Download FINANCIAL ECONO MICS MAY 2012 - Institute of Bankers in Malawi

FINANCIAL ECONOMICS MAY 2012 – SOLUTIONS
SECTION A
(60 MARKS)
Answer ALL questions from this section.
QUESTION 1
a. State and define the three components of interest rate that are considered in
investment analysis. (9 marks)
1. Risk-free rate – This is a rate that investors could invest fund at no or little
risk. Normally this is a ten-year government bond as a proxy to a risk-free
rate. (3 marks)
2. Risk premium – This is a rate above the risk-free rate that investors demand
as compensation for losing the use of the money today and potentially
investing in more risky assets than government bonds at the risk-free rate. (3
marks)
3. Inflation premium – inflation eats away at real returns and again investors
need compensation for the loss of purchasing power. This would however
lead to different results due to the intervals between payments.
b. Differentiate between effective and nominal interest rate. Provide clear examples
for each. (6 marks).
Nominal Interest rate
This is the interest rate that makes no allowance for inflation and this is the rate that many
banks advertise also known as annual percentage yield (APY). It is the return on the principal
amount over an entire year. For example, a 5% rate compounded monthly would have an
approximate APY of 5.12%.
6%
12 m onths
Example: Let's assume a nominal interest rate of 6% per annum, which is credited as of
= 0.5% every month.
After one year, the initial investment is increased by the factor (1+0.005)12 ≈ 1.0616. As a
result, this nominal interest rate of 6% is equivalent to an effective interest rate of 6.16%.
Effective Interest rate
This is the interest rate that makes allowance for inflation and is the actual rate paid (or
received) after accounting for compounding that occurs during the year. If you want to compare
two alternative investments with different compounding periods you need to compute the
effective interest rate also known as effective annual rate (EAR) and use that for comparison.
An interest rate is called nominal if the period of time after that the interest is credited (e.g. a
month) is not identical to the basic time unit (normally a year).
QUESTION 2
a. What do you understand by the term annuity and under what circumstance could
it be used? (4 marks)
The term annuity is used in finance theory to refer to any terminating stream of fixed
payments over a specified period of time.
It is mostly used in connection with the valuation of the stream of payments, taking into
account time value of money concepts such as interest rate and future value.
b. Give two types of annuities with clear examples for each. (6 marks
4. Ordinary annuity – payments are required at the end of each period. For
example, straight bonds usually pay coupon payments at the end of every six
months until the bond's maturity date. (3 marks)
5. Annuity due – payments are required at the beginning of each period. Rent is
an example of the annuity due. (3 marks)
c. Calculate the payment at the beginning of a contract for a warehouse at 10% per
annum whose payment is K5, 000 per annum. (5 marks)
QUESTION 3
a. Compare and contrast current yield and adjusted current yield. Please give
examples for each. (10 marks)
Current yield
A simple yield calculation that is often used to calculate the yield on both bonds and the
dividend yield for stocks is the current yield. The current yield calculates the percentage return
that the annual coupon payment provides the investor. In other words, this yield calculates what
percentage the actual dollar coupon payment is of the price the investor pays for the bond. The
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multiplication by 100 in the formulas below converts the decimal into a percentage, allowing us
to see the percentage return:
Current Yield = (Annual Kwacha Interest Paid/ Market price) * 100. So, if you purchased a bond
with a par value of Mk100 for Mk95.92 and it paid a coupon rate of 5%, the current yield will be
= ((0.05 * Mk 100)/Mk 95.92) * 100% = 5.21%
Adjusted yield
The modified current yield formula then takes into account the discount or premium at which the
investor bought the bond. This is the full calculation:
Adjusted Current yield = (Annual coupon/Market price) * 100 + ((100- Market price)/years of
maturity)
To re-calculate the yield of the bond in our first example, which matures in 30 months and has a
coupon payment of Mk 5
Adjusted current yield = (Mk 5/Mk 95.92) * 100 + ((100- 95.92)/2.5) = 6.84%
b. In the absence of a financial calculator and a programme, define how you would
use an approximation method to define yield to maturity. (5 marks)
Review the relationship between a bond's price and its yield. In general, as a bond's price
increases, yield decreases. This relationship is measured using the price value of a basis point
(PVBP). By taking into account factors such as the bond's coupon rate and credit rating, the
PVBP measures the degree to which a bond's price will change when there is a 0.01% change
in interest rates.
The charted relationship between bond price and required yield appears as a negative curve
below.
Figure 1: Price Yield Curve
This is due to the fact that a bond's price will be higher when it pays a coupon that is higher than
prevailing interest rates. As market interest rates increase, bond prices decrease.
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QUESTION 4
Regression analysis is the statistical technique that identifies the relationship between
two or more quantitative variables. The analysis has however, has strengths and
limitations.
a. Give four limitations of regression analysis (8 marks).
