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 Blue Llama Mining Inc. (BLM):

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

1. While BLM 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 BLM for 2014 to 2018 are:

2014 - 2015 - 2016 - 2017 - 2018

Stock return 25.00% 17.00% 30.00% 42.00% 13.00%

Given the preceding data, the average realized return on BLM’s stock is .?

The preceding data series represents ??? of BLM’s historical returns.

Based on this conclusion, the standard deviation of BLM’s historical returns is ???.

If investors expect the average realized return from 2014 to 2018 on BLM’s stock to continue into the future, its coefficient of variation (CV) will be .???

Answer 1

Solution:

Year	Return r	(r-rbar)^2
2014	25	0.16
2015	17	70.56
2016	30	21.16
2017	42	275.56
2018	13	153.76
Total	127	521.2

Average realized return on BLM stock (r bar) = 127/5 = 25.4

Standard deviation = square root of( (r-rbar)^2 / n-1)

= square root of (521.2/4)

=130.3

the peceding data series represents value of BLM,s historical return. Based on this conclusion, the standard deviation is 130.3

Coefficient of variance = standard deviation/mean

= 130.3/25.4

=5.1299