INSTITUTE OF BANKERS OF SRI LANKA
Intermediate in Applied Banking and Finance (IABF)
Business Mathematics and Statistics - Guidance Questions
a) The questions below are provided to guide students and teachers in their
studies on the subject as per the syllabus.
b) Each question will carry 20 marks distributed as 5 marks for each subquestion.
c) It is expected that about 30-35 minutes will take to answer a question.
d) Precise answers are expected in points. Detailed essay typed long answers
are not expected.
1.
Observations obtained from measuring length of 252 cables for maintaining the quality
control in a manufacturing firm are shown in the following table.
Length (Approximate cm)
199-201
202-204
205-207
208-210
Frequency
51
107
70
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Calculate the following statistical values and explain the importance of each to identify
the nature of cable production.
i) Mean
ii) Variance
iii) Standard deviation
iv) Coefficient of variation
2.
Answer the following questions.
i)
Suppose that A and B are two probable events so that P(A∩B)=1/4 and
P(A)=P(A/B’)=5/12. Here, B’ is the complement of B. Using the information given
above, find the following.
a) P(B/A)
b) P(B)
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ii)
iii)
c) P(A/B)
d) P(AUB)
Probability is a statistical measure of the likeliness that a probable event will
occur. A coin is tossed thrice to observe such a probable event. Consider H as the
head turning up and T as the tail turning up. Answer following questions related
to this experiment.
a) Sample space of this event
b) Probability of head turning up thrice.
c) Probability of head turning up at least once
Suppose a school hockey team is going to play a match. If F is the event of having
a favourable weather condition and V is the event that the school hockey team
wins the match, the relevant tree diagram and the probabilities of possible
events are given below. F’ and V’ are the compliments of F and V, respectively.
Find the probability of the event that the school hockey team wins the match.
V
0.8
F
0.75
0.2
0.3
0.25
V’
V
F’
0.7
V’
iv)
The probability of occurring the event A is 0.3 and that of B is 0.6. If A and B are
mutually independent, find AUB.
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3.
Answer the following questions.
i)
X is a variable that denotes the distribution of the marks obtained by students in
a class for Statistics. The behavior of the variable X is a normal distribution. The
mean and the standard deviation is given so that X~N (60, 15). Using the
information given above, find the following probabilities.
a) Pr (X<50)
b) Pr (55<X<65)
ii)
The mean income (µ) of employees in a commercial bank is Rs.50, 000.00, and
the standard deviation (σ) is Rs.20, 000.00. Find the standard error of the sample
mean (X̅ ) when the magnitude of the sample (n) randomly obtained from the
population is 10. Mention your assumptions in this regard and propose a
measure to minimize this standard error.
iii)
Calculate the confidence interval for a population mean (µ) of 95%, using data
given in (II) above if the sample mean (X̅ ) =Rs.55, 000.00. (Consider that Z0.025
=1.96)
iv)
State three qualities which should be with the mean of the sample distribution.
4.
The following relationship between interest rates (Y) and fixed deposits (X) has been
derived by using observations received by a commercial bank has been estimated in the
regression model Y = β1X+ β0
log (interest rates) = 0.2617-1.4379 x log (Deposits)
Coefficient of determination R2 = 71.35%
Answer the following questions.
i)
ii)
iii)
iv)
5.
Explain the usefulness of coefficient, β1, for deciding the change in interest rate
on deposits.
Calculate the coefficient of correlation (r) for the variables X and Y. Mention
what information is provided by the coefficient of correlation.
State key assumptions made when estimating a Linear Regression Equation.
State the meaning of coefficient of determination (R2) for the above regression
model.
An investor deposits savings in a two year term deposit of Rs.10, 000.00 in a commercial
bank. Interest at rates (interest paid annually) 2% and 4% is paid for the first and second
year, respectively. Answer the following questions.
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i)
ii)
iii)
iv)
What is the value of the deposit belonging to the investor at the end of the two
years?
What is the Annual Average Rate of Return received by the investor within this
period?
Calculate the Geometric Average Rate of Return of those returns.
Discuss what the most useful rate is by comparing (II) and (III) above.
6.
When a security is purchased by an investor between the coupon periods, the number
of days between the purchase settlement date and the next coupon period is 115. The
normal coupon period has 183 days. Assume that the coupon rate of the security is 7.4%
and if there are 10 semi-annual coupon payments remaining.
i) Describe the dirty price and clean price of a security.
ii) What is the dirty price of the security if the discount rate is 5.6%
iii) What is the interest accrued for this security within this period?
iv) What is the clean price of security?
