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/â (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 2âs 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.
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/â (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 2âs 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.
