7. Let X1 and X2 denote the prices of Stock 1 and Stock 2. The price of Stock 1

Question

7. Let X1 and X2 denote the prices of Stock 1 and Stock 2. The price of Stock 1 is $1.00 and that of Stock 2 is also $1.00. I invest $3.00 to buy the stocks. Based on historical data, the mean price of Stock 1 is $1.00 and that of Stock 2 is also $1.00. The variance of Stock 1 is 0.25 (dollar2 ) and that of Stock 2 is also 0.25.

7-1. (1 point) What is the variance of 3X1? Answer: V[3X1] = ______________

7-2. (2 points) Assume that X1 and X2 are independent.

What is the variance of X1 + 2X2? Answer: V[X1 + 2X2] = ____________________

7-3. (2 points) Assume that the correlation between X1 and X2 is – 1 (negative one).

What is the variance of X1 + 2X2? Answer: V[X1 + 2X2] = _______________

7. Let X1 and X2 denote the prices of Stock 1 and Stock 2. The price of Stock 1 is $1.00 and that of Stock 2 is also $1.00.linvest $3.00 to buy the stocks. Based on historical data, the mean price of Stock 1 is $1.00 and that of Stock 2 is also $1.00. The variance of Stock 1 is 0.25 (dollar 2) and that of Stock 2 is also 0.25 7-1. (1 point) What is the variance of 3X1? Answer: V13X 7-2. (2 points) Assume that X1 and X2 are independent. What is the variance of X1 2X2? Answer: V 2X 7-3. (2 points) Assume that the correlation between X1 and X2 is-1(negative one). What is the variance of X1 +2X2? Answer: V 2X

Explanation / Answer

7.1)Var(3X1) =32*Var*(X1) =9*0.25=2.25

7.2)V(X1+2X2) =Var(X1)+4*Var(X2)=0.25+4*0.25=1.25

7.3) V(X1+2X2) =Var(X1)+4*Var(X2) +2*1*2*(-1)*(Var(X1)*Var(X2))1/2 =0.25+4*0.25-4*(0.25*0.25)1/2

=1.25-1 =0.25

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