Reference no: EM132510389
AFIN2070 Stochastic Methods in Applied Finance - Macquarie University
Problem 1
ZCF wants to see if their weekly sales values have any impact on their weekly share returns (with a one-week delay). The relevant values over a two-month period are shown below.
|
Week
|
Sales revenue in week ($millions)
|
Share return for (week + 1)
|
|
1
|
21
|
-5.16%
|
|
2
|
14
|
-2.34%
|
|
3
|
18
|
2.67%
|
|
4
|
25
|
7.50%
|
|
5
|
30
|
-4.40%
|
|
6
|
9
|
4.55%
|
|
7
|
15
|
-3.26%
|
|
8
|
23
|
-2.42%
|
a) Calculate Spearman's rho for this data. Show full working.
b) Calculate Kendall's tau for this data. Show full working.
(HINT: The use of Excel may help you here. If you do choose to use Excel, include any relevant explanation of the calculation used as part of your submission)
Problem 2
The daily returns over a selected period for shares in Aaron's Adventures and Bradley's Boats (A and B) have been recorded and provided to you in the Assignment Data spreadsheet under "Q2". Use this data to answer the following questions.
a) Make an appropriate graph of the pairs of daily returns. Include all relevant labels to make your graph clear.
b) State the Pearson's correlation coefficient for these daily returns. You do not need to show any working for this part.
c) (W) Explain what your result in part b) means with reference to your graph in part a).
d) (W) Suppose you wanted to simulate more data points to help predict future returns. First describe what features (in particular, dependencies) of the current data you would try to preserve. What process would you choose to simulate your data? Explain how you chosen method would preserve your chosen features.
Problem 3
Harry has collected data on years of work experience and annual salaries from 500 different office workers in his home city of Everwork. Work experience is measured to the nearest half-year, and annual salaries are measured in thousands of dollars. This data has been recorded and provided to you in the Assignment Data spreadsheet under "Q3". Use this data to answer the following questions.
a) (C) Harry would like to use this data to build a model to estimate the annual incomes of office workers based on years of work experience. Plot an appropriate graph based on the data provided.
b) (C) State the correlation between years of work experience and annual salary. You do not need to show any working for this part.
Tom, one of Harry's colleagues, has performed a linear regression on this data to assist Harry.
c) (W) Tom has found the values of ?? and ?? to be 56.41061 and 2.627692 respectively. Explain what these numbers represent.
d) (W) Under Tom's model, state explicitly the assumptions for the error term ??i. By looking at the graph in part a), comment on the appropriateness of the use of a linear regression model.
(Hint: although not strictly necessary for this question, it may be useful to run a regression by yourself on this data)
Problem 4
Roy is modelling the maximum daily loss in any month for shares in Emblem Industries. He believes this maximum loss
L follows a GEV (0.04,0.025, -0.02) distribution.
a) (C) Write down the CDF for this distribution and clearly state what this function represents. Also, calculate the mean and variance of L under Roy's model. Clearly state any values of the Gamma function that are used in your model.
b) (C) Using part a) or otherwise, calculate the 2% VaR for L. Show all relevant calculation steps.
Problem 5 Bob works for an insurance company that currently has a portfolio of 200 home insurance contracts in the region of Floyd. A large river flows through Floyd, and the region has been experiencing heavier than usual rainfall in the last year. Bob has been asked to undertake a risk analysis of the home insurance portfolio. By looking at home insurance portfolios from other regions, he assumes that the number of claims follows a Poisson process with an average of 6 claims per year.
a) (C) What is the probability that the first claim from this portfolio does not happen within six months? Clearly state what distribution(s) you are using and show all relevant calculation steps.
b) (C) Bob's boss is worried about the company going bankrupt. He says that if the company receives 40 or more claims from this portfolio within the next 5 years they won't be able to afford it. Under Bob's model, what is the probability that this occurs? Clearly state what distribution(s) you are using and show all relevant calculation steps.
(HINT: The use of Excel may help you here. If you do choose to use Excel, include any relevant explanation of the calculation used as part of your submission)
c) (W) As it turns out, a couple of years later, the insurance company suffered huge losses due to a surge of claims, was forced into administration, and Bob was fired. Explain why Bob's risk model was inappropriate for this particular insurance portfolio.
Attachment:- Stochastic Methods in Applied Finance.rar