UNISA EXAMINATIONS
JANUARY/FEBRUARY 2021
RSK4805
MARKET RISK MANAGEMENT
100 Marks
Duration: 3 hours
This timed online assessment consists of 9 pages.
INSTRUCTIONS FOR EXAMINATION PAPER:
1.
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Open Rubric
Answer ALL THE QUESTIONS in this paper. You only need to supply your answer and don’t
have to rewrite the question.
Pay special attention to the structuring and numbering of your answers.
Number the questions the same as in the exam paper. And make sure that your student
number appears on each page.
Round all calculations to four (4) decimal places, with final answer to two decimal places,
unless otherwise stated.
Make sure that you number your pages and that all pages are part of one PDF document
before you upload your answers.
Name your upload file as follows: Your student number_RSK4805_Exam.
The first page should clearly state your name, student number and the module code.
Instructions for the invigilator app is on the next page.
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RSK4805
JAN/FEB 2021
INSTRUCTIONS FOR INVIGILATOR APP
Day of the assessment instructions:
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RSK4805
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Question 1
[30]
Question 1.1
A hedge fund manager gathered the following information regarding his portfolio:
State of economy
Expansion
Sustainable growth
Recession
Probability
0.4
0.2
0.4
(10)
Return
15%
10%
4%
The return of the market last year was 11.5% and the risk-free rate was 6%. The hedge fund manager
has a beta of 0.9 and alpha of 2.1%.
1.1.1
Calculate the expected return and standard deviation of the portfolio.
(4)
1.1.2
What return can the hedge fund manager earn?
(2)
1.1.3
Explain what a hedge fund manager can do to produce a positive alpha.
(2)
1.1.4
A bank estimates that its profit next year is normally distributed with a mean of 0.95% of
assets and the standard deviation of 5% of assets. How much equity (as a percentage of
assets) does the hedge fund manager need in order to be 99% sure that he will have positive
equity at the end of the year?
(2)
Question 1.2
(10)
1.2.1
An investment bank has been asked to underwrite an issue of 12 million shares by a
company. It is trying to decide between a firm commitment where it buys the shares for $25
per share and a best efforts arrangement where it charges a fee of 30 cents for each share
sold. As part of the procedure to assess the risk, it considers two scenarios: firstly where the
price that it can obtain per share is $30 and secondly where it can only receive a price of $23
per share. Explain the difference between the two alternatives.
(5)
1.2.2
Explain property-casualty insurance and give an example of both.
(2)
1.2.3
Explain the advantages of exchange traded funds (ETF) over mutual funds.
(3)
Question 1.3
(10)
1.3.1
Assets within Beta Bank consist of $230 million in corporate loans and $50 million in OECD
government bonds. Calculate the total risk-weighted assets of Beta Bank.
(2)
1.3.2
Basel II.5 relates to changes in the calculation of capital for market risk. Indicate the three
changes that were implemented under Basel II.5 and the effect this had on the banking
industry.
(4)
1.3.3
Explain the difference between the banking book and the trading book and the risk capital
that form part of these.
(4)
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Question 2
RSK4805
JAN/FEB 2021
[30]
Question 2.1
(10)
2.1.1
The current price of a stock is R150, and three-month European call options with a strike
price of R155 currently sell for R7.10. An investor who feels that the price of the stock will
increase is trying to decide between buying 100 shares and buying 2 000 call options. Both
strategies involve an investment of R17 000. Calculate the profit for both alternatives if the
price increases to R162 and indicate which alternative the investor should choose. How high
does the stock price have to rise for the option strategy to be more profitable?
(4)
2.1.2
The price of gold is currently trading at $1,800 per ounce. The forward price for delivery in
one year is $2,000. An arbitrageur can borrow money at 6% per annum. Assume there are
no storage costs and that gold provides no income. What should the arbitrageur do if he
wants to invest in 100 ounces of gold?
(3)
2.1.3
A company’s investments earn LIBOR minus 0.75%.
Table 1
Swap quotes made by market maker (per cent per annum)
Maturity (years)
Bid
Offer
Swap rate
2
2.55
2.58
2.565
3
2.97
3.00
2.985
4
3.15
3.19
3.170
5
3.26
3.30
3.280
10
3.48
3.52
3.500
Explain how the company can use the quoted rates in the table to convert the investments
to a ten-year fixed-rate investment.
(3)
Question 2.2
2.2.1
(10)
The CEO received the following information regarding a European call option with a stock
price of R145, strike price of R150, risk-free rate of 6%, stock price volatility of 25% and time
to exercise of 25 weeks. The table gives the delta, gamma, vega, theta and rho for the option
for a long position in one option and a short position in 10 000 options.
