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- 1. CAPITAL ASSET PRICING MODEL AN INTRODUCTION by Richard Diamond September 2011
- 2. PRESENTATION INTRODUCTION• What is CAPM? Background to model derivation, purposes and issues that CAPM aims to address• Statistical workings and pre-requisites of in-depth understanding of CAPM (Modern Portfolio Theory)• CAPM weaknesses and applications in ﬁnancial management• Issues of presentation to the UG cohort. Pedagogic advice stemming from the threshold concepts paradigm
- 3. CAPM INVENTION• Capital AssetPricing Model was developed as an attempt to predict capital markets’ behaviour under the condition of risk• CAPM is based on equilibrium assumption and used to estimate a risk-adjusted return on asset (‘cost of equity’)• Anacademic paper that presented CAPM is Sharpe (1964). Capital Asset Prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19 (3), 425-442
- 4. Optimization and Application to Portfolio Selection” for more details);;e–Capital Asset Pricing Model (CAPM)predict asset prices; Is an equilibrium model: it can be used to – Can be factor to any in which portfolio; Is a linear appliedmodel,security orthe factor is the market return; – Is expressed FORMULATION USING CAPM in from the mean-variance analysis (see “Fundam Is derived directlyterms of expectations. Optimization and Application to Portfolio Selection” for more detail EXPECTATIONS ALGEBRAForan equilibrium model: it can be used to predict asset prices; Is an investment I, It takes the form Can be applied to any r R portfolio; R E security or I E rM I Is • This reads as “expected excess return on Individual asset equals beta expressed in terms of expectations.or, alternatively excess return on Market” times expected an investment I, ItEtakes R E r R rI return r form M free rate R. Excess • Excess return is historical the minus risk I is r R E r R return on market E regarded as ‘the market price of risk’ I I M • Most of textbooks present a re-arranged expression as follows:alternatively E rI R I E rM R
- 5. THE STRUCTURE OF CAPMThis kind of explanation is typical for a US classroom. Being difﬁcult to comprehend, it shows a complex structure
- 6. WHAT IS BETA OF AN ASSET?• Betais a parameter that gives information about individual stock and its speciﬁc (idiosyncratic) risk• Betais calculated as the slope of the simple linear regression (You can remember ‘beta’ from regression formulae before!)• What is an independent variable in the regression? (Excess return on the market or market price of risk)
- 7. Monthly Stock PricesMonth S&P 500 MSFT 1 1,147.39 30.16 Security Characteristic Line y = 0.9939x - 0.0035 2 1,076.92 26.13 R² = 0.31031 3 1,067.14 25.46 40.00% 4 989.82 27.35 5 911.62 23.99 6 916.07 24.54 30.00% 7 815.28 21.87 8 885.76 26.74 9 936.31 28.84 20.00% 10 879.82 25.85 Stock Returns 10.00% MSFT 0.00% Returns S&P 500 MSFT -6.14% -13.35% -10.00% -0.91% -2.58% -7.25% 7.44% -20.00% -7.90% -12.29% 0.49% 2.29% -11.00% -10.88% -30.00% 8.64% 22.25% -30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00% 40.00% S&P 500 Returns 5.71% 7.87% BETA CALCULATIONStep-by-step Excel demonstration together with re-explanationof the linear regression model and Q&A. Offer Youtube links
- 8. BETA ILLUSTRATIONSTwo examples: beta is similar for a conservative mutual fund andInternet video streaming service. Betas for different industries
- 9. HOW EQUILIBRIUM WORKS• Sincethe optimal policy is to invest a fraction of wealth into the tangency portfolio, ultimately every investor will hold the tangency portfolio• Asa consequence, equilibrium will be achieved and the market value of each risky asset will become proportional to their weights in the tangency portfolio• Another formulation: expected returns and variances will become equal to ones of the tangency portfolio
- 10. TANGENCY PORTFOLIO?? TOPICREQUIRES SOME MPT KNOWLEDGE The tangency portfolio Line parametrized by wt: Return wt t 1 wt R R wt t R wt t t CAPM A Tangency portfolio B R B A t Risk 41It is a portfolio of risky assets (equity, commodity) allocated in such a waythat it provides ‘the same’ return as a risk free asset (cash, bond) portfolioBonds are not strictly risk-free: they have interest rate and credit risks
- 11. CAPM IS A MODELLove based on outer beauty--of the elegant CAPM formulation, of course--can be a good start but only love based on deep understanding and acceptance of weakness endures
- 12. WHAT CAPM PREDICTS• CAPM is an equilibrium model and is based on expectations. That means that its use for prediction is theoretically justiﬁed• It follows from the CAPM expectations formulation that the risk premium (excess return) of an individual asset in linear relationship with the risk premium of the market (times beta). The principle is scaleable to a portfolio of assets• Hence a conclusion that, on average, the market will only compensate for taking on the systematic risk (adjusted by beta that reﬂects non-systematic risk but as a constant parameter)
- 13. PRACTICAL FORMULATION OFCAPM FOR MANAGEMENT This formulation is used when estimating ‘cost of equity’ for the ﬁrm’s capital structure Risk free rate can be found using the yield curve of USAdvice: use input from Treasuries (Bloomberg website)ﬁnancial markets for corporatebudgeting and investment Market rate of return isplanning but trading requires averaged return on a marketmore sophisticated tools index (e.g., Dow Jones or DAX)
- 14. PEDAGOGIC ISSUES• An introduction to undergraduate students warrants step-by- step explanation and guidance through mathematics• Itis important make students accustomed to ‘the tools of the trade’ and generate linkages to the underlining knowledge while avoiding the ﬁtting of CAPM to too many theories • Important opportunity to do an application of the simple regression model and give understanding of ‘mechanics’ • Justiﬁcation with equilibrium and MPT rather than utility
- 15. THRESHOLD CONCEPT ISSUES APPLIED TO CAPM PRESENTATION• “Thethreshold concept approach is concerned with how students can be helped to acquire integrating ideas.” (Davies & Mangan 2007b)• Flashingthe CAPM formula on a slide and then doing some cost of capital examples would be the exactly wrong approach • Itis better of focus on intricacies of WACC and exercise practice closer to the time of examination, as a revision. However, past exam papers are to be released at the start
- 16. THRESHOLD CONCEPT ISSUESAPPLIED TO CAPM PRESENTATIONTo stimulate open mindset and memory retention:• Demonstrate the workings of the model (statistics). Opaqueness will lead to rote learning of symbols’ deﬁnitions• Show where the inputs can practically come from--the short- term part of US Treasury yield curve--stimulate informed guess and recognition based on prior knowledge• Behonest about the model’s weaknesses and application of the outputs. Provide the idea of where the model was coming from and for what purposes it was derived and is used

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