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Reference no: EM131133273

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Harvard
Referencing

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Learning
Outcomes

On successful completion of this assignment you will be able to:

1. Design and apply quantitative tools in financial markets
2. Critically evaluate the changes that might occur if certain assumptions in the models used are changed
3. Compute basic valuation analysis for financial markets instruments

4. Evaluation of the inputs variables and their outputs in the use of quantitative tools in financial markets
5. Synthesis and evaluate findings and present same in a professional manner to a varied audience
Grading Criteria Postgraduate Grading Criteria for this assignment is available at the end of this document.

Your Task QUESTION 1

The managing partner for Westwood One Investment Managers Inc. gave a public seminar in which she discussed a number of issues, including investment risk analysis. In that seminar, she reminded people that the coefficient of variation can often be used as a measure of risk of an investment. To demonstrate her point of view, she used two hypothetical stocks as examples. She let x equal the change in assets for a $1,000.00 investment in stock1 and y reflect the change in assets for a $1,000.00 investment in stock2. She showed the seminar participants the following probability distributions:

a. Compute the expected values for the random variables x and y. (2 marks)
b. Compute the standard deviations for the random variables x and y.(3 marks)
c. Compute the coefficient of variation for each random variable.(2 marks)
d. Referring to part c, suppose the seminar director said that the first stock was riskier since its standard deviation was greater than the standard deviation of the second stock. How would you respond to her assertion? (3 marks)

QUESTION 2

MainStay Investments is one of the investment vehicles used by New York Life Investment Management (NYLIM). The respondents to a survey conducted by NYLIM and who are aged between 26 and 82 indicated that 66% o f seniors, 61 % of baby boomers, and 58% of Generation X expect Individual Retirement Accounts (IRAs) to be their primary source of income in retirement. The margin of error was given as ±5 percentage points.

a. Calculate a 95% confidence interval for the proportion of seniors who expect IRAs to be their primary source of income in retirement. (5 marks)
b. Although the sample size for the entire survey was listed, the sample size for each of the three generations was not given. Assuming the confidence level was 95%, determine the sample size for each of the three generations. (5 marks)

QUESTION 3
About 74% of Freddie Mac-owned loans were refinanced in the second quarter of 2005 (USA Today, Lifeline, August 3, 2005), resulting in new mortgages carrying loan amounts at least 5% above the original mortgage balance. The median loan refinanced in the second quarter was 2.6 years old.

If a sample size of 2,500 was used to obtain this information,

a. Determine if the sample size for the test is large enough to warrant approximating the sample proportion's distribution with a normal
distribution. (5 marks)
x P(x) y P(y)
-$1,000 0.1 -$1,000 0.2
$0 0.1 $0 0.4
$500 0.3 $500 0.3
$1,000 0.3 $1,000 0.05
$2,000 0.2 $2,000 0.05

b. Use this information to determine if less than 75% of new mortgages had a loan amount at least 5% above the original mortgage balance.
Use a test statistic approach with a = 0.025. (5 marks)

QUESTION 4
Before the unprecedented decline in home sales that started in late 2008, the National Association of Realtors profile of home buyers and sellers indicated that the percentage of home buyers who are single women has more than doubled since 1981, whereas the percentages of home buyers who are single men has declined. This occurred despite evidence indicating that women's salaries still lag behind those of men.

The Association's profile states that the median income for men and women home buyers was $58.939 and $47,315, respectively. Assume the respective standard deviations and sample sizes were $10,000 and $9,000, and 200 and 302

a. Conduct a hypothesis test to determine if the median income for men buying homes is more than $10,000 larger than that of women. Use
a significance level of 0.05. (5 marks)

b. Describe any additional assumptions required to validate the results of the hypothesis test in part a. (5 marks)

QUESTION 5
In conjunction with the housing foreclosure crisis of 2009, many economists expressed increasing concern about the level of credit card debt and efforts of banks to raise interest rates on these cards. The banks claimed the increases were justified. A Senate sub-committee decided to determine if the average credit card balance depends on the type of credit card used. The cards under consideration are Visa, MasterCard, Discover, and American Express. The sample sizes to be used for each level are 25, 25, 26, and 24, respectively.

a. Describe the parameter of interest for this analysis. (1 mark)
b. Determine the factor associated with this experiment. (2 marks)
c. Describe the levels of the factor associated with this analysis. (1 mark)
d. State the number of degrees of freedom available for determining the between-samples variation. (2 marks)
e. State the number of degrees of freedom available for determining the within-samples variation. (2 marks)
f. State the number of degrees of freedom available for determining the total variation.

