In July 2004, six-month futures on the FTSE 500 stock index traded at 16,000. The spot was 13,300. The interest rate was 19% p.a. and the dividend yield was 4% (for six months). Assume that the entire dividend is paid on contract maturity, and the contract concerns the ex-dividend price. Are the futures are fairly priced? If not, illustrate an arbitrage strategy to take advan- tage of this opportunity.
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Answer using futures pricing formulas
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- The current value of BSE SENSEX is 10000 and the annualized dividend yield on the index is 5%. A six-month-futures contract on the BSE SENSEX is quoted at 10200. If the return on Treasury Bills available in the market for the same maturity is 5% and 25 % of the stocks included in the index will pay dividends during the next six months, you are required to a. Determine whether index futures is overpriced or under priced. b. Show risk-free arbitrage profits, if any, available to the investor irrespective of the value of the SENSEX on maturity with detail workings, assuming that the SENSEX on maturity can be i. 9900 orii. 10250 Solve fast pleaseThe one-year futures price on a particular stock - index portfolio is 1,124.91, the stock index currently is 1, 116, the one-year risk-free interest rate is 2.61%, and the year-end dividend that will be paid on a $1,116 investment in the index portfolio is $13.73. By how much is the contract mispriced? future price - parity priceA non-dividend-paying stock has a futures contract with a price of $82.20 and a maturity of six months. If the risk-free rate is 3.9 percent, what is the price of the stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
- 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.A non-dividend-paying stock is currently priced at $16.40. The risk-free rate is 3 percent and a futures contract on the stock matures in six months. What price should the futures be?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
- What would be the spot price if a stock index futures price were $75, the risk-free rate were 10 percent, the dividend yield 3 percent, and the futures expires in three months? A. $73.70 B. $77.48 C. $72.60 D. $76.32 E. none of the above Please explain step by stepSuppose that the value of the S&P 500 stock index is 2,000.a. If each E-mini futures contract (with a contract multiplier of $50) costs $25 to trade with a discount broker, how much is the transaction cost per dollar of stock controlled by the futures contract?b. If the average price of a share on the NYSE is about $40, how much is the transaction cost per “typical share” controlled by one futures contract?c. For small investors, a typical transaction cost per share in stocks directly is about 10 cents per share. How many times the transactions costs in futures markets is this?A stock will pay a dividend of $3 in 4 months and $4 in 8 months. The current price of the stock is $408. If the risk-free rate for all maturities is 5.19%, what is the arbitrage profit of a 12-month forward contract on the stock if its current price is $600? Group of answer choices $230.685 $195.195 $177.45 $195.195 $221.813
- 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?The stocks of Cee Mobile Limited is currently trading at $73 each. The call option on the company’s stock has an exercise price of $70, with fifty (50) days remaining to expiration. It is assumed that the yield on treasury bills is currently 2%, while the volatility of the stock price is estimated as being 35%. a. Using the Black-Scholes-Merton (BSM) model, calculate the value of the Call option, given the above parameters. Show all relevant workings. b. Of the value computed, how much is the intrinsic value and the time value of the Call option? c. Using the BSM model and the information given above, calculate the value of the Put option on the stock, with a similar strike price and days to expiration.Consider the futures contract on XYZ Inc. stock. Suppose that the annual dividend yield for the stock is 2.5% and the risk-free rate is 6.3%. Both rates are based on continuous compounding. The current futures price of the XYZ Inc. futures contract maturing in 18 months is $900 per share. Assume that the no arbitrage Futures-Spot parity when asset provides a known yield holds. What is the current spot price of XYZ Inc. per share? Please explain and show calculation. a. $934.39 b. $952.79 c. $850.13 d. $900.00 e. $944.37