ABCDEFGHIJKLMNOPQRST
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Asset 1 (e.g., equity fund)Asset 2 (e.g., fixed income fund)
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Expected return (daily, %)0.0743142840.015546375
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Standard deviation (%)1.7260443050.281412607
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Covariance (S12, %^2)0.3442356393
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Efficient Portfolio Frontier
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aS = sqrt(bR^2 + cR + d)
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Where
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a = R1 - R2
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a =0.058767909
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b = S1^2 + S2^2 - 2S12
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b =2.36995072
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c = 2[(R1 + R2)S12 - R2S1^2 - R1S2^2]
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c =-0.04253628833
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d = (R2^2)(S1^2) + (R1^2)(S2^2) - 2R1R2S12
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d = 0.0003619986839
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Sample PortfoliosX1X2R (%)S (%)Notes
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10.50.50.04493032950.9678446772
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20.20.80.02729995680.5291579327
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3-0.11171.11170.0089819995650.2226031369Minimum variance portfolio
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AnnualDaily (%)
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Risk free rate (Rf)1.249%0.0034007820
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Slope = (bR + c)/(aS)
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V1 = R1 - Rf0.07091350195
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V2 = R2 - Rf0.01214559295
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Weight of Asset 1 in Optimal Portfolio = X1 =
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(V1S2^2 - V2S12)/[V1S2^2 + V2S1^2 - (V1 + V2)S12]
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10.86%
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Weight of Asset 2 in Optimal Portfolio = X2 =
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89.14%
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Daily (%)Annual
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Optimal Portfolio Return = Rp =0.021930671578.33%
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Optimal Portfolio Standard Deviation = Sp =0.4058925684
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Slope of Capital Allocation Line/Sharpe Ratio0.04565220201
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