You enter into a 1-year futures contract on a non-dividend paying stock when the stock price is $100 and the risk-free interest rate is 5% per annum. Six months later the stock price has fallen to $90, and the interest rate is 4% per annum. Which of the answers below is closest to the change in the futures price? Assume discrete compounding and discounting. Question 6Answer a. -12.34 b. -11.40 c. -10.00 d. -13.20
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- You enter into a 1-year futures contract on a non-dividend paying stock when the stock price is $100 and the risk-free interest rate is 5% per annum. Six months later the stock price has fallen to $90, and the interest rate is 4% per annum. Which of the answers below is closest to the change in the futures price? Assume discrete compounding and discounting. Question 6Answer a. -12.34 b. -11.40 c. -10.00 d. -13.20a. A single-stock futures contract on a non-dividend-paying stock with current price $260 has a maturity of 1 year. If the T-bill rate is 5%, what should the futures price be? (Round your answer to 2 decimal places.) Futures price b. What should the futures price be if the maturity of the contract is 4 years? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Futures price c. What should the futures price be if the interest rate is 8% and the maturity of the contract is 4 years? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Futures priceA non-dividend paying asset is current priced at $25 and the risk-free interest rate is 8% per annum. Today, you enter into a six-month futures contract to buy a unit of this asset. Three months from now the underlying price has fallen to $18 (but note that the interest rate has not moved). Which of the answers below is closest to the fall in the futures price? Use discrete discounting. Question 7Answer a. $6.50 b. $5.50 c. $7.50 d. $4.50
- Suppose the quoted futures price for delivery in 1 year is $7.10. The current underlying price is $7 and the continuously compounded interest rate is 5%. The underlying does not pay dividends. How could you make a riskless arbitrage profit? Question 2Answer a. buy futures contracts, short sell the stock and invest in a bank account b. borrow from the bank to buy futures contracts and short sell the stock c. sell futures contracts, borrow and buy the stock d. sell future contacts, short sell the stock and invest in a bank accountA non-dividend paying asset is current priced at $25 and the risk-free interest rate is 8% per annum. Today, you enter into a six-month futures contract to buy a unit of this asset. Three months from now the underlying price has fallen to $20 (but note that the interest rate has not moved). Which of the answers below is closest to the fall in the futures price? Use discrete discounting. a. $4.50 b. $6.50 c. $7.50 d. $5.50Question 2. You have been asked to value a Arithmetic Lookback option which expires in six months time. At the end of the six months the buyer is paid the arithmetic mean of the underlying stock over the contract period. Using the compressed stock tree presented in Figure 1 and assuming an annual interest rate of 4.5% determine the fair price of the Arithmetic Lookback option. Why are Lookback options considered to he expensive? 182.5 158.7 138 138 120 120 104.4 104.4 90.8 79 Figure 1: Compressed stock tree
- a. A single-stock futures contract on a non-dividend-paying stock with current price $150 has a maturity of 1 year. If the T-bill rate is 3%, what should the futures price be?b. What should the futures price be if the maturity of the contract is 3 years?c. What if the interest rate is 6% and the maturity of the contract is 3 years?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?There is a futures contract available on a dividend paying stock. The current stock price is $7.25 and a dividend of $2 will be paid after 6 months. The interest rate is 12% per annum (assuming discrete compounding). The fair price of the futures for delivery one year ahead is closest to which of the values below? Question 8Answer a. $5.90 b. $8.12 c. $5.50 d. $10.40
- 5. Suppose the one-year futures price on a stock-index portfolio is 1218, the stock index currently is 1200, the one-year risk-free interest rate is 3%, and the ybar-end dividend that will be paid on a $1,200 investment in the index portfolio is $15. 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. Assume a zero bid-ask spread in security and futures transactions. Now assume that if you short sell the stocks in the index portfolio, the proceeds are kept with the broker, and you do not receive any interest income of the funds. Is there still an arbitrage opportunity (assuming that you don't already own the shares in the index)? d. Given the short sale rules, what is the no-arbitrage band for the stock-futures price relationship? Specifically, how high and how low can the futures price be without giving rise to arbitrage opportunities. C.Suppose XYZ stock pays no dividends and has a current price of $50. The forward price for delivery in 1 year is $55. Suppose the 1-year eective annual interest rate is 10%. (a) Graph the payo and prot diagrams for a forward contract on XYZ stock with a forward price of $55. (b) Is there any advantage to investing in the stock or the forward contract? Why? (c) Suppose XYZ paid a dividend of $2 per year and everything else stayed the same. Now is there any advantage to investing in the stock or the forward contract? Why?Suppose a stock is currently (time t = 0) worth 100. Further, suppose the one year annually compounded interest rate is 2%, and the two year annually compounded rate is 3%. Find the following:a) The forward price for a forward contract on the stock with maturity year T1 = 1. b) The forward price for a forward contract on the stock with maturity year T2 = 2.c) The forward price for a forward contract with maturity T1 = 1 on a ZCB with maturity T2 = 2.d) The forward price for a forward contract with maturity T1 = 1 on a forward contract on the stock with maturity T2 = 2 and delivery price K = 101.