D4 Finance Bond portfolio currently has a duration of 4.7 and a value of $800,000. The price of the cheapest to deliver treasury is $97,425 and has a duration of 7.63, and the conversion factor of for this cheapest to deliver bond is 1.29. The portfolio manager wants to temporarily change the duration of the portfolio and uses futures contracts to reach the duration objective. Determine the number of futures contracts to be bought or sold if the new duration objective is: 3.5. 6.2. 10.8
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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?
- . A portfolio manager follows a duration-matched strategy in his funds. His bond portfolio has a durationof 5.3 years, with a market value $8,400,500. He plans to reduce the duration of his bond portfolio to 4.5years. Assume that he can use 5-year T-note futures contracts to hedge the risk, with one-tick changes ininterest rates, this futures contract value will change by $25. Calculate the number of futures contracts thatthe manager should long or short.Consider the following scenario analysis attached in the images: Assume a portfolio with weights of 0.60 in stocks and 0.40 in bonds. a. What is the rate of return on the portfolio in each scenario? (Enter your answer as a percent rounded to 1 decimal place.) Rate of Return Recession % Normal economy % Boom % b.What are the expected rate of return and standard deviation of the portfolio?(Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Expected Return : % Standard Deviation: %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?
- Consider a treasury bill with a rate of return of 5% and the following risky securities:Security A: E(r) = .15; variance = .0400Security B: E(r) = .10; variance = .0225Security C: E(r) = .12; variance = .1000Security D: E(r) = .13; variance = .0625The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. The security the investor should choose as part of his complete portfolio to achieve the best Sharpe ratio would be?The following data are available to you as portfolio manager: Security Estimated return (%) Beta A 40 3.0 B 35 2.5 C 30 1.0 D 17.5 1.8 E 20.0 1.5 Market Index 25 2.0 Government Security 17 0 In terms of the security market line, which of the securities listed above are underpriced? Assuming that a portfolio is constructed using equal proportions of the five securities listed above, calculate the expected return and risk of such a portfolioA portfolio manager decides to adjust the beta of his $101148 equity portfolio from 0.5 to 1.3 for the next five months. The manager selects a future on the market index, which is currently traded at $487, to adjust the beta of his equity portfolio. The expectation about the market underpinning the adjustment of beta and the number of futures contracts the manager should take are: a. The market will be moving up, and a long position in 166 futures contracts should be held b. The market will be moving down and a short position in 104 futures contracts should be held c. The market will be moving down, and a long position in 270 futures contracts should be held d. The market will be moving up, and a short position in 166 futures contracts should be held Which of the following best describes the role of central clearing parties a. CCPs are used to manage price risk of futures transactions b. CCPs services are used in all OTC derivative transactions c. CCPs help market participants to…
- 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 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?Assignement B Abacus Ltd is an investment fund that specializes in fixed income securities. At the end of2010 the fund’s bond portfolio has the following information BOND YIELD TO MATURITY PRICE DURATION CONVEXITY A 12% 1045 2.35 16.46 B 14% 2265 4.26 22.80 C 8% 1430 3.45 11.96 D 10% 1100 4.20 15.56 Assume that the yield to maturity on each bond increases by 4%, calculate(i) The percentage by which the price of each bond will decrease(ii) The amount in cedis by which the price of each bond will decrease (iii) The percentage and the cedi decrease in the total value of the portfolio.