Ideas are cheap, execution is everything – Part I

In one of the episodes of Shark Tank reality TV show, one of the sharks, Chris Sacca,  said “Ideas are cheap, execution is everything”. This statement resonates with any person who puts their money at risk and expects a return based on a realistic projection that would allow them to cover their initial cost and compensate them for the risk taken. This is not that different when allocating your money among equities, debt. commodities and currencies. Kevin O’Leary would always throw out innovative payback structures to ensure that is comfortably compensated for the risk he’s taking. For example, if taking equities is too risky for an investor, given that the startup is too early, in which its products or services have yet to been tested in the market, and hence resulting in no historical supportive evidence to provide certainty in its growth projection, Kevin would make offers that include royalties that would allow them to earn more in the early stage than would their equity apportion to, or debts paying out  market equivalent interest rate with a mark up to compensate them for the risk taken. They are being creative with how they invest their money all because they are seeking to maximise their reward-to-risk ratio. If structured correctly, investors can easily have returns with little or zero cost.

To most who are not aware of the math behind it, the unfamiliarity deters them from being creative as they sense more risk than returns. There are times when you have a view on where things can go off based on some catalyst or trend. Say that your judgement is spot on, but you took an outright directional long/short with no netting in exposure. This requires a large upfront capital, exposes you to unlimited upside/downside directional risk, and your source of return is solely on the direction of the price. In this post, I would shed enough light on how to be creative in structuring your legs such that you will be able to maximise your reward-risk payoff.

Recap the basics


On options trading

Be mindful of the spread between buying and sell options. Typically at prices beyond the visibility of the ladder, brokers will not allow selling but do accept your purchase at the minimum tick. For very near dated options, the spread could make the credit generated on selling the option not worth the risk undertaken. Selling an option does not directly lead to profit, since the option is tradeable and on selling, its MTM to the asking price if you decide to liquidate by buying it back. That said, on selling, P/L typically would be in red as you paid the spread and as time passes, would a positive theta (time decay) imply a backwardation adjustment to your option bid price such that approaching expiration, the option’s bid price converges to 0 as it loses its extrinsic value and only then, would your P/L be green. Eventually, on expiration, if both intrinsic and extrinsic value expired  at 0, you are entitled to the credit you signed up for when selling. For DvP settlement, choose spot (or delivery) if the option is a hedge to be package with the underlying, otherwise, choose cash as that saves on delivery cost, which is another bid-ask spread to pay. Likewise, it does not mean that you pay the entire cost of the option on purchase at ask price, as the option is still tradeable in the market. MTM of an option bought will be to the bid price if you were to sell at market. At any time before expiry, you can liquidate the option bought by selling it. However, theta is negative and as time pass, option price will be adjusted lowered and your P/L MTM will be more negative if intrinsic value is increasing as extrinsic value decreases.

Put-Call Parity (Synthetic equivalence)

long C + Cash (Future Strike Price discounted to PV * Quantity per Contract)

= long P + long underlying

Since LHS is a synthetic equivalent to RHS, a market neutral position (cash) would be short C, long P, long underlying aka conversion structure. However, since cash is discounted to PV because you are taking a neutral stance on a future price, you will be exposed to the time value of money. Given rates are positive, Exp(Rate * Time) will be a steepening curve. This is similar in cases of any positive carry e.g. EURUSD forward curve is upward sloping,  since US dollar pays a higher ON rate than Euro dollar. The difference between spot and the forward prices along the curve is the implied forward (swap) points. Counter-intuitively, this doesn’t mean your EURUSD price is projected to go up since you have locked in the spot rate (fixed today, settled T+2). but it means that your opening price in terms of FV will be going with the forward prices. Given that EURUSD 1m fwd points is currently ~ +35 points, holding a long EURUSD with a upward sloping forward curve and closing 1m later means your opening price is going to be adjusted 0.0035 (35 points / 10,000) higher. Here, some will say that since the forward curve is in contango, it produces negative roll yield for long positions. This is a debiting (negative) carry that requires financing over time. That said, unless time value of money is negative, it doesn’t make any sense to hold market neutral positions locked to a future value.

We can also negate the need for holding a long underlying by combining a long call time spread + short put time spread. It is a market neutral position until the expiry (before settlement aka maturity date) of the nearer legs. Market neutral means no delta, no gamma, no vega, no theta.

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Long Jelly Roll = long call time spread + short put time spread

This is a long jelly roll which explains the difference in the pricing between call and put time spread. Calendar spread and Jelly Roll is explained in the next post, part II.

Vice versa, one can earn the time value of money between the time differentials with a short jelly roll.

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Short Jelly Roll = short call time spread + long put time spread

Synthetics

Two or more trading instruments packaged to emulate another trading instrument or vehicle. Synthetics have resemblance in greeks (sensitivity to price, time, IV), but not necesasry similar in cash flow (debit vs credit) and financing needs.

