A financial institution has the following portfolio of over-the-counter options on sterling:
|
Type |
Position |
Delta of Option |
Gamma of Option |
Vega of Option |
|
Call |
-2,000 |
0.5 |
2.2 |
1.8 |
|
Call |
-1000 |
0.8 |
0.6 |
0.2 |
|
Put |
-4,000 |
-0.40 |
1.3 |
0.7 |
|
Call |
-1000 |
0.70 |
1.8 |
1.4 |
A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8.
Is it possible to find a position in the traded option and in sterling that make the portfolio gamma neutral, vega neutral and delta neutral? Explain.
In: Finance
A financial institution has the following portfolio of over-the-counter options on sterling: Type, Position, Delta of Option, Gamma of Option, Vega of Option ,Call -2,000 ,0.5, 2.2, 1.8; Call -1000, 0.8, 0.6 ,0.2 ;Put -4,000 ,-0.40, 1.3, 0.7 ;Call -1000 ,0.70, 1.8, 1.4;
A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8.
a. Is it possible to find a position in the traded option and in sterling that make the portfolio gamma neutral, vega neutral and delta neutral? Explain.
In: Finance
Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts & Brown, 2005). Based on pretreatment depression scores, patients were divided into four groups based on their level of depression. After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study.
| Low Moderate |
High Moderate |
Moderately Severe |
Severe |
|---|---|---|---|
| 3.3 | 0.7 | 2 | 2.8 |
| 0 | 2.7 | 2.3 | 3.2 |
| 3.2 | 4 | 1.1 | 1.9 |
| 2.6 | 1.4 | 1 | 4.2 |
| 0.8 | 2.8 | 2.7 | 1.4 |
| 2.9 | 2.5 | 3.3 | 1.7 |
| 1.1 | 0 | 1.8 | 1.1 |
| 2.9 | 2.6 | 1.8 | 3.2 |
| 4.5 | 2 | 4.7 | 3.5 |
| 1.6 | 0.3 | 1.5 | 1.5 |
| 3.3 | 1.6 | 0.7 | 3.4 |
| 1 | 1.5 | 3 | 3.2 |
| 0.6 | 2.2 | 1.8 | 2.1 |
| 2.3 | 2.6 | 2.7 | 1.4 |
| 3.7 | 1.9 | 1.1 | 2.1 |
| 2.8 | 4.7 | 1.9 | 1.5 |
| 1.7 | 1.2 | 1.5 | 2.6 |
| 1.6 | 0.9 | 0 | 4.1 |
| 1.8 | 3.4 | 1.4 | 3.6 |
| 2.1 | 2 | 1.4 | 2.3 |
| 2.1 | 0.2 | 2.4 | 0.7 |
| 2.4 | 1.1 | 2.1 | 1.9 |
| 3.3 | 3.4 | 2.2 | 2.4 |
| 0.1 | 0.3 | 2.2 | 2.6 |
| 4.5 | 2.5 | 1.1 | 3.5 |
| 2.6 | 1.9 | 3.7 | 3.1 |
| 2.7 | 1.3 | 3.1 | 2.5 |
| 1.9 | 2.5 | 1.1 | 2.6 |
| 1.7 | 2 | 1.7 | 3.8 |
| 1.3 | 2.5 | 2.9 | 2.5 |
| 1.5 | 1.5 | 2.2 | 3.3 |
| 2.5 | 4.2 | 1.6 | 3.2 |
| 4.2 | 3.3 | 2.1 | 3.4 |
| 2.1 | 1.4 | 3.3 | 2.1 |
| 1.5 | 2.7 | 0.4 | 1.5 |
| 1.2 | 3 | 1.4 | 1.5 |
| 1.9 | 1 | 1.7 | 3.8 |
| 1.1 | 1.5 | 2.8 | 2.6 |
| 3.4 | 1.5 | 1.5 | 1.1 |
| 1.2 | 2.5 | 1.3 | 2.5 |
| 3.5 | 1.8 | 0 | 1.9 |
| 1.1 | 3.7 | 0.2 | 2.5 |
| 2.8 | 1.5 | 0.9 | 2.5 |
| 1.2 | 0.7 | 3.7 | 0 |
| 1.1 | 1.5 | 1.3 | 3.4 |
| 3.2 | 2.5 | 2.7 | 1.9 |
| 0.3 | 1.2 | 1.3 | 3.1 |
| 0.4 | 1.9 | 3.8 | 2.1 |
| 1.6 | 2.8 | 2.5 | 4.1 |
| 2.2 | 2.2 | 2 | 4.1 |
| 3.5 | 2.6 | 0.3 | 2.1 |
| 2 | 3.9 | 4 | 3.8 |
| 2.4 | 1.6 | 2 | 4.1 |
| 0 | 1.3 | 1.4 | 3.6 |
| 3.7 | 2 | 2.8 | 2.5 |
| 0.8 | 1.5 | 2.4 | 1.5 |
| 4.4 | 0.5 | 2.2 | 3.2 |
| 2.8 | 2.1 | 1.8 | 1.5 |
| 3 | 3.1 | 2.4 | 1.8 |
| 1.6 | 0.7 | 1 | 2.6 |
| 1.7 | 1.8 | 3.7 | 3.9 |
This is the summary table for the ANOVA test:
| S.S. | d.f. | M.S. | |
| Between | 14.348360655737 | 3 | 4.7827868852458 |
|---|---|---|---|
| Within | 260.6737704918 | 240 | 1.0861407103825 |
| TOTAL | 275.02213114754 | 243 |
From this table, you obtain the necessary statistics for the
ANOVA:
F-ratio: 4.4034689424001
p-value: 0.00489
η2=η2= 0.052171658316617
What is your final conclusion? Use a significance level of
α=0.02α=0.02.
