Question 1 (25 marks) 1.1 An analyst for LevelUP gathered the following information regarding a futures contract: Current spot-market price of R60 The continuous compounded risk-free interest rate of 8.5% per annum The actual futures prices of the contract are R61 Calculate the price of the future contract for delivery in six months and indicate whether the contract is overpriced, underpriced, or correctly priced. (6) 1.2 The gamma and vega of a delta-neutral portfolio are 55 and 27, respectively, where vega is a percentage (%). 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 R5 and its volatility to increase by 5%. (4) 1.3 What does it mean to state that the theta of an option position is 150 per day? If a trader feels that neither a stock price nor its implied volatility will change, what type of option position is appropriate? (4) 1.4 Suppose that the price of an asset at the close of trading yesterday was R500 and its volatility was estimated as 1.5% per day. The price at the close of trading today is R495. Update the volatility estimate using the EWMA model with = 0.95. (Round your calculations to 8 decimal places) (6) 1.5 You enter a futures contract to buy white maize for R1,900 per tonne, for delivery in three months. The contract size is for the delivery of 1,000 tonnes. The initial margin is R250,000 and the maintenance margin is R80,000. When will you receive a margin call? What change in the futures price led to this margin call? (Show all your calculations) (5) Total Question 1 = 25 marks Page 3 Question 2 2.1 Suppose that each of two investments has a 3% chance of a loss of R15 million, a 2% chance of a loss of R1.5 million and a 95% chance of a profit of R1.5 million. They are independent of each other. Calculate the expected shortfall (ES) when the confidence level is 95%. (4) 2.2 If 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, which of these is expected to have a higher value? Please explain your answer. (2) 2.3 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 7.3. If the daily volatility of the exchange rate is 0.5% and a linear model is assumed, calculate the estimated 10- day 95% VaR for the portfolio. (4) 2.4 Suppose we estimate the one-day 97.5% VaR from 1,100 observations (in millions of dollars) as 5. By fitting a standard distribution to the observations, the probability density function of the loss distribution at the 97.5% point is estimated to be 0.08. Calculate the standard error of the VaR estimate in dollar terms. (Round your calculations to 8 decimal places) (4) 2.5 List two ways of handling interest-rate-dependent instruments when the model-building approach is used to calculate VaR. (2) 2.6 A binary option pays off R240 if a stock price is greater than R50 in six months. The current stock price is R45, and its volatility is 25%. The risk-free rate is 7% and the expected return on the stock is 11%. Calculate the value of the option. (5) 2.7 The probability that the loss from a portfolio will be greater than R20 million in one month is estimated to be 5%. What is the one-month 99% VaR assuming the change in the value of the portfolio is normally distributed with zero mean? (4)