Mastering Derivatives: Avoiding Active Management of Delta-neutral Trades

Delta-neutral trades require active management. These are trades that involve taking long positions in, say, lower strike calls and short positions in higher strike calls such that the delta of the long position is equal to the delta of the short position. The strategy is typically setup to bet on the relation between implied volatility and realised volatility. The issue is that option delta changes as the underlying price changes. You must, therefore, continually manage the position so that its delta is close to zero. This requires time and effort. This week, we discuss a strategy that is intentionally not delta-neutral, but setup to take a bet on volatility.

Implied volatility

A long stock position has a delta of one, and gamma and vega of zero. That is, the change in the stock price with respect to itself (delta of the stock) is always one. Gamma, which is the change in delta, is therefore zero. So, a position that is long the stock and short the ATM call will carry short gamma and short vega. The position may be hurt if there is a sharp change in the underlying price; for then the ATM call will rise significantly as its delta will increase, driven by its gamma.

The objective of this position is to bet on the option’s implied volatility. Note that time value of an option, one component of the option price, consists of time to expiry and implied volatility. Short options gain from time decay (or loss in time value). This means short options can gain if the option’s implied volatility decreases through expiry. Put differently, by going long on the stock and short on the ATM call, you are betting that the current implied volatility is higher and will decrease as the option approaches expiry. The long stock protects your naked short call from gathering losses if the underlying moves up.

The position is subject to downside risk, which is cushioned by the premium collected on the short call. Suppose you buy 550 shares of HDFC Bank and short one contract of near-month 1460 call (permitted lot size is 550 shares) for 45 points. Your downside break-even price is 1410 (the spot price, 1455, less premium collected). If the underlying declines below this level, the position will incur losses. If the underlying moves up sharply, the position will have lower gains; the gains from the long stock will be greater than the losses from the increase in option price. This is because the delta of the stock is greater than the delta of the call option.

Optional reading

Setting up this trade requires large trading capital as the number of shares you buy must equal the permitted lot size of the option contract. If this were a delta-neutral trade, you would have bought half of the permitted lot size, as the delta of an ATM call is likely to be close to 0.50.

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