Explain what this tells us about the equality of mean?
Let's look at the boxplot for each treatment:
012345Depression ScoresLow ModerateHigh ModerateModerately SevereSevere
How could boxplots refine our conclusion in an ANOVA test? Your answer should address this specific problem.
Edit
Insert
Formats
In: Statistics and Probability
Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts & Brown, 2005). Based on pretreatment depression scores, patients were divided into four groups based on their level of depression. After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study.
| Low Moderate |
High Moderate |
Moderately Severe |
Severe |
|---|---|---|---|
| 3.3 | 0.7 | 2 | 2.8 |
| 0 | 2.7 | 2.3 | 3.2 |
| 3.2 | 4 | 1.1 | 1.9 |
| 2.6 | 1.4 | 1 | 4.2 |
| 0.8 | 2.8 | 2.7 | 1.4 |
| 2.9 | 2.5 | 3.3 | 1.7 |
| 1.1 | 0 | 1.8 | 1.1 |
| 2.9 | 2.6 | 1.8 | 3.2 |
| 4.5 | 2 | 4.7 | 3.5 |
| 1.6 | 0.3 | 1.5 | 1.5 |
| 3.3 | 1.6 | 0.7 | 3.4 |
| 1 | 1.5 | 3 | 3.2 |
| 0.6 | 2.2 | 1.8 | 2.1 |
| 2.3 | 2.6 | 2.7 | 1.4 |
| 3.7 | 1.9 | 1.1 | 2.1 |
| 2.8 | 4.7 | 1.9 | 1.5 |
| 1.7 | 1.2 | 1.5 | 2.6 |
| 1.6 | 0.9 | 0 | 4.1 |
| 1.8 | 3.4 | 1.4 | 3.6 |
| 2.1 | 2 | 1.4 | 2.3 |
| 2.1 | 0.2 | 2.4 | 0.7 |
| 2.4 | 1.1 | 2.1 | 1.9 |
| 3.3 | 3.4 | 2.2 | 2.4 |
| 0.1 | 0.3 | 2.2 | 2.6 |
| 4.5 | 2.5 | 1.1 | 3.5 |
| 2.6 | 1.9 | 3.7 | 3.1 |
| 2.7 | 1.3 | 3.1 | 2.5 |
| 1.9 | 2.5 | 1.1 | 2.6 |
| 1.7 | 2 | 1.7 | 3.8 |
| 1.3 | 2.5 | 2.9 | 2.5 |
| 1.5 | 1.5 | 2.2 | 3.3 |
| 2.5 | 4.2 | 1.6 | 3.2 |
| 4.2 | 3.3 | 2.1 | 3.4 |
| 2.1 | 1.4 | 3.3 | 2.1 |
| 1.5 | 2.7 | 0.4 | 1.5 |
| 1.2 | 3 | 1.4 | 1.5 |
| 1.9 | 1 | 1.7 | 3.8 |
| 1.1 | 1.5 | 2.8 | 2.6 |
| 3.4 | 1.5 | 1.5 | 1.1 |
| 1.2 | 2.5 | 1.3 | 2.5 |
| 3.5 | 1.8 | 0 | 1.9 |
| 1.1 | 3.7 | 0.2 | 2.5 |
| 2.8 | 1.5 | 0.9 | 2.5 |
| 1.2 | 0.7 | 3.7 | 0 |
| 1.1 | 1.5 | 1.3 | 3.4 |
| 3.2 | 2.5 | 2.7 | 1.9 |
| 0.3 | 1.2 | 1.3 | 3.1 |
| 0.4 | 1.9 | 3.8 | 2.1 |
| 1.6 | 2.8 | 2.5 | 4.1 |
| 2.2 | 2.2 | 2 | 4.1 |
| 3.5 | 2.6 | 0.3 | 2.1 |
| 2 | 3.9 | 4 | 3.8 |
| 2.4 | 1.6 | 2 | 4.1 |
| 0 | 1.3 | 1.4 | 3.6 |
| 3.7 | 2 | 2.8 | 2.5 |
| 0.8 | 1.5 | 2.4 | 1.5 |
| 4.4 | 0.5 | 2.2 | 3.2 |
| 2.8 | 2.1 | 1.8 | 1.5 |
| 3 | 3.1 | 2.4 | 1.8 |
| 1.6 | 0.7 | 1 | 2.6 |
| 1.7 | 1.8 | 3.7 | 3.9 |
This is the summary table for the ANOVA test:
| S.S. | d.f. | M.S. | |
| Between | 14.348360655737 | 3 | 4.7827868852458 |
|---|---|---|---|
| Within | 260.6737704918 | 240 | 1.0861407103825 |
| TOTAL | 275.02213114754 | 243 |
From this table, you obtain the necessary statistics for the
ANOVA:
F-ratio: 4.4034689424001
p-value: 0.00489
η2=η2= 0.052171658316617
