Reference no: EM132547633
Quantitative Finance and Financial Markets Assignment
Learning Outcome 1: Apply quantitative tools in financial markets.
Learning Outcome 2. Critically evaluate the impact of changes to financial models.
Learning Outcome 3. Compute basic valuation analysis for financial markets instruments.
Learning Outcome 4. Evaluation of the inputs variables and their outputs in the use of quantitative tools in financial markets.
Learning Outcome 5. Critically evaluate the relative importance of the key elements in successful performance measurement and control.
Problem 1 During the recession that began in 2008, not only did some people stop making house payments, but they also stopped making payments for local government services such as trash collection and water and sewer services. The following data has 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 was 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
|
Y
|
|
$4,300.00
|
3900 + NM
|
|
$100.00
|
200 + NM
|
|
$300.00
|
300 + NM
|
|
$900.00
|
900 + NM
|
|
$1,400.00
|
1400 + NM
|
|
$1,900.00
|
1600 + NM
|
|
$1,600.00
|
1300 + NM
|
|
$3,700.00
|
3000 + NM
|
|
$6,400.00
|
5100 + NM
|
|
$2,100.00
|
1900 + NM
|
|
$200.00
|
300 + NM
|
Where NM is the last two digits of your student ID number.
a. Compute the least squares regression equation.
b. If the computer-generated account balance was 120, what would you expect to be the actual account balance as verified by the accountant?
c. The computer-generated balance for Oliver Buxton is listed as 100 in the computer-generated account record. Calculate a 95% interval estimate for Mr Buxton's actual account balance.
Problem 2
A real estate investor in the city of Santa Monica, California wishes to determine the selling price of California residences using the size (square feet) and whether the residence is a condominium or a single-family home. A sample of 20 residences was obtained with the following results:
|
Price ($)
|
Type
|
Square feet
|
|
$424,000.00
|
f
|
2500 + NM
|
|
$428,000.00
|
c
|
2400 + NM
|
|
$421,000.00
|
f
|
2100 + NM
|
|
$465,000.00
|
f
|
2500 + NM
|
|
$446,000.00
|
f
|
2300 + NM
|
|
$397,000.00
|
c
|
2100 + NM
|
|
$583,000.00
|
f
|
3300 + NM
|
|
$572,000.00
|
c
|
3200 + NM
|
|
$479,000.00
|
f
|
2600 + NM
|
|
$389,000.00
|
c
|
2100 + NM
|
|
$412,000.00
|
c
|
2200 + NM
|
|
$423,000.00
|
c
|
2300 + NM
|
|
$438,000.00
|
f
|
2300 + NM
|
|
$471,000.00
|
f
|
2500 + NM
|
|
$393,000.00
|
c
|
2100 + NM
|
|
$390,000.00
|
c
|
2100 + NM
|
|
$543,000.00
|
f
|
3000 + NM
|
|
$434,000.00
|
f
|
2300 + NM
|
|
$506,000.00
|
f
|
2800 + NM
|
|
$429,000.00
|
f
|
2200 + NM
|
Where NM is the last two digits of your student ID number.
a. Produce a regression equation to predict the selling price for residences using a model of the following form:
γi = β0 + β1x1 + β2x2 + ε
Where
1 Square Footage
1, if a condomnium
2 0, if a single-family home
b. Interpret the parameters β1, and β2 in the model given in part a.
c. Calculate P-values and a 95% confidence interval for both slopes of both variables. Interpret them.
d. Produce an equation that describes the relationship between the selling price and the square footage of (1) condominiums and (2) single-family homes.
Problem 3
A major sausage producer has an office in Wolfsburg, Germany. The sales manager of the office is evaluated based on the number of new clients signed up every quarter. The following data reflects the number of new customers added during each quarter between 2016 and 2019.
|
Quarter
|
Year
|
No. of
Clients
|
|
Qtr1
|
2016
|
466 + NM
|
|
Qtr2
|
2016
|
480 + NM
|
|
Qtr3
|
2016
|
433 + NM
|
|
Qtr4
|
2016
|
534 + NM
|
|
Qtr1
|
2017
|
500 + NM
|
|
Qtr2
|
2017
|
535 + NM
|
|
Qtr3
|
2017
|
512 + NM
|
|
Qtr4
|
2017
|
581 + NM
|
|
Qtr1
|
2018
|
542 + NM
|
|
Qtr2
|
2018
|
615 + NM
|
|
Qtr3
|
2018
|
584 + NM
|
|
Qtr4
|
2018
|
666 + NM
|
|
Qtr1
|
2019
|
632 + NM
|
|
Qtr2
|
2019
|
682 + NM
|
|
Qtr3
|
2019
|
680 + NM
|
|
Qtr4
|
2019
|
755 + NM
|
Where NM is the last two digits of your student ID number.
a. Calculate the multiple linear regression equation using quarterly data as dummy variables.
b. Interpret each slope and the intercept in the multiple linear regression equation from part a. Calculate a 90% confidence interval for each variable slope and assess whether it is statistically significant.
c. Create a forecast for 2020 and 2021.
Problem 4
James Anderson is the COO of a leading financial institution. He has asked you, a portfolio manager, to calculate the best combination of assets, stock, bonds, and commodities in the firm's portfolio. James has also provided you with the following information from the firm's financial history:
|
Three-Asset Case
|
Stocks
|
Bonds
|
Commodities
|
|
Expected return E(R)
|
13%
|
3%
|
4%
|
|
Variance
|
218%
|
60%
|
140%
|
|
Standard deviation
|
148%
|
77%
|
118%
|
|
Correlation between stocks and
bonds
|
0.2 +
NM/1000
|
|
|
|
Correlation between stocks and
commodities
|
0.4 +
NM/1000
|
|
|
Correlation between bonds and
commodities
|
0.7 +
NM/1000
|
Where NM is the last two digits of your student ID number.
Given the information above, you are required to produce a report that consists of the following:
a. Calculate all expected returns and standard deviations of all portfolio combinations. Use 10% as the smallest unit of the combination, so for example the first combination will be stock 100%, bonds 0%, and commodities 0%, the second combination will be stock 90%, bonds 10%, commodities 0%, and so on (there are 66 possible combinations).
b. Plot the efficient frontier for all combinations.
Problem 5
A black swan is a very rare bird which (unless you venture to South Australia) you will not happen to see in your lifetime. The black swan event, which takes its name from the rare bird, is also an unexpected and extremely rare occurrence. Or at least it should be.
A black swan event is an event so unlikely that its probability is almost zero. Yet, black swan events are nightmares any portfolio analyst or risk manager needs to live with. Portfolio analysts calculate the overall risk levels based on historical data and historical correlations between asset prices (and probabilities of the change of these correlations). Yet, black swan events tend to turn up in the most unexpected places. The credit crunch in 2007 was an instance of a black swan event, triggered by a previously impossible coordinated decline in house prices everywhere in the United States. The Fukushima Daiichi Accident, a tsunami that caused a nuclear disaster which temporarily disrupted supply chains in Japan, was another. More recently, the Covid-19 pandemic was yet another such event.
Write a critical essay where you critically evaluate the risk of unknown future developments and their impact on the world of finance.
Attachment:- Quantitative Finance and Financial Markets.rar