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Var can never be negative,

and since (std dev)^2 = variance

when you squared root the Var to get Std Dev, mathematically, you will get 2 values which is one +ve and one -ve, with same magnitude

usually we will take +ve value to express, so if the std dev is 5%, it is interpreated as the extimated value can be 5% higher or 5% lower from the mean

for the equation quoted : The variance of a 2 asset port = (Wa^2)(Var a) + (Wb^2)(Var b) + 2(Wa)(Wb)(Std a)(Std b)(Correl (a,b))

for any value of correlation you input from -1 to 0, play around with the weight & std dev of each asset, you will never get -ve value as the answer, you can try and see

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