a. In order to reduce risk when financing his new business, Linda intends to use a 3-month index futures contract. Assume that the index's current value is 2,040, the constantly compounded risk-free interest rate is 7.5% annually, and the dividend yield of that stock is 1% annually. What is the future price?

a. In order to reduce risk when financing his new business, Linda intends to use a 3-month index futures contract. Assume that the index's current value is 2,040, the constantly compounded risk-free interest rate is 7.5% annually, and the dividend yield of that stock is 1% annually. What is the future price?

International Financial Management

14th Edition

ISBN:9780357130698

Author:Madura

Publisher:Madura

Chapter11: Managing Transaction Exposure

Section: Chapter Questions

Problem 35QA

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In order to reduce risk when financing his new business, Linda intends to use a 3-month index futures contract. Assume that the index's current value is 2,040, the constantly compounded risk-free interest rate is 7.5% annually, and the dividend yield of that stock is 1% annually. Later, Linda believes that futures contracts on currencies can offer a greater return than futures contracts on indices. Consider storing a 3-year futures contract at a cost of MYR 6 per unit. Assume that the risk-free rate is 6% per year for all maturities and that the current price is MYR 760 per unit. Estimate the predicted price in the future. What will Linda do if she is an arbitrageur, and the real future price is higher than the predicted future price?
Later, Linda believes that futures contracts on currencies can offer a greater return than futures contracts on indices. Consider storing a 3-year futures contract at a cost of MYR 6 per unit. Assume that the risk-free rate is 6% per year for all maturities and that the current price is MYR 760 per unit. Estimate the predicted price in the future. What will Linda do if she is an arbitrageur, and the real future price is higher than the predicted future price?
Suppose an investor sells 100 stocks by short selling for 6 months, the stock price is 30 yuan, and the annual interest rate of 6 months is fixed at 3%. How can I use forward contracts to avoid risks? What is the execution price? Please analyze if the stock price rises to 35 yuan or falls to 25 yuan after 6 months of hedging, what are the losses of this investor?
Donna Doni, CFA, wants to explore potential inefficiencies in the futures market. The TOBEC stock index has a spot value of 185. TOBEC futures contracts are settled in cash and underlying contract values are determined by multiplying $100 times the index value. The current annual risk-free interest rate is 6.0%.a. Calculate the theoretical price of the futures contract expiring six months from now, using the cost-of-carry model. The index pays no dividends.The total (round-trip) transaction cost for trading a futures contract is $15.b. Calculate the lower bound for the price of the futures contract expiring six months from now.
a) When the December gold futures contract was trading at US$408 per 10 gram, expecting a fall in the price, Mr Joey Tuwai sells ten December gold futures contracts of 1 kg each in September. As expected, the gold prices fall with the December futures contracts trading at US$406 by October. Joey decides to close out the contract, and lock in his gain. Required: What is the amount of profit that Joey makes? Show your working. b) You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The Treasury-bill rate is 7%. One of your clients chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. Required: What is the expected value and standard deviation of the rate of return on your client’s portfolio?
Suppose the 1-year futures price on a stock-index portfolio is 1,914, the stock index currently is 1,900, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,900 investment in the market index portfolio is $40.a. By how much is the contract mispriced?b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing.c. Now assume (as is true for small investors) that if you short sell the stocks in the market index, the proceeds of the short sale are kept with the broker, and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming that you don’t already own the shares in the index)? Explain.d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relation-ship? That is, given a stock index of 1,900, how high and how low can the futures price be without giving rise to arbitrage opportunities?
Suppose an investor buys 300 stocks for 3 months, the stock price is 10 yuan, and the annual interest rate for 3 months is fixed at 5%. How can I use forward contracts to avoid risks? What is the execution price? Please analyze if the stock price rises to 15 yuan or falls to 8 yuan after 3 months of hedging, what are the losses of this investor?
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Suppose that the current spot price of corn is $720 per bushel. The one year risk-free rate is 6% per annum. The futures price for delivery of one bushel of corn in one year’s time is $792 per bushel. Assume that net costs (storage costs minus convenience yield) are $15 per bushel (over the next one year). Is the futures contract correctly priced? If not, what is the theoretically correct price for the futures contract and how could you take advantage of any mispricing? Please show full steps and explain.
Suppose that Ace Insurance Company forecasts that stock market prices are going to increase considerably over the next three months and that they want to purchase500S&P 500 index futures contracts that have settlements that are six months out. If the index has a value of 3,000, and the value of a contract is 250 times the index’s value, then Ace Insurance Company will have invested $______ in the futures contracts.