Historically the S&P 500 Stock Index has returned about 8% a year but returns are very uneven as recent experience has reminded us - the INDEX declined by more than 50% from its peak in 2007 and took 7 years to attain that peak level again. This year (2019) the S & P 500 Index has gained about 10% through today’s date after declining almost 10% for last year( 2018). It has since recovered. In contrast a typical Money Market Fund has returned about 2% a year with minimal fluctuation. Given this, evaluate the following:

d) How risky would it be if you planned to use the Money Market fund as the major component of your retirement fund, 40 years from now? Briefly discuss your perception of risk in this decision, given your objective!

Very low                                                                                               Very high

                 risk              ____    ____    ____    ____    ____    ____    ____        risk

                                       1          2          3       4        5           6          7

            .

Briefly explain your decision: (2 points)

Do questions E-G

The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 8 varieties of Kellogg’s cereal.

Sugar (grams), ? 4 14 12 10 8 6 7 3

Calories, ? 110 140 130 110 120 100 120 190

a. Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between the amount of sugar and the number of calories per serving? We want to fit a straight-line model to relate calories y to the amount of sugar x. ? = ?0 + ?1 ? + ?

b. Compute: ????, ????, ????, ?̂ 0, ?̂ 1 .

c. Using your answer in part ( b ), find the predictive regression equation of the number of calories on the amount of sugar. Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain.

d. Give a practical interpretation of the value of ?̂ 1. Find the estimated standard error of the regression model and provide an interpretation.

e. For the fifth observation, Compute the predicted value ?̂5, the residual ?̂5.

f. Compute standard error of ?̂ 1 . Find a 97 % Confidence interval for ?1

g. Conduct a test to determine whether the two variables, sugar x and calories y, are positively linearly related. Use ? = 0.05.

41. Intergovernmental organization (IGO)
42. International law
43. Bilateral treaty
44. Multilateral treaty
45. North Atlantic Treaty Organization (NATO)
46. North American Free Trade Agreement (NAFTA)
47. The United Nations
48. The European Union
49. Cosmopolitanism
50. Schengen area
51. Eurozone
52. International treaty
53. Immanuel Kant
54. US Carrier Group
55. State of Nature (Hobbesian)

MATLAB NEEDED.

This lab will use functions and arrays.   The task within is to Add, Sub, or Multiply 2 Matrix. See Manipulate Matrix doc for the methods. My reference to matrix below is because we are doing matrix math. The matrix are arrays.

Matlab built-in functions not allowed

You will write 3 functions (call those functions): 1. ADD two matrix,   2. SUBTRACT two matrix, and 3. MULTIPLY two matrix.

Requirements:

1. Write the script to cycle until user chooses to stop.
2. Using any input format, you pick um,
   1. Have the user choose to ADD, SUB, or MULTIPLY matrix
   2. Using a switch case
      1. ADD matrix for this task you have the user enter the size of the matrix. That is enter row and column.   (NOTE row and col must apply to both matrix so you only ask once.)

Using random fill create two different matrix.

NOTE in code example used: b = int16(rand(r,c)*n);      int allows signed integers.

% digits 0 to n integers

For this lab we care about signed number so please use int not uint.

Call a function to add these 2 matrix and return the SUM

2. SUB matrix for this task you have the user enter the size of the matrix. Same rule apples for SUM as applied for ADD.

Using random fill create two different matrix

Call a function to subtract these two matrix and return the DIFFERENCE

3. MULTIPLY matrix for this task you have to ask the user for 3 dimension rows of A, columns of A,

and columns of B. (From theory Columns of A are the rows of B)

Using random fill create two different matrix

Call a function to multiply these two matrix and return the PRODUCT

3. Write 3 functions ADD, SUB, and MULTIPLY (Use your own names)
   1. Please do not pass the rows and columns thru the parameter list. Each parameter list should have only 2 array names, to be processed (added, subtracted, or multiplied ).
   2. Instead use the size function in Matlab.  For ADD and SUB only need size of one array. For MULTIPLY need size of both arrays because you need 3 of the 4 row, column numbers for the 3 for loops i, j, k.
   3. OUTPUT from each function is the resultant array.

ADD (SUB) MATRIX

C = A + B   Requires 2 for loops to move throught the arrays

Equation   C(i,j) = A(i,j) + B(i,j)   Fundamentally you are adding each element of A to its corresponding element of B and putting the sum into the corresponding element of C

MULTIPLYING MATRICES

There are some strick rules that must be applied.

C = A * B     requires that the columns of A must equal the rows of B.   C’s dimensions are the Rows of A by the Columns of B.

A(Ar,Ac)    B(Br,Bc)   C(Cr,Cc) given these dimensions for the three matrices

Rules above require Ac = Br    thus the # of columns of A equal the rows of B.

