FIN 400 Financial Theory & Analysis Test 2, University of Botswana

This document is a solution to the FIN 400 Financial Theory & Analysis Test 2 from the University of Botswana, conducted in November 2021. The exam covers key concepts in financial theory and analysis, including portfolio return and risk calculation, differentiation between Capital Market Line (CML) and Security Market Line (SML), and the demonstration of beta for risk-free assets and market portfolios. It explores asset pricing models like CAPM and APT, explains the Runs Test for market efficiency, and presents equations for correlation and covariance, along with their distinctions. The solution also touches on Herbert Simon's concept of satisficing and the components of total variance, including systematic and unsystematic risks. The solutions are presented with formulas, explanations, and point-form answers to provide a comprehensive understanding of the topics.

UNIVERSITY OF BOTSWANA
FACULTY OF BUSINESS
DEPARTMENT OF ACCOUNTING & ACCOUNTING
TEST 2
FRONT PAGE
COURSE NO: FIN 400 DATE: November 2021
TITLE OF THE PAPER: FINANCIAL THEORY & ANALYSIS
SUBJECT: FINANCE DURATION: 1 HR
INSTRUCTIONS:
1. There are Eight (8) Questions. ANSWER ALL
2. The question paper carries a total of 40 marks
3. Neatness and presentation will be considered in grading.
4. Show all the supporting work & Formulae
5. Give your answers to 2 decimal places where appropriate.
6. Be brief and to the point. Write in point form where possible.
7. Possession of unauthorised material is strictly prohibited.
DO NOT OPEN THIS PAPER UNTIL YOU ARE TOLD TO DO SO BY THE SUPERVISOR/INVIGILATOR
No. of Pages 4 (Including Cover Page)

1. Given a risk free asset and portfolio M, present the formula for calculating a two asset
portfolio return and also demonstrate how to arrive at portfolio risk (standard
deviation) which is given by p = m . (7 marks)
Rp = E[Rm] + (1 - )Rf (2 marks)
p2 = 2VAR[Rm]+ (1- )2VAR[Rf]+ 2(1- )COV[Rm,Rf]
= 2VAR[Rm]+ (1- )20+ 2(1- )0 = 2VAR[Rm]
p = m (5 marks)
2. Differentiate between the Capital Market Line (CML) and Security Market Line
(SML). (4 marks)
The CML is sometimes confused with the security market line (SML). The SML is
derived from the CML. While the CML shows the rates of return for a specific
portfolio, the SML represents the market’s risk and return at a given time, and shows
the expected returns of individual assets. And while the measure of risk in the CML
is the standard deviation of returns (total risk), the risk measure in the SML
is systematic risk or beta. (4 marks)
3. With the help of relevant formulae, demonstrate why beta of a risk free security is
zero and that of a market portfolio is 1. (6 marks)
Risk free Security
Beta for risk-free asset is zero because its covariance with market portfolio is zero
The numerator of the above function is zero because Since COV(Rf, Rm)= QfQmRf,m=
0*QmRf,m = 0
Market Portfolio
Beta for market portfolio is 1 because the covariance of market portfolio with itself is
identical to the variance of the market portfolio.
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4. State the two competing asset pricing models and explain how they diverge.
(5 marks)
CAPM and APT (2 marks), Students should be able to indicate that the CAPM is a
single factor model which compensate the investor for exposure to market risk
through Market risk premium but APT is a multifactor model which decompose
market risk into several factors which could include Inflation Premium, default risk
premium and term structure of interest rate. (3 marks)
5. One of the tests of independence used under the weak form market efficiency is the
Runs Test. Describe how the Runs Test works. (4 marks)
• Given a series of price changes, each change is designated as a plus (+) or minus
(-). A run occurs when two consecutive changes are the same. (2 marks)
• You compare the number of runs for a given series to the expected value of the
number of runs that should occur in a random series. (2 marks)
6. Present the equation for correlation coefficient and that of a covariance between asset
(i) and assets (j) and also differentiate between covariance and correlation coefficient.
(5 marks)
COVi,j = ri,jQi Qj (1 mark)
ri,j = COVi,j/Qi Qj (1 mark)
Covariance measures the direction of the relationship between two assets or
portfolios or how they co-move over time. Correlation coefficient on the other hand
measures the extent/ magnitude of the relationship between two assets or
portfolios. (3 marks)
7. Briefly explain what you understand by Nobel Laureate Herbert Simon’s concept of
satisficing. (4 marks)
Satisficing is a decision-making strategy that aims for a satisfactory or adequate
result, rather than the optimal solution. Instead of putting maximum exertion toward
attaining the ideal outcome, satisficing focuses on pragmatic effort when confronted
with tasks. This is because aiming for the optimal solution may necessitate a needless
expenditure of time, energy, and resources. (4 marks)
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8. Total Variance (σ2m) of the ith security can be written as follows:
What are the two constituents of the total variance function and how do they differ?
(5 marks)
b2i σ2(Rmt) is the component of systematic risk and (1 mark)
is the component of unsystematic risk. (1 mark)
Systematic risk is undiversifiable risk which affects all firms in the industry and is the
risk that the investor is compensated for, for investing in the market. Unsystematic
risk is the risk that can be diversified away and is peculiar to a particular organization.
(3 marks)
***END OF TEST***
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