8-1: EXPECTED RETURN A stock’sreturns have the following distribution: Demandfor

ID: 2662282 • Letter: 8

Question

8-1: EXPECTED RETURN A stock’sreturns have the following distribution:

Demandfor the Probabilityof This Rateof Return If This

Company’sProducts Demand Occurring DemandOccurs

Weak 0.1 (50%)

BelowAverage 0.2 (5)

Average 0.4 16

Aboveaverage 0.2 25

Strong 0.1 60

1.0

Calculate thestock’s expected return, standard deviation, and coefficientof variation.

Explanation / Answer

Answer:

We know that,

Expected Return = P1R1 +P2R2 + P3R3 +P4R4 + P5R5

Expected Return = [0.1 * -50%] + [0.2 * -5%] + [0.4 * 16%] +[0.2 * 25%] + [0.1 * 60%]

Expected Return = [-5%] + [-1%] + [6.4%] + [5%] + [6%]

Expected Return = 11.4% or 0.114

(1)

Demand for theCompany’s Products

(2)

Probability of thisDemand Occurring

(3)

Return Deviation fromExpected Return

(4)

Squared ReturnDeviation from Expected Return

(5)

Product

(2) X (4)

Weak

0.1

-0.5 – 0.114 = -0.614

(-0.614)2 = 0.376996

0.1*0.376996 = 0.0376996

Below Average

0.2

-0.05 – 0.114 = -0.164

(-0.164)2 = 0.026896

0.2*0.026896 = 0.0053792

Average

0.4

0.16 – 0.114 = 0.046

(0.046)2 = 0.002116

0.4*0.002116 = 0.0008464

Above Average

0.2

0.25 – 0.114 = 0.136

(0.136)2 = 0.018496

0.2*0.018496 = 0.0036992

Strong

0.1

0.60 – 0.114 = 0.486

(0.486)2 = 0.236196

0.1*0.236196 = 0.0236196

Summation of the fifth column Product (5) = Variance

Variance = 2 = [0.0376996] + [0.0053792] +[0.0008464] + [0.0036992] + [0.0236196]

Variance = 2 = 0.071244

Standard Deviation () = 2

Standard Deviation () = 0.071244

Standard Deviation () = 0.266916 or 26.69% mightbe a higher risk.

Coefficient of variation = Standard deviation / Expectedreturn

Coefficient of variation = 26.6916% / 11.4%

Coefficient of variation = 2.3414 relatively a highvariation in the returns of the stock.

(1)