Mathematics of Finance
Mathematics of Finance
Mathematics of Finance (Bachelors Degree – BSF 418)
CAT 1 (Continues Assessment Test 1)
(Online Take-Home Exam)
This CAT 1 incorporates 19 questions.
You are required to answer ALL questions.
To be handed in by ….., Mid-day in Google Classroom) –
NO acceptance after set deadline
1. Total 5% Marks: The following figures show the annual salaries in CHF of 20 GBS Mathematics of Finance
students doing Internship at Bank chains in Barcelona and Geneva.
Calculate the arithmetic mean, median, and mode Salary of the students.
Mathematics of Finance
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15’180, 19’870, 14,375, 15’767, 15’870, 15’180, 14’375, 36’938, 15’180, 46’132, 15’525, 19’600, 14’375, 23’069, 16’767, 16’767, 17’880, 14’375, 14’375, 14’375
2. Total 5% Marks: A Mathematics Investment analyst receives the following data showing the percentage
changes in Labor costs of Junior managers in an investment bank Chain over a 12-months
period. The highest change observed was +172 per cent for a senior manager in one of
the banks in Madrid.
Percentage Change Frequency -5 to under 0 2 0 to under 5 32 5 to under 10 25 10 to under 15 10 15 to under 20 8 20 to under 25 3 25 to under 30 2 30 to under 35 5 35 to under 40 4 40 to under 100 3 100 to 172 4
a). What is the mean annual percentage change in Labor costs for Junior managers in this investment bank?
b). What is the estimate of the Median Value? (3% Marks)
c). What is the modal class interval? (2% marks)
3. Total 5% Marks:
The following information applies to a portfolio composed of Fund A and Fund B.
Fund A Fund B
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Portfolio weights (%) 70 30
Expected returns (%) 10 16
Standard deviations (%)
7 13
Correlation between the returns of Fund A and Fund B
0.80
The portfolio’s standard deviation of return is closest to:
A. 7.38%.
B. 8.80%. C. 8.35%.
4. Total 5% Marks: You open a bank account today (06th April 2022) expecting that your dad will credit
your account three years later. If indeed your dad puts in CHF 15’500, how much
money will have in your account after 10 years if your earn 6% interest semi-annually
compounded?
5. Total 5% Marks:
Your dad has been asked to retire today and take his retirement benefits either as a
lump sum or as an annuity. The pension officer presents him with two alternatives:
● An immediate lump sum of CHF 2 million ● An annuity with 20 payments of 200’000 each year starting today
The interest rate at your bank is 7% per year annually compounded. Which option
would you recommend your dad to take?
6. Total 5% Marks:
Your pension Fund manager estimates that the corporate sponsor will make CHF 10
Million contributions, 5 years from now. The rate of return on the plan assets is
estimated to be 9% per year. The Pension Fund manager wants to calculate the FV of
this contribution 15 years from (the date at which the funds will be distributed to
retirees). Compute that FV?
7. Total 5% Marks: Using five years of monthly data, an analyst computes the following risk and return measures for three portfolios:
Portfolio Mean Monthly Portfolio Beta Portfolio Return Standard deviation
X 1.0% 1.5 1.3
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Y 1.5% 2.3 2.0 Z 2.5% 3.0 1.7
The mean monthly return on Treasury bills (T-bills) is 0.5% over this period. The most preferred portfolio, based on its Sharpe ratio, is: A. Portfolio X B. Portfolio Y C. Portfolio Z
Mathematics of Finance
8. Total 5% Marks: Based on historical returns, a portfolio has a Sharpe ratio of 2.0. If the mean return to the portfolio is 20%, and the mean return to a risk-free asset is 4%, what is the standard deviation of return on the portfolio?
