Question

2. Measuring stand alone risk using realized data

2. Measuring standalone risk using realized data Aa Aa E 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 2015 are: stock turm 1750 1.90 2.0 2.0 2010 2012 17.50% 2013 11.90% 2014 21.00% 2015 29.40% 2016 9.10% Stock return Given the preceding data, the average realized return on CCC's stock is of CCC's historical returns. Based on this conclusion, the The preceding data series represents standard deviation of CCC's historical returns is

Answer 1

Average Return = [0.1750 + 0.1190 + 0.2100 + 0.2940 + 0.0910] / 5
Average Return = 0.8890 / 5
Average Return = 0.1778 or 17.78%

Variance = [(0.1750 - 0.1778)^2 + (0.1190 - 0.1778)^2 + (0.2100 - 0.1778)^2 + (0.2940 - 0.1778)^2 + (0.0910 - 0.1778)^2] / 4
Variance = 0.0255388 / 4
Variance = 0.0063847

Standard Deviation = (0.0063847)^(1/2)
Standard Deviation = 0.0799 or 7.99%

Coefficient of Variation = Standard Deviation / Average Return
Coefficient of Variation = 0.0799 / 0.1778
Coefficient of Variation = 0.45

Given the preceding data, the average realized return on CCC’s stock is 17.78%.
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 7.99%
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.