Stanford University Montgomery Bus Boycott Civil Rights Movement Paper Post must be 300 words minimum-600 words maximum. Post word count at the end of you

Stanford University Montgomery Bus Boycott Civil Rights Movement Paper Post must be 300 words minimum-600 words maximum.

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Initial Post

Make sure you review: http://kingencyclopedia.stanford.edu/encyclopedia/encyclopedia/enc_montgomery_bus_boycott_1955_1956/ (Links to an external site.)Links to an external site. which is a timeline of events for the entire boycott start to finish and
review the overview on http://www.montgomeryboycott.com/overview/ (Links to an external site.)Links to an external site.

Go to Voices of the boycott

http://www.montgomeryboycott.com/voices-of-the-boycott/ (Links to an external site.)Links to an external site.

Select 2 individuals from the Voices of the Boycott link . You can also find “stories” of individuals on the right side of the page under Biographies or Profiles. Click on “full list” under each to see all the selections.

Read the story for two different people. You must choose the story for 2 indivduals.

Answer the following 2 questions for each person you pick:

Person #1

Name the person you picked and summarize the story of the individual you picked.

Make sure you explain how the person you chose is related to the events in Montgomery and/or the boycott

How does reading their first hand stories and watching the video interviews add to your understanding of the boycott and segregation in the 1950’s? Be specific.
Give illustrations and examples from the entire story. Be thorough

Person #2

Answer the above 2 questions for the 2nd person you chose.

Do not number your points and do not repeat the questions by typing them in your written response.

Additional Resources if you desire more information

Montgomery Bus Boycott website

http://www.montgomeryboycott.com/ (Links to an external site.)Links to an external site.

General information with good links

http://mlk-kpp01.stanford.edu/index.php/encyclopedia/encyclopedia/enc_montgomery_bus_boycott_1955_1956/ (Links to an external site.)Links to an external site.

