BUS6032 Quantitative Analysis for Financial Studies Assignment 2
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BUS6032 Quantitative Analysis for Financial Studies
Assignment 2
Due on Nov 20
. There are 6 questions.
. The assignment will be marked out of 20.
. Handwrite the answers to all questions neatly and legibly in the space provided.
. Show your steps clearly when answering the questions.
1) For a stock with price P and earning per share E, the price-to-earning ratio (PE ratio) is defined as P/E. The PE ratio of EDU company is normally distributed with a standard deviation of 3.9541 and 95% of the time EDU is trading at a PE ratio between 15.1 and 30.6. The latest earning forecast for EDU is $1.47 per share.
1a. Find the mean of the PE ratio. (1 mark)
1b. EDU is considered as “overvalue” by investment banks if it is traded at the upper confidence limit of the 90% confidence interval for its PE ratio. What is the “overvalue” price? (1 mark)
2) A well-known investment bank has job openings for the position of management trainee. Candidates should take the aptitude test and have a good result to proceed to the next stage of the recruitment process. The test score is normally distributed with a mean of 690.2 and a standard deviation of 202.2. Let X be the random variable representing the test score. Using the standard normal table attached at the last page of this assignment to answer the following questions.
2a. Find the values of the standard normal variable Z if X are equal to 850 and 431.3, respectively (1 mark)
2b. What is the probability that a candidate scored between 431.3 and 850 ? (1 mark)
2c. If only the top 9% scored candidates can go to the next stage, what is the minimum score required? (1 mark)
3) An asset management company STARS manages two stock funds A and B where A is called Japan Equity Fund and B is called Vietnam Opportunities Fund. The rates of return of A and B are 9.6% and 24.5%, respectively. There are many stock funds managed by other companies also investing in Japan and Vietnam. STARS wants to know how well its funds perform compared to other companies. A random sample of 50 Japan stock funds has a mean rate of return of 6.5% and sample standard deviation of 10.6%. Another random sample of 35 Vietnam stock funds has a mean rate of return of 17.9% and population standard deviation of 21.1%.
3a. Find the standard errors of the mean rate of return for Japan stock funds and Vietnam stock funds, respectively. (1 mark)
3b. Construct a 95% confidence interval for the mean rate of return for Japan stock funds. (0.5 mark)
3c. Construct a 95% confidence interval for the mean rate of return for Vietnam stock funds. (0.5 mark)
3d. Simply just based on the mean rate of return, which equity fund A or B, could STARS claim it to be the top 5% highest performance funds in its own category? Explain your answer. (1 mark)
4) Suppose three stocks A, B and C only have a limited number of potential values and let these potential values be random variables X, Y, and Z, respectively. X is related to Y and Z by the linear equation 3X = Y – 2Z. The expected value of X is $14.42. All possible values of X and their corresponding probabilities are shown below:
Possible values of X |
$7 |
v |
$15 |
$21 |
1.8v |
P(X = x) |
0.25 |
0.2 |
0.35 |
p |
0.1 |
The variance of Y is $106.7. The expected value and variance of Z are $5.3 and $16.9, respectively.
4a. Find the value of vand p (1 mark)
4b. Find the variance of X (0.5 mark)
4c. Find the expected value of Y (0.5 mark)
4d. Are stock B and stock C (or Y and Z) negatively linearly correlated? Explain your answer (1 mark)
5) From a financial website, the month-end closing prices of Crude Oil and Bitcoin from December 2022 to July 2023 are shown in the table below.
|
Closing Price (USD) |
|
End of Quarter |
Crude Oil |
Bitcoin |
December 2022 |
Missing |
23,139.28 |
January 2023 |
76.41 |
23,147.35 |
February 2023 |
75.67 |
28,478.48 |
March 2023 |
76.78 |
29,268.81 |
April 2023 |
68.09 |
27,219.66 |
May 2023 |
70.64 |
30,477.25 |
June 2023 |
81.8 |
29,230.11 |
July 2023 |
82.82 |
29,429.59 |
Given that monthly rates of return for Crude Oil and Bitcoin are independent and they are normally distributed. The population standard deviations of monthly rate of return for Crude Oil and Bitcoin are 9.7% and 13.8%, respectively.
5a. By using the formula for monthly rate of return as shown below and using only non-missing data for both Crude Oil and Bitcoin, write down the 6 monthly rates of return and the corresponding months in the table below. (1.5 marks)
cpcurrent − cpprevious
R current = cpprevious x 100%
where
Rcurrent = monthly rate of return at current month
CPcurrent = month-end closing price at current month
CPprevious = month-end closing price at one month before current month
|
R current |
|
End of Month |
Crude Oil |
Bitcoin |
|
|
|
|
|
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|
|
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5b. Let the sample mean monthly rates of return for Crude Oil and Bitcoin be X(̅) 1 and X(̅)2, respectively. FindX(̅)1 and X(̅)2 (use arithmetic mean). (1 mark)
5c. Construct a 95% confidence interval forX(̅)2 -X(̅)1 and give the interpretation. (1.5 marks)
5d. Can we say that the performance of Crude Oil is worse than Bitcoin ? Explain your answer. (1 mark)
6) The research team of an investment bank issues analytical reports on listed stocks trading in different stock exchanges. To declare the conflict of interest, an analytical report on a listed stock in which the investment bank or the investment analyst holds is considered as an “ownership” report. From historical data, the number of analytical reports issued by investment bank JJM and BS per quarter identified as “ownership” reports are both approximately normally distributed. The mean number of “ownership” reports per quarter for JJM is 6.1 while it is 18.1 for BS. The standard deviation of number of “ownership” reports per quarter for JJM and BS are 7 and 15, respectively.
6a. In a particular quarter, what is the probability of less than 10 “ownership” report in BS ? (1 mark)
6b. A random sample of 35 reports in JJM and another random sample of 65 reports in BS are
drawn. Let the sample mean number of “ownership” reports per quarter for JJM and BS beX(̅)A
andX(̅)B, respectively. Write down the mean and standard deviation of the sampling distribution of
X(̅)A andX(̅)B, respectively. (1 mark)
6c. Suppose the two normal distributions are independent, write down the mean and standard
deviation of the sampling distribution of X(̅)B -X(̅)A (1 mark)
6d. Based on the two random samples in 6b, find the probability that the mean number of “ownership” reports in BS are 9 more than in JJM ? (1 mark)
2023-11-18