Since long call + long K cash = long put + long stock,

  • synthetic long call = long stock + long put
  • synthetic short call = short stock + short put
  • synthetic long put = short stock + long call
  • synthetic short put = long stock + short call
  • synthetic long stock = long call + short put (credit on entry if put written more valuable than call bought
  • synthetic short stock = short call + long put
  • covered call = long stock + short call = short put

Implied volatility smile (over strike price)

volatility-smile.gif
Sampled from a set (call and put) options that share the same expiration date

IV is an effective proxy for the options premium. Notably, desks quote in terms of IV delta or premium, where the only difference is that the former implied a simultaneous delta hedge while the latter doesn’t.

Reverse skews (Smirk) occur when the IV is higher on lower options strikes. It is most commonly seen in equity index options or other longer-term options. This model seems to occur at times when investors worry about crashes and buy OTM puts as alternatives to stop losses in long positions without drawing down available capital for other uses e.g. posting IM/VM or funding settlement. Another explanation is that money managers prefer writing OTM call over OTM put i.e. covered call strategy is crediting since you are long underlying that pays a dividend. Likewise, if underlying is debiting (i.e. long CL has storage cost, long EURUSD), a covered put is preferred.

Graph showing an example of the Reverse Volatility Skew
As strike price fall, IV increase. As strike price rise, IV fall.

Forward skew (Inverted Smirk) IV values go up at higher strike prices. This is best represented within the commodities market. When supply is tight, businesses would rather pay more to secure supply than to risk supply disruption. For example, if weather reports indicates a heightened possibility of an impending frost, fear of supply disruption will cause businesses to drive up demand for OTM calls for the affected crops. Chart showing an example of the Forward Volatility Skew

IV term structure

Term structure means the IV over time. A growth of a “kink” on a specified expiration date is a result of a high risk event appearing on that date, where market is pricing in more upside and downside risk. A separation of put IV term structure against call IV term structure can reveal the market directional bias. That is, selecting the IV smile for the chosen date where there is a IV is above average against other period, and looking at the skew of that smile. A comparison of the IV term structure against other underlying IV term structure can reveal whether the event risk on that date is contained or widespread beyond that underlying. implied vol term structure.png

Greek FormulasImage result for gamma theta formula

Covered Call Strategy (Bonus Income generation)


Scenario: Post financial release, you intend to continue holding a long underlying (e.g. equity) through the current quarter till the release of the next financial statement. However, referencing the industry and the company’s cash flow seasonality, cash flow had always been depressed in the current quarter. Knowing that this would be a one-off disappointment, and you are willing to endure the expected drawdown, you wish to open a secondary position that leverages on this seasonality as well as your long position. Entering into an agreement to lend your equities to your custodian to allow other of its participants to short sell not only encourage others to act against your favor but is not feasible with your primary strategy as you wish to retain the flexibility of your portfolio.

Selling call options referencing your underlying is a strategy to express your secondary position while retaining your primary position. You have reasons to believe that area around the next key technical level at 105 would have many large sell-stop orders and neither would the IDBs or price makers acting as principals anticipate buy orders towards that key level which requires pre-hedging. To avoid spillage triggers, a slight markup in price above that resistance makes a reliable strike price for the short call. Downsides are, this strike price is a cap on profits from further upside risk, you are opening your long position to be called away should the call owner exercise its right, and you are taking unlimited downside risk from the owner. Upsides are, you are are compensated a premium for taking his risk and this helps generate income while you are in drawdown, notwithstanding that the contracts of calls you can short is limited by your long position quantity (divided by the shares per option).

Selling calls to pre-cover your longs can be part of your primary strategy to call a top. Earning premium makes the long a crediting carry (excluding dividend) that, again, adjusts your long opening price downwards. Say, if your views change along the quarter and you think the market is tipping, instead of generating income while in a drawdown holding for good, you switch to an exit strategy. Now, getting your long called away isn’t a bad thing as you get to sell at a top on top of earning a premium. If strike is 105, your opening price is 100, and premium earned is 5, your return to call would be 105/(100-5) instead of 105/100. If you are right, the top would not stretch to 110 i.e. 110/100 ~= 105/95. Moreover, if dividends are typically paid out before the expiry of the call, there could be mispricing opportunities that is in your favor by moving away from the unadjusted strike price.

Say your long didn’t get called away, instead of drawing down X, you only drawdown X – premium earned. Tantamount to net income, whether income generated parked as an income or as a drawdown buffer, its a credit (+). Its always better to generate income then pay expenses. However, as an average worker can be a millionaire if he works long enough, the difference lies in whether the covered call is consistently executed leveraging on a strategic hold-for-good long position in the underlying. Of course one may argue, if the expectations for its future is so dark, put-call skew will be exaggerated upwards aka negative RR (25 RR = 25 delta call vol – 25 delta put vol) such that the income generated selling consecutive calls will diminish over time and be less able to adequately cover each consecutive drawdown. Worst case, selling a deep ITM call at  100 delta (if there’s a buyer) where premium = 1*(S-K), remains less than the subsequent drawdown. (Would the lowest transacted strike price of a 100 delta call say anything?)

