Question

3. Measuring standalone risk using realized (historical) data Aa Aa E Returns eamed over a given time period are called realized retums. 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 Falcon Freight Inc. (FF): Five years of realized returns for FF are given in the following table. Remember: 1. While FF 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 FF for 2012 to 2016 are: 2012 11.25% 2013 7.65% 2014 13.50% 2015 18.90% 2016 5.85% Stock return Given the preceding data, the average realized return on FF's stock is 11.43% of FF's historical returns. Based on this conclusion, the The preceding data series represents a sample standard deviation of FF's historical returns is If investors expect the average realized return from 2012 to 2016 on FF's stock to continue into the future, its coefficient of variation (CV) will be

Answer 1

1)

Average return = (0.1125 + 0.0765 + 0.135 + 0.189 + 0.0585) / 5

Average return = 0.1143 or 11.43%

2)

Sample

3)

Standard deviation = {[(0.1125 - 0.1143)² + (0.0765 - 0.1143)² + (0.135 - 0.1143)² + (0.189 - 0.1143)² + (0.0585 - 0.1143)²] / 5 - 1}^1/2

Standard deviation = {[0.000003 + 0.001429 + 0.000428 + 0.00558 + 0.003114] / 4}^1/2

Standard deviation = {0.002639}^1/2

Standard deviation = 0.0514 or 5.14%

4)

Coefficient of variation = 0.0514 / 0.1143

Coefficient of variation = 0.45