(1 point) Asset 1 has expected rate of return T1-0.08 and volatility 1 0.12, and
ID: 2812188 • Letter: #
Question
(1 point) Asset 1 has expected rate of return T1-0.08 and volatility 1 0.12, and asset 2 has expected rate of return T2 =0.13 and volatility 2-02. The covariance of the rates of return T1 and T2 is 1.2 0.0072. Consider portfolios that combine the two assets with weights wi and 2, where wi + 21 To find the weights for the minimum variance portfolio using Lagrange multipliers, we first define Then using the known values for 1, 2, and 1,2, equation (1) becomes (2) f(w1,w2) (type wi as w1, w2 as w2) We next define The partial derivative of F with respect to w is (4) Fan- The partial derivative of F with respect to w2 is (type A as lambda) (type X as lambda) The partial derivative of F with respect to is (6) F Requiring that Ful-0, FWy0, and ¾ 0, gives algebraic equations for wi, W2 and The minimum variance portfolio corresponds to weights WI = , W2 The minimum variance portfolio has expected return rate and volatilityExplanation / Answer
f(w1,w2)=0.5*(w1^2*0.12^2+w2^2*0.2^2+2*w1*w2*0.0072)
Fw1=w1*0.12^2+w2*0.0072-lambda
Fw2=w2*0.2^2+w1*0.0072-lambda
Flambda=-w1-w2+1
w1*0.12^2+w2*0.0072-w2*0.2^2-w1*0.0072=0
=>w1=0.82
w2=0.18
rP=0.82*0.08+0.18*0.13=0.089
standard deviaiton=sqrt(0.82^2*0.12^2+0.18^2*0.2^2+2*0.82*0.18*0.0072)=0.114472704
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