Your portfolio consists of two assets: $10,500 of Intel's corporate bonds and $15,700 of Microsoft stock. The standard deviations of returns for Intel's bonds and Microsoft stock are 12% and 27%, respectively. The correlation between these two investments is 0.33. What is the standard deviation of your portfolio?

Answer:18.35%Step-by-step explanation:The proportion of the standard deviation of return of the portfolio combining two assets A and B is given by [tex]\large \sigma_P=\sqrt{W_A^2\sigma_A^2+W_B^2\sigma_B^2+2R(A,B)W_A\sigma_AW_B\sigma_B}[/tex] where [tex]\large W_A[/tex] = proportion of asset A in the investment. [tex]\large W_B[/tex] = proportion of asset B in the investment. [tex]\large \sigma_A[/tex] = proportion of standard deviation of return for asset A. [tex]\large \sigma_B[/tex] = proportion of standard deviation of return for asset B. R(A,B) = correlation between the two investments The total investment is $10,500 + $15,700 = $26,200 Let A be the asset of Intel's corporate bonds and B the asset of Microsoft stocks [tex]\large W_A=\frac{10,500}{26,200}=0.4[/tex] [tex]\large W_B=\frac{15,700}{26,200}=0.6[/tex] [tex]\large \sigma_A=0.12[/tex] [tex]\large \sigma_B=0.27[/tex] R(A,B) = 0.33 Replacing in our formula [tex]\large \sigma_P=\sqrt{(0.4)^2(0.12)^2+(0.6)^2(0.27)^2+2*0.33*0.4*0.12*0.6*0.27}\Rightarrow\\\\\boxed{\sigma_P=0.1835=18.35\%}[/tex]