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. 2. 3. 4. 5. 6. 7. 8. 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. Page 2 of 9 RSK4805 JAN/FEB 2021 INSTRUCTIONS FOR INVIGILATOR APP Day of the assessment instructions: o Please remember to keep your cell phone fully charged for the duration of the assessment. o Please log into The Invigilator App if you have not done so yet. You need to be connected to the internet in order to log in. o Scan the QR code below once the examination starts. If you encounter difficulty with scanning of the QR code, you can also enter the QR access code as indicated at the bottom of the QR code to start the online invigilation. Please ensure that you are connected to the internet if you need to enter the QR access code at the bottom of the QR code. o Once the QR code is scanned, avoid any disturbances by putting your phone on airplane mode if possible. No internet connection is needed during the assessment. o Keep the Invigilator app open at all times on your cell phone during the assessment. o You may place your cell phone next to you. Your cell phone does not need to face you however should be close enough to hear the notifications from The Invigilator App. o The Invigilator App will notify you when an action is required. In order to receive notifications do not put your cell phone on silent mode and ensure media volume is turned up. o When an action is required, a notification beep will be heard, and an instruction will be visible for you to action promptly. o Please take note that once the examination time is over, firstly focus on scanning and uploading your script to your assessment platforms. Uploading your script is time sensitive. o Once your script is uploaded on your assessment platform, you may switch on your data to start the uploading process on The Invigilator app. o Good Luck! RSK4805 QR access code: 1e337e0b [TURN OVER] Page 3 of 9 RSK4805 JAN/FEB 2021 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) [TURN OVER] Page 4 of 9 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) [TURN OVER] Page 5 of 9 RSK4805 JAN/FEB 2021 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) [TURN OVER] Page 6 of 9 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) [TURN OVER] Page 7 of 9 RSK4805 JAN/FEB 2021 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. [TURN OVER] Page 8 of 9 RSK4805 JAN/FEB 2021 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. [TURN OVER] Page 9 of 9 4.8 RSK4805 JAN/FEB 2021 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] © UNISA 2020 [TURN OVER]