7.
The following table shows prices and quantities of items in a basket of goods selected to
construct a hypothetical consumer price index in 1980 and 1990.
Commodity
Beans (kg.)
Milk (Littre)
Fossil fuel (Gallons)
Shoes (a pair)
i)
ii)
iii)
iv)
8.
1980
Quantity
Price
40
75
150
60
200
180
2
400
1990
Quantity
Price
40
80
100
80
250
200
3
500
Calculate the Consumer Price Index using the Laspeyres Formula for the year
1990 using 1980 as the base year.
Calculate the average Inflation Rate for the year 1990.
Outline the problems associated with the use of Laspeyres Formula based price
indices.
Explain the importance of Consumer Price Index to banks.
Suppose that a multiple regression equation has been estimated by conducting a survey
to study the efficiency of employees recruited to handle financial transactions with
customers of a commercial bank. The multiple regression equation in the predicted
form is as follows:
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Y
Y
X1
X2
i)
ii)
iii)
iv)
= 2.0+0.5 X1 + 0.2 X2
Number of transactions finished within an hour - a proxy for
Efficiency.
Period of service in the commercial bank in months – a proxy for
Experience.
Marks received for the recruitment examination - a proxy for
Intelligence
What are the key assumptions made for estimating the above regression model?
Kamal has received 70 marks for the recruitment examination. He was recruited
very recently. Which efficiency do you expect from him when compared with the
overall efficiency estimate in the model?
Which will be Kamal’s efficiency when his service period reaches 6 months?
Outline the key problems, additional information required and
statistical/technical problems confronted when using the results of the above
multiple regression equation.
9.
Answer the following questions.
i)
What is the future value in 10 years of Rs.1,500/- payments received at the end
of each year for the next 10 years, Assume an interest rate of 8% prevailing in
the 10 – year period.
ii)
A bond with a coupon rate of 8% paid annually and a face value of $ 1,000
matures in 12 years. If the current annual market interest rate is 8%, what is the
bond’s market value?
iii)
If the market interest rate rises to 10%, what will be the new price for the bond?
iv)
Investor purchases a Treasury bill for Rs.9,600 with time to maturity of 182 days.
Its face value is $ 10,000. If the investor holds it up to maturity, what is the yield
of the Treasury bill?
10.
Answer the following questions relating to foreign exchange calculations.
i.
Spot exchange rates of USD against JPY and GBP against USD are as follows.
USD/JPY
=
108.00
GBP/USD
=
1.6150
Calculate the exchange rate of GBP against JPY (GBP/JPY) spot exchange rate.
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ii.
Assume the following information.
Currency
GBP
EURO
Interbank
Interest Rate
2%
Spot Rate
$ 1.6185
Expected Spot
Rate in 5 Days
$ 1.6135
4%
$ 1.8150
$ 1.8200
Explain how a XYZ bank can speculate by taking a short position in one currency and a
long position in the other. What will be the gain if expectations come true? Assume
that the bank can borrow two million units of either currency.
iii.
Dealer in a bank quotes you USD/JPY spot as 105.50/75 and one week forward premium
as 10/20. If you want to buy USD 1 million against JPY what will be the 1 week forward
rate applicable for your transaction?
iv.
USD/LKR spot rate quoted as 130.25 in the market. Interbank market interest rates for
USD and LKR for 1 month periods are 3% and 8%, respectively. What will be the
theoretical 1 month forward premium for USD/LKR transaction? (Hint. Use day count;
360 days per year and 30 days per month).
11.
Time series analysis is a statistical technique used to analyse the behavior of a variable
over a medium to long-term period. Answer the following questions.
i.
Describe the meaning of trend, cyclical, seasonal and irregular components of a time
series of a variable.
ii.
Identify the movement components of the time series relevant to the following and
write the reasons for the above categorization.
a) Decline of paddy production due to floods.
b) Monthly price variations of vegetable.
iii.
Which time series components could determine by using the least square method?
iv.
Write the advantages and disadvantages of using the least square method for the
above determination.
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12.
Explain the usefulness of the following statistical techniques in analysis of data.
i)
Dummy Variables
ii)
Time Series Trend
iii)
Hypothesis Testing
iv)
Non-linear regression
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