Montgomery City Code http://www.archives.state.al.us/teacher/rights/lesson1/doc1.html(Links to an external site.) FNAN 491 Computational Finance Using Excel and Mathematica
© Problem Set 6: Monte Carlo Simulation of a Markov Process to Generate Options Price
Estimates
DUE: TUESDAY, May 6, 2019 BY 6:00 PM
In this problem, worth 25 points, the procedure of Monte Carlo simulation of Markov processes
will be used to generate options price estimates and compare these to actual options prices for put and
call options for at least 3 of the stocks that you used in Problem Set 1. Update the stock and options
prices for calls and puts at strike prices at the money of the option at the most recent date using
finance.yhaoo.com for the options. Use at least a 3-month time period to expiration such as the
September 20, 2019 expiration date. Employ the implied volatility for each stock as given in the options
table in Yahoo Finance. Use the Mathematica program provided on Blackboard for the course under the
Problem Set 6 item. The data you will need are:
1. market values of the stock (s),
2. market implied volatility of each stock’s returns for calls and puts (sigmav and sigmaput
respectively),
3. strike price of call and put options for each stock, x, (use the same strike price for calls and puts),
4. time to expiration (proportion of a year of 252 days,( t),
5. the risk-free rate for the time period say 3-months (rf), and
6. the number of iterations (n of 1000, 5,000 and 10,000).
Computational Requirements
Use Mathematica to perform your calculations.
First compute the Black -Scholes call and put prices using the respective volatility values for future
comparison. These are given by functions bsfc for call option prices and bsfput for put options prices.
Then, using the assumption that stock prices follow a Geometric Brownian Motion (GBM) with a drift
factor of rf, so that with the change in the natural logarithm of stock prices, dlns = ln (st) – ln (s0) and
eta a standard normal random variate : dlns = (rf – 0.5*sigmav^2)*dt + sigmav*eta*Sqrt[t]
stating in terms stock values st = s0*Exp[(rf – 0.5*sigmav^2)*t + sigmav*eta*Sqrt[t]] by taking the
exponential of each side of the equation. This is the stock generating process.
The next step is to find the standard normal random variables eta by using the Mathematica
functions eta = Table[RandomVariate[NormalDistribution[0, 1]], n]; after defining n=1000 or n=5000
or n=10000. Following this the stock prices can be computed using the Table function again as:
st = Table[ s0*Exp[((rf – 0.5*sigmav^2)*t) + sigmav*eta[[i]]*Sqrt[t]], {i, 1, n}]; (use sigmaput for put
option calculations).
Using these computations the call prices and put prices can be estimated as shown in the program
by computing the mean of the random call or put values and these estimates then compared to the BlackScholes estimates and actual options prices.
The Analysis
Analyze your results for each stock option by:
1. How do the estimates of the Monte Carlo method compare with the Black-Scholes for each of
the increasing number of iterations? With more iterations do the values get closer to BlackScholes?
2. Compare the closeness of the Monte Carlo method with the actual options prices. Are they closer
for the call or the put and are they closer than the Black-Scholes formula and as the number of
iterations increases?
3. Which one of your stocks had the closest estimates to the actual options prices?
4. Use the tabular form provided in the program to present your results in your analysis.
Instructions for Use of the Efficient Frontier Calculator – Problem Set 1: Efficient Frontier from a cho
1
2
3
4
5
6
This calculator finds the efficient frontier from a group investments assuming the variances and covariances are constants
and that the investments can’t be sold short.
Refer to the spreadsheet titled Efficient Frontier.
The data that must be input to the program:
a. Variance-Covariance matrix computed from the returns of each investment.
In the example the this matrix is of 6 stocks.
This matrix is named VarCov (see Insert/Name/Define)
b. The mean returns at an annual rate from the data on investment returns.
The locations of the variables that must be changed using the Insert/Name/Define function are:
Constant
Means
nsec
Portfolio Mean
Portfolio Sigma
RESULTS
theta
Total
VarCov
weights
x_1
x_2
x_3
x_4
x_5
x_6
x_7
x_8
x_9
x_10
x_11
x_12
x_13
x_14
x_15
etc
For example, the location of VarCov is the range B6:G11.
If you expand the number of investments to 15 from 6, the range of VarCov would be: B6:P20.
These ranges are changed by using the Insert/Names/Define function by entering the new range for VarCov.
