RSK4805 Assignment 3 (DETAILED ANSWERS) 2024 - DISTINCTION GUARANTEED

RSK4805 Assignment 3 (DETAILED ANSWERS) 2024 - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED Answers, guidelines, workings and references .. Question 1 (25 marks) 1.1 A bank estimates that its profit next year is normally distributed with a mean of 0.8% of assets and a standard deviation of 2% of assets. How much equity (as a percentage of assets) does the company need to be 99% sure that it will have positive equity at the end of the year? (Use z-values rounded to two decimal places) (2) 1.2 Given the following information for a listed company, the expected return if invested in the shares of this company is 7.80%. Calculate the variance and the standard deviation of this expected return. (3) State of Economy Probability Percentage Return State 1 0.30 13% State 2 0.35 8% State 3 0.15 2% State 4 0.20 4% 1.3 Describe an exchange-traded fund (ETF) and identify an advantage of an ETF compared to a closed-end fund (CEF). (2) 1.4 Suppose you currently hold a security valued at R750, and the prevailing risk-free rate is 5.5%. You plan to sell this security in three months. The theoretical forward contract price is calculated at R760.12 and will be used to hedge against potential price declines. Now, if the dealer offers a tradable price to unlock the arbitrage profit of R745 on the forward contract, determine the arbitrage opportunity available to you, and subsequently, provide a calculation for the potential arbitrage profit. (5) 1.5 You are a risk manager at a big corporation. How can you update the volatility estimate for an asset when the closing price yesterday was R375, and the estimated daily volatility was 1.2%? Today’s closing price is R371. You need to consider the following two methods for updating the volatility estimate: a) EWMA model with λ = 0.95 b) GARCH (1,1) model with ω = 0.000003, α= 0.05, and β = 0.95 (Round all calculations to eight decimal places) (5) Page 3 1.6 An analyst provided data for two assets, Asset A and Asset B, including their current daily volatilities, prior and current daily closing prices, coefficient of correlation between the returns of these two assets, the covariance, and the parameter λ used in the EWMA model. With today's closing prices at R55 and R35 for Asset A and Asset B respectively, the new covariance estimate between the two assets is 0.000120. Additionally, the new variance estimates for Asset A and Asset B are 0.000392 and 0.000189, respectively. The analyst now seeks an update on the correlation estimate between the two assets, considering the current trading prices of these assets. Calculate the revised correlation estimate between the assets. (3) 1.7 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 35% per annum. The risk-free rate is 6% (continuously compounded) and the expected return on the stock is 11.5% (continuously compounded). Calculate the value of this option. (5) Total (Question 1): 25 marks Page 4 Question 2 (25 marks) 2.1 How will a 0.5% decrease in the yield to maturity (YTM) affect the price of a ten-year bond with a current YTM of 6.5% and an annual coupon rate of 5.2%? The bond's current price is R975.20, and its duration is 7.8. Calculate the new bond price after the decrease in YTM. (4) 2.2 Portfolio A consists of a one-year zero-coupon bond with a face value of R2000 and a 10-year zero-coupon bond with a face value of R6000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of R5000. The value of Portfolio A is R4016.95 and the value of Portfolio B is R2757.81. The current yield on all bonds is 10% per annum. The values of Portfolio A and Portfolio B with a 6% increase in the yield is R2915.67 and R1929.84 respectively. Calculate the percentage reduction in the values of Portfolio A and Portfolio B when the yield increases by 6% per annum. (2) 2.3 Assuming that the daily changes in a portfolio’s value follow a normal distribution with a mean of zero and a standard deviation of R6 million, calculate the following: (5) a) Calculate the one-day 99% Value at Risk (VaR). b) Calculate the five-day 97.5% VaR. c) Calculate the five-day 99% VaR. d) Which two parameters play a role in the calculation of VaR? 2.4 Explore the risk management of a portfolio, which combines a R400,000 investment in gold and a R600,000 investment in silver. Given the respective daily volatilities of 1.6% for gold and 1.3% for silver, along with a coefficient of correlation between their returns of 0.65, calculate the 10-day 97.5% VaR and VaR diversification benefit for the portfolio. (5) 2.5 Explain whether the following statement is true/false and give a reason for your answer. (3) The Basel recommendations to banks state that backtesting should form an integral part of the overall governance and risk management culture within the bank. Page 5 2.6 Suppose we estimate the one-day 95% VaR from 1,100 observations (in millions of dollars) at 5. By fitting a standard distribution to the observations, the probability density function of the loss distribution at the 95% point is estimated to be 0.08. Calculate the standard error of the VaR estimate. (Round calculations to eight decimal places) (3) 2.7 The gamma and vega of a delta-neutral portfolio are 50 and 25, 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 increase by R3 and its volatility to decrease by 4%.