I have the answer key for this question, but I specifically need explanations for the following, please look at the question and provide a detailed explanation. Thanks.

1. From part B, why is the covariance between the stock A (or stock B) with the tangency portfolio found using the covariance between stocks A and B times the weight of B (or A)?

2. From part C, please explain the denominator in the formula for the weight for the riskless asset. What is a? Why is a = 2?

3. The stock market comprises two stocks, A and B, and a risk-free asset. The return on the risk-free asset is Rs = 1%. The table below gives next period's returns of the two stocks, RA and RB, in each state of the world. 1 State RA RB Probability Good 8% 1% 30% So-so 6% 2% 40% Bad -2% 3% 30% (a) Calculate the expected returns of stocks A and B and the standard deviations of these returns. Also, calculate the covariance between A and B's returns, Cov(RA, Rb), and their correlation coefficient, PA,B. (8 marks) (b) Suppose that you are told that the tangengey portfolio T of A and B satisfies the so-called the first-order condition: E[RA] Rf E[RB] RF BT where o at is the covariance between the returns on stock A and portfolio T, and OBT is the covariance between the returns on stock B and portfolio T. Using the first-order condition, calculate the tangency portfolio of stocks A and B. (8 marks) (e) Suppose that Tom's utility function is E(Rp) 2Var(Rp), where R, is his portfolio return formed from stocks A and B as well as the risk-free asset. What is Tom's optimal portfolio? (8 marks) 3. (a) The expected returns on stocks A and B are E[RA] E[RB] = 0.08 x 0.3+0.06 x 0.4 0.02 x 0.3 = 0.042, = 0.01 x 0.3+0.02 x 0.4+0.03 x 0.3 = 0.02. The standard deviations of the returns on stocks A and B are = (0.08 0.042) x 0.3+(0.06 0.042) x 0.4+(-0.02 0.042) x 0.3 = 0.0414, (0.01 0.02)2 x 0.3+(0.02 0.02) x 0.4+ (0.03 0.02) x 0.3 = 0.0077 OB = The covariance between RA and RB is O AB = E[RARB] ERA]E[RB] = 0.08 x 0.01 x 0.3+0.06 x 0.02 x 0.4+(-0.02)