Lecture_12-spring

# Lecture_12-spring - Lecture 12 Formulas: statistics review...

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Unformatted text preview: Lecture 12 Formulas: statistics review Present value: Future value: Expected value: Variance: Correlation: Bond value: Holding Period Return: t t r P P ) 1 ( + = i N i i r p r E * ) ( 1 ∑ = = t o t r P P ) 1 ( * + = 2 1 )) ( ( * ) ( r E r p r Var i N i i- = ∑ = y x y x y x corr σ σ ) , cov( ) , ( = T T t t r Face r Coupon ) 1 ( ) 1 ( 1 + + + ∑ = P D P P H P R 1 1 +- = Formulas: Utility and portfolio choice p c y σ σ = 2 01 . ) ( p f p A r r E y σ- = ) ( * ) 1 ( ) ( p f complete r E y r y r E +- = Formulas: portfolio theory E{r p } = w*E(r MS ) + (1-w)*E(r GM ) p f p r r E CAL of Slope σ- = } { . . ) , ( * ) 1 ( * * 2 * ) 1 ( * 2 2 2 2 GM MS Cov w w w w GM MS p- +- + = σ σ σ CAPM 2 * 01 . ) ( m f m A r r E y σ-- = ] } { [ * ] } { [ ) , ( } { 2 f m e f m m m e f e r r E r r E r r Cov r r E- =- =- β σ m e e m m e m e m m e m e r r Corr r r Corr r r Cov σ σ σ σ σ σ β ) , ( ) , ( ) , ( 2 2 = = = 2 01 . ) ( m A rf rm E σ- =- – E{r e }- r f = α e + β e *[E{r m } - r f ] where in equilibrium alpha equals to zero Midterm • Three multiple choice questions • Choice of three out of 5 definitions • Choice of one of the two short calculation questions (one line of calculation) • Five long calculation questions Review problems Problem 1 You are evaluating the expected performance of two stocks . Risk-free rate is 5% Expected Return on market portfolio is 11.5% The beta of stock1 is 1.5 The beta of stock 2 is 0.8 Based on your own analysis , the return on stock one should be 13.25 and return on stock 2 should be 11.25.Calculate the required rate of return on stock 1and 2. Indicate whether each stock is undervalued, fairly valued or overvalued. • E(r) = rf + β × [E(r M ) rf ] − • Stock1 : E(r) = 5 + 1.5 × [11.5 5.0] = 14.75% − • Stock2: E(r) = 5 + 0.8 × [11.5 5.0] = 10.20% − • If the forecast rate of return is less than (greater than) the required rate of return, then the security is overvalued (undervalued). • Stock 1: Forecast return – Required return = 13.25% − 14.75% = 1.50% − • Stock 2: Forecast return – Required return = 11.25% − 10.20% = 1.05% • Therefore, stock 1 is overvalued and stock 2 is undervalued. Problem 2 • Risk-free rate=5%,expected rate of return required by the market for a portfolio with beta of 1 is 12%. According to CAPM: a. What is the expected return on market portfolio? b. What would be the expected rate of return on a stock with beta=0? c. Suppose you consider buying a share of stock at \$40. The stock is expected to pay \$3 dividends next year and you expect to sell it for \$41. Beta=-0.5. Is the stock overpriced or underpriced? • Since the market portfolio, by definition, has a beta of 1, its expected rate of return is 12%....
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## This note was uploaded on 04/17/2008 for the course ECON 171A taught by Professor Yusim during the Spring '08 term at Brandeis.

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Lecture_12-spring - Lecture 12 Formulas: statistics review...

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