Question

You find a certain stock that had returns of 8 percent, −3 percent, 12 percent, and 17 percent for four of the last five years. The average return of the stock for the past five-year period was 6 percent. What is the standard deviation of the stock's returns for the five-year period?

Answer 1

Answer:

Standard deviation of stock's return =  8.27%

Step-by-step explanation:

Average = sum/ total no.

Since the given average is for 5 years but the yearly returns are given for four years, we have to first find the missing return for fifth year

Average = sum/ total number

Since average=0.06 and total no. is 5, we can find the missing no. X

            (0.08 - 0.03 + 0.12 + 0.17 + X)÷5 = 0.06

                    X = - 0.04

       

Variance is the the average of the squared differences from the Mean.

Variance = 1/5[$(0.08 - 0.06)^{2}$ + $(- 0.03 - 0.06)^{2}$ + $(0.12 - 0.06) ^{2}$+ $(0.17 - 0.06)^{2}$ + $(-0.04 - 0.06)^{2}$]

                = 0.0342 ÷ 5

                = 0.00684

Standard deviation = squar-root of variance

       S.D = √0.00684

              = 8.27%

Answer 2

Answer:

Standard deviation = 8.27 percent

Step-by-step explanation:

Average = (Σx)/N

The average is the sum of variables divided by the number of variables.

x = each variable

N = number of variables = 5

Let the unknown percent be y

6 = (8 - 3 + 12 + 17 + y)/5

y = 30 - 34 = - 4

The standard deviation is the square root of variance. And variance is an average of the squared deviations from the mean.

Mathematically,

Standard deviation = σ = √[Σ(x - xbar)²/N]

x = each variable

xbar = mean = 6 percent

N = number of variables

σ = √[{(8 - 6)² + (-3 - 6)² + (12 - 6)² + (17 - 6)² + (-4 - 6)²}]/(5)]

σ = √[[(2)² + (-9)² + (6)² + (11)² + (-10)²]/(5)]

σ = √[(4 + 81 + 36 + 121 + 100)/(5)] = √(342/5) = 8.27 percent.