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[]
[]
[]
[]
[null,"Input Parameters"]
[]
[null,"rhist","Expected historical returns on the stocks"]
[null,"rrf","Risk-free rate of return"]
[null,"ω","Observed market portfolio (supply of assets)"]
[null,"Σ","Asset historical covariance matrix"]
[null,"γ","Parameter of the utility function (measures risk-aversion)"]
[null,"U","Utility function: U = rx - (γ/2) * (x Σ x)"]
[]
[null,"CAPM Problem"]
[]
[null,"Investor's problem","Equilibrium prices"]
[null,"maxx U(x)","rCAPM: x = ω"]
[null,"1 * x = 1"]
[]
[null,"Estimated Output Values"]
[]
[null,"CAPM Equilibrium Values"]
[]
[null,"β","Security beta coefficients","β = Σω / ωΣω"]
[null,"rmin","Return on portfolio uncorrelated with market index","rmin = rrf"]
[null,"rMkt","Return on market index portfolio","rMkt = rmin + γ (ωΣω)"]
[null,"rCAPM","Returns derived from the CAPM model","rCAPM = rmin + β x [rMkt - rmin]"]
[null,"λ","Security alpha coefficients","λ = rhist - rCAPM"]
[]
[null,"Security Efficiency Measures"]
[]
[null,"Treynor","T = (rhist - rmin) / β"]
[null,"Sharpe","S = (rhist - rmin) / σ"]
[null,"Jensen","J = λ / β"]
[]
[null,"Investors' Decision Problem"]
[]
[null,"Funds (in two-fund separation):"]
[null,"xmin","Σ-1 1 / A","µ = B/A","σ2 = 1/A"]
[null,"xM","Σ-1 r / B","µ = C/B","σ2 = C / B2"]
[]
[null,"A","1 Σ-1 1","C","r Σ-1 r"]
[null,"B","1 Σ-1 r","D","A*C - B*B"]
[]
[null,"Efficiency frontier","σ2 = (1 + (Aμ-B)2 / D) / A"]
[]
[null,"CAPM Calculator Parameters"]
[]
[null,"Σ-1","Inverse covariance matrix"]
[]
[null,"Output Tabs"]
[]
[null,"input","CAPM Inputs tab","γ, rhist, Σ"]
[null,"output","CAPM output tab",", rmin, rMtk, rCAPM"]
[null,"investors","Output for investors' problem (the solution is constructed for both the historical and CAPM returns)","rhist, demand (x), xmin, xM, A, B, C, D, Efficiency frontier"]
[null,"calc","CAPM calculator fields","Σ-1"]
[null,"test","CAPM tests"]
[null,"charts","Efficiency frontier, excess demand/supply, alphas, betas"]

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["EOAN"]
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[]
[null,"2017-01-01"]
[null,"2017-04-30",null,null,null,null,null,"Column1","Column2","Column3"]
[null,"MSFT"]

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