- Earlier chapters covered features, contract details, and payoff profiles of futures and options.
- Focus now shifts to applying these instruments for hedging, trading, and arbitrage.
- The chapter first explains hedging, trading, and arbitrage with futures.
- It then introduces various trading strategies using options.
- The concept of arbitrage using options via put-call parity is discussed.
- Lastly, the process of delta-hedging an options portfolio is explained.
Futures contracts for hedging, speculation and arbitrage :
- Purpose of Derivatives: Futures and options are primarily designed to manage financial risk.
- Hedging Strategies:
- Long Hedge: Used to hedge future stock purchases against price rises by taking a long futures position.
- Short Hedge: Used to hedge future stock sales against price falls by taking a short futures position.
- Example Outcomes: Gains or losses on futures positions offset price movements in the spot market, effectively locking in the desired price.
- Portfolio Hedging:
- Index futures hedge systematic market risk for diversified portfolios.
- Hedge ratio calculated based on portfolio value, beta, index futures price, and lot size.
- Trading and Speculation:
- Bullish View: Go long on futures contracts expecting price rises, leveraging high returns with lower capital outlay.
- Bearish View: Short futures contracts anticipating price drops, profiting from falling prices without owning the asset.
- Arbitrage Opportunities:
- Cash-and-Carry: Profits when futures are overpriced by buying in the cash market and selling futures.
- Reverse Cash-and-Carry: Profits when futures are underpriced by shorting in the cash market and going long on futures.
- Leverage Advantage: Futures trading provides higher returns relative to capital invested due to margin requirements.
Use of options for trading and hedging :
- Options Trading Strategies include spreads, straddles, and strangles.
- Spreads involve combining options on the same underlying asset and type (call/put) with different strikes or expiries — yielding limited profit and loss positions.
- Vertical Spreads: Same expiry, different strikes.
- Bullish Vertical Spread:
- Using Calls: Long lower strike call, short higher strike call.
- Using Puts: Short higher strike put, long lower strike put.
- Bearish Vertical Spread:
- Using Calls: Short lower strike call, long higher strike call.
- Using Puts: Long higher strike put, short lower strike put.
- Horizontal (Calendar) Spread: Same strike, different expiries — bets on the change in time value.
- Diagonal Spread: Different strikes and expiries — complex, more suited for OTC markets.
- Straddles:
- Long Straddle: Buy a call and a put with the same strike and expiry — profits from large price swings either way, with two breakeven points.
- Short Straddle: Sell a call and a put with the same strike and expiry — profits if the price remains stable, but has unlimited risk if the price moves sharply.
- Payoff Examples were provided for each strategy, illustrating profit, loss, breakeven points, and risk profiles using numerical scenarios.
- The text emphasizes the risk-reward balance in each strategy, noting where gains are capped and where losses could be potentially unlimited.
- Long Strangle:
- Similar to a straddle but with different strike prices for the call and put options.
- Both options are out-of-the-money, making the premium lower.
- Maximum loss is the total premium paid, and maximum profit is unlimited if the stock moves significantly.
- Two break-even points (BEPs) exist.
- Short Strangle:
- Opposite of the long strangle, involves selling out-of-the-money options.
- Profit occurs if the underlying remains stable, with a limited maximum profit and unlimited potential losses.
- Two BEPs at different price points.
- Covered Call:
- Strategy for generating extra income by selling a call option against a stock held in the cash market.
- Limits profit on the stock but allows the investor to keep the premium received.
- Can lead to a net profit or loss depending on the stock price movement.
- Collar:
- An extension of the covered call strategy.
- Adds a long put to limit downside risk while capping the upside.
- Helps reduce potential losses if the stock price falls below a certain level.
- Butterfly Spread:
- A strategy to limit the downside of a short straddle by adding long out-of-the-money calls or puts.
- Involves using three different strikes and the same maturity dates.
- The payoff structure forms a “butterfly” pattern, with limited profit and limited loss.
Arbitrage using options: Put-call parity :
- Put-Call Parity Concept: It defines the relationship between call and put options with the same strike price and expiry. The formula is:
c+X×e−rt=p+S0c + X \times e^{-rt} = p + S_0c+X×e−rt=p+S0
Where:
- ccc: Call option premium
- ppp: Put option premium
- XXX: Strike price
- S0S_0S0 : Spot price of the underlying
- rrr: Interest rate
- ttt: Time to expiry
- Fair Price Calculation: Knowing the spot price and call option price, one can derive the fair price of the put option. If the traded price of the put deviates from this price, an arbitrage opportunity arises.
- Example:
- Stock price: Rs.1251
- Call option strike price: Rs.1240
- Call option price: Rs.47.50
- Interest rate: 8% p.a.
- Put option fair price: Rs.28.26
- Traded put price: Rs.23.15 (underpriced, arbitrage opportunity)
- Arbitrage Strategy:
- Buy the put and stock, short the call, resulting in a net outflow of Rs.1226.65.
- If the stock price rises or falls, the arbitrageur still makes a net gain of Rs.5.14.
- Execution Risks:
- The strategy requires precise, simultaneous execution of transactions. Delays can lead to losses, especially if one leg of the transaction is left unexecuted, exposing the arbitrageur to large risks.
Delta-hedging :
- Delta and Sensitivity: Delta measures an option’s sensitivity to changes in the underlying asset’s price. A delta of 0.6 means a 1-unit price change in the underlying stock causes a 0.60 change in the option price.
- Example Setup: A trader short sells 10 at-the-money (ATM) call options on a stock trading at Rs 100, with a delta of 0.50. The options have a lot size of 50.
- Hedging Risk: Since the trader is short on calls, they are at risk if the stock price rises. To hedge, the trader needs to take a long position in the underlying stock.
- Determining Long Position: If the stock price rises by Rs 1, the loss on the short call position is Rs 250. The trader offsets this by going long on stock futures, which have a delta of 1.
- Delta-Neutral Position: The trader needs to buy 5 futures contracts, creating a delta-neutral position, where the total delta of short calls and long futures equals zero.
- Adjusting for Price Changes: If the stock price rises, the delta of the calls increases, requiring the trader to adjust their futures position. For instance, if the delta increases to 0.60, the trader needs to buy one more future contract to maintain delta-neutral.
- Ongoing Adjustments: Delta-hedging requires continuous adjustments, buying or selling futures contracts to keep the portfolio’s delta close to zero, mitigating the risk of the short option position.
Interpreting open interest and put-call ratio for trading strategies :
- Open Interest: Refers to the number of open positions in the market, not yet closed (e.g., 2,56,000 contracts in May index futures).
- Traded Volume: The total number of contracts traded on a particular day.
- Put-Call Ratio (PCR): The ratio of put option volume to call option volume, calculated based on trading volumes or open interest.
- Trading Strategy based on Open Interest and Futures Price:
- Bullish Signal: Rising futures price and increasing open interest.
- Short-Covering: Rising futures price with declining open interest (existing short positions being squared).
- Bearish Signal: Declining futures price with increasing open interest (short positions being built).
- Squaring of Long Positions: Declining futures price with declining open interest.
- Put-Call Ratio as a Contrarian Indicator:
- PCR < 1: Indicates a bearish trend (more calls than puts).
- PCR > 1: Indicates a bullish trend (more puts than calls).