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Corporate Finance

Corporate Finance. Risk and Return Prof. André Farber SOLVAY BUSINESS SCHOOL UNIVERSITÉ LIBRE DE BRUXELLES. Risk and return. Objectives for this session: 1. Review 2. E fficient set 3. Optimal portfolio 4. CAPM. Review : Risk and expected returns for porfolios.

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Corporate Finance

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  1. Corporate Finance Risk and Return Prof. André FarberSOLVAY BUSINESS SCHOOLUNIVERSITÉ LIBRE DE BRUXELLES

  2. Risk and return • Objectives for this session: • 1. Review • 2. Efficient set • 3. Optimal portfolio • 4. CAPM A.Farber Vietnam 2004

  3. Review : Risk and expected returns for porfolios • In order to better understand the driving force explaining the benefitsfrom diversification, let us consider aportfolio of two stocks (A,B) • Characteristics: • Expected returns : • Standard deviations : • Covariance : • Portfolio: defined by fractions invested in each stockXA ,XBXA+ XB= 1 • Expected return on portfolio: • Variance of the portfolio's return: A.Farber Vietnam 2004

  4. The efficient set for two assets: correlation = 0 A.Farber Vietnam 2004

  5. Example A.Farber Vietnam 2004

  6. Marginal contribution to risk: some math • Consider portfolio M. What happens if the fraction invested in stock Ichanges? • Consider a fraction Xinvested in stock i • Take first derivative with respect to X for X = 0 • Risk of portfolio increase if and only if: • The marginal contribution of stock i to the risk is A.Farber Vietnam 2004

  7. Marginal contribution to risk: illustration A.Farber Vietnam 2004

  8. Choosing portfolios from many stocks • Porfolio composition : • (X1, X2, ... ,Xi, ... ,XN) • X1 + X2+... +Xi+... +XN=1 • Expected return: • Risk: • Note: • Nterms for variances • N(N-1) terms for covariances • Covariances dominate A.Farber Vietnam 2004

  9. Some intuition A.Farber Vietnam 2004

  10. The efficient set for many securities • Portfolio choice: choose anefficient portfolio • Efficient portfolios maximiseexpected return for a given risk • They are located on the upperboundary of the shaded region (each point in this regioncorrespond to a given portfolio) Expected Return            Risk A.Farber Vietnam 2004

  11. Choose the asset with the highestratio of excess expected return torisk: Example: RF =6% Exp.Return Risk A9% 10% B15% 20% Asset Sharpe ratio A(9-6)/10 =0.30 B(15-6)/20 =0.45 ** A Choosing between 2risky assets Expected return B A Risk A.Farber Vietnam 2004

  12. Optimal portofolio with borrowing and lending Optimal portfolio: maximize Sharpe ratio A.Farber Vietnam 2004

  13. Capital asset pricing model (CAPM) • Sharpe (1964) Lintner (1965) • Assumptions • Perfect capital markets • Homogeneous expectations • Main conclusions: Everyone picks the same optimal portfolio • Main implications: • 1. M is the market portfolio : a market value weighted portfolio of all stocks • 2. The risk of a security is the beta of the security: • Beta measures the sensitivity of the return of an individual security to the return of the market portfolio • The average beta across all securities, weighted by the proportion of each security's market value to that of the market is 1 A.Farber Vietnam 2004

  14. Optimal portfolio: property Slope = M x j RF Slope = A.Farber Vietnam 2004

  15. Risk premium and beta • 3. The expected return on a security is positively related to its beta • Capital-Asset Pricing Model (CAPM) : • The expected return on a security equals: the risk-free rate plus the excess market return (the market risk premium) times Beta of the security A.Farber Vietnam 2004

  16. CAPM - Illustration Expected Return 1 Beta A.Farber Vietnam 2004

  17. CAPM - Example • Assume: Risk-free rate = 6% Market risk premium = 8.5% • Beta Expected Return (%) • American Express 1.5 18.75 • BankAmerica 1.4 17.9 • Chrysler 1.4 17.9 • Digital Equipement 1.1 15.35 • Walt Disney 0.9 13.65 • Du Pont 1.0 14.5 • AT&T 0.76 12.46 • General Mills 0.5 10.25 • Gillette 0.6 11.1 • Southern California Edison 0.5 10.25 • Gold Bullion -0.07 5.40 A.Farber Vietnam 2004

  18. Pratical implications • Efficient market hypothesis + CAPM: passive investment • Buy index fund • Choose asset allocation A.Farber Vietnam 2004

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