What is your final conclusion? Use a significance level of
α=0.02α=0.02.
Explain what this tells us about the equality of mean?
Let's look at the boxplot for each treatment:
012345Depression ScoresLow ModerateHigh ModerateModerately SevereSevere
How could boxplots refine our conclusion in an ANOVA test? Your answer should address this specific problem.
Edit
Insert
Formats
In: Statistics and Probability
|
Group1 |
Group2 |
d |
|
5.6 |
6.4 |
-0.8 |
|
1.3 |
1.5 |
-0.2 |
|
4.7 |
4.6 |
0.1 |
|
3.8 |
4.3 |
-0.5 |
|
2.4 |
2.1 |
0.3 |
|
5.5 |
6 |
-0.5 |
|
5.1 |
5.2 |
-0.1 |
|
4.6 |
4.5 |
0.1 |
|
3.7 |
4.5 |
-0.8 |
In: Statistics and Probability
If x is a binomial random variable, use the binomial probability table to find the probabilities below.
|
a. P(x=3) for n=10, p=0.5 b. P(x≤4) for n=15, p=0.3 c. P(x>1) for n=5, p=0.2 d. P(x<6) for n=15, p=0.8 e. P(x≥14) for n=25, p=0.8 f. P(x=3) for n=20, p=0.1 |
In: Statistics and Probability
Imagine you are a pipeline company trying to sell a new project to a shipper of oil for a new refinery.
Pipeline Length: 266 miles (16,853,760 inches)
The refinery is scheduled to take 300,000 barrels per day of Bakken Crude at typical temperatures. Temperature: 60 degrees Fahrenheit. Flow rate = 33687.5 in3/s. Kinematic viscosity: 3.337 centistokes or 0.0051723603 in2/s. Specific Gravity = 0.7
Calculate Reynold's number.
Friction Factor: 0.0275.
Calculate Pressure Drop.
Pipeline flows entirely through class I locations except for 10 miles located in a class IV location. You have the option of bypassing the class IV location by running the pipeline an additional 50 miles.
Pipe Diameter: 12 inches X-42 Schedule 20
Calculate Maximum Pressure
The inlet pressure of pumping stations should not fall below 400 psi.
Set distance between pumping stations optimally.
Calculate horsepower requirements
In: Mechanical Engineering
Question 3. - Please do c, d and e
An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut of a particular manufacturing machine. An experiment is conducted and the data can be found in SurfaceFinish.jmp on eCampus.
a. State the two-way ANOVA model corresponding to this data. Be sure to define each term in your model and list any assumptions that are made.
b. Perform the test to determine if the model from part a) is significant.
c. Prepare a profile plot for the cell mean surface finish scores. Does it appear that any interaction effects are present? Explain.
d. Test whether or not interaction effects are present.
e. Given that low surface finish scores are desirable, which combination(s) of feed rate and depth of cut do you recommend?