The program to compute the effcient frontier is executed by entering Ctrl-A.
The proportions for each of the constants (risk-free or borrowing and lending rates) is given in the RESULTS table.
To find the efficient asset allocation shares for any borrowing-lending rate, enter the
borrowing-lending rate value as the constant.
For the example this is cell c23. Enter the value in percent annual rate.
Once these entries have been made, go to Tools/Solver and run the Solver program.
The results for the allocations associated with this rate will be the cells to the right
of the x_i, starting in cell C38 in the example.
Chart 1 plots the columns Sigma and Mean giving the efficient frontier.
Frontier from a choice of Common Stocks and a Default Risk Free Asset
Microsoft Excel 16.0 Answer Report
Worksheet: [Frontier_Report.xls]Efficient Frontier
Report Created: 2/8/2019 7:05:14 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: GRG Nonlinear
Solution Time: 9.437 Seconds.
Iterations: 9 Subproblems: 0
Solver Options
Max Time 100 sec, Iterations 100, Precision 0.000001
Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%,
Solve Without Integer Constraints, Assume NonNegative
Objective Cell (Max)
Cell
Name
Original Value Final Value
$B$31 theta
7.48%
7.52%
Variable Cells
Cell
Name
$C$38 x_1
$C$39 x_2
$C$40 x_3
$C$41 x_4
$C$42 x_5
$C$43 x_6
$C$44 x7 Weights
$C$45 x8 Weights
$C$46 x9 Weights
$C$47 x10 Weights
Constraints
Cell
Name
$C$48 Total
$C$38 x_1
$C$39 x_2
$C$40 x_3
$C$41 x_4
$C$42 x_5
$C$43 x_6
$C$44 x7 Weights
$C$45 x8 Weights
$C$46 x9 Weights
$C$47 x10 Weights
Original Value Final Value
Integer
0.42699
0.34884 Contin
0.03150
0.08546 Contin
0.00000
0.00000 Contin
0.54151
0.54859 Contin
0.00000
0.00197 Contin
0.00000
0.00000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
0.0000
0.0151 Contin
Cell Value
1.0000
0.34884
0.08546
0.00000
0.54859
0.00197
0.00000
0.0000
0.0000
0.0000
0.0151
Formula
$C$48=1
$C$38>=0
$C$39>=0
$C$40>=0
$C$41>=0
$C$42>=0
$C$43>=0
$C$44>=0
$C$45>=0
$C$46>=0
$C$47>=0
Status
Binding
Not Binding
Not Binding
Binding
Not Binding
Not Binding
Not Binding
Binding
Binding
Binding
Not Binding
x1
x2
x3
x4
x5
x6
x7
x8
x9
theta
Slack
0
0.34884
0.08546
0.00000
0.54859
0.00197
0.00000
0.0000
0.0000
0.0000
0.0151
r=-3%
r=1%
r=5%
r=9%
r=13%
42.7%
34.9%
44.7%
47.0%
56.4%
3.1%
8.5%
1.7%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
54.2%
54.9%
53.7%
53.0%
43.6%
0.0%
0.2%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
7.52%
6.01%
4.55%
3.14%
1.85%
Microsoft Excel 16.0 Answer Report
Worksheet: [Frontier_Report.xls]Efficient Frontier
Report Created: 2/8/2019 7:05:39 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: GRG Nonlinear
Solution Time: 6.64 Seconds.
Iterations: 6 Subproblems: 0
Solver Options
Max Time 100 sec, Iterations 100, Precision 0.000001
Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%,
Solve Without Integer Constraints, Assume NonNegative
Objective Cell (Max)
Cell
Name
Original Value Final Value
$B$31 theta
5.99%
6.01%
Variable Cells
Cell
Name
$C$38 x_1
$C$39 x_2
$C$40 x_3
$C$41 x_4
$C$42 x_5
$C$43 x_6
$C$44 x7 Weights
$C$45 x8 Weights
$C$46 x9 Weights
$C$47 x10 Weights
Constraints
Cell
Name
$C$48 Total
$C$38 x_1
$C$39 x_2
$C$40 x_3
$C$41 x_4
$C$42 x_5
$C$43 x_6
$C$44 x7 Weights
$C$45 x8 Weights
$C$46 x9 Weights
$C$47 x10 Weights
Original Value Final Value
Integer
0.34884
0.39552 Contin
0.08546
0.05517 Contin
0.00000
0.00000 Contin
0.54859
0.54931 Contin
0.00197
0.00000 Contin
0.00000
0.00000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
0.0151
0.0000 Contin
Cell Value
1.0000
0.39552
0.05517
0.00000
0.54931
0.00000
0.00000
0.0000
0.0000
0.0000
0.0000
Formula
$C$48=1
$C$38>=0
$C$39>=0
$C$40>=0
$C$41>=0
$C$42>=0
$C$43>=0
$C$44>=0
$C$45>=0
$C$46>=0
$C$47>=0
Status
Binding
Not Binding
Not Binding
Binding
Not Binding
Binding
Not Binding
Binding
Binding
Binding
Binding
Slack
0
0.39552
0.05517
0.00000
0.54931
0.00000
0.00000
0.0000
0.0000
0.0000
0.0000
Microsoft Excel 16.0 Answer Report
Worksheet: [Frontier_Report.xls]Efficient Frontier
Report Created: 2/8/2019 7:06:46 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: GRG Nonlinear
Solution Time: 3.828 Seconds.
Iterations: 3 Subproblems: 0
Solver Options
Max Time 100 sec, Iterations 100, Precision 0.000001
Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%,
Solve Without Integer Constraints, Assume NonNegative
Objective Cell (Max)
Cell
Name
Original Value Final Value
$B$31 theta
4.55%
4.55%
Variable Cells
Cell
Name
$C$38 x_1
$C$39 x_2
$C$40 x_3
$C$41 x_4
$C$42 x_5
$C$43 x_6
$C$44 x7 Weights
$C$45 x8 Weights
$C$46 x9 Weights
$C$47 x10 Weights
Constraints
Cell
Name
$C$48 Total
$C$38 x_1
$C$39 x_2