QUESTION 6
A senior analyst working for Ameritrade has reviewed purchases his customers have made over the last six months. He has categorized the mutual funds purchased into eight categories: Aggressive Growth (AG) - Growth (G)

- Growth-Income (G-I) - Income Funds (IF) - International (I) - Asset Allocation (AA) - Precious Metal (PM) - Bond (B).

The percentage gains (%) accrued by 3 randomly selected customers (C1, C2 and C3) in each group are as follows:

a. Develop the appropriate ANOVA table to determine if there is a difference in the average percentage gains accrued by his customers
among the mutual fund types. Use a significance level of 0.05. (5 marks)
b. Use the Tukey-Kramer procedure to determine which mutual fund type has the highest average percentage gain. Use an experimentwide
error rate of 0.05. (5 marks)

QUESTION 7
A study was conducted to determine if there is a difference between the investing preferences of mid-level managers working in the public and private sectors in New York City. A random sample of 320 public sector employees and 380 private sector employees was taken. The sampled participants were then asked about their retirement investment decisions and classified as being either "aggressive," if they invested only in stocks or stock mutual funds, or "balanced," if they invested in some combination of stocks, bonds, cash, and other. The following results were found:

a. State the hypothesis of interest and conduct the appropriate hypothesis test to determine whether there is a relationship between employment sector and investing preference. Use a level of significance of 0.01.

b. State the conclusion of the test conducted in part a.

c. Calculate the p-value for the hypothesis test conducted in part a.

QUESTION 8
During the recession that began in 2008, not only did some people stop making house payments, but they also stopped making payments for localgovernment services such as trash collection and water and sewer services.

The foll owing data have been collected by an accountant who is performing an audit of account balances for a major city billing department.

The population from which the data were collected represents those accounts for which the customer had indicated the balance was incorrect. The dependent variable, y, is the actual account balance as verified by the accountant. The independent variable, x, is the computer-generated account balance.

X 233 10 24 56 78 102 90 200 344 120 18
Y 245 12 22 56 90 103 85 190 320 120 23

Mutual Fund AG G G-I I F I AA PM B
C1 6 7 5 1 14 - 3 5 - 1
C2 7 - 2 6 0 13 7 7 3
C3 12 0 2 6 10 7 5 2

Agressive Balanced
Public 164 156
Private 236 144

a. Compute the least squares regression equation. (2 marks)
b. If the computer-generated account balance was 100, what would you expect to be the actual account balance as verified by the accountant? (2 marks)
c. The computer-generated balance for Timothy Jones is listed as 100 in the computer-generated account record. Calculate a 90% interval
estimate for Mr. Jones's actual account balance. (3 marks)

d. Calculate also a 90% interval estimate for the average of all customers' actual account balances in which a computer-generated account balance is the same as that of Mr. Jones (part c). Interpret your results. (3 marks)

QUESTION 9

A real estate agent wishes to determine the selling price of residences using the size (square feet), and whether the residence is a condominium or a single-family home. A sample of 20 residences was obtained with the following results:

Price ($) Type Square Feet
199,700 F 1,500
211,800 C 2,085
197,100 F 1,450
228,400 F 1,836
215,800 F 1,730
190,900 C 1,726
312,200 F 2,300
313,600 C 1,650
239,000 F 1,950
184,400 C 1,545
200,600 C 1,375
208,000 C 1,825
210,500 F 1,650
233,300 F 1,960
187,200 C 1,360
185,200 C 1,200
284,100 F 2,000
207,200 F 1,755
258,200 F 1,850
203,100 F 1,630
F: Single-Family Home
C: Condomnium Residence

a. Produce a regression equation to predict the selling price for residences using a model of the following form: (2 marks) Where,

b. Interpret the parameters β1, and β2 in the model given in part a

c. Produce an equation that describes the relationship between the selling price and the square footage of (1) condominiums and (2)
single-family homes.

d. Conduct a test of hypothesis to determine if the relationship between the selling price and the square footage is different between
condominiums and single-family homes.

QUESTION 10
A major brokerage company has an office in Miami, Florida. The manager of the office is evaluated based on the number of new clients generated each quarter. The following data reflect the number of new customers added during each quarter between 2006 and 2009.

a. Plot the time series and discuss the components that are present in the data.

b. Referring to part a, fit a linear trend model to the data for the years 2006- 2008. Then use the resulting model to forecast the number of
new brokerage customers for each quarter in the year 2009. Compute the MAD and MSE for these forecasts and discuss the results.

c. Using the data for the years 2006-2008, determine the seasonal indexes for each quarter.

d. Develop a seasonally unadjusted forecast for the four quarters of year 2009.

e. Using the seasonal indexes computed in part d; determine the seasonally adjusted forecast for each quarter for the year 2009.
Compute the MAD and MSE for these forecasts.

 

Reference no: EM131133273

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