3. Measuring standalone risk using realized data Returns earned over a given tim

ID: 2771703 • Letter: 3

Question

3. Measuring standalone risk using realized 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.

Five years of realized returns for Celestial Crane Cosmetics Inc. (Crane Cosmetics) are given in the following table:

Also note that:

Given this return data, the average realized return on Celestial Crane Cosmetics Inc.’s stock is:

a)27.94%

b)43.31%

c)13.97%

d)34.93%

The preceding data series represents _____________ of Crane Cosmetics’s historical returns.

a) the universe

b) the population

c) a sample

Based on this conclusion, the standard deviation of Crane Cosmetics’s historical returns is:

a) 6.2782%

b) 5.6154%

c) 8.4756%

d) 4.8342%

If investors expect the average realized return on Celestial Crane Cosmetics Inc.’s stock from 2009 to 2013 to continue into the future, its expected coefficient of variation (CV) is expected to equal:

a) 0.8314

b) 0.5168

c) 0.4494

d) 0.3775

2009 2010 2011 2012 2013 Stock return 13.75% 9.35% 16.50% 23.10% 7.15%

Explanation / Answer

QUESTION 1

Average realized return on CCC’s stock can be calculated by computing arithmetic mean of returns given for 2009-2013.

Arithmetic mean = (13.75% + 9.35% + 16.50% + 23.10% + 7.15%)/5 = 13.97%

Hence, answer is Option (c) 13.97%

QUESTION 2

Answer is Option (c) Sample.

Let us reject other options, rather than selecting the correct one here.

CCC has been trading for 25 years, but the data provided is only for 5 years. Population would have been if the returns were provided for 25 years. So ‘Population’ is not the answer.

CCC has been in business for around 40 years. If the data provided was for 40 years (25 years public trading and 15 years private trading), then it would have been ‘universe’ of data. That is complete data available for company, since inception. So ‘Universe’ is also ruled out.

QUESTION 3

Standard deviation is square root of the sum of squared deviations divided by one less than the number of observations. Mathematically, it is represented as:

(Xi - Mean)^2

13.75%

0.00000484

9.35%

0.00213444

16.50%

0.00064009

23.10%

0.00833569

7.15%

0.00465124

Sum of (Xi – Mean)^2 = 0.01576630

This divided by one less than number of observations = 0.01576630/(5 – 1) = 0.003942

Square root of this number = 6.2782% - - > Standard deviation. Answer

QUESTION 4

Coefficient of Variation = Standard deviation of Sample/Mean of Sample = 6.2782%/13.97% = 0.4494. Answer