Corporate Finance Risk and Return Prof Andr Farber
Corporate Finance Risk and Return Prof. André Farber SOLVAY BUSINESS SCHOOL UNIVERSITÉ LIBRE DE BRUXELLES A. Farber Vietnam 2004
Risk and return • Objectives for this session: • 1. Review • 2. Efficient set • 3. Optimal portfolio • 4. CAPM A. Farber Vietnam 2004 2
Review : Risk and expected returns for porfolios • In order to better understand the driving force explaining the benefits from diversification, let us consider a portfolio of two stocks (A, B) • Characteristics: – Expected returns : – Standard deviations : – Covariance : • Portfolio: defined by fractions invested in each stock XA , XB XA+ XB= 1 • Expected return on portfolio: • Variance of the portfolio's return: A. Farber Vietnam 2004 3
The efficient set for two assets: correlation =0 A. Farber Vietnam 2004 4
Example A. Farber Vietnam 2004 5
Marginal contribution to risk: some math • Consider portfolio M. What happens if the fraction invested in stock I changes? • Consider a fraction X invested 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 6
Marginal contribution to risk: illustration A. Farber Vietnam 2004 7
Choosing portfolios from many stocks • Porfolio composition : ü (X 1, X 2, . . . , Xi, . . . , XN) ü X 1 + X 2 +. . . + Xi +. . . + XN = 1 • Expected return: • Risk: • Note: ü N terms for variances ü N(N-1) terms for covariances ü Covariances dominate A. Farber Vietnam 2004 8
Some intuition A. Farber Vietnam 2004 9
The efficient set for many securities • Portfolio choice: choose an efficient portfolio • Efficient portfolios maximise expected return for a given risk • They are located on the upper boundary of the shaded region (each point in this region correspond to a given portfolio) Expected Return Risk A. Farber Vietnam 2004 10
Choosing between 2 risky assets • Choose the asset with the highest ratio of excess expected return to risk: A Expected return B • A Example: RF = 6% • Exp. Return Risk • A 9% 10% • B 15% 20% • Asset Sharpe ratio • A (9 -6)/10 = 0. 30 • B (15 -6)/20 = 0. 45 ** Risk A. Farber Vietnam 2004 11
Optimal portofolio with borrowing and lending Optimal portfolio: maximize Sharpe ratio A. Farber Vietnam 2004 12
Capital asset pricing model (CAPM) • Sharpe (1964) Lintner (1965) • Assumptions ü Perfect capital markets ü 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 13
Optimal portfolio: property Slope = M RF xj Slope = A. Farber Vietnam 2004 14
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 15
CAPM - Illustration Expected Return 1 Beta A. Farber Vietnam 2004 16
CAPM - Example • Assume: Risk-free rate = 6% • Market risk premium = 8. 5% Beta Expected Return (%) • American Express 1. 5 18. 75 • Bank. America 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 5. 40 -0. 07 A. Farber Vietnam 2004 17
Pratical implications • Efficient market hypothesis + CAPM: passive investment ü Buy index fund ü Choose asset allocation A. Farber Vietnam 2004 18
- Slides: 18