Then Cr = Ar   The rows of C must equal the rows of A

Then Cc = Bc The columns of C must equal the columns of B

The equation for filling the Matrix C is:

C(i,j) = ∑Ai,k) *B(k,j)

This notation uses i, j , k:

1. i runs from 1 to Ar
2. j runs from 1 to Bc

These 2 for loops fill Matrix C

3. k controls the summation of a sum of products of each row element in Matrix A times each respective column element in Matrix B
4. (   Note that ∑ demands a third for loop using k from 1 to Ac)

This is similar to Add and Sub the Answer array must be filled by 2 for loop.   This only adds a third for loop to manage the summation. use equation for summation. (∑).  

Consider the following work breakdown structure: Given a due date of 210 days, what is the earliest you can start activity D without delaying the project?

Benefits of diversification.

Sally Rogers has decided to invest her wealth equally across the following three assets.  

a.  What are her expected returns and the risk from her investment in the three​ assets? How do they compare with investing in asset M​ alone?  

Hint​: Find the standard deviations of asset M and of the portfolio equally invested in assets​ M, N, and O.

b.  Could Sally reduce her total risk even more by using assets M and N​ only, assets M and O​ only, or assets N and O​ only? Use a​ 50/50 split between the asset​ pairs, and find the standard deviation of each asset pair.

______________________________________________________________________

using the table below:

a.  

What is the expected return of investing equally in all three assets​ M, N, and​ O? (Round to two decimal​ places.)

What is the expected return of investing in asset M​ alone? ​(Round to two decimal​ places.)

What is the standard deviation of the portfolio that invests equally in all three assets​ M, N, and​ O? ​(Round to two decimal​ places.)

What is the standard deviation of asset​ M? ​(Round to two decimal​ places.)

By investing in the portfolio that invests equally in all three assets​ M, N, and O rather than asset M​ alone, Sally can benefit by increasing her return by ______ and decrease her risk by _________ ?  ​(Round to two decimal​ places.)

b.  

What is the expected return of a portfolio of​ 50% asset M and​ 50% asset​ N? ​(Round to two decimal​ places.)

What is the expected return of a portfolio of​ 50% asset M and​ 50% asset​ O? ​(Round to two decimal​ places.)

What is the expected return of a portfolio of​ 50% asset N and​ 50% asset​ O? (Round to two decimal​ places.)

What is the standard deviation of a portfolio of​ 50% asset M and​ 50% asset​ N? (Round to two decimal​ places.)

What is the standard deviation of a portfolio of​ 50% asset M and​ 50% asset​ O? ​(Round to two decimal​ places.)

What is the standard deviation of a portfolio of​ 50% asset N and​ 50% asset​ O? ​(Round to two decimal​ places.)

c.

Could Sally reduce her total risk even more by using assets M and N​ only, assets M and O​ only, or assets N and O​ only?  ​(Select the best​ response.)

a. not enough info to answer question

b. yes, a portfolio of 50% of asset M and 50% of asset O, could reduce risk to 1.5%

c. no, none of the portfolios using 50-50 split reduce risk

d. yes, a portfolio of 50% of asset M and 50% of asset N, could reduce risk to 1.5%

The accompanying table lists a random selection of usual travel times to​ school, in​ minutes, for 40 secondary school students in country A. A second selection of usual travel times to​ school, in​ minutes, was randomly selected for 40 students in country B. Complete parts​ a) and​ b).

Sample Country A   Sample Country B
45   29
5   10
4   9
14   30
50   5
21   8
21   7
19   15
21   10
21   36
24   16
36   10
14   24
29   22
19   20
11   26
45   29
10   10
2   25
60   7
24   15
19   19
5   25
16   15
5   10
15   26
18   5
30   2
40   4
20   25
11   20
30   14
10   48
14   21
20   20
10   12
14   19
16   5
10   14
24   11

Calculate the test statistic.

t = _ ?

​(Round to two decimal places as​ needed.)

Calculate the degrees of freedom.

df = _ ?

Determine the​ P-value.

P-value = _ ?

​(Round to four decimal places as​ needed.)

Make a conclusion.

Comparing the​ P-value to the level of​ significance, a = ​0.05, the decision is to (reject/fail to reject) the null hypothesis. There (is/is not) sufficient evidence to conclude that​ students' travel times in each country are (same/different).

Construct a​ 95% confidence interval for​(μ1−μ2​).

( _ , _ )

​b) Are your​ P-value and confidence level in part​ a) trustworthy?

yes or no

An investor obtains the following information:

• Stock price today = $120

• Stock price one year from today can take two values: $110 or $130

• Exercise price = $120

• Risk free interest rate = 5% per annum

What should be the price of a put option on the given stock under these conditions (use discrete discounting)?

What is the F statistic to test for a difference in mean THC yield between the control and heat-treated seeds?