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

Question

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] = _______________

Explanation / Answer

7-1. Var[3X1] = 3^2 * var[X1] = 9*0.25 = 2.25

7-2. V[X1 + 2X2] = V[X1] + 2^2 * V[X2] = 0.25+4*0.25 = 1.25

7-3 V[X1 + 2X2] =  V[X1] + 2^2 *  V[X2] + 2*(-1)*sqrt(0.25)^2 = 0.25+4(0.25) - 1 =0.25

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