Question

1. The return on shares of Valley Transporter is predicted under the following various economic conditions:
Recession  -0.14
Normal +0.07
Boom +0.24
If each economy state has the same probability of occurring, what is the variance of the stock?
Place your answer in decimal form using four decimal places.

2. The return on shares of the Orange Company are predicted under the following states of nature. The states of nature are all equally likely, and because there are a total of three states, each state has a 33.333% chance of occurring.

Recession  -0.14
Normal +0.07
Boom +0.20

What is the standard deviation of Orange?
Place your answer in decimal form, for example as say .0675 and not 6.75.

3. The return on the Rush Corporation in the state of recession is estimated to be -24% and the return on Rush in the state of boom is estimated to be 35%. The return on the Oberman Corporation in the state of recession is estimated to be 42% and the return on Oberman in the state of boom is estimated to be -19%. Given this information, what is the covariance between Rush and Oberman if there is a 0.70 probability that the economy will be in the state of boom and a 0.30 probability that the economy will be in the state of recession.

Place your answer in decimal form and not as a percentage.

****Please show how to get all anwsers

Answer 1

1) Variance of the stock is the square of the Standard Deviation of the returns from a stock.

Each economy state has equal probability which is equal to 1/3 = 0.3333

We can calculate variance directly as follows :

	State of Economy	Probability (p)	Return (X)	Expected Return = p * X	Dx = X - Expected Return*	(Dx)2	p x (Dx)2
	Recession	0.3333	-0.14	-0.046662	-0.196661	0.038675549	0.01289056
	Normal	0.3333	0.07	0.023331	0.013339	0.000177929	0
	Boom	0.3333	0.24	0.079992	0.183339	0.033613189	0.011203276
				0.056661			0.024093836
	* Note : We have calculated expected return as sum of p*X = 0.056661
			Variance = Sum of (p x Dx2) = 0.0241 (rounded off)

Variance of the stock = 0.0241

2) Standard Deviation of Orange = 0.1401 (calculated below)

Variance is p x Dx² , and the square root of this value is equal to Standard Deviation

3) Covariance between Rush and Oberman = [ p * (X - Expected return of X) * (Y - Expected return of Y) ]

Covariance = -0.0756 (shown below)