(2) The spot price of the S&P 500 index is currently at 1200 per share. The 3-month futures price is the same as the spot price. The simple interest rate is 2% for 3 months and the simple dividend yield is 1% for 3 months. (a) Calculate the arbitrage-free futures price. (b) Provide an arbitrage trading strategy.
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- (i) A forward contract with 12 months to maturity is written on an underlying stock. The stock price is $45, and it is expected to pay dividends of $2 after 6 months and $3 immediately prior to maturity. The relevant riskless rate of interest is 4%. Calculate the theoretical forward price and initial value of the forward contract and explain the forward pricing relationship. (ii) Provide a numerical example of an arbitrage strategy for situations where the forward is trading above, and below the theoretical forward price.Suppose that the risk-free interest rate is 6% per annum with continuous compounding and the dividend yield on a stock index is 4% per annum. The index is standing at 400 and the futures price for a contract (on that index) deliverable in 9 months is 405. What arbitrage opportunity does this create? • Borrow to buy shares underlying the index and enter a short position in index futures contracts • Enter a long position in index futures contracts, short sell shares underlying the index and invest excess funds • Borrow to buy shares underlying the index and enter a long position in index futures contracts • Enter a short position in index futures contracts, short sell shares underlying the index and invest excess funds • No arbitrage opportunityGiven the following quotes: FBM KLCI spot = 747 points, risk-free rate = 4.5% annualised, FBM KLCI dividend yield = 1.75% annualised. i) If the 90-day KLCI futures is quoted at 762 points, show that arbitrage is possible ii) Calculate the arbitrage profit if FBM KLCI is 10% higher by futures maturity.
- Consider these futures market data for the June delivery S&P 500 contract, exactly one year from today. The S&P 500 index is at 2,145, and the June maturity contract is at Fo = 2,146. a. If the current interest rate is 2.5%, and the average dividend rate of the stocks in the index is 1.9%, what fraction of the proceeds of stock short sales would need to be available to you to earn arbitrage profits? (Enter your answer in numbers and not in percentage. Eg; Enter 0.12 and not 12%. Do not round intermediate calculations. Round your answer to 4 decimal places.) Answer is complete but not entirely correct. Fraction 0.7787In two-months the price of stock will be either $23 or $27. The risk-free interest rate is 10%. The current price of the stock is $25. Suppose the price of the stock will be ST at the end of the two-months and the derivative on the stock will pays off St². Find the value of the derivative. (A) $621.39 (B) $729.39 (C) $529.39 (D) $639.26You observe that the settlement price of a one-year futures contract for 1 share of a dividend paying stock is currently at $52. The current stock price is $50 and the risk-free interest rate is 10% p.a. (compounded annually). It is also known that the dividend yield on the stock is 4% p.a. (compounded annually). Set up a strategy to realize an arbitrage profit today and show the initial and terminal cash flows from each position taken in the strategy. Assume that investors can short-sell or buy the stock on margin and that they can borrow and lend at the risk-free rate. Thank you!
- Consider these futures market data for the June delivery S&P 500 contract, exactly one year from today. The S&P 500 index is at 1,950, and the June maturity contract is at F0 = 1,951.a. If the current interest rate is 2.5%, and the average dividend rate of the stocks in the index is 1.9%, what fraction of the proceeds of stock short sales would need to be available to you to earn arbitrage profits?b. Suppose now that you in fact have access to 90% of the proceeds from a short sale. What is the lower bound on the futures price that rules out arbitrage opportunities?c. By how much does the actual futures price fall below the no-arbitrage bound?d. Formulate the appropriate arbitrage strategy, and calculate the profits to that strategy.In two-months the price of stock will be either $23 or $27. The risk-free interest rate is 10%. The current price of the stock is $25. Suppose the price of the stock will be ST at the end of the two-months and the derivative on the stock will pays off Sr?. Find the value of the derivative. (A) $621.39 (B) $729.39 (C) $529.39 (D) $639.26The value of the S&P 500 index is 4,815. The continuously compounded risk - free rate is 5.5% and the continuous dividend yield is 1.1% . You consider trading 1 E- mini futures on the S&P 500 (symbol: ES) with a contract unit of $5 x S&P 500 Index listed on CME and 115- days to expiration. a. Calculate the no - arbitrage futures price of the position. b. Calculate the value of a long futures position after 46 days if the index value is $3,852.
- Suppose the 6-month Mini S&P 500 futures price is 1,345.99, while the cash price is 1,335.81. What is the implied difference between the risk-free interest rate and the dividend yield on the S&P 500? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Implied difference %Consider a six-month futures contract on the FTSE 100. Assume the stocks underlying the index provide an annual dividend yield of 6.2% and the value of the index is 6754.5. Calculate the price of the index (to the nearest full index point) if the continuously compounded risk-free interest rate is (i) 6.9% and (ii) 5.A stock is currently priced at $40. The risk-free rate of interest is 8% p.a. compounded continuously and an 18-month maturity forward contract on the stock is currently traded in the market at $38. You suspect an arbitrage opportunity exists. Which one of the following transactions do you need to undertake at time t = 0 to arbitrage based on the given information? Long the forward, short-sell the share and invest at risk-free rate Long the forward, borrow money and buy the share Short the forward, borrow money and buy the share Short the forward, short-sell the share and invest at risk-free rate