Depth of Cut (in) = 0.15 0.15 0.15 0.18 0.18 0.18 0.2 0.2 0.2 0.25 0.25 0.25 0.15 0.15 0.15 0.18 0.18 0.18 0.2 0.2 0.2 0.25 0.25 0.25 0.15 0.15 0.15 0.18 0.18 0.18 0.2 0.2 0.2 0.25 0.25 0.25
Feed Rate (in/min) = 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
Surface Finsih Score = 74 64 60 79 68 73 82 88 92 99 104 96 92 86 88 98 104 88 99 108 95 104 110 99 99 98 102 104 99 95 108 110 99 114 107 111
| Depth of Cut (in) | Feed Rate (in/min) |
|
|||
| 0.15 | 0.2 | 74 | |||
| 0.15 | 0.2 | 64 | |||
| 0.15 | 0.2 | 60 | |||
| 0.18 | 0.2 | 79 | |||
| 0.18 | 0.2 | 68 | |||
| 0.18 | 0.2 | 73 | |||
| 0.2 | 0.2 | 82 | |||
| 0.2 | 0.2 | 88 | |||
| 0.2 | 0.2 | 92 | |||
| 0.25 | 0.2 | 99 | |||
| 0.25 | 0.2 | 104 | |||
| 0.25 | 0.2 | 96 | |||
| 0.15 | 0.25 | 92 | |||
| 0.15 | 0.25 | 86 | |||
| 0.15 | 0.25 | 88 | |||
| 0.18 | 0.25 | 98 | |||
| 0.18 | 0.25 | 104 | |||
| 0.18 | 0.25 | 88 | |||
| 0.2 | 0.25 | 99 | |||
| 0.2 | 0.25 | 108 | |||
| 0.2 | 0.25 | 95 | |||
| 0.25 | 0.25 | 104 | |||
| 0.25 | 0.25 | 110 | |||
| 0.25 | 0.25 | 99 | |||
| 0.15 | 0.3 | 99 | |||
| 0.15 | 0.3 | 98 | |||
| 0.15 | 0.3 | 102 | |||
| 0.18 | 0.3 | 104 | |||
| 0.18 | 0.3 | 99 | |||
| 0.18 | 0.3 | 95 | |||
| 0.2 | 0.3 | 108 | |||
| 0.2 | 0.3 | 110 | |||
| 0.2 | 0.3 | 99 | |||
| 0.25 | 0.3 | 114 | |||
| 0.25 | 0.3 | 107 | |||
| 0.25 | 0.3 | 111 |
In: Statistics and Probability
| Q4Y4 | Q1Y5 | Q2Y5 | Q3Y5 | Q4Y5 | Total | |
| Budgeted Sales (Actual for Q4Y4) | 10000 | 11000 | 14000 | 15000 | 17000 | 57000 |
| Selling Price/per unit | 9 | 9 | 9 | 9 | 9 | 9 |
| Sale Collection | ||||||
| In quarter of sale | 0.8 | |||||
| In following quarter | 0.2 | |||||
| Desired ending finished goods inventory | 2500 | 2200 | 2400 | 2100 | 2100 | |
| Raw Materials/per unit | 5 | 5 | 5 | 5 | 5 | 5 |
| Desired Ending raw material inventory Inventory | 5000 | 8000 | 7000 | 6000 | 5000 | 5000 |
| Raw material price/per unit | 2 | 2 | 2 | 2 | 2 | 2 |
| Accounts payable | ||||||
| In quarter of purchase | 0.7 | |||||
| In following quarter | 0.3 | |||||
| Q4Y4 raw material cost | 100000 |
REQUIRED:
| Sale Budget | Year 5 Quarters | |||||
| 1 | 2 | 3 | 4 |
Year |
||
| Production Budget |
| Material Budget |
|
Cash Receipts |
| Cash Payments |
In: Accounting
Almost all U.S. light-rail systems use electric cars that run on
tracks built at street level. The Federal Transit Administration
claims light-rail is one of the safest modes of travel, with an
accident rate of .99 accidents per million passenger miles as
compared to 2.29 for buses. The following data show the miles of
track and the weekday ridership in thousands of passengers for six
light-rail systems.
| City | Miles of Track | Ridership (1000s) |
| Cleveland | 13 | 16 |
| Denver | 15 | 36 |
| Portland | 36 | 82 |
| Sacramento | 19 | 32 |
| San Diego | 45 | 76 |
| San Jose | 29 | 31 |
| St. Louis | 32 | 43 |
| SSE | |
| SST | |
| SSR | |
| MSE |
In: Statistics and Probability