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Unformatted text preview: 10. CAPM (part 1) • In this chapter we go into more detail about the riskreward relationship. • Also, we will learn about – the role of diversification in risk management. – the security market line (SML) and the capital asset pricing model (CAPM) . – how to construct efficient portfolios Constructing portfolios • Suppose there are two possible assets available to invest in, A and B : – the expected return of A is E ( R A ) and the standard deviation is σ A . – the expected return of B is E ( R B ) and the standard deviation is σ B . – the correlation between the returns of A and B is ρ . • Now, suppose we invest some fraction of our money in A and some fraction in B , say w A and w B , where w A + w B = 1 (these are called the portfolio weights ). The portfolio thus formed has expected return E ( R p ) = w A E ( R A ) + w B E ( R B ) and variance σ 2 p = w 2 A σ 2 A + w 2 B σ 2 B + 2 w A w B ρσ A σ B 2 Correlation If the returns on two assets are positively correlated , it means that when one stock has a positive return, the return on the other tends to be positive as well. If the returns on two assets are negatively correlated , it means that when one stock has a positive return, the return on the other tends to be negative. 3 Figure — correlation The returns of assets A and B have correlation of .75 4 Figure — correlation 5 Example Suppose E ( R A ) = 9% , σ A = 15% , E ( R B ) = 15% , σ B = 20% and ρ = . 2 . What are the expected return and standard deviation of a portfolio with 40% of its value in asset A and 60% in asset B? If the riskfree rate is 5%, what are the Sharpe ratios for each asset and for the portfolio? 6 Example — continued Construct portfolios using the weights below and compute the ex pected return, standard deviation, and Sharpe ratio for each port folio. Solution: w A w B E ( R p ) σ p Sharpe0.2 1.2 16.2 24.8 0.452 0.0 1.0 15.0 20.0 0.500 0.2 0.8 13.8 15.7 0.561 0.4 0.6 12.6 12.3 0.618 0.6 0.4 11.4 10.8 0.594 0.8 0.2 10.2 11.9 0.438 1.0 0.0 9.0 15.0 0.267 1.20.2 7.8 19.2 0.146 Note: It is easiest to do this using a spreadsheet. 7 • The expected return for the portfolio is a weighted average of the individual assets’ returns. • But, this is not true for the standard deviation: diversification reduces risk . • Some, but not all risk can be eliminated by diversification . • Using a little bit of algebra, it is possible to determine the portfolio with minimum variance ....
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 Fall '07
 DONCHEZ,RO
 Capital Asset Pricing Model, Corporate Finance, Financial Markets, Modern portfolio theory, idiosyncratic risk

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