Going with the drift (carry) can be a tactical short term long, whereby its not a secondary position that leverages on your primary position, but a complete primary position (package of 2 legs) in itself. Unless you own a large portfolio, typically you would not endure through a large drawdown. That said, following positive carry is not free money rolling in as what most would say and it requires active management and constant adjustments to the legs. Notably, rolls are not guaranteeed unlike carry which has the nearest leg fixed. Rolls are earned only if the forward curve remains unchanged.

Irregardless covered call is a primary (short or secondary position, avoiding costly adjustments is key. In other words, adjustments is like deferring your primary position losses with secondary positions, and depending on the adjustment, it would cost more (debiting) or generate more income (crediting) to close old or open new positions. To avoid more than unneeded adjustments along the life of the package, a close forecast of where the price would be at the time of expiry (i.e. Vanilla call), deciding the max risk appetite, and knowing the current state of IV term structure and its expected change.

If forecast at expiry is neutral, writing ATM call would generate more income than would a OTM call. However, if forecast at expiry is moderately bullish, writing a slightly OTM call with a closer strike to forecast zone will maximise return, given that a similar ATM call will generate slightly more premium but you lose a larger chunk of the meat. 2018_12_17_23_20_29_Clipboard.pngSince the unlimited downside risk is from the underlying, having a higher risk appetite means affording to take a lower upfront reward/risk ratio, that is, able to accept lower premium which allows them to write calls that are further OTM or of nearer expiry. Typically, they are insensitive to underlying drawdown as they will stick to their primary position e.g. diversified portfolio. Being aggressive allows you to sell further OTM calls which is a stronger bullish stance (underlying move is of 1 delta, OTM premium earned is of <0.5 delta). Here, risk is premium earned might be inadequate to cover underlying drawdown. Or writing nearer expiry consecutively to generate faster income but smaller premium (since shorter duration, theta not necessarily higher except if its ATM). Here, risk is gamma is high and its possible taking a drawdown below breakeven point (S-K). Note, reward is smaller but underlying risk remains unchanged. (Long-term covered call strategy)2018-12-18 00_08_53-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro2018-12-18 00_04_32-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro

Likewise, a lower risk appetite suggests a higher upfront reward/risk ratio. That is, he is more concerned on the premium earned because he is more sensitive to underlying drawdown risk i.e. will not hold underlying long enough to recoup drawdown. He is more focus on the short term direction, and less interested in any long term view. For example, higher IV pricing before the date of (next earliest) call expiry results in higher premiums. Risk is that IV indeed remains high and underlying long will experience a large drawdown more than the premium earned through expiry. That said, forecast takes precedence over favoring calls that pay high premiums, since it only reflects the elevated risk call seller has to take. Writing ATM or ITM calls generates larger premium than OTM calls but leaves no headroom for earning income from underlying appreciation or even a slight bearish stance (sold ITM call). In other words, maximising (upfront) premium earned / (potential) drawdown is tricky because he’s not into income generation from secondary positions but more into speculation that market has mipriced the call option IV above its fair value or expectations on the underlying is above the roof and is near a top i.e. having a speculative view opposite to market pays since by your forecast, call will appear expensive (Short-term covered call strategy)

Ideally, duration of call sold should be not that long (say 45 days) so that theta is higher which generates fast income (up to you to open new shorts) and expiring early gives more flexibility, more time for adjustments to forecast given recent changes which avoids large drawdown in excess of premium earned. Counterintuitively, you seek a balance where underlying price on expiry is above the breakeven point (S-K) but not way above your strike price as that meant that you cap your profit. Worse comes to worst, it mitigates your drawdown.

Adjustments

If your forecast is modified from neutral to moderately bullish or bearish, not mild deviation from neutral, covered call becomes inappropriate and should be liquidated. You exit  a covered call by either A) selling the underlying + buying an equivalent call with the same time to expiry and strike price or B) buying an synthetic equivalent put without change to underlying and written call. This leaves a residual arbitrage position (conversion i.e. S+P-C = PV(strike*option contract size) ) that has very little risk but may require some capital to hold. Latter is for emergency bail out situations where you have to pay the implied time value of money calculated in the conversion package, but you get to postpone liquidating your long underlying or call on that day unfavourably, say due to liquidity and unfavorable market impact. Note that since covered call is synthetically equivalent to selling put, a covered put is to sell put and long cash to buy stock at strike price, if exercised at maturity. Difference between covered call and covered put is that you do not hold a long underlying position, hence maximum profit is the premium received, maximum risk is the (strike price – underlying price at expiry + premium received), breakeven when underlