Pricing Futures Essay

2204 words - 9 pages

Abstract
This assignment is divided into two parts. Part 1 aims to construct a hedging strategy using index futures through a simple regression, with the change in spot price as the dependent variable and the change in futures price as the independent variable. We have used historical prices of the S&P 500 index and its index futures. Hypothetical examples of how to utilise the optimal hedging ratio obtained from the regression were also discussed. Part 2 explores various option trading strategies using options of three firms listed on NASDAQ:  News Corporation (NWS), market capitalisation: \$ 13,208 million Seagate Technology (STX), market capitalisation: \$ 5,109 million  Titan Machinery ...view middle of the document...

Therefore we can use our hedge ratio, contract size and portfolio size to calculate the optimal number of index futures contracts to hedge our exposure as shown by the formula below.

3
(Assuming contracts sold on 31st December 2010 to hedge for a three year period.) Hence: ( )

We would need to sell 31 index futures contracts on the 31st of December 2010 to optimally hedge our three year underlying index exposure, which we will close out by buying 31 futures contracts on the 31st of December 2013. In the above calculation we are assuming that there is no mismatch between our portfolio and the index, which is quite unrealistic. If we do not hold an index portfolio, then h2 will be the beta of our portfolio, and the optimal number of contracts for the hedge is subject to change as shown below.

    Hence:

(assuming our portfolio has a beta of 0.9)

(Assuming contracts sold on 31st December 2010 to hedge for a three year period.)

It is important to note than using the optimal number of contracts to hedge an exposure may not necessarily yield the best outcome in every scenario. An optimal hedge simply eliminates as much of the risk as possible, resulting in a more certain (but may not be more favourable) outcome. For example, if the price of the underlying asset moves in favour of the investor, an optimal hedge will offset just about all gains from the investor.

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2.1

Selected Strategies

To construct a profitable options trading strategy, one must consider the underlying stock price movements. This depends on not only the fundamentals of the general economy, industry and the firm itself, but also investor’s expectations of them. We have formed our predictions of the firms’ future stock price movements by referring to recent news articles. For simplicity purposes, we have constructed our strategies using the last settlement price on each day. These prices can be found in Appendices 2, 3 and 4.

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The payoffs for each strategy are calculated using the option intrinsic value formulas (i.e. for a call MAX [(S − K), 0], and for a put MAX [(K – S), 0]), taking into consideration the premiums. Please note these calculated payoffs in the graphs are only indications of potential gains or losses assuming that we hold our positions to maturity. As we calculated profit and loss on 26/09/2011 and 03/10/2011 (rather than at maturity), our recorded profit and loss may differ from the payoffs calculated using the formulas above and indicated in the graphs.

2.1.1 News Corporation (NWS)
News Corporation is a diversified broadcast and print media conglomerate which includes many different subsidiaries. It has operations mainly in the US, Europe and Australia. The company recently had two journalism scandals, and has reshuffled its board members.1 Although NWS’s business fundamentals have not changed, investors’ confidence levels may be lowered due to the increased uncertainty of the company’s future prospects....

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