Question

Q1/Calculate the expected return for a stock, given the following information about its returns in different states of the economy.

State of economy	Probability	Stock return
Recession	0.16	-0.15
Normal	0.43	0.07
Boom	--	0.25

Enter return in percents, not in decimals.

Q2/Given the following information about the returns of stocks A, B, and C, what is the expected return of a portfolio invested 30% in stock A, 40% in stock B, and 30% in stock C?

State of economy	Probability	Stock A	Stock B	Stock C
Boom	0.19	0.37	0.26	0.35
Good	0.22	0.23	0.15	0.27
Poor	0.2	0.09	0.04	0.02
Bust	--	-0.17	-0.14	-0.25

Enter answer in percents.

Q3/

Given the following information about a stock's return in the various states of the economy, calculate the standard deviation of its return.

State of economy	Probability	Stock return
Recession	0.16	-0.27
Normal	0.49	0.04
Boom	--	0.24

Enter answer in percents, accurate to two decimal places.

Answer 1

Q1. Expected Return = 10.86%

State of economy	Probability	Stock return	Probability* Return
Recession	0.16	-0.15	-0.024
Normal	0.43	0.07	0.0301
Boom	0.41	0.25	0.1025
expected return for a stock			0.1086
expected return for a stock %			10.86

Note : For Boom Probability = 1- 0.16-0.43

-----

2. the correct answer is 4.582%

Note :

a. For Poor Probability = 1- 0.19- 0.22- 0.2

= 0.39

b.

		Stock A		Stock B		Stock C		Total
State of economy	Probability	Stock A	Probability* Return	Stock B	Probability* Return	Stock C	Probability* Return
Boom	0.19	0.37	0.0703	0.26	0.0494	0.35	0.0665
Good	0.22	0.23	0.0506	0.15	0.033	0.27	0.0594
Poor	0.2	0.09	0.018	0.04	0.008	0.02	0.004
Bust	0.39	-0.17	-0.0663	-0.14	-0.0546	-0.25	-0.0975
			7.26		3.58		3.24
Weights			30%		40%		30%
expected return			2.178		1.432		0.972	4.582

3. The correct answer is 17.02%

Note :

For Boom , Probability = 1-0.16-0.49

	Probability	Stock Return	Expected Return ( Probability * Expected Return)
Recession	0.16	-0.27	-0.0432
Normal	0.49	0.04	0.0196
Boom	0.35	0.24	0.0840
	Expected Return		0.06
	Expected Return   %		6.04
Stock A	Probability	Probable Return	Deviation ( Probable Return- Expected Return)	Deviation Squared	Product ( Deviation Squared* Probability)
Recession	0.16	-27.00	-33.04	1,091.64	174.66
Normal	0.49	4.00	-2.04	4.16	2.04
Boom	0.35	24.00	17.96	322.56	112.90
			Variance		289.60
			Standard Deviation (Square root of Variance)		17.02