Single option
Value (R)
Delta
Gamma
Vega (per %)
Theta (per day)
Rho (per %)
R12.49
0.600
0.015
0.402
-0.041
0.373
Short position in 10 000
options
- 124 900
- 6 000
-150
-4 020
410
-3 730
Explain to the CEO what will happen to the delta, gamma, vega, theta and rho when the
variables change as follows:
 stock price increases by R0.10 with no other changes
 volatility increases by 0.75% with no other changes
 interest rate increases by 1% with no other changes
 one day goes by without changes in the stock price or volatility
(5)
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2.2.2
The gamma and vega of a delta-neutral portfolio are 74 and 30, respectively, where vega is
per %. Estimate what happens to the value of the portfolio when there is a shock to the market
causing the underlying asset price to decrease by R7.50 and its volatility to increase by 7%.
(2)
2.2.3
A portfolio manager created a portfolio consisting of a 1-year zero-coupon bond with a face
value of R1 500 and a 5-year zero-coupon bond with a face value of R5 500. The current
yield on all bonds is 10% per annum (continuously compounded). What is the percentage
change in the value of the portfolio for a 0.6% per annum increase in yield?
(3)
Question 2.3
2.3.1
(10)
Suppose the parameters in a GARCH(1,1) model are α = 0.03, β = 0.93 and ω = 0.000005.
The current daily volatility is estimated to be 1.3%
(a) What is the long-run average volatility?
(b) Estimate the daily volatility in 20 days.
(2)
(2)
2.3.2
Explain the difference between the exponentially weighted moving average module and the
GARCH (1,1) module with regard to long-run average variance.
(2)
2.3.3
An analyst gathered the following information on two assets:
Current daily volatilities
Prices at close of business
yesterday
Prices at close of business
today
Asset A
2.20%
R53
Asset B
1.60%
R33
R54
R34
The estimate of coefficient of correlation between the returns of the two assets was 0.25
and the covariance 0.000088. The parameter λ used in the EWMA model is 0.95.
The analyst has asked you to update the correlation estimate between the two assets,
taking the trading prices of the assets today into consideration (round to 6 decimal places).
(4)
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Question 3
Question 3.1
RSK4805
JAN/FEB 2021
[30]
(10)
3.1.1
A fund manager announces that the fund’s 3-month 99% VaR is 8.2% of the size of the
portfolio being managed. You have an investment of R1 000 000 in the fund. How do you
interpret the portfolio manager’s announcement?
(2)
3.1.2
Which four conditions should a risk measure satisfy to be seen as a coherent risk measure?
(4)
3.1.3
Describe two ways of handling interest-rate-dependent instruments when the model-building
approach is used to calculate VaR.
(2)
3.1.4
A financial institution owns a portfolio of options dependent on the US dollar–sterling
exchange rate. The delta of the portfolio with respect to percentage changes in the exchange
rate is 8.2. If the daily volatility of the exchange rate is 0.6% and a linear model is assumed,
calculate the estimated 10-day 95% VaR for the portfolio.
(2)
Question 3.2
(10)
3.2.1
A binary option pays off R240 if a stock price is greater than R50 in 6 months. The current
stock price is R43 and its volatility is 35%. The risk-free rate is 6% and the expected return
on the stock is 11.5%. Calculate the value of the option.
(4)
3.2.2
An analyst wants to compare the expected future value of a stock index in real-world terms
with the expected future value in the risk-neutral world. Explain to the analyst which one will
give the higher expected value.
(2)
3.2.3
Indicate whether the following statements are true/false and give a reason for your answer:
(a) The Basel recommendations to banks state that back testing should form an integral part of
the overall governance and risk management culture within the bank.
(2)
(2)
(b) Objective probability is calculated from data.
Question 3.3
(10)
3.3.1
During the last few years an organisation has experienced large losses due to the activities
of a single trader within the organisation. What was seen as the main reason for these
losses?
(3)
3.3.2
Explain why it is important for organisations to monitor risks when derivatives are used. (2)
3.3.3
Explain the main lessons learnt from managing the trading room in order to avoid large losses
within the organisation trading.
(5)
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Question 4
[10]
Read the case study and answer the question that follows:
The Postgrad Advisory Group manages the assets for individual investors. Mercy Chisasa, the chief
risk officer, is meeting with one of the investors, Mr Ngwenya. Mr Ngwenya would like to discuss the
risk management strategies for his portfolio as he is concerned about the recent volatility in the
market and would like to find out about the use of options in risk management.