1. The technique is demanding because it requires quantitative data
relating to several thousand individuals.
2. Implementing the data collection can be time-consuming and
expensive.
3. Regression analysis is likely to reach the conclusion that there is
a strong link between two variables, whereas the influence of
other, more important, variables may not have been estimated
(this error is called "data snooping"). The tool should therefore be
used with care.
4. Relations between the different explained and explanatory
variables are often circular (X explains Y and Y explains X). In
this case, the method is inapplicable.
5. The observations must present sufficiently contrasted evolutions
to allow for adjustment. For example, if all the observations
concern the 30-40 age group, it will not be possible to estimate
the influence of age on employment.
b. Explain and define two factors that analysts must consider when making
their estimates for investment evaluation. (7 marks)
SECTION B
Answer ANY TWO questions from this section.
QUESTION 5
a. Explain the sinking funds and give two common uses of sinking funds. (5
marks)
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A sinking fund is defined as an annuity invested in order to meet a known commitment
at some future date. (1 mark)
Common uses of Sinking funds –
(i)
Repayment of debts (2 marks)
(ii)
(ii) Providing funds to purchase a new asset when the existing one is fully
depreciated. (2 marks)
b. Mr Jones has acquired a loan of K 650, 000 from one of the local banks at
an interest rate of 7.75%. The loan is to be paid back over a period on 20
years. Calculate the annual payment necessary to amortize a debt for Mr.
Jones. (15 marks)
P = K 650,000, n = 20 and i = 7.75/100 = 0.0775. Working through the formula, the
annual payment necessary to amortise the debt is K64, 977.08
QUESTION 6
a. What is dispersion in financial economics? (2 marks)
It is how spread or variability the data is in statistics. It describes how
spread out or scattered a set or distribution of numeric data is.
b. Compare and contrast with examples the range and mean deviation. (8
marks)
Both the range and the mean deviation are the particular measures of dispersion.
However, the range is defined as the numerical difference between the smallest and
largest values of the items in a set or distribution. Thus, it can be calculated as largest
value minus smallest value.
An example for the range: two industrial machines over fourteen days were:
machine 1: 4,7,1,2,2,6,2,3,0,4,5,3,7,4
machine 2: 3,2,2,3,3,2,4,1,1,3,2,4,2,2
The range of values for machine 1 is 7-0=7 and for machine 2 is 4-1=3. Thus the daily
production of rejects is more variable for machine 1.
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On the other hand, mean deviation is a measure of dispersion that gives the average
absolute difference between each item and the mean. It is a much more representative
measure than the range since all item values are taken into account in its calculation.
An example of the mean deviation: Suppose an assembly line produced 3,10,5 and 2
defective products on four successive runs. the mean number of defectives is
3  10  5  2 20


 5.
4
4
The absolute differences between each value and the mean (5) are respectively:
3-5=-2(or 2 ignoring the minus sign)
10-5=5
5-5=0
2-5=-3 (or 3 ignoring the minus sign)
The mean deviation can now be calculated as the average of the above absolute
differences. that is:
2  5  0  3 10


 2.5
4
4
Mean deviation
c. Outline the main steps involved in rejecting a hypothesis and what does this
mean?. (10 marks)
The hypothesis is tested basing on the assumptions about the population, assumptions
which may or may not be true. This is always given in the form of a statement about the
statistical nature of the population. Then if, on the evidence from a single sample taken
from the population, it is found that the results obtained from the sample would have
been unlikely to occur if the hypothesis were true, we would be inclined to reject the
hypothesis.
Steps involved in rejecting the hypothesis.
STEP 1:
State the null hypothesis H0 and the alternative hypothesis Ha.
To do a significance test, you need 2 hypotheses: a). Null Hypothesis (H0): the
statement being tested and b), Alternative Hypothesis (Ha): the statement we hope or
suspect is true instead of H0.
Hypotheses can be one-sided or two-sided.
One-sided hypothesis: covers just part of the range for your parameter
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H
H
0
:   10
:   10
a
:   10
0
:   10
:   10
a
OR
Two-sided hypothesis: covers the whole possible range for your parameter
H 0 :   10
H
a
H
H
Even though Ha is what we hope or believe to be true, our test gives evidence for or
against H0 only.
STEP 2: Calculate the value of the test statistic.
A test statistic measures compatibility between the H0 and the data. The formula for the
test statistic will vary between different types of problems.
STEP 3: Draw a picture of what Ha looks like, and find the P-value.
P-value: the probability, computed assuming that H0 is true, that the test statistic would
take a value as extreme or more extreme than that actually observed due to random
fluctuation. It is a measure of how unusual your sample results are.
The smaller the P-value, the stronger the evidence against H0 provided by the data.
