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Lecture09c - Lecture 9 Capital Asset Pricing Model(CAPM 2...

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Unformatted text preview: 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 r We can safely assume that all rational investors will prefer A or B over C r That is, portfolio C is inefficient and is dominated dominated by A and B r However, the choice between A and B will depend on the investor’s risk preference r A more risk averse investor will prefer portfolio B to A 4 RisklessLending r Let us now assume that you can invest in portfolio A at 17%, as well as a risklessasset such as Treasury Bills at 4% (risk-free rate) r By investing in Treasury bills, you are effectively lending to the Federal Government 5 14 10 17 Adding the Risk-Free Asset 4 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 (%) RisklessBorrowing 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 r Invest 40% in portfolio A and 60% in Treasury Bills r Expected return on your overall position = + E() E ) ) ( ( ff p A A r w w r r E()0.6(0.04)0.4(0.17) 0.092 9.2% p r = + = = 8 Verify the point on the plot r Variance of your overall position Std dev of risk free asset is zero 2 2 2 2 2 , 2 2 2 2 2 2 2 () 2 ()() 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 9 Weights must add to one RisklessBorrowing r Borrowing $600 at the risklessrate, you can invest this together with your original wealth of $1,000, a total of $1,600, in portfolio A = ×- × ( 0.04)+( 0.17)=0.248 or 0.6 1.6 24.8% = + E() () E() p f f A A r wr w r r The standard deviation of your overall position is × 1.60.22=0.352or35.2% σ σ = = p A A w 10 Standard Deviation Expected Return (%) RisklessBorrowing and Lending A 22 4 8.8 17 9.2 24.8 35.2 Riskless Lending Riskless Borrowing 11 14 10 17 4 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 Standard Deviation Expected Return (%) risk-free asset 22 A C But we can do marginally better 13 The Capital Market Line Standard Deviation Standard Deviation Expected Return (%) 4% (r f ) Capital Market Line (CML) 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) Market Market Portfolio Portfolio What is Portfolio M? In theory the market portfolio contains every asset in the world. What is Portfolio M?...
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