Question

Returns earned over a given time period are called realized returns. Historical data on realized returns is often used to estimate future results. Analysts across companies use realized stock returns to estimate the risk of a stock.

Consider the case of Celestial Crane Cosmetics Inc. (CCC):

Five years of realized returns for CCC are given in the following table. Remember:

1.	While CCC was started 40 years ago, its common stock has been publicly traded for the past 25 years.
2.	The returns on its equity are calculated as arithmetic returns.
3.	The historical returns for CCC for 2012 to 2016 are:

	2012	2013	2014	2015	2016
Stock return	22.50%	15.30%	27.00%	37.80%	11.70%

Given the preceding data, the average realized return on CCC’s stock is ___ .

The preceding data series represents   of CCC’s historical returns. Based on this conclusion, the standard deviation of CCC’s historical returns is___ .

If investors expect the average realized return from 2012 to 2016 on CCC’s stock to continue into the future, its coefficient of variation (CV) will be ___ .

Answer 1

Average Return = [0.2250 + 0.1530 + 0.2700 + 0.3780 + 0.1170] / 5
Average Return = 1.1430 / 5
Average Return = 0.2286 or 22.86%

Variance = [(0.2250 - 0.2286)^2 + (0.1530 - 0.2286)^2 + (0.2700 - 0.2286)^2 + (0.3780 - 0.2286)^2 + (0.1170 - 0.2286)^2] / 4
Variance = 0.0422172 / 4
Variance = 0.0105543

Standard Deviation = (0.0105543)^(1/2)
Standard Deviation = 0.1027 or 10.27%

Coefficient of Variation = Standard Deviation / Average Return
Coefficient of Variation = 0.1027 / 0.2286
Coefficient of Variation = 0.45

Given the preceding data, the average realized return on CCC’s stock is 22.86%.
The preceding data series represents a sample of CCC’s historical returns. Based on this conclusion, the standard deviation of CCC’s historical returns is 10.27%
If investors expect the average realized returns from 2012 to 2016 on CCC’s stock to continue into the future, its coefficient of variation (CV) will be 0.45.