You find a certain stock that had returns of 14.8 percent, –22.4 percent, 28.4 p
ID: 2802234 • Letter: Y
Question
You find a certain stock that had returns of 14.8 percent, –22.4 percent, 28.4 percent, and 19.4 percent for four of the last five years. Assume the average return of the stock over this period was 12.8 percent.
What was the stock’s return for the missing year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Stock's return %
What is the standard deviation of the stock’s returns? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Standard deviation %
Explanation / Answer
Missing return = 23.8%
Standard deviation = .2032 or 20.32%
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The arithmetic mean, also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables.
Arithmetic mean = (Sum of all the values in the data set)/ Number of data
Let’s put the values in the formula
.128 = [(.148 + (-.224) + .284 + .194 + X]/5
.128 * 5 = .402 + X
.64 = .402 + X
X = .64 - .402
X = .238 or 23.8%
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Standard deviation is a measure of the dispersion of a set of data from its mean. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. In finance, standard deviation is a statistical measurement; when applied to the annual rate of return of an investment, it sheds light on the historical volatility of that investment. The greater the standard deviation of a security, the greater the variance between each price and the mean, indicating a larger price range.
Standard deviation = UNDROOT[Sigma(X-µ)^2/N-1]
Where,
X = Value in the data set
µ= Sum of all the data sent divided by number of data
N = Number of data points
Let's find the mean of the numbers
µ = (Sum of numbers in data set)/number of data
= (0.148 + -0.224 + 0.284 + 0.194 + 0.238 + 0 + 0 + 0 + 0 + 0)/ 5
= 0.64/ 5
= 0.128
Data (X)
(X-µ)
(X-µ)^2
0.148
0.02
0.0004
-0.224
-0.352
0.1239
0.284
0.156
0.0243
0.194
0.066
0.0044
0.238
0.11
0.0121
Total
0.1651
Let's put the values in the formula to find standard deviation
Standard deviation = UNDROOT[0.1651/ (5- 1)]
= UNDROOT[0.1651/ 4]
= UNDROOT[0.0413]
= 0.2032
So standard deviation of numbers is 0.2032
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Hope that helps.
Feel free to comment if need further assistance J
Data (X)
(X-µ)
(X-µ)^2
0.148
0.02
0.0004
-0.224
-0.352
0.1239
0.284
0.156
0.0243
0.194
0.066
0.0044
0.238
0.11
0.0121
Total
0.1651
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