A portfolio has to be created that includes two assets, X an Y. THe standard dev

Question

A portfolio has to be created that includes two assets, X an Y. THe standard deviation of X and Y are 9% and 0% respectively. The correlation between the two assets is 0. What proportion of your portfolio must be invested in X so that the standard deviation of your portfolio is 6%? (The answer is 0.67 - need to know how it's calculated.) Step -by-step calculation applying relevant formula is required. EXCEL IS NOT ALLOWED (I know the answer because I used Excel - the solution I seek here is the one based on non-excel calucation)

Explanation / Answer

let w be proportion of portfolio invested in X

hence 1-w is invested in Y

w * Sa + (1-w) *sb = S

=>

w * 9% + (1-w) * 0 = 6%

=>

w = 2/3 = 0.67

proportion of protfolio invested in X = 0.67

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