Question

3. Measuring stand-alone risk using realized (historical) data 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 2014 to 2018 are: 2014 2015 2016 2017 2018 Stock return 20.00% 13.60% 24.00% 33.60% 10.40% Given the preceding data, the average realized return on CCC’s stock is20.32% . The preceding data series representsa sample 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 2014 to 2018 on CCC’s stock to continue into the future, its coefficient of variation (CV) will be .

Answer 1

Computation of Standard Deviation

Year	Realized Returns	Mean (Average return)	Deviation from Mean (Return - Mean)	Square of Deviation from Mean
2014	20.00%	20.32%	-0.32%	0.0010%
2015	13.60%	20.32%	-6.72%	0.4516%
2016	24.00%	20.32%	3.68%	0.1354%
2017	33.60%	20.32%	13.28%	1.7636%
2018	10.40%	20.32%	-9.92%	0.9841%
Step 1: Sum of (Squared deviation from Mean)	3.3357%
Step 2 : Step 1 / (Sample no. of years - 1)*	0.8339%
Step 3 ---> Standard Deviation ---> Square root of Step 2	9.1319%

Computation of Coefficient of Variation

Standard Deviation	9.1319%
Mean	20.32%
Coefficient of Variation ---> (Standard Deviation) / Mean	0.45