Calculate the P-value by using the sampling distribution of the test statistic
STEP 4: Compare your P-value to a significance level. State your conclusion about the
data in a sentence. Compare P-value to a significance level, .
If the P-value ≤, we can reject H0.
In this case, we reject H0, meaning that the results significant.
QUESTION 7
c. What is risk diversification under modern portfolio theory? (6 marks)
The risk on an individual asset is derived from the probability distribution and it is
usually assumed that the wealth owner cannot change that. But one of the most
important ideas in financial economics is that the portfolio owners can reduce the
average risk on the asset he/she owns by holding more than the same amount of wealth
placed in one share. The notion that risk can be reduced by owning more than an asset
is called risk diversification. In other words, the process of spreading an investment
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across assets (and thereby forming a portfolio) is called diversification. The principle of
diversification indicates that spreading an investment across many assets will eliminate
some of the risk.
d. Mention any three approaches to risk diversification. (4 marks)
1. Random or Naïve Diversification
2. Inter-industry diversification
3. Inter-quality rating diversification
4. Markowitz Risk diversification
e. Under
Capital
Asset
Pricing
Model
(CAPM)
describe
systematic
and
unsystematic risk and how the risk can be reduced. (10 marks)
Systematic Risk (also known as non-diversifiable risk, non-specific, unavoidable or
market risk) refers to that portion of risk of individual security’s returns caused by factors
affecting market as a whole (macroeconomic variables) such as changes in interest
rates, inflation, taxation etc. Indeed, systematic risks have market wide effects.
Unsystematic Risk (diversifiable risk, specific or avoidable risk) refers to risk unique to
a particular firm such a firm going bankrupt or staff of Post Office going on strike.
Unsystematic risk accounts for approximately 70% of a firm’s total risk and can be
reduced through diversification. Reducing unsystematic risk through holding diversified
portfolios of share form the basis of Markwitz’s portfolio theory. The area labeled
‘unsystematic risk’ is the part that can be eliminated by diversification. CAPM uses the
systematic risk of individual securities to determine the fir price.
Systematic and Unsystematic Risks
Risk
(Std. dev)
Unsystematic risk
Total risk
Systematic risk
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20
30
No. of securities in a portfolio
CAPM uses the systematic risk of individual securities to determine the fair price.
QUESTION 8
a. According to Say's Law, when an economy produces a certain level of real GDP,
it also generates the income needed to purchase that level of real GDP. It is
believed that the economy is always capable of achieving the natural level of real
GDP. Please illustrate with a diagram how an economy would move out of
natural real GDP. (10 marks)
If aggregate demand falls below aggregate supply due to aggregate saving, suppliers
will cut back on their production and reduce the number of resources that they employ.
When employment of the economy's resources falls below the full employment level, the
equilibrium level of real GDP also falls below its natural level. Consequently, the
economy may not achieve the natural level of real GDP if there is aggregate
saving. The classical theorists' response is that the funds from aggregate saving are
eventually borrowed and turned into investment expenditures, which are a component
of real GDP. Hence, aggregate saving need not lead to a reduction in real GDP.
Consider, however, what happens when the funds from aggregate saving exceed the
needs of all borrowers in the economy. In this situation, real GDP will fall below its
natural level because investment expenditures will be less than the level of aggregate
saving. This situation is illustrated in the figure below.
Figure 2: Classical theory of interest rate adjustment in the money market
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Aggregate saving, represented by the curve S, is an upward-sloping function of the
interest rate; as the interest rate rises, the economy tends to save more. Aggregate
investment, represented by the curve I, is a downward-sloping function of the interest
rate; as the interest rate rises, the cost of borrowing increases and investment
expenditures decline. Initially, aggregate saving and investment are equivalent at the
interest rate, i. If aggregate saving were to increase, causing the S curve to shift to the
right to S′, then at the same interest rate i, a gap emerges between investment and
savings. Aggregate investment will be lower than aggregate saving, implying that
equilibrium real GDP will be below its natural level.
b. How would you deal with the situation, explain with the aid of classical theory. (10
marks).
The figure below, considers a decrease in aggregate demand from AD1 to AD2.
The immediate, short-run effect is that the economy moves down along the SAS curve
labeled SAS1, causing the equilibrium price level to fall from P1 to P2, and equilibrium
real GDP to fall below its natural level of Y1 to Y2. If real GDP falls below its natural
level, the economy's workers and resources are not being fully employed. When there
are unemployed resources, the classical theory predicts that the wages paid to these
resources will fall. With the fall in wages, suppliers will be able to supply more goods at
lower cost, causing the SAS curve to shift to the right from SAS1 to SAS2. The end
result is that the equilibrium price level falls to P3, but the economy returns to the
natural level of real GDP.
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END OF THE EXAMINATION PAPER
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