Question

Take it to the Bank

Daryl Bank is an investment broker with Bank, Tank, & Shank a full service financial services firm serving the regional area of southern West Virginia. From the corporate offices in Beckley, Daryl manages a large number of clients throughout the southern part of the state.

Daryl is very customer service oriented and makes a personal effort to visit every client at least twice a year, even if it means traveling to his or her hometown. He usually travels to different county seats throughout the state and stays a couple of days in a local hotel so clients can visit him in these various locations. With his laptop Daryl can access account information and the latest information about traded securities using any number of software programs. His clients also enjoy seeing the demonstrations of portfolio programs for their specific accounts.

Daryl also uses these trips to visit West Virginia companies for potential investment possibilities. He likes to know the companies he invests in, and wants to get a competitive advantage in any investment decision. Since not many investment brokers are taking the time to visit some of the smaller publicly traded West Virginia companies, Daryl feels that he knows substantially more about these companies and their potential for excess returns than the general market. He is always looking for undervalued opportunities for investment purposes so that his customers can also enjoy many happy returns on their portfolios.

On a recent trip to Curveintheroad in the far southwestern part of the state, Daryl had the opportunity to visit three companies. He has been able to maintain a friendship with the top management of these companies and was given access to important financial data, which he planned to use to determine stock valuation.

The first company is Dig Deep, a regional coal mining company. They have been in operation for over 20 years and have the mining rights to over 100 square miles of land. Most of the coal they mine is the more clean burning anthracite coal. Even though they are a relatively small, company, they possess modern equipment and a very efficient mining operation.

The stock price for Dig Deep was $32 on January 1, 20x0, $36 on December 31, 20x0, $33 for 12/31/x1, $35 for 12/31/x2, $42 for 12/31/x3 and $44 for 12/31/x4. In the year 20x0 they paid a dividend of $1.00, the same for 20x1, $1.10 in 20x2, $1.25 in 20x3 and that amount again in 20x4. The standard deviation for their stock is 6%, beta is 0.80, and correlation coefficient is .60.

The second company is Moon Shine, a regional medicinal spirits company. This company got its start about 75 years ago and has been very successful establishing a niche market in all natural herbal remedies. What makes this company especially appealing to Daryl is its ability to do well during times when the general economy is in a depression or recession.

The stock price for Moon Shine was $14 on January 1, 20x0, $18 on December 31, 20x0, $15 for 12/31/x1, $22 for 12/31/x2, $32 for 12/31/x3 and $28 for 12/31/x4. The company does not pay a dividend. The standard deviation for their stock is 14%, beta is 1.25, and correlation coefficient is -0.30.

Finally Daryl met the management team at Pork, Byrd and Belly. In spite of the name, this was not an agricultural company, but a heavy construction company with major government contracts for roads and bridges. The company has had some very successful contracts in the past which have led to great growth, but their rate of growth has slowed a little in the last couple of years.

The stock price for Pork, Byrd and Belly was $10 on January 1, 20x0, $15 on December 31, 20x0, $25 for 12/31/x1, $30 for 12/31/x2, $28 for 12/31/x3 and $25 for 12/31/x4. In the year 20x0 they paid a dividend of $0.80, $0.90 in 20x1, $1.20 in 20x2, $0.50 in 20x3 and that amount again in 20x4. The standard deviation for their stock is 20%, beta is 1.05, and correlation coefficient is .45.

Since these are all small regional companies, Daryl uses the Russell 4000 index as a measure of the market standard. He likes to compare the performance of his companies against this index along with other criteria to determine if a company stock price offers a good value.

The index price for the Russell 4000 was 1200 on January 1, 20x0, 1400 on December 31, 20x0, 1800 for 12/31/x1, 1750 for 12/31/x2, 1600 for 12/31/x3 and 1700 for 12/31/x4. The standard deviation for the index is 5%, beta is 1.0, and correlation coefficient is 1.00. Currently the rate of return on a Treasury bill is 5.0%.

Required:

1. Compute the coefficient of variation for each stock plus the market for the 5 year period from 20x0 to 20x4.

Answer 1

Given:

(1) Dig Deep

Standard deviation is 6%

Stock Price
January 1, 2x10	$32
December 31, 2x10	$36
December 31, 2x11	$33
December 31, 2x12	$35
December 31, 2x13	$42
December 31, 2x14	$44

Dividend
Year 2x10	$1
Year 2x11	$1
Year 2x12	$1.1
Year 2x13	$1.25
Year 2x14	$1.25

(2) Moon Shine

Stock Price
January 1, 2x10	$14
December 31, 2x10	$18
December 31, 2x11	$15
December 31, 2x12	$22
December 31, 2x13	$32
December 31, 2x14	$28

Standard deviation is 14%

(3) Pork, Byrd and Belly

Stock Price
January 1, 2x10	$10
December 31, 2x10	$15
December 31, 2x11	$25
December 31, 2x12	$30
December 31, 2x13	$28
December 31, 2x14	$25

Dividend
Year 2x10	$0.8
Year 2x11	$0.9
Year 2x12	$1.2
Year 2x13	$0.5
Year 2x14	$0.5

Standard deviation is 20%

(4) 4000 index

Index Price
January 1, 2x10	1200
December 31, 2x10	1400
December 31, 2x11	1800
December 31, 2x12	1750
December 31, 2x13	1600
December 31, 2x14	1700

Standard deviation is 5%.

Solution:

Coefficient of variation = standard deviation/ Mean---------------(1)

Mean = Return for each period/ no. of period-----(2)

To calculate coefficient of variation for each stock and index, first of all, we will have to calculate the returns for each category.

Returns =( Stock price at T+1 - Stock Price at T + Dividend in the year) / (Stock price at T)

Applying the same formula, we will calculate the returns for each category foe each period from year 2x10 to 2x14.

Returns, mean and coefficient of variation for Dig Deep:

Returns
Year 2010	15.6%
Year 2011	-5.6%
Year 2012	9.4%
Year 2013	23.6%
Year 2014	7.7%

Mean of return = 10.2%----From (2)

Coefficient of variation = 6/10.2 = 0.59---------From (1)

Returns, mean and coefficient of variation for Moon Shine:

Returns
Year 2010	28.6%
Year 2011	-16.7%
Year 2012	46.7%
Year 2013	45.5%
Year 2014	-12.5%

Mean of return = 18.3%--------From (2)

Coefficient of variation = 14/18.3 = 0.77---------From (1)

Returns, mean and coefficient of variation for Pork, Byrd and Belly

Returns
Year 2010	58.0%
Year 2011	72.7%
Year 2012	24.8%
Year 2013	-5.0%
Year 2014	-8.9%

Mean of return = 28.3%--------From (2)

Coefficient of variation = 20/28.3 = 0.71---------From (1)

Returns, mean and coefficient of variation for Market

Returns
Year 2010	16.7%
Year 2011	28.6%
Year 2012	-2.8%
Year 2013	-8.6%
Year 2014	6.3%

Mean of return = 8%--------From (2)

Coefficient of variation = 5/8 = 0.63---------From (1)