Fundamentals of Hedging Derivatives and Swaps

Question: 1. The yield curve is flat at 6% per annum. What is the value of a Forward Rate Agreement where the holder receives interest at the rate of 8% per annum for a six-month period on a principal of $1,000 starting in two years? All rates are compounded semi-annually. Explain your answer. 2. A trader has a portfolio worth $5 million that mirrors the performance of a stock index. The stock index is currently 1,250. Futures contracts trade on the index with one contract being on 250 times the index. To remove market risk from the portfolio the trader should short or long in the forward or futures market? A company enters into a short futures contract to sell 50,000 units of a commodity for 70 cents per unit. The initial margin is $4,000 and the maintenance margin is $3,000. What is the futures price per unit above which there will be a margin call? 3. In which of the following cases is an asset NOT considered constructively sold? Explain your reasoning. A. The owner shorts the asset B. The owner buys an in-the-money put option on the asset C. The owner shorts a forward contract on the asset. D. The owner shorts a futures contract on the stock Answer: 1. FV of $1000 in five semi-annual periods 1000*(1+0.08/2) = 1040 PV= $ 1040/ (1+ 0.06/2) ^5 = $ 862.60878 Rounding it to $ 862.61 Investment does not start with accruing interest rate for the period of 2 years, that is 4 Semi-annual periods starting from today) After that, interest is paid after an additional 6 month of period on total of 5 semi-annual periods starting from today 2.1) Particulars Amount Portfolio $5,000,000 Stock Index price 1250 Future contract (1250 * 250) = 312,500 The number of contract required = 5,000,000 / (1250 * 250) = 5,000,000 / 312,500 = 16 contracts The portfolio mainly mirrors the stock index so selling 16 contracts might mainly help in nullifying the risk that might be incurred from volatility. Thus, short future position comprising of 16 contracts might mainly help in reducing the risk of market declines in the future. 2.b) Particulars Amount Future contracts 50,000 units Initial margin $4000 Maintenance Margin $3000 Commodity price 70 cent Calculation = (0.72-0.70) * 50,000 = 0.02 * 50,000 = 1,000 The difference between initial margin and maintenance margin is $1,000. Thus, if the contract attains a loss of $1,000 then a margin call will be activated. The future price of the commodity is 70 cents. Thus, if the price rises to 72 cents then the margin call will be activities [(0.72-0.70) * 50,000] = $1,000. Furthermore, it could be concluded that if the prices rises of 72 cents the margin call of the short position will be activated (Webber 2011). 3. From the options given, B is the correct answer. This is because profits on the assets have to be recognized in the options A, C and D. As far as holder of the asset is concerned, it cannot be deferred in profit recognition matters with indication of trading activities (RheinlaÃÅ'ˆnder and Sexton 2011). In the given case, B option is the answer, as asset is not considered for constructively sold in any form (Barnett and Cohn 2011). In other words, purchasing money by using put option is profit-locking system in the asset without triggering immediate liability of tax activities. Reference List Barnett, Gary and Joshua D Cohn. 2011.Fundamentals Of Swaps Other Derivatives, 2011. New York, NY: Practising Law Institute. RheinlaÃÅ'ˆnder, Thorsten and Jenny Sexton. 2011.Hedging Derivatives. New Jersey: World Scientific. Webber, Nick. 2011.Implementing Models Of Financial Derivatives. Chichester, U.K.: Wiley.