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Futures, Swaps, and Risk Management


  1. Foreign exchange futures trade on several foreign currencies, as well as on a European currency index. The interest rate parity relationship for foreign exchange futures is

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    with exchange rates quoted as dollars per foreign currency. Deviations of the futures price from this value imply an arbitrage opportunity. Empirical evidence, however, suggests that generally the parity relationship is satisfied.

  2. Futures contracts calling for cash settlement are traded on various stock market indexes. The contracts may be mixed with Treasury bills to construct artificial equity positions, which makes them potentially valuable tools for market timers. Market index contracts are used also by arbitrageurs who attempt to profit from violations of the stock-futures parity relationship.

  3. Hedging requires investors to purchase assets that will offset the sensitivity of their portfolios to particular sources of risk. A hedged position requires that the hedging vehicle provide profits that vary inversely with the value of the position to be protected.

  4. The hedge ratio is the number of hedging vehicles such as futures contracts required to offset the risk of the unprotected position. The hedge ratio for systematic market risk is proportional to the size and beta of the underlying stock portfolio. The hedge ratio for fixed-income portfolios is proportional to the price value of a basis point, which in turn is proportional to modified duration and the size of the portfolio.

  5. Many investors such as hedge funds use hedging strategies to create market-neutral bets on perceived instances of relative mispricing between two or more securities. They are not arbitrage strategies, but pure plays on a particular perceived profit opportunity.

  6. Interest rate futures contracts may be written on the prices of debt securities (as in the case of Treasury-bond futures contracts) or on interest rates directly (as in the case of Eurodollar contracts).

  7. Swaps, which call for the exchange of a series of cash flows, may be viewed as portfolios of forward contracts. Each transaction may be viewed as a separate forward agreement. However, instead of pricing each exchange independently, the swap sets one "forward price" that applies to all of the transactions. Therefore, the swap price will be an average of the forward prices that would prevail if each exchange were priced separately.

  8. Commodity futures pricing is complicated by costs for storage of the underlying commodity. When the asset is willingly stored by investors, the storage costs net of convenience yield enter the futures pricing equation as follows:

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    The non–interest net carrying costs, c, play the role of a "negative dividend" in this context.

  9. When commodities are not stored for investment purposes, the correct futures price must be determined using general risk–return principles. In this event,

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    The equilibrium (risk–return) and the no-arbitrage predictions of the proper futures price are consistent with one another for stored commodities.











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