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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.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?An option trader has built a portfolio of three different call options onthe same underlying with the same maturity. The trader has boughtone call with a strike of 20 and also bought a call with a strike of50. The trader has sold two calls with a strike of 35. The currentunderlying price is 35. Tabulate, plot and describe the total payoffsfrom this portfolio. Given your payoff profile, what must be true aboutthe cost of building this portfolio?
- 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.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?This example is part of "Hedged Portfolios" to minimize risk. Assume you have $9000 to invest; A stock is trading at $90.00. A call option that expires in one year with a strike price of $90.00 is trading at $10.00. What is your portfolio's 1-year return if you invest in "Only Stocks" and the the stock price after one year is $48.00? Enter your answer in the following format: + or - 0.1234 Hint: Answer is between -0.4212 and -0.5042 ___________? ANSWER IN TYPING
- You 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.Consider a portfolio consisting of 6 stocks and 10 put options on the stocks. The current stock price is S0 = 100 and the stike price of the options is X = 100. The stock pricecan take on only two values at maturity T given by Su = 120 and Sd = 90. The risk-free rate is given by 5%. (1) How many put options with strike price X = 110 are necessary in the portfolio to have a certain payoff at maturity?(2) Find the value of a put option P0 with strike price X = 100.(3) Find the value of a call option C0 with X = 100 by using the Put-Call-Parity. Verify that your answer by calculating the price C0 directly.An analyst wants to evaluate Portfolio X consisting entirely of US common stocks, using both the Treynor and Sharpe measures of the portfolio performance. The following table provides the average annual rate of return for the portfolio X the market portfolio (as measured by the Standard & Poor's 500 index) and US Treasury billds (Tbills) during the past eight years Average Return Standard deviation Beta Portfolio X 10% 18% 0.6 S & P 500 12% 13% 1 T bills 6% n/a n/a a. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Briefly explain whether portfolio X underperformed, equalled, or outperformed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure. b. Based on the performance of…
- Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean? Explain what is meant by basis risk when futures contracts are used for hedging.You are planning to make a hedging. The standard deviation of semiannual changes in a futures price on the gold is $0.96. The standard deviation of semiannual changes of the gold price is $0.87 and the coefficient of correlation between the two changes is 0.9. What is the optimal hedge ratio for a 6-month contract? Choose correct answer: a. The optimal hedge ratio is 0.8352 b. The optimal hedge ratio is 0.1 c. The optimal hedge ratio is 0.9931 d. The optimal hedge ratio is 0.8156An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table provides the average annual rate of return for Portfolio X, the market portfolio (as measured by the Standard and Poor’s 500 Index), and U.S. Treasury bills (T-bills) during the past eight years. Rate Annual Averageof Return STANDARD DEVIATION OF RETURN BETA Portfolio X 10 13 0.40 S&P 500 12 10 1.00 T-bills 7 n/a n/a n/a = not applicable Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Round your answers for the Treynor measure to one decimal place and for the Sharpe measure to three decimal places. Treynor measure Sharpe measure Portfolio X 7.5 S&P 500 5