Mercy begins by explaining that analysts make assumptions about investors in that they
 care only about the expected returns and the standard deviation of returns of their portfolios
 can lend and borrow at the same risk-free rate and taxes are considered at a set rate
 all have homogeneous expectations
Information on the RRT index that Mr Ngwenya has in his portfolio is indicated below:
Table 1
Index price
1 200
Table 2
Delta
0.45
Variables for European option on RRT index
Strike price Risk-free
Dividend
Index
rate
yield
volatility
1 250
5%
2%
20%
Option Greeks
Gamma
Theta daily
0.0023
-0.22
Rho per %
2.44
Time
0.5
Value of
option
R53,44
Vega per %
3.33
After reviewing table 2, Mr Ngwenya asked Mercy which of these Greek letters will best describe the
change in value of the portfolio due to changes in the volatility. Mercy explains to him that the theta
of -0.22 per day means that if one day passes without changes in the stock price or volatility, the
option position will decline by R2.20, and that the delta of 0.45 means that when the price of the
stock increases by a small amount, the price of the option will decrease by 45% of this amount. Mr
Ngwenya asked Mercy to explain how a short position in 1 000 options can be made delta neutral
when the delta of the long position in each option is 0.45.
Value at risk and expected shortfall
Table 3
Information on overall portfolio (normally distributed) owned by Mr Ngwenya
Time
Mean
Standard
Confidence
deviation
level
6 months
R5 million
R12 million
95%
Mr Ngwenya has two assets within his portfolio with R120 000 invested in both. The daily volatility
of both assets is 1% and the coefficient of correlation between the returns 0.4. Mercy makes the
following statements about the assets in the portfolio:
Statement 1: The standard deviation of each asset is R1 000.
Statement 2: The variance of the portfolio’s daily change is equal to R4 032 000.
Statement 3: The standard deviation of the portfolio’s daily change is R2 000.
Statement 4: The 5-day 95% VaR and ES are R7 408 and R9 183, respectively.
Statement 5: Both VaR and ES will satisfy the subadditivity condition.
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Questions
4.1
Mercy’s statement about the assumptions of investors is accurate with regard to …
A. lending/borrowing rate but not expectations.
B. expected return and standard deviation but not taxes.
C. taxes but not borrowing rate.
4.2
Which of the following is the correct answer to Mr Ngwenya’s question about the
option Greek letter?
A. vega
B. theta
C. gamma
4.3
Mercy’s statements about theta and delta are accurate with regard to …
A. theta but not delta.
B. delta but not theta.
C. Both statements are incorrect.
4.4
Which of the following is the correct answer to Mr Ngwenya’s question about making
the portfolio delta neutral?
A. A short position in 1 000 options has a delta of -550 and can be made delta neutral by buying
550 shares.
B. A short position in 1 000 options has a delta of -450 and can be made delta neutral by selling
450 shares.
C. A short position in 1 000 options has a delta of -450 and can be made delta neutral by buying
450 shares.
4.5
Assume that the gamma in table 2 is for a delta-neutral portfolio. What will happen to
the value of the portfolio when the price of the underlying asset suddenly increases
by R200?
A. The value of the portfolio decreases by R46.
B. The value of the portfolio increases by R46.
C. There is no change in the value of the portfolio.
4.6
Each of the following statements about VaR is true except …
A. VaR will be larger when it is measured over a month than when it is measured over a day.
B. VaR is the loss that would be exceeded by a given probability over a specific time period.
C. VaR will be larger when it is measured at 5% probability than when it is measured at 1%
probability.
D. Estimating VaR involves several decisions such as probability and time period over which
the VaR will be measured.
4.7
Which of the following statements is correct regarding the values in table 3?
A. VaR for the portfolio with a time horizon of 6 months and confidence level of 97.5% is R16.3
million.
B. There is a 95% level of confidence that the maximum 6-month loss on the portfolio will not
exceed R16.3 million.
C. There is a 1% probability that the portfolio will suffer a decline in the value equal to/exceeding
R16.3 million during the following 6 months.
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4.8
RSK4805
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The statement made by Mercy about VaR and expected shortfall that is incorrect is …
A. statement 2.
B. statement 3.
C. statement 4.
4.9
Indicate whether statement 5 that Mercy made about subadditivity conditions is
true/false for value at risk and expected shortfall.
A.
B.
C.
4.10
A.
B.
C.
VaR
True
True
False
ES
True
False
True
The standard deviation of daily changes in investment for each asset is …
Asset A
R1 200
R1 200
R1 000
Asset B
R1 200
R1 000
R1 000
[100]
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UNISA 2020
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