Question

7. Measuring standalone 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 Happy Dog Soap Inc. (HDS):

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

1.	While HDS 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 HDS for 2012 to 2016 are:

	2012	2013	2014	2015	2016
Stock return	21.25%	14.45%	25.50%	35.70%	11.05%

Given the preceding data, the average realized return on HDS’s stock is _________ .

The preceding data series represents _________ of HDS’s historical returns. Based on this conclusion, the standard deviation of HDS’s historical returns is _________ .

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

Answer 1

	Year	Returns(%)	Standard Deviation
	2012	21.25		0.1156
	2013	14.45		50.9796
	2014	25.50		15.2881
	2015	35.70		199.0921
	2016	11.05		111.0916
			Total	=(0.1156+50.9796+15.2881+199.0921+111.0916)/(5-1)
				9.702667
				9.702667
a)	Average	= sum of all the returns / no.of years
		=(21.25+14.45+25.50+35.70+11.05)/5
		21.59
b)	The preceding data series represents sample of HDS 's historical returns
c)	standard deviation of HDS's historical return is 9.702667
d)	coefficient of variation = standard deviation/ mean
			=9.702667/21.59
			0.449406