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A Better Risk Gauge For Options Portfolios

Consider a complex portfolio that includes numerous options combinations corresponding to different underlying assets and created under various options strategies. A proper risk management system requires indicators that forecast risk on the portfolio level. The common tools used to evaluate risks of options are the Greeks. These measures reflect the extent to which the value of the option responds to changes in variables such as price, volatility, time and the interest rate. These variables can be regarded as risk factors causing option price fluctuations. The Greeks are calculated as partial derivatives of the option price based on a given variable. Delta is the first derivative of the option price with respect to the underlying asset price. The derivative with respect to volatility is called vega. Theta measures time decay, and rho measures the sensitivity to the interest rate. Derivatives of the second and higher orders also are used. The risks of option positions on the same underlying asset can be evaluated by mere summation of corresponding Greeks. However, this does not work when the portfolio contains several combinations related to different underlying assets. Because delta and vega are not additive for options corresponding to different underlyings, their summing is impossible here. The index delta is an alternative risk indicator that measures how much the value of a complex portfolio is likely to change in response to changes in the value of the index. We can solve the non-additivity problem by expressing the delta of each option as a derivative based on some composite index. This approach will transform delta into an additive characteristic, thereby clearing the way to express the risk of the complex portfolio. The utility of the index delta is not limited to the evaluation of the portfolio risk. It can be useful for hedging and restructuring complex positions in the course of realizing various dynamic options trading strategies based on delta-neutrality. The following steps are necessary to compute the index delta: (1) Select the appropriate index. It can be either ready-made (S&P 500) or an index created by the investor.