► You want to protect the value of a $185,000,000 portfolio over the near term (so, you will "short-hedge"). The beta of this portfolio is 1.25. ► The Mini S&P futures contract with 3-months to expiration has a price of 2,880. ▸ How many futures contracts do you need to sell? 1,606. Here's why: Mini S&P 500 Multiplier: = 1,605.9 Suppose two other portfolio betas are 1.45 and 0.75. What then?
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- The manager of a well-diversified portfolio with a market value of $200 million that mirrors the S&P 500 wants to hedge the portfolio against a market decline in value over the next six months. The portfolio manager wants to use the Mini-S&P 500 contract for hedging. The contract multiplier for this futures contract is $50. The futures price for the contract at the date that the hedge is put on is 4,200. a. Should the portfolio manager buy or sell the futures contract. Explain why. b. How many contracts should the portfolio manager sell or buy? c. Suppose at the delivery date (six months from now), the value of the S&P 500 is 3,800. Show what the outcome for this hedge will be.A company has $20 million portfolio with beta of 0.8. It would like to use futures contracts on the S&P 500 to hedge its risk. The index is currently standing at 1050, and each contract is for delivery of $250 per index points. What is the hedge that minimises its risk? What should the company do if it wants to reduce the beta of the portfolio to 0.2? a. Buying 76 futures contracts minimises the risk. To reduce the beta to 0.2, the company should instead buy 61 contracts. b. Buying 61 futures contracts minimises the risk. To reduce the beta to 0.2, the company should instead buy 46 contracts. c. Selling 76 futures contracts minimises the risk. To reduce the beta to 0.2, the company should instead sell 61 contracts. d. Selling 61 futures contracts minimises the risk. To reduce the beta to 0.2, the company should instead sell 46 contracts.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 KLSE CI is at 1250. The value of your portfolio is RM2.5 million. if you wish to hedge against a market downturn as completely as possibile, do you buy or sell futures contractYou are currently long on a portfolio of stocks that has a beta of 1.60. Given recent uncertainties, you intend to reduce the portfolio beta to 1.20. Your portfolio currently worth RM2.8 million and FBM KLCI is at 800 points. Show how the objective can be achieved using SIF contracts.The S&P 500 futures price is 4372 and you have a portfolio of stocks valued at $20,000,000. Each futures contract is worth $250. If the portfolio moves exactly like the index, how many contracts do you need to hedge this portfolio and what is the implied beta?
- 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? b. 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?You want to use S&P 500 index options to hedge your portfolio. • Portfolio has a beta of -1.0. • It is currently worth $500,000 and index stands at 1000. • The risk-free rate is 0% per annum. • There is no dividend yield on both the portfolio and the index. 1) What option contracts would you consider? 2) How many option contracts should be purchased? 3) What strike price should we consider for insurance against the portfolio value falling below $450,000 in three months? 4) What happens if index level turns out to be 1200 after three months?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?
- A fund manager has a portfolio worth $100 million with a beta of 1.5. The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on the S&P 500 to hedge the risk. The current level of the index is 2250, one contract is on 250 times the index, the risk-free rate is 2%, and the dividend yield on the index is 1.7% per year. (Assume all the rates are continuously compounded.) What is the theoretical futures price for the three-month futures contract? What position should the fund manger take to eliminate all exposure to the market over the next two months? Calculate the effect of your strategy on the fund manager’s returns if the level of the market in two months is 2,000, 2,200, 2,500, 2,800, and 3,000.A ) A portfolio manager desires to generate $10 million 100 days from now from a portfolio that is quite similar in composition to the S&P 100 index. She requests a quote on a short position in a 100-day forward contract based on the index with a notional amount of $I0 million and gets a quote of $25.2. If the index level at the settlement date is $35.7. calculate the amount the manager will payor receive to settle the contract B) A forward contract covering a $10 million face value of T-bills that will have 100 days to maturity at contract settlement is priced at 1.96 on a discount yield basil. Compute the dollar amount the long must pay at settlement for the T-bills. C) Consider an FRA that: • Expires/settles in 30 days. • Is based on a notional principal amount of $1 million. • Is based on 9O-dayLIBOR. • Specifics a forward rate of 5%. Assume that the annual 9O-day LIBOR 30-days from now (at expiration) is 6%. Compute the cash settlement payment at expiration and identify which…A company has a £10 million portfolio with a beta of 0.8 to the stock market. The futures price for a contract on the stock market is 500. Futures contracts can be traded with value equal to £10 multiplied by the futures price. What position should one take in order to completely hedge the market risk? a. Short 2000 contracts b. Long 2000 contracts c. Short 1600 contracts d. Long 1600 contracts