16.g Delta Hedging

Introduction to Delta Hedging

  • Final video for Chapter 16 on options, focusing on hedging portfolios using Delta hedging.

  • Delta hedging allows for active management of risk and the potential for earning while hedging.

Understanding Delta

  • Delta measures the sensitivity of an option's price to changes in the price of the underlying stock.

    • Positive Delta: Associated with call options (value increases as stock price increases).

    • Negative Delta: Associated with put options (value decreases as stock price increases).

  • It is critical in determining the risk and management strategy when using options.

Example of Delta Hedging

  • Consider a call option with a Delta of 0.5:

    • If the stock price increases by $1, the call option value increases by $0.50.

  • Simple Strategy: Buying 1 share of stock and selling 2 call options:

    • If stock price increases by $1:

      • Gain from the stock = $1

      • Loss from selling calls = -$1 (due to 2 calls increasing by $0.50 each)

      • Overall: No gain/loss (break even).

    • If stock price decreases by $1:

      • Loss from the stock = -$1

      • Gain from calls = $1 (due to rises when the price decreases)

      • Overall: No gain/loss (break even).

  • This illustrates how selling calls provides hedging against stock price declines.

Active Management of Delta Hedging

  • Delta changes with stock price fluctuations, necessitating adjustments to the number of options sold/bought.

  • This type of hedging is termed dynamic because it requires continuous monitoring and adjustment.

Hedging Large Portfolios

  • Example: Hedging a $10 million stock portfolio using options:

    • Use index options where contract size = 100 times index value (as opposed to futures which was 250 times).

    • The hedge calculations involve:

      • Beta: Measure of volatility relative to the index.

      • Adjust the number of contracts based on the ratio of portfolio beta to option Delta.

Adjustments in Delta Hedge Calculation

  • When hedging with call options:

    • If Beta > 1, more options are needed.

    • If Beta < 1, fewer options are needed.

    • A negative sign can help determine whether to sell or buy:

      • Positive Delta indicates a requirement to sell calls to hedge.

      • Negative Delta (in case of puts) indicates a need to buy puts.

Example Calculation

  • $10 million portfolio with Beta = 1, needing to hedge using call options:

    • Calculate number of options sold using formula: Portfolio Value / Option Contract Size X (Portfolio Beta / Option Delta).

    • For a given Delta, this might indicate selling 84 call options to hedge.

  • This reflects a dynamic approach, requiring ongoing adjustments based on market conditions.