Problem 13-7 Calculating Returns and Standard Deviations [LO1]

Problem 13-7 Calculating Returns and Standard Deviations [LO1]

Consider the following information:

  

				Rate of Return If State Occurs
State of	Probability of
Economy	State of Economy			Stock A			Stock B
Recession		.15			.06		−	.19
Normal		.60			.09			.10
Boom		.25			.14			.27

  

Calculate the expected return for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	Expected return
Stock A	%
Stock B	%

  

Calculate the standard deviation for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	Standard deviation
Stock A	%
Stock B	%

 

Explanation:

The expected return of an asset is the sum of each return times the probability of that return occurring. So, the expected return of each stock asset is:

E(RA) = .15(.06) + .60(.09) + .25(.14)

E(RA) = .0980, or 9.80%

E(RB) = .15(−.19) + .60(.10) + .25(.27)

E(RB) = .0990, or 9.90%

To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, then add all of these up. The result is the variance. So, the variance and standard deviation of each stock is:

  

σA2 =.15(.06 − .0980)2 + .60(.09 − .0980)2 + .25(.14 − .0980)2

σA2 = .00070

  

σA = (.00070)1/2

σA = .0264, or 2.64%

  

σB2 =.15(−.19 − .0990)2 + .60(.10 − .0990)2 + .25(.27 − .0990)2

σB2 = .01984

  

σB = (.01984)1/2

σB = .1409, or 14.09%