$C$40 x_3
$C$41 x_4
$C$42 x_5
$C$43 x_6
$C$44 x7 Weights
$C$45 x8 Weights
$C$46 x9 Weights
$C$47 x10 Weights
Original Value Final Value
Integer
0.44674
0.46966 Contin
0.01665
0.00000 Contin
0.00000
0.00000 Contin
0.53661
0.53034 Contin
0.00000
0.00000 Contin
0.00000
0.00000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
Cell Value
1.0000
0.46966
0.00000
0.00000
0.53034
0.00000
0.00000
0.0000
0.0000
0.0000
0.0000
Formula
$C$48=1
$C$38>=0
$C$39>=0
$C$40>=0
$C$41>=0
$C$42>=0
$C$43>=0
$C$44>=0
$C$45>=0
$C$46>=0
$C$47>=0
Status
Binding
Not Binding
Binding
Binding
Not Binding
Binding
Not Binding
Binding
Binding
Binding
Binding
Slack
0
0.46966
0.00000
0.00000
0.53034
0.00000
0.00000
0.0000
0.0000
0.0000
0.0000
Microsoft Excel 16.0 Answer Report
Worksheet: [Frontier_Report.xls]Efficient Frontier
Report Created: 2/8/2019 7:07:08 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: GRG Nonlinear
Solution Time: 4.031 Seconds.
Iterations: 3 Subproblems: 0
Solver Options
Max Time 100 sec, Iterations 100, Precision 0.000001
Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%,
Solve Without Integer Constraints, Assume NonNegative
Objective Cell (Max)
Cell
Name
Original Value Final Value
$B$31 theta
3.11%
3.14%
Variable Cells
Cell
Name
$C$38 x_1
$C$39 x_2
$C$40 x_3
$C$41 x_4
$C$42 x_5
$C$43 x_6
$C$44 x7 Weights
$C$45 x8 Weights
$C$46 x9 Weights
$C$47 x10 Weights
Constraints
Cell
Name
$C$48 Total
$C$38 x_1
$C$39 x_2
$C$40 x_3
$C$41 x_4
$C$42 x_5
$C$43 x_6
$C$44 x7 Weights
$C$45 x8 Weights
$C$46 x9 Weights
$C$47 x10 Weights
Original Value Final Value
Integer
0.46966
0.56417 Contin
0.00000
0.00000 Contin
0.00000
0.00000 Contin
0.53034
0.43583 Contin
0.00000
0.00000 Contin
0.00000
0.00000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
Cell Value
1.0000
0.56417
0.00000
0.00000
0.43583
0.00000
0.00000
0.0000
0.0000
0.0000
0.0000
Formula
$C$48=1
$C$38>=0
$C$39>=0
$C$40>=0
$C$41>=0
$C$42>=0
$C$43>=0
$C$44>=0
$C$45>=0
$C$46>=0
$C$47>=0
Status
Binding
Not Binding
Binding
Binding
Not Binding
Binding
Not Binding
Binding
Binding
Binding
Binding
Slack
0
0.56417
0.00000
0.00000
0.43583
0.00000
0.00000
0.0000
0.0000
0.0000
0.0000
Microsoft Excel 16.0 Answer Report
Worksheet: [Frontier_Report.xls]Efficient Frontier
Report Created: 2/8/2019 7:07:29 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: GRG Nonlinear
Solution Time: 4.078 Seconds.
Iterations: 3 Subproblems: 0
Solver Options
Max Time 100 sec, Iterations 100, Precision 0.000001
Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%,
Solve Without Integer Constraints, Assume NonNegative
Objective Cell (Max)
Cell
Name
Original Value Final Value
$B$31 theta
1.76%
1.85%
Variable Cells
Cell
Name
$C$38 x_1
$C$39 x_2
$C$40 x_3
$C$41 x_4
$C$42 x_5
$C$43 x_6
$C$44 x7 Weights
$C$45 x8 Weights
$C$46 x9 Weights
$C$47 x10 Weights
Constraints
Cell
Name
$C$48 Total
$C$38 x_1
$C$39 x_2
$C$40 x_3
$C$41 x_4
$C$42 x_5
$C$43 x_6
$C$44 x7 Weights
$C$45 x8 Weights
$C$46 x9 Weights
$C$47 x10 Weights
Original Value Final Value
Integer
0.56417
0.85663 Contin
0.00000
0.00000 Contin
0.00000
0.00000 Contin
0.43583
0.14337 Contin
0.00000
0.00000 Contin
0.00000
0.00000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
0.0000
0.0000 Contin
Cell Value
1.0000
0.85663
0.00000
0.00000
0.14337
0.00000
0.00000
0.0000
0.0000
0.0000
0.0000
Formula
$C$48=1
$C$38>=0
$C$39>=0
$C$40>=0
$C$41>=0
$C$42>=0
$C$43>=0
$C$44>=0
$C$45>=0
$C$46>=0
$C$47>=0
Status
Binding
Not Binding
Binding
Binding
Not Binding
Binding
Not Binding
Binding
Binding
Binding
Binding
Slack
0
0.85663
0.00000
0.00000
0.14337
0.00000
0.00000
0.0000
0.0000
0.0000
0.0000
NO SHORT SALES
Variance-covariance matrix
VarCov
AAPL
BAC
C
COST
DAL
F
GE
S
TGT
WMT
AAPL
15.07189
5.802067 6.183366 4.1182467 6.408248
4.355189 4.294686
5.072176 3.459114
BAC
5.8020674
16.45575 13.43382 3.4612701 8.199968
7.092645 5.979071
8.413615 3.953163 2.514918
C
6.1833661
13.43382 14.74231 3.6389718 7.960136
7.43879 6.449818
COST
4.1182467
3.46127 3.638972 8.4821331 4.158879
3.212775 2.641782
3.343705 5.210687 4.314958
DAL
6.4082479
8.199968 7.960136 4.1588795 22.55181
6.615596 4.285459
6.858148 4.596389
F
4.3551886
7.092645
7.43879 3.2127747 6.615596
14.02841 5.470291
6.537876 4.429088 2.620664
GE
4.2946865
5.979071 6.449818 2.6417816 4.285459
5.470291 16.46064
5.696009 3.404217 2.414262
S
5.0721759
8.413615 8.230685 3.3437049 6.858148
6.537876 5.696009
60.2303 4.505286 2.773751
TGT
3.4591136
3.953163 4.211674 5.2106871 4.596389
4.429088 3.404217
4.505286 15.85477 5.482395
WMT
2.8894403
2.514918
2.620664 2.414262
2.773751 5.482395 9.505575
2.70844 4.3149585
3.2456
8.230685 4.211674
10
c
Portfolio mean
13.00%
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