9. Total 5% Marks: The expected returns and standard deviations for the three portfolios are shown in the table below.
Portfolio Expected Return Standard Deviation Beta One 21% 9.3% 1.4 Two 13% 6.4% 1.1 Three 11% 6.0% 1.0
An investor wants to select the optimal portfolio using Roy’s safety-first criterion with a threshold return of 3%. Assuming the risk-free rate is 2%, this investor should select Portfolio: A. One B. Two C. Three
10. Total 5% Marks:
Don Thompson plans to work for ten years and then take an extended vacation. He expects to save $3,000 a year for the first five years and $5,000 a year for the following five years. These savings will start one year from now. Thompson has $10,000 in an account paying 6% compounded annually and will begin putting his future savings into the same account when they begin. Given these assumptions, the
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amount of money that Thompson will have at the end of year 10 is closest to: A. $64,372 B. $68,725 C. $71,774
11. Total 5% Marks: Mike Ellers is evaluating a Venture capital investment that requires an initial investment of $2 million and, if it survives, the venture is expected to have a value of $15 million at the end of four years.
Year 1 2 3 4 Probability of failure 20% 20% 15% 10%
What is the NPV of this investment given the conditional failure rates above and a required rate of return of 25%? A. $1,008,102 B. $1,133,440 C. $1,710,560
12. Total 5% Marks: An investor bought 1,000 shares of Revland Co. on January 1, 2018, for $50 a share. He recorded the following data about the stock over the next three years: Year Year-End Stock Price Dividends During the Year 20X4 $45.00 $2.00 20X5 $50.00 $2.00 20X6 $60.75 $2.25
The geometric mean return over this 3-year period is closest to: A. 11% B. 12% C. 13%
13. Total 5% Marks: A portfolio manager has a two-asset portfolio with the following characteristics:
Asset Portfolio Weight Return Standard Deviation Correlation A 0.20 6% 5% 0.50 B 0.80 12% 20% 0.50
The standard deviation of this two-asset portfolio is closest to?: 14. Total 5% Marks:
Compute the Coefficient of Variation CV = Std / mean – assuming mean is 172.25
Height cm Frequency (Nr. of Students)
150 and under 155 1
5
155 and under 160 1
160 and under 165 2
165 and under 170 3
170 and under 175 6
175 and under 180 2
180 and under 185 4
185 and under 190 1
15. Total 5% Marks:
Find the median height of GBS students from the below data:
Height cm Frequency (Nr. of Students)
150 and under 155 1
155 and under 160 1
160 and under 165 2
165 and under 170 3
170 and under 175 6
175 and under 180 2
180 and under 185 4
185 and under 190 1
16. Total 5% Marks:
Mathematics of Finance
Distribution showing the weekly output of stock Traders at an Investment Bank in
Barcelona:
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Output (Stock Units) Number of Traders 100 – 160 1 160 – 180 5 180 – 200 10 200 – 220 35 220 – 240 55 240 – 260 74 260 – 300 20
a). Find mean of weekly Output
b). Find Median weekly Output
17. Total 5% Marks: From the below data, assess the average deviation from the mean price per unit of stock
Stock Price Number of Stocks sold
1.5 – 2.5 15
2.5 – 3.5 2
3.5 – 4.5 19
4.5 – 5.5 10
5.5 – 6.5 14
18. Total 5% Marks:
You are asked to arrange some Corporate Bonds in order of their maturity. What is the number of ways that are possible to arrange 4 Bonds from a total of 10 Bonds?
19. Total 10% Marks: – Use the below info to answer questions 19a-19e
Records show that for every 100 items produced in a factory during the day shift, two
are defective, and for every 100 produced during the night shift, four are defective. If
during the 24-hour period, 2000 items are produced during the day and 800 during
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the night, what is the probability that an item picked at random from the 2’800
produced during the 24-hour period;
a). Was produced on the day shift and was defective? (2 % marks)
b). Was produced on the Night shift and was defective? (2 % marks)
c). Is defective irrespective of the shift? (2% marks)
d). If a selected item is defective, what is the probability that it came from the day
shift? (2% marks)
e). If a selected item is defective, what is the probability that it came from the night
shift? (2% marks)
