Considering the stocks in the previous question, where Stock Xillow has an expected return of 16%...

Considering the stocks in the previous question, where Stock Xillow has an expected return of 16% and a standard deviation of 4% and Stock Yash has an expected return of 12% and a standard deviation of 3%. The stocks have a correlation coefficient of -0.3. What is the weight of the investment in Stock Xillow that creates the minimum variance portfolio of the two stocks? A. From 0% to 20% B. From 20% to 40% C. From 40% to 60% D. From 60% to 80% E. From 80% to 100%

Expert Solution

Minimum Variance Portfolio:

A minimum variance portfolio is a collection of securities that combine to minimize the price volatility of the overall portfolio. with the given weights to securities/ Assets in portfolio, portfolio risk will be minimal.

Weight in A = [ [ (SD of B)^2] - [ SD of A * SD of B * r(A,B) ] ] / [ [ (SD of A)^2 ]+ [ (SD of B)^2 ] - [ 2* SD of A * SD of B * r (A, B) ] ]
Weight in B = [ [ (SD of A)^2] - [ SD of A * SD of B * r(A,B) ] ] / [ [ (SD of A)^2 ]+ [ (SD of B)^2 ] - [ 2* SD of A * SD of B * r (A, B) ] ]

A =Xillow

B = Yash

Particulars	Amount
SD of A	4.0%
SD of B	3.0%
r(A,B)	-0.3000

Weight in A = [ [ (SD of B)^2] - [ SD of A * SD of B * r(A,B) ] ] / [ [ (SD of A)^2 ]+ [ (SD of B)^2 ] - [ 2* SD of A * SD of B * r (A, B) ] ]
= [ [ (0.03)^2 ] - [ 0.04 * 0.03 * -0.3 ] ] / [ [ (0.04)^2 ] + [ ( 0.03 )^2 ] - [ 2 * 0.04 * 0.03 * -0.3 ] ]
= [ [ 0.0009 ] - [ -0.00036 ] ] / [ [ 0.0016 ] + [ 0.0009 ] - [ 2 * -0.00036 ] ]
= [ 0.00126 ] / [ 0.00322 ]
= 0.391304

Weight of Investment in Xillow is 39.13%

Option B is correct.

jeff jeffy answered 1 year ago

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