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Hedging
Hedging is an important consideration in modern finance. The decision of whether or not to hedge, how much portfolio insurance is adequate, and how often to rebalance a portfolio are important considerations for traders, portfolio managers, and financial institutions alike.
Without transaction costs, financial professionals would prefer to rebalance portfolios continually, thereby minimizing exposure to market movements. However, in practice, the transaction costs associated with frequent portfolio rebalancing may be very expensive. Therefore, traders and portfolio managers must carefully assess the cost needed to achieve a particular portfolio sensitivity (e.g., maintaining delta, gamma, and vega neutrality). Thus, the hedging problem involves the fundamental tradeoff between portfolio insurance and the cost of such insurance coverage.
The major topics covered in this chapter include:
Hedging Functions
The Financial Derivatives Toolbox offers two functions for assessing the fundamental hedging tradeoff, hedgeopt and hedgeslf.
The first function, hedgeopt, addresses the most general hedging problem. It allocates an optimal hedge to satisfy either of two goals:
hedgeopt allows investors to modify portfolio allocations among instruments according to either of the goals. The problem is cast as a constrained linear least squares problem. For additional information about hedgeopt, see Hedging with hedgeopt.
The second function, hedgeslf, attempts to allocate a self-financing hedge among a portfolio of instruments. In particular, hedgeslf attempts to maintain a constant portfolio value consistent with reduced portfolio sensitivities (i.e., the rebalanced portfolio is hedged against market moves and is closest to being self-financing). If hedgeslf cannot find a self-financing hedge, it rebalances the portfolio to minimize overall portfolio sensitivities. For additional information on hedgeslf, see Self-Financing Hedges (hedgeslf).
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