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Finance homework check! Risk loving, calculations, etc. I just need my answers checked! Suppose Joe has the choice of two investments. He can invest in

Finance homework check! Risk loving, calculations, etc. I just need my answers checked!

Suppose Joe has the choice of two investments. He can invest in a bond, which in 10 years (not accounting for inflation), will have a 50% probability of a 50% return and a 50% probability of a 40% return. On the other hand, he could invest in a mutual fund that in 10 years would have a 50% chance of returning 100% and a 50% chance of returning -20%. If he chose the latter investment, would he be considered Risk Neutral, Risk Averse, or Risk Loving?

Joe would be considered as risk loving.

The later investment is high risk high return investment compared to the one before.

Now, Dr. Pennyworth has a chance to purchase one of two professional cricket clubs, the Miami Manatees or the Jacksonville Gemini. At the beginning of last year, the Manatees were purchased for $100 million, provided $10 million in profits, and are currently on sale for $110 million. On the other hand, the Gemini started the year purchased at $80 million, provided $30 million in profits, and are currently on sale for $140 million. Calculate the rate of return for the owners of each team last year. Which team would you suggest that Dr. Pennyworth purchase today?

Miami Manatees

Investment =$100 million

Return = $10 million

Rate of return = 10/100 = 10%

Selling price = $110 million

Jacksonville Gemini

Investment = $80 million

Return = $30 million

Rate of Return = 30/80 = 37.5%

Selling Price = $140 million

Dr. Pennyworth should purchase Jacksonville Gemini cricket club.

For the above problem, you project that the most optimistic profits for the Manatees this year is $35 million, while the most pessimistic projection is $5 million. Your projections for the Gemini are $32 million and $7 million, respectively. Based only on the range, which do you think is the riskier investment? Which one would you choose?

Game

Most optimistic

Most pessimistic

Manatees

$35million

$5million

Gemini

$32 million

$7million

Based only on the range, Manatees is a riskier investment i.e. $30 million compared to $25million difference between the most optimistic and most pessimistic projection.

I would choose Manatees.

4. Imagine there are two free agent outfielders available. They both cost the same price, but you only have the money to sign one. Assume home runs alone are a proxy for performance. Suppose Player 1 has a 20% chance of hitting 20 home runs and a 20% chance of hitting 25 home runs, a 25% chance of hitting 30 home runs, a 20% chance of hitting 35 home runs, and a 15% chance of hitting 40 home runs. Player 2 has a 10% chance of hitting 10 home runs and a 10% chance of hitting 15 home runs, a 10% chance of hitting 25 home runs, a 30% chance of hitting 30 home runs, a 30% chance of hitting 35 home runs, and a 10% chance of hitting 50 home runs.

Which player has the highest expected return?

Player one expected return

0.2 *20 + 0.2*25 + 0.25*30 + 0.2*35 + 0.15*40 = 25.9 homes

Player two expected return

0.1*10+0.1*15+0.1*25+0.3*30+0.3*35+0.1*50= 24.5 homes

Which player would represent the riskier investment?

Player one

0.2

20

4

-25.5

650.25

130.05

0.2

25

5

-24.5

600.25

120.05

0.25

30

7.5

-22

484

121

0.2

35

7

-22.5

506.25

101.25

0.15

40

6

-23.5

552.25

82.8375

Expected return

29.5

VARIANCE

555.1875

STD DEV

23.56

Player Two

0.1

10

1

-23.5

552.25

55.225

0.1

15

1.5

-23

529

52.9

0.1

25

2.5

-22

484

48.4

0.3

30

9

-15.5

240.25

72.075

0.3

35

10.5

-14

196

58.8

0.1

50

5

5

25

2.5

Expected return

24.5

VARIANCE

287.4

STD DEV

16.95

Player 1 is a riskier investment i.e. Player 1 has higher variance and standard deviation

Which player would you choose?

I would choose player two

What does this say about your risk preferences?

I am risk loving

If there is a high chance of a negative return, why would a general manager invest in a very risky player? How might this conflict with the goals of the team as a whole?

A general manager would invest in a very risky player with a high chance of a negative return since probably the investment would generate huge profits if the estimation of the manager turns out to be correct is high.

The goals of the team as a whole are to maximize returns and minimize risk. Investing in a risky player raises the risk profile of the team as a whole.

