I need help with these homework questions.

For full marks please show all calculations/formulas.

1. Consider the following information on three stocks in four possible future states of the economy:

Rate of return if state occurs

State of economy Probability of state of economy Stock A Stock B Stock C

Boom 0.3 0.35 0.45 0.38

Good 0.3 0.15 0.20 0.12

Poor 0.3 0.05 -0.10 -0.05

Bust 0.1 0.00 -0.30 -0.10

a. Your portfolio is invested 30% in A, 50% in B, and 20% in C. What is the expected return of your portfolio?

b. What is the variance of this portfolio?

c. What is the standard deviation of this portfolio?

2 a) Suppose we observe two stocks with the following characteristics:

Stock expected return Beta

K 20% 1.6

L 12% 0.9

An asset is said to be overvalued if its price is too high given its expected return and risk. The risk-free rate is currently 6%. Is one of the two stocks overvalued relative to the other? Explain your answer fully (i.e., provide reasons why you think the stock is or is not overvalued).

b) Suppose we observe two stocks with the following characteristics:

Stockexpected returnBeta

M 20%1.6

N 12%0.9

An asset is said to be undervalued if its price is too low given its expected return and risk. The risk-free rate is currently 6%. Is one of the two stocks undervalued relative to the other? Explain your answer fully (i.e., provide reasons why you think the stock is or is not undervalued).

c)In a well-functioning, well-organized, active market, can a stock be persistently over- or undervalued relative to an average asset in the market? Explain why or why not. How and when is equilibrium achieved?

3 - Suppose we have two risky assets, Stock I and Stock J, and a risk-free asset. Stock I has an expected return of 25% and a beta of 1.5. Stock J has an expected return of 20% and a beta of 0.8. The risk-free asset's return is 5%.

a.Calculate the expected returns and betas on portfolios with x% invested in Stock I and the rest invested in the risk-free asset, where x% = 0%, 50%, 100%, and 150%.

b.Using the four portfolio betas calculated in part (a), reverse engineer (i.e., derive mathematically) the portfolio weights for a portfolio consisting of only Stock J and the risk-free asset.

Hint: For example, if we wished to obtain a portfolio beta of 0.5, then the weights on Stock J and the risk-free asset must be 62.5% and 37.5%, respectively, and the expected return for this portfolio must be 14.375%.

c.Calculate the reward-to-risk ratios for Stock I and Stock J.

d.Plot the portfolio betas against the portfolio expected returns for Stock I on a graph, and link all the points together with a line. Then plot the portfolio betas against the portfolio expected returns for Stock J on the same graph and link all these points together with another line. Ensure that the x-axis and y-axis are clearly labelled. (Hint: This can be done easily with the charting function in Microsoft Excel.) Please show the steps to create the graph in Excel.

e. Using the graph in part (d) above, together with your answers in part (c) above, elaborate on the efficiency of the market containing Stock I and Stock J.