Bill Broodiest, star quarterback for the Spring Bay Smashers, would like to inve

Question

Bill Broodiest, star quarterback for the Spring Bay Smashers, would like to invest a small portion of his earnings in stocks of one of three firms. His estimated dividends and the probabilities of their occurrence follow.

Galaxy Communications

.1

$500

.3

800

.4

1,000

.2

1,200

Grasshopper Tractor

.2

$0

.3

700

.3

800

.2

900

Breathiest Electronics

.1

$500

.2

700

.4

900

.2

1,100

.1

1,200

Question 1: Calculate the coefficient of variation for all 3 firms (round to three decimal places).

Question 2: Rank the three firms from the least risky to the most risky.

Galaxy Communications

.1

$500

.3

800

.4

1,000

.2

1,200

Explanation / Answer

First we need to calculate the expected value of each investement: Galaxy: Expected return = 0.1 *$500 + 0.3*$800 + 0.4 * $1000 + 0.2 * $1200                          = $930 For Grass hoper: ER = 0.2 * $0 + $0.3 * $700 + $0.3 * $800 + 0.2 * $900       = $630 For Breathiest: ER = 0.1 * $500 + 0.2 * $700 + 0.4 * $900 + 0.2 * $1100 + 0.1 * 1200       = $890 Now, calculating the standard deviation for each firm: SD of Galaxy: SD = SQrt [ (500 - 875)^2 + (800 - 875)^2 + (1000 - 875)^2 + (1200 - 875)^2 / 4]       = Sqrt [ (140625 + 5625 + 15625 + 105625) / 4]      = Sqrt [ 66,875]      = 285.6 Calculating SD for Grass hoper: SD = Sqrt [ (0 - $600)^2 + ($700 - $600)^2 + ($800 - $600)^2 + ($900 - $600)^2 / 4]       = Sqrt [ 360,000 + 10,000 + 40,000 + 90,000 / 4]      = Sqrt [ 500,000 / 4]     = Sqrt[ 125,000]     = 353.55 Calculating the SD for Breathiest: SD = Sqrt [ (500 - 880)^2 + (700 - 880)^2 + (900 -880)^2 + (1100 - 880)^2 + (1200 - 880)^2 / 5]       = Sqrt [ 144,400 + 32,400 + 400 + 48,400 + $102,400 / 5]      = Sqrt [ 65,600]      = 256 Calculating the Coefficient of variation for each firm: For Galaxy: CV = 286 / 930       = 0.307 For Grasshoper: CV = 353.55 / 630       = 0.56 For Breathiest: CV = $256 / 890       = 0.28 The least risky investment is the Breathiest , the next riskiest is the Galaxy and the most riskiest is the Grasshoper.

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