Assume Mike Trout has the following distribution of outcomes for 2012. If he gets hurt, he will need some time to recover even while in the lineup, so he cannot produce at his highest level even if he comes back from an injury. If he does not get hurt, then he is certain to either Produce A, B or C, with A > B > C.

Outcome

Probability

Return/Production

Gets Hurt, Misses Whole Season

10%

0 wins

Gets Hurt, Misses 1/2 season, Produces B

20%

1.5 wins

Gets Hurt, Misses 1/2 season, Produces C

10%

0.75 wins

Gets Hurt, Misses 1/4 season, Produces B

10%

3 wins

Gets Hurt, Misses 1/4 season, Produces C

10%

1.5 wins

No Injury, Produces A

20%

10 wins

No Injury, Produces B

10%

6 wins

No Injury, Produces C

10%

3 wins

Using the above information, calculate Mike Trout's expected production for next year. What is his range of possible performances?

Outcome

Probability

Return/Production

Expected Return

Ri - ER

Ri - ER)SQUARED

Gets Hurt, Misses Whole Season

10%

0

0

-3.725

13.87563

Gets Hurt, Misses 1/2 season, Produces B

20%

1.5

0.3

-3.425

11.73063

Gets Hurt, Misses 1/2 season, Produces C

10%

0.75

0.075

-3.65

13.3225

Gets Hurt, Misses 1/4 season, Produces B

10%

3

0.3

-3.425

11.73063

Gets Hurt, Misses 1/4 season, Produces C

10%

1.5

0.15

-3.575

12.78063

No Injury, Produces A

20%

10

2

-1.725

2.975625

No Injury, Produces B

10%

6

0.6

-3.125

9.765625

No Injury, Produces C

10%

3

0.3

3.425

11.73063

Total expected Return

3.725

Variance

87.91188

Standard deviation

9.37

What about his standard deviation?

= 9.37

Using the standard deviation, calculate the interval within which Trout's performance should fall 95% of the time. Does anything seem strange about this calculation?

Standard error = 9.37/ (8) = 9.37/2.83 = 3.31

Margin of error = 3.31 x 2 = 6.61

95% confidence interval: 3.725 + 6.61 = -2.885 to 10.335

Something seems strange with this calculation. Margin of error is larger than the expected return

Suppose you could make an investment. With Investment 1, there is a 20% chance of making $10, a 15% chance of making $20, a 20% chance of making $25, a 20% chance of making $30, a 20% chance of making $40, and a 5% chance of making $100. For Investment 2, there is a 25% chance of making $1,000, a 50% chance of making $2,000, and a 25% chance of making $7,500. Use the coefficient of variation to evaluate the risk involved in these two investments. How does this result differ from using the range? How does it differ from comparing the two using only the standard deviation? Why is this important?

Investment 1

Expected return

Variance

Square of Variance

0.2

10

2

-27

729

0.15

20

3

-26

676

0.2

25

5

-1

1

0.2

30

6

-23

529

0.2

40

8

-21

441

0.05

100

5

-24

576

Expected Return

29

Variance

2952

STD Dev

54.33

Coefficient of variation = STD DEV/EXPECTED RETURN

1.8734

Investment 2

Expected return

Variance

Square of Variance

0.25

1000

250

-2875

8265625

0.5

2000

1000

-2125

4515625

0.25

7500

1875

-1250

1562500

Expected Return

3125

Variance

14343750

STD Dev

3787

Coefficient of variation = STD DEV/EXPECTED RETURN

1.2118

Range

Investment 2s returns are more skewed than investment 1 and therefore investment two would be considered riskier. However, using coefficient of variation shows that investment 1 is riskier.

Standard deviation

Investment has a higher standard deviation compared to investment 1 and therefore investment two would be considered riskier. However, using coefficient of variation shows that investment 1 is riskier.

Coefficient of variation measures the variability of the outcomes relative to the expected return. Since the two sets of data are different, coefficient of variation is the best measure of risk.

Based on the following table of yearly revenues, do you think the two teams are compliments or substitutes? Why?

Year

Manatees

Gemini

2005

$10

$10

2006

$5

$15

2006

$15

$20

2008

$25

$35

2009

$12

$12

2010

$12

$15

2011

$20

$25

The teams are compliments. The price movements and range shows that Manatees and Gemini prices neither affect each other directly nor are they driven by the same set of factors as would be in the case of substitutes.

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