Lecture09 - Efficient Frontier Expected Return 17 Lecture 9...

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Lecture 9 Capital Asset Pricing Model (CAPM) 2 Efficient Frontier 14 22 10 17 Which portfolio would a risk averse investor choose? Standard Deviation Expected Return (%) A B C 3 Dominant Portfolios ring4 We can safely assume that all rational investors will prefer A or B over C ring4 That is, portfolio C is inefficient and is dominated dominated by A and B ring4 However, the choice between A and B will depend on the investor’s risk preference ring4 A more risk averse investor will prefer portfolio B to A 4 Riskless Lending ring4 Let us now assume that you can invest in portfolio A at 17%, as well as a riskless asset such as Treasury Bills at 4% (risk-free rate) ring4 By investing in Treasury bills, you are effectively lending to the Federal Government
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5 14 10 17 Adding the Risk-Free Asset 4 0 Standard Deviation Expected Return (%) risk-free asset 22 A B C Now assume that we can invest in a risk-free asset such as Treasury Bills at 4% (risk- free rate) 6 Standard Deviation Expected Return (%) Riskless Borrowing and Lending A 22 4 8.8 17 9.2 24.8 35.2 We could invest in a combination of the Risk Free Asset and A The range of portfolios lie on the straight line shown 7 Verify the point on the plot ring4 Invest 40% in portfolio A and 60% in Treasury Bills ring4 Expected return on your overall position = + E( ) E ) ) ( ( f f p A A r w w r r 8 Verify the point on the plot ring4 Variance of your overall position 2 2 2 2 2 , 2 2 2 2 2 2 0 0 2 ( ) 2 0 ( )( ) p f f A A f A f A f A f A A f A A A A w w w w w w w w w σ σ σ ρ σ σ σ σ σ = + + = + + = σ σ σ σ σ σ = = = = = 2 2 2 0.4x0.22=0.088or8.8% p p A A A A p A A w w w
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9 Riskless Borrowing ring4 Borrowing $600 at the riskless rate, you can invest this together with your original wealth of $1,000, a total of $1,600, in portfolio A = + E( ) ( ) E( ) p f f A A r w r w r ring4 The standard deviation of your overall position is σ σ = = p A A w 10 Standard Deviation Expected Return (%) Riskless Borrowing and Lending A 22 4 8.8 17 9.2 24.8 35.2 11 14 10 17 4 0 Standard Deviation Expected Return (%) risk-free asset 22 A B C We could also invest in the risk free asset and B 12 14 10 17 4 0 Standard Deviation Expected Return (%) risk-free asset 22 A C But we can do marginally better
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13 The Capital Market Line Standard Deviation Expected Return (%) 4% (r f ) The line which runs at a tangent to the efficient frontier (from the risk-free return on the Y axis) is called the Capital Market Line (CML) What is Portfolio M? In theory the market portfolio contains every asset in the world.
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