Let X, Y, Z be the three assets, with VAR(X) = VAR(Y) = VAR(Z) = 1. Z is independent from X and Y , and COV(X, Y) = 0.2 . Assuming no short selling, what is the portfolio weight on Z that gives the smallest variance? (Hint: since Z is independent with X and %3D %3D Y, you may express wx and wy as a function of 1 - wz , and then find wz)

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Let X, Y, Z be the three assets, with VAR(X) = VAR(Y) = VAR(Z) = 1. Z is
independent from X and Y , and COV(X, Y) = 0.2 .Assuming no short selling, what is the
portfolio weight on Z that gives the smallest variance? (Hint: since Z is independent with X and
Y, you may express wx and wy as a function of 1- wz , and then find wz.)
Transcribed Image Text:Let X, Y, Z be the three assets, with VAR(X) = VAR(Y) = VAR(Z) = 1. Z is independent from X and Y , and COV(X, Y) = 0.2 .Assuming no short selling, what is the portfolio weight on Z that gives the smallest variance? (Hint: since Z is independent with X and Y, you may express wx and wy as a function of 1- wz , and then find wz.)
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