What is Hedging?
In its broadest definition, ‘hedging’ involves reducing risk by leveraging correlations or lack thereof between hazardous investments. Hedging aims to optimise risk/return ratios. The standard Modern Portfolio Theory paradigm allows for several portfolios with similar anticipated returns but distinct variances (‘risk’). When two portfolios offer the same projected return, the one with lesser risk is the better investment.
A Short Example
When you purchase a call option, its value may fluctuate based on the underlying asset’s performance. So, sell some stock short. Selling the proper amount short can reduce risk by balancing stock and option fluctuations.
A Deep Dive into Hedging
To appreciate the benefits of hedging, consider the different types of hedging.
There are two main types of hedging strategies: model-independent and model-dependent.
Model Independent Hedging
Put-call parity is one example of this type of hedging. Calls and puts on a European asset with identical strikes and expires, as well as the underlying stock and zero-coupon bond with the same term, have a straightforward relationship. This link is independent of the underlying asset’s value change.
Another example is spot forward parity. Finding a hedge does not need specifying the asset’s dynamics, including volatility. There are few model-independent hedges.
Model Dependent Hedging
Finance hedging strategies typically rely on a model of the underlying asset. Hedging in Black-Scholes analysis establishes a theory for determining derivative values. Pricing derivatives requires knowledge of the underlying asset’s volatility. If the model is incorrect, it may potentially affect the option value and hedging strategy.
Delta Hedging
Delta hedging is a fundamental concept in derivatives theory. A clever hedge between the option and its underlying eliminates all risk, making it theoretically perfect. Delta hedging uses the perfect correlation between changes in option value and stock price.
This is an example of ‘dynamic’ hedging, which requires regular monitoring and adjustment based on the sale or purchase of the underlying asset. Any dynamic hedging approach that involves frequent rehedging will incur transaction costs and lead to losses. In some markets, this can be crucial.
In a delta-hedged portfolio, the ‘underlying’ could be a tradable asset like a stock or a random factor that sets a price, such as a risk of default. To acquire two instruments with the same risk of default, compute their price sensitivities, or deltas, then buy them in inverse proportion to these deltas (one long, one short). This is also called delta hedging. If two underlyings are highly connected, one can be used as a proxy for the other for hedging. You would only be subject to the basic risk. Exercise caution as the close relationship may not always work out.
Combining uncorrelated financial instruments can create a portfolio with lower risk compared to individual instruments. Having a huge portfolio can potentially reduce risk to minimal levels. While not precisely hedging, this nonetheless achieves the same aim.
Gamma Hedging
Gamma hedging is a cost-effective approach that reduces the magnitude of each rehedge and increases the duration between them. Delta hedged portfolios are insensitive to modest fluctuations in the underlying asset. The portfolio’s convexity relative to the underlying causes a slight mistake in this calculation. Gamma hedging eliminates second-order effects, making it a more accurate method of hedging. Typically, an exotic contract is hedged against a vanilla contract and its underlying. The vanilla and underlying quantities are chosen to result in a zero portfolio delta and gamma.
Vega Hedging
The effectiveness of prices and hedging methods depends on the model for the underlying asset. The volatility of the underlying asset is a major factor in determining the contract value. Unfortunately, measuring this metric is challenging. Simple theories often presuppose a constant, which is not always true. We can use vega hedging to ensure a portfolio’s value is not affected by this parameter,. We hedge one option with both the underlying and another option to achieve zero delta and vega, which represent the portfolio’s volatility sensitivity.
Using a constant volatility (basic Black-Scholes) model to calculate sensitivities to parameters that are supposed to be constant is generally satisfactory in practice, although it is inconsistent theoretically. Distinguishing between factors (underlying asset price and time) and parameters (volatility, dividend yield, interest rate) is crucial.
Prices are sensitive to variables, but not necessarily to parameters. To address this issue, it’s possible to model volatility and other variables separately. This approach enables the development of a consistent hypothesis.
Static Hedging
Delta hedging presents both practical and theoretical challenges. Hedging can be costly and requires precision timing. To apply the principle, a significant amount of the underlying asset may need to be purchased or sold. This is a difficulty with barrier options and those with discontinuous payoffs. Theoretically, the model for the underlying is imperfect, as we do not have accurate parameter values. Delta hedging alone exposes us to model risk.
It’s recommended to use both static and delta hedging strategies to address these issues. This involves purchasing or selling more liquid traded contracts to limit cash flows from the initial contract. The static hedge is activated immediately and will remain in place until it expires. If an exotic contract’s cash flows match those of traded options, its value is determined by the cost of establishing a static hedge, without the need for a model. (But it wasn’t an exotic option to begin with.)
Super Hedging
Classical dynamic delta hedging cannot fully reduce risk in incomplete markets. Superhedge refers to building a portfolio with a favourable payback regardless of market conditions. To superhedge a short call strategy, simply buy one stock and do not rebalance. Superhedging can result in prices that are significantly different from the market, as demonstrated in this example.
Margin Hedging
During volatile markets, banks and other institutions can face unexpected margin calls that require substantial amounts of capital to cover, rather than changes in asset values. Met-allgesellschaft and Long Term Capital Management are two examples of how margins have caused major damage.
Writing options is quite dangerous. Buying an option has only one downside: the upfront price. However, the potential upside is boundless. The benefits of writing an option are minimal, but the drawbacks could be significant.
Clearing houses require option writers to deposit a margin to mitigate the risk of default in case of an adverse outcome. There are two types of margins: initial margin and maintenance margin. The initial margin refers to the amount placed upon contract beginning.
The overall margin amount must remain above a predetermined maintenance margin. If it goes below this level, additional funds (or equivalent in bonds, stocks, etc.) must be deposited. Margin deposit requirements vary by contract.
The overall margin amount must remain above a predetermined maintenance margin. If it goes below this level, additional funds (or equivalent in bonds, stocks, etc.) must be deposited. Margin deposit requirements vary by contract.
A significant market shift may necessitate a big margin call that is challenging to meet. Margin hedging can help avert this problem. Create a portfolio that balances margin calls on one section with refunds from others. Over-the-counter contracts typically do not require a margin and are therefore excluded from the computation.
Crash (Platinum) Hedging
The final type of hedging is tailored to extreme markets. Market crashes have two clear effects on hedging strategies. The huge and quick nature of the moves makes delta hedging ineffective. The convexity impact is not negligible. Second, regular market correlations become irrelevant. Typically, correlations become one (or minus one). Crash or Platinum hedging uses the latter effect to minimise the worst-case scenario for the portfolio. The CrashMetrics technique is a strong hedge as it does not rely on volatility factors. Platinum hedging has two types: hedging the portfolio’s paper value and hedging margin calls.
Related Readings
- Value At Risk in Finance: All You Need To Know
- Arbitrage in Quantitative Finance: All You Need To Know
- Modelling Approaches in Quantitative Finance: All You Need To Know
- Central Limit Theorem In Finance: Power Your Portfolio Now
- Capital Asset Pricing Model