RSK4805_Assignment 03_Requirements_2022_68a69a4b083c28340a3b5f95e9ea33ab.pdf - Adobe Acrobat Pro DC (32-bit) File Edit View E-Sign Window Help Home Tools RSK4805_Assignme... x 1 /2 100% H RSK4805 - Market risk management Assignment 03 Assignment due date Contribution to year mark Written assignment 10 August 2022 35% C Subscribe 0 NB: Do NOT wait until the last date provided before you complete the assignment on myUnisa, as the system might be very busy or down for routine maintenance. Required: This assignment consists of two questions of 25 marks each. This assignment covers Topics 2 and 3. Round all your calculations to four decimal places and only the final answer to two decimal places unless otherwise stated. Question 1 (25 marks) 1.1 1.2 A trader buys 350 shares of a stock on margin. The price of the stock is R75. The initial margin is 65% and the maintenance margin is 30%. Calculate the initial margin and indicate at what share price there will be a margin call? (5) A trader 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 Short position in 10, 000 options lu Type here to search ENG 11:03 INTL 2022/06/23 22 RSK4805_Assignment 03_Requirements_2022_68a69a4b083c28340a3b5f95e9ea33ab.pdf - Adobe Acrobat Pro DC (32-bit) File Edit View E-Sign Window Help Home Tools RSK4805_Assignme... x 1 /2 100% Single option Value (R) R12.49 Delta 0.600 Gamma 0.015 Vega (per %) 0.402 Theta (per day) -0.041 Rho (per %) 0.373 Short position in 10, 000 options - 124,900 - 6,000 -150 -4,020 410 -3,730 Subscribe Explain to the trader what the impact will be on the short options position in each of the following scenarios: 1.3 1.4 a. stock price increases by R0.15, with no other changes b. volatility increases by 0.75%, with no other changes c. one day goes by without changes in the stock price or volatility (6) The current price of a stock is R200 and three-month European call options, with a strike price of R205, currently sell for R12.50. An investor, who feels that the price of the stock will increase, is trying to decide between buying 100 shares or buying 1 600 call options. Both strategies involve an investment of R20 000. Calculate the profit for both alternatives, if the price increases to R210, 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?(5) A five-year bond, with a yield to maturity (YTM) of 11% (continuously compounded), pays an 8% coupon at the end of each year. The bond price is R86.80 and the duration 4.256. What effect will an increase of 0.3% in the yield to maturity (YTM) have on the bond price? Type here to search d (3) 1 0 c+ lu ENG 11:04 INTL 2022/06/23 22 RSK4805_Assignment 03_Requirements_2022_68a69a4b083c28340a3b5f95e9ea33ab.pdf - Adobe Acrobat Pro DC (32-bit) File Edit View E-Sign Window Help Home Tools RSK4805_Assignme... x 1.5 2 / 2 100% H Type Position A financial institution has the following portfolio of over-the-counter options on sterling: Delta of Gamma of Vega of option option option Call -1,000 0.50 2.2 1.8 Call -500 0.80 0.6 0.2 Put -2,000 -0.40 1.3 0.7 Call -500 0.70 1.8 1.4 Subscribe 0 c+ A traded option is available with a delta of 0.7, gamma of 1.2 and vega of 0.8. What position in the traded option and in sterling would make the portfolio both gamma neutral and delta neutral? (4) The volatility of an asset is 3.2% per day. What is the standard deviation of the percentage price change in four days? (2) Total Question 1 = 25 marks 1.6 lu Type here to search Question 2 (25 marks) 2.1 2.2 Consider a position consisting of a R400,000 investment in gold and a R600,000 investment in silver. Suppose that the daily volatilities of these two assets are 1.6% and 1.3%, respectively, and that the coefficient of correlation between their returns is 0.65. Calculate the 10-day 97.5% VaR and VaR diversification benefit for the portfolio. (6) Suppose that each of two investments has a 4% chance of a loss of R15 million, a 1% chance of a loss of R1.5 million and a 95% chance of a profit of $1.5 million. They are independent of each other. Calculate the expected shortfall (ES) when the confidence level is 95%? (3) < > ENG 11:04 INTL 2022/06/23 22 RSK4805_Assignment File Edit View E-Sign Window Help 03_Requirements_2022_68a69a4b083c28340a3b5f95e9ea33ab.pdf - Adobe Acrobat Pro DC (32-bit) Home Tools RSK4805_Assignme... x 2/2 + 100% ! independent of each other. Calculate the expetitu shortfall (L) with the commence level is 95%? (3) 2.3 What assumption is being made when VaR is calculated using the historical simulation approach and 250 days of data? (1) Type here to search 2.4 2.5 A stock has an expected return of 15%, a volatility of 25% and is currently priced at R56. Calculate the price of the stock that has a 5% probability of being exceeded in two years' time? (2) A binary option pays off R240, if a stock price is greater than R50 in six months. The current stock price is R43 and its volatility is 30%. The risk-free rate is 7% and the expected return on the stock is 11%. Calculate the value of the option? (6) 2.6 2.7 Explain the three areas to be aware off when managing liquidity risk in the trading room? (3) Explain three different ways that scenarios can be generated for stress testing. (4) Total for Question 2 = 25 marks Unisa 2022 d 2 Subscribe 0 lu ENG 11:05 INTL 2022/06/23 22