Topic09_capm[1]

# Topic09_capm[1] - Thomas Moeller FINA 30153 Financial...

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Thomas Moeller FINA 30153: Financial Management 1 Topic 9 Capital Asset Pricing Model (CAPM) Objectives 1. Discuss efficient portfolios with borrowing and lending opportunities 2. Understand market portfolio and separation theorem 3. Discuss capital market line 4. Define beta and characteristic line 5. Explain security market line 6. Understand differences between capital market line and security market line 7. Discuss the empirical evidence on the CAPM

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Thomas Moeller FINA 30153: Financial Management 2 1. Efficient portfolios Portfolio: combination of different securities Expected return of a portfolio of N securities: = = i r E N 1 i i w p r E Variance of a portfolio of N securities: = = = N 1 i N 1 j ) j r , i Cov(r j w i w 2 p σ where w i = proportion of funds invested in security i E(r i ) = expected return on security i N = number of securities in the portfolio Cov(r i ,r j ) = covariance between the returns of asset i and asset j
Thomas Moeller FINA 30153: Financial Management 3 By changing the proportion of investment in each security (the w's in the equations), one can change the expected return and the variance of the portfolio. Rational investors will choose their portfolio weights so that their portfolios are "efficient." An efficient portfolio has the largest expected return for a given level of risk . Efficient set: Set of all assets and portfolios that are efficient Since investors try to maximize expected returns and minimize risk, they choose portfolios from the efficient set.

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Thomas Moeller FINA 30153: Financial Management 4
Thomas Moeller FINA 30153: Financial Management 5 2. Efficient portfolios with borrowing and lending By combining risky securities, we were able to generate an efficient portfolio frontier. If we assume the existence of risk-free assets, we can obtain even better risk/return combinations. A lending portfolio includes risk-free and risky assets. A borrowing portfolio involves investing total capital plus borrowed funds in risky asset.

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Thomas Moeller FINA 30153: Financial Management 6 Expected return of a portfolio of risk-free and risky asset: E(r p ) = w f r f + w j E(r j ) Variance of two-asset portfolio including risk-free asset: σ 2 p = w j 2 σ j 2 Expected Return on Portfolio (%) Standard Deviation of Portfolio (%)
Thomas Moeller FINA 30153: Financial Management 7 3. Market portfolio and separation theorem In a world with homogeneous expectations,

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## This note was uploaded on 04/21/2008 for the course FINA 30153 taught by Professor Moeller during the Spring '08 term at TCU.

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Topic09_capm[1] - Thomas Moeller FINA 30153 Financial...

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