Warrants: risk control in Greek

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  Serge Nussbaumer
  Chefredaktor

Delta hedging is one of the best-known risk management strategies. This approach originally comes from options trading, where it is mainly used by institutional investors and market makers to hedge against price risks. However, private investors can also use delta hedging to protect themselves against losses. This type of hedging focuses on the delta. This sensitivity indicator is one of the most important “Greeks” and indicates how much the price of an option or warrant changes if the price of the underlying asset changes by one unit. A call option with a delta of 0.6 means that if the price of the underlying asset, such as a share, rises by CHF 1, the price of the option rises by CHF 0.60. For calls, the delta is between 0 and 1 and for puts between 0 and -1.

The aim of delta hedging is to minimize or neutralize the delta risk. As a rule, the underlying asset is bought or sold in a certain ratio to the option position held. Call options have a positive delta. To offset the risk, a corresponding number of the underlying asset must therefore be sold short. The delta of a put option is negative. Here, a corresponding position must be built up by buying the underlying. The position in the underlying must therefore be adjusted so that the total delta of the portfolio is 0 or close to 0 and price changes in the underlying have little or no effect on the value of the portfolio.

Example of a delta hedge

A typical options contract on shares traded on futures exchanges usually has a contract size of 100 units. For a put option with a delta of -0.6, 60 units of the underlying share (100 x 0.6) must therefore be purchased to offset the negative delta. The sum of the deltas is therefore 0 (delta-neutral). For example, if the share rises by CHF 1, the put position is reduced by CHF 60, while the value of the share position increases by CHF 60. Gains and losses from the option and share position therefore balance each other out. To achieve the same effect with a call with a delta of 0.6, 60 shares must be sold short. If the share falls by CHF 1, the call position is reduced by CHF 60, while the value of the shares sold short increases by CHF 60.

Delta hedging with put warrants

The previous explanations referred primarily to delta hedging in professional options trading. However, private investors can also benefit from this concept to hedge existing positions in their portfolio against price losses. This can be achieved using put warrants. An example: Let’s assume an investor has 200 shares of the model share in his portfolio and wants to protect this position against possible price losses. The sample share is currently trading at CHF 100, resulting in a position value of CHF 20,000. In order to offset any losses, 400 put warrants with a subscription ratio of 1:1 and a delta of -0.5 on the sample share would be required. If the sample share falls by CHF 1, this results in a loss of CHF 200 for 200 shares, while the 400 put warrants gain CHF 200 (400 shares x CHF 0.50 per put). For a put warrant with a delta of -0.8, the same neutralizing effect would already be achieved with 250 shares (250 x CHF 0.80). This shows that The closer the delta is to -1, the fewer put warrants are required for hedging.

Continuous rebalancing required

Delta hedging can be used to secure a share’s price gains in the short term without having to sell the share. However, this type of risk control is also associated with a number of challenges. On the one hand, the delta is not a constant value, but changes with every movement of the underlying. The gamma provides information about this. However, the price development of
options and warrants also depends on other influencing factors. These include
changes in the implied volatility of the underlying (Vega) or the loss of time value (Theta), for example. Delta hedging requires continuous monitoring and adjustment of the positions (rebalancing) in order to keep the delta as neutral as possible. This leads to increased transaction costs as frequent trading is required. Without regular adjustments, it can quickly happen that the position to be hedged is over- or under-hedged, which jeopardizes the hedging objective. It is generally advisable to hedge with put warrants that have the highest possible (negative) delta and the lowest possible gamma. This is because the lower the gamma, the less the delta changes when the underlying changes.

Omega: Managing the risk of loss

Another key figure for risk management in warrant trading is the so-called omega. Although it is not a classic Greek, it provides a valuable guide for assessing the risk/reward profile of warrants. It indicates the percentage by which the price of the warrant theoretically changes if the price of the underlying rises or falls by 1%. This figure is a combination of simple leverage and delta and is referred to as theoretical leverage. The simple leverage is calculated by dividing the price of the underlying by the price of the warrant (multiplied by the subscription ratio). For example, a simple leverage of 10 means that the capital invested to buy a share is 10 times higher than the capital invested in the warrant. However, it is not possible to deduce from this how the warrant will react if the price of the underlying changes. This is achieved by multiplying the simple leverage by the delta. The omega is important because it gives investors a feeling for the profit opportunities, but also the risk of loss of a warrant. A warrant with an omega of 10, for example, is significantly riskier than a warrant with an omega of 3. Nevertheless, it should also be noted here that the omega is not a fixed value, but is subject to fluctuations due to changes in the delta and other price parameters.