Question

Expected rate of return and risk. Syntex, inc is considering an investment in one of two common stocks. Given the information that follows, which invest is better, based on the risk (as measured by the standard deviation) and return? Common stock A Common stock B Probability Return Probability Return 0.36 13% 0.10 -6% 0.30 17% 0.40 8% 0.35 21% 0.40 16% 0.10 21%

Answer 1

Stock A

Expected return(Stock A)

(0.35*13%)+(0.3*17%)+(0.35*21%)=

17%

Std. deviation of Returns(Stock A)from expected return(A)

is the Square root of

the sum of

the squared deviations

of the individual returns

from the mean /most probable return.

ie.

((p1*(R1-ER A)^2)+(p2*(R2-ER A)^2)+(p3*(R3-ER A)^2))^(1/2)

((0.35*(13%-17%)^2)+(0.3*(17%-17%)^2)+(0.35*(21%-17%)^2))^(1/2)

3.35%

Stock B

Expected return(Stock B)

(0.1*-6%)+(0.4*8%)+(0.4*16%)+(0.1*21%)=

11.1%

Std. deviation of Returns(Stock A)from expected return(A)

is the Square root of

the sum of

the squared deviations

of the individual returns

from the mean /most probable return.

ie.

((p1*(R1-ER A)^2)+(p2*(R2-ER A)^2)+(p3*(R3-ER A)^2))+(p4*(R4-ER 4)^2))^(1/2)

((0.1*(-6%-11.1%)^2)+(0.4*(8%-11.1%)^2)+(0.4*(16%-11.1%)^2))+(0.1*(21%-11.1%)^2)^(1/2)=

3.56%

Summary
	ER	Std. devn
Stock A	17%	3.35%
Stock B	11.1%	3.56%

From the above, Stock A is preferred as it has greater probable returns & also lesser volatility ,ie. Comparatively less tendency to deviate from the most expected return--inferred from the standard deviation %