Question

Question 1:

You are planning about putting some money in the stock market. There are two stocks in your mind: stock A and stock B. The economy can either go in recession or it will boom in the coming years. Being an optimistic investor, you believe the likelihood of observing an economic boom is two times as high as observing an economic depression. You also know the following about your two stocks:

State of the Economy	Probability	RA	RB
Boom		3%	–2%
Recession		6%	6%

a. Calculate the expected return for stock A and stock B

b. Calculate the total risk (variance and standard deviation) for stock A and for stock B

c. Calculate the expected return on a portfolio consisting of equal proportions in both stocks.

d. Calculate the expected return on a portfolio consisting of 10% invested in stock A and the remainder in stock B.

e. Calculate the covariance between stock A and stock B.

f. Calculate the correlation coefficient between stock A and stock B.

g. Calculate the variance of the portfolio with equal proportions in both stocks using the covariance from answer e.

h. Calculate the variance of the portfolio with equal proportions in both stocks using the portfolio returns and expected portfolio returns from answer c.

Answer 1

An economic boom is 2 times as high as observing an economic depression .. F economic depression bex then economic boom will be ax. . Probability of economic depression = 722 = 13. Probability of economic boom = 20 = ²/3 a Calculation of Expected Return Expected Return = { Probability of economy x Rerwn of that economy in 1. Expected Return of Stock A =RA s = 2/3 * 3% + 13x6% = 2% +2% 4% . 3 . dici . it Expected Return of Stock B = Rs = 23* (-2%) + 13x6% -1.33%. + 2% = 0.67%

DATE: 1 b Calculation of Variance 4 Standard Deviation Variance = {P.(RA-RA) ² Standard Deviation = Variance Variance of Stock A = 2/3* (4-3) + 13 (4-6)2 -0-67 +1:33 - 2 Standard Deviation of Stock A = √2 -1-41 Variance of StockB - 213 (067-(-2)) + 1/3 (0-67-6)* = 4.75 + 9.47 - 12.22 Standard Deviation of Stock B=√14.22 = 3.77 a Expected Rerum of Portolio with equal proportion in both Stock j.e. 50% in both stock. . Expected Return of Portfolio = MG{Weight & Return of Stock = 50% x 4% + 50%x 0.67% = 2% + 0.335 % - 2.335% d Expected Return of Portfolio it 10% in StockA & go% in stock B = 10%x 4% + 90%x0.67% = 0.4% + 0.603% = 1.003%