Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 16% and a standard deviation of return of 18.0%. Stock B has an expected return of 12% and a standard deviation of return of 3%. The correlation coefficient between the returns of A and B is 0.50. The risk-free rate of return is 10%. The proportion of the optimal risky portfolio that should be invested in stock A is

Answer 1

The proportion of the optimal risky portfolio that should be invested in stock A is 0%.

Using this formula

Stock A optimal risky portfolio=[(Wa-RFR )×SDB²]-[(Wb-RFR)×SDA×SDB×CC] ÷ [(Wa-RFR )×SDB²+(Wb-RFR)SDA²]- [(Wa-RFR +Wb-RFR )×SDA×SDB×CC]

Where:

Stock A Expected Return  (Wa) =16%

Stock A Standard Deviation (SDA)= 18.0%

Stock B Expected Return  (Wb)= 12%

Stock B Standard Deviation(SDB) = 3%  

Correlation Coefficient for Stock A and B (CC) = 0.50  

Risk Free rate of return(RFR) = 10%

Let plug in the formula

Stock A optimal risky portfolio=[(.16-.10)×.03²]-[(.12-.10)×.18×.03×0.50]÷ [(.16-.10 )×.03²+(.12-.10)×.18²]- [(.16-.10 +.12-.10 )×.18×.03×0.50]

Stock A optimal risky portfolio=(0.000054-0.000054)÷(0.000702-0.000216)

Stock A optimal risky portfolio=0÷0.000486×100%

Stock A optimal risky portfolio=0%

Inconclusion the proportion of the optimal risky portfolio that should be invested in stock A is 0%.

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