Lecture Notes 4 Portfolio Diversification

# Lecture Notes 4 Portfolio Diversification - Special ρ B B...

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1 Portfolio Diversification Consider a portfolio with 2 assets, A & B Let W A and W B be the proportions in invested in each asset respectively Also, let E(r A ) and E(r B ) be the expected rates of return on each asset Finally, let σ A and σ B be the expected return standard deviations and let ρ A,B be the correlation among the assets’ returns

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2 Portfolios with 2 assets Expected return & Std. Dev B A B B A A B B A A B B A A W W W W r E W r E W r E , 2 2 2 2 p p 2 ) ( ) ( ) ( ρ σ σ σ σ σ + + = + =
3 Portfolios with one risky asset and a risk-free asset Let ‘y’ be the proportion of wealth invested in the risky asset Let the risky asset’s expected rate of return be E(r A ) and standard deviation be σ A The risk-free asset has a rate of return equal to r f

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4 Portfolios with one risky asset and a risk-free asset ? ) ) ( ( ) ( investor particular a for y optimal the is What : Question A p f A f p y r r E y r r E σ σ = - + =
5 1 , - = B A I: Case Special ρ Portfolios with 2 risky assets B B A A p B B A A W W r E W r E W r E σ σ σ - = + = ) ( ) ( ) ( p

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6 Portfolios with 2 risky assets

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Unformatted text preview: Special ρ B B A A p B B A A W W r E W r E W r E σ + = + = ) ( ) ( ) ( p 7 Minimum Variance Portfolio (with 2 risky assets) ( 29 A W B W B A B A B A B A B A B A W-=-+-= 1 , 2 2 2 , 2 ρ σ 8 What if a risk-free asset is available in addition to the risky assets? • The feasible set of portfolios becomes more attractive ( Why? ) • There is an optimal risky portfolio which dominates all other risky portfolios (irrespective of risk preferences) • The optimal (tangency) portfolio has the highest Sharpe ratio among all feasible portfolios 9 Optimal risky portfolio in presence of a risk-free asset Standard Deviation Expected Return Risk-free C B A CAL for Portfolio C CAL for Portfolio B CAL for Portfolio A Optimal CAL has the steepest slope....
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