ࡱ> !# ` @)bjbjss ..,4$UhEYZ @n}3zto0CCCj  Minimum Variance Portfolio Weight  EMBED Equation.3  Portfolio Variance with Weights and Standard Deviations  EMBED Equation.3  Optimal Portfolio (Weight in Bonds)  EMBED Equation.3  Covariance and Correlation Coefficient Covariance (rS , rB ) = S B S,B Or S,B = Covariance (rS , rB ) / (S B ) Correlation Coefficient = S,B Portfolio Problem Use the following two portfolios to answer parts one to four. PortfolioExpected ReturnStandard DeviationBond Portfolio6%10%Stock13%30% If the correlation coefficient (() is -0.40 for these two risky assets, what is the minimum variance portfolio you can construct? (Hint: What percent of your wealth is invested in each portfolio?)  EMBED Equation.3  Weight in the stock is 1 minus weight in the bond or 1 0.8226 = 0.1774 82.26% in Bond, and 17.74% in Stock What is the expected return on the MVP (minimum variance portfolio) in part one using your allocation of wealth to bonds and stocks? E(rMVP) = (0.8226) x (0.06) + (0.1774) x (0.13) = 0.0724 or 7.24% What is the standard deviation of the minimum variance portfolio? 2 = (.1774)2 (0.30)2 + (0.8226)2 (0.10)2 + 2 (.8226) (.1774) (0.30) (0.10) (-0.4) 2 = 0.002833 + 0.006766 - 0.003593 = 0.006097  EMBED Equation.3!"$%89:;vwx ͼܥ䴌xiXxPPhPCJaJ!j$h!hCJEHUaJjHG hCJUVaJh!CJaJjh!CJUaJhuCJaJ!jWh_h!CJEHUaJjG h!CJUVaJhvCJaJ!jh_h_CJEHUaJj~G h_CJUVaJh_CJaJjh_CJUaJhGjCJaJhd/yCJaJ"#$<=uvw  " t v x $a$gdhf$a$gdP$a$gdv$a$gdd/y@)        " $ * L N V X d f h l n r x   % & Ĺwhj"G h*CJUVaJhfCJaJjhfCJUaJ jrhnh&hnhvCJaJhvhvCJaJhvhhfCJH*aJhvhhfCJaJhhfCJaJhPhPCJaJhvhPCJH*aJhvhPCJaJhPCJaJhPCJH*aJ&x ^ ` t `kd $$IflF ,"   06    4 la $IfgdP/gdn$a$gdd/y$a$gdv  ukd< $$IflF ,"   06    4 la $IfgdP/   . / V W X ~yyyyyyyyyyyyygdnkd $$IflF ,"   06    4 la  # ( , - . / 2 7 F K V X Y &.6>@JR $&(*04<DLPxz|~ڻֳֳ޷ַַַ hM3hnh ThM3 hM3H* hfH* hfH*h&hfhfH*h*hfhnjhfCJUaJ!jZ h*h*CJEHUaJD BDFHJz| $$$$$$%%%&&(&&& ' ''gd5Lgdn$$$$ $ $$$$$%%%%%%%%%& &"&$&&&t&|&&&&&&''((((,(.(D(F(T(V(ŽŮѽŒ}}}}x}s}s}s}s}s h5LH* h5LH*h5Lhvj4h Th5LEHUj"G h5LCJUVaJjih Th TEHUj5H G h TCJUVaJjh TUh Thnh&hITjhM3hAfUEHUj"G hAfUCJUVaJUhM3jhM3U-  Hint, must be less than 10% the standard deviation of the bond portfolio. What is the optimal portfolio of these two assets if the risk-free rate is 3% (i.e., how do you allocate of your wealth in stocks and bonds)?  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