimal portfolio. The Capital Asset Pricing model, or ‘CAPM’, produced by John Lintner in 1965, is a product that branched from the Single-Index model. While it does not use an alpha, it does use a beta that is specified...
Words: 1415 - Pages: 6
...Damodaran’s Country Risk Premium: A Serious Critique Lutz Kruschwitz∗Andreas Löffler†& Gerwald Mandl‡ , Version from July 31, 2010 Contents 1 Introduction 2 2 2 CRP concept 3 Critique of the CRP concept 7 3.1 The theoretical foundation of Damodaran’s equations – built on sand 7 3.2 Damodoran’s empirical basis – a hotchpotch of ad hoc ideas . . . . . 12 4 Conclusion 19 ∗ Freie Universität Berlin, Germany, Chair of Finance and Banking, E-Mail LK@wacc.de. † Universität Paderborn, Germany, Chair of Finance and Investment, E-Mail AL@wacc.de. ‡ Universität Graz, Austria, Chair of Accounting and Auditing, E-Mail Gerwald.Mandl@uni-graz.at. 1 Electronic copy available at: http://ssrn.com/abstract=1651466 1 Introduction For several years, when setting discount rates Damodaran has advocated more consideration of country risk premiums (CRP ) when it comes to assessing companies with activities in emerging markets. We have to acknowledge that his approach is enjoying growing support among investment banks and auditing firms. At the same time, it is to be noted that Damodaran’s concept has failed to resonate sufficiently with the academic community. This is reason enough to perform a systematic analysis and critical discussion of his country risk premium concept. Damodaran’s initial considerations concerning a country risk premium can be found in Damodaran (1999a) and Damodaran (2003), with further essentially unchanged mentions in his more recent publications. In our contribution...
Words: 7452 - Pages: 30
...plant requires a large onetime investment but will provide significant capacity addition as well as cost savings over the next 10 years. Should you approve the proposal for the new plant? □ “HSBC FTSE 100” is a index fund that replicates FTSE 100 index. The fund offers investors a convenient diversification at a low price. Would you be interested in investing in the fund (or somewhere else)? » What if it was TESCO that was considering HSBC FTSE 100 as an investment vehicle? □ In 2004, Sergey Brin and Larry Page, the founders of Google Inc., were talking to investment bankers from Morgan Stanley. They hope to finance a number of potential opportunities through IPO (initial public offering). One of the most important concerns is of course what the offering price should be. Part 1 Project Valuation Dr. Kirak Kim MSc Corporate Finance EFiMM0017 Project Valuation Investment decision Revisit: Valuing unlevered cash flows Revisit: Uncertainty and the notion of risk Weighted average cost of capital Adjusted present value Two Main Decisions in Corporate Finance What is the objective of the firm (corporation)? max{ Shareholder Value } i.e., owners’ wealth “How should the firm evaluate its investment alternatives?” Investment Decisions “How should the firm (optimally) finance its investment projects?” Financing Decisions Investment-side (capital budgeting) was where you left off in Finance &...
Words: 8376 - Pages: 34
...cash flows are discounted at 12% their shares are overpriced, however, when discounted at rates below 11.17% the firm is undervalued. Cohen is tasked to further analyze Nike’s cost of capital to accurately estimate what rate their cash flows should be discounted back at. Joanna Cohen’s WACC Calculations Cohen decides to use a single cost of capital rather than multiple costs of capital. This is accurate as Nike operates primarily in the same business segments and each segment assumes similar risks. To find Nike’s Weighted Average Cost of Capital (WACC), she must first find the capital structure of the firm. Cohen incorrectly uses the book value of equity, rather than the market value. Additionally, she uses the book value of debt, however this is acceptable because the market values are not provided in the case. With Nike’s capital structure in hand, Cohen begins calculate the cost of capital for debt and equity. To calculate the cost of debt, Cohen uses historical interest expenses as a proxy, however this is not a forward looking estimation and using the materials provided a better estimation of cost of debt can be made by calculating the yield-to-maturity on Nike’s outstanding bonds. To calculate cost of equity Cohen uses the Capital Asset Pricing Model (CAPM), however incorrectly inputs an average beta instead of the most current beta. The most current beta should be used because it is most representative of the future beta of Nike. The other inputs used in...
Words: 1146 - Pages: 5
... 4. Capital Asset Pricing Model 4 5.1 Limitations of CAPM 4 5.2 The APT Model 4 5.3 The Three-Factor Model 4 5.4 Required Rate of Return using APT or Three-Factor 5 Model 5. Bonds 5 6.5 How bond prices are determined 5 6.6 The Rate of Return on the bonds 6 6. Conclusion 7. Appendices 6.1 Appendix 1 – after tax rate of return on bonds 7 6.2 Appendix 2 – Excel Working and screen shot 8. References 9. Bibliography 1. Introduction Naturally Fresh Plc are considering converting a number of their farms in Southern Europe into campsites following difficult trading conditions. This report will look at the required rate of returns on the equity as well as the bonds, whilst explaining the models used to calculate the returns and also provide a recommendation on whether the investment opportunity should be accepted by Naturally Fresh Plc. 2. Required Rate of Return on Equity Key | | E(R) | Expected/Required Rate of Return | R(f) | Risk Free Rate | B | Beta | R(m) | Market Return | R(m)-R(f) | Market Premium | Capital Asset Pricing Model (CAPM): E(R) = Rf + B(Rm-Rf) E(R) = 2% + 0.8(12%-2%) E(R) = 10% The required rate of return, which is the minimum yield that investors require in order to select a particular investment, was calculated using the CAPM. The CAPM is a model that describes the relationship between risk and return and...
Words: 2713 - Pages: 11
...1. Calculation of WACC of a Multi-Division Corporation 2. Sources of Data and their limitation 3. Use of CAPM, Cost of Equity, Effect of Leverage on the Ce, WACC 4. Use of data for comparable to estimate asset betas for division-specific cost of capital 5. Biases and Limitations No financial modeling. In the previous years they would include WACC as part of case study 3 – Now it has been changed to 2 – without any actual financial statements. No excel modeling. Focused on how to address the issues. Multi-Divisional Comapnies Discount Rate, based on the U.S. The company has three divisions. The profit making divisions, marketing… blah, blah. Very different with each other in terms of how to make the products. Growth, maturity. This issue will become more apparent. For WACC, looking at the formula for WACC, Percentage of debt over the value, cost of debt * Tax Rate, + Equity Value. (1-T) Interest payment to debt holders reflects the benefit of the tax shields, lowering your cost of debt. Capital Structure in general, debt and equity together. Cost of debt… tends to be of a lower percentage as it represents the risk to debt holders thus a lower & compared to risk to equity holders. Why is debt lower than equity? Contractual obligations – Debt Obligations Risk comes into play when the company is at default. Equity shareholders are of a nature of “Residual claim” = they get whatever that is left after all the debt holders have been paid. When the company...
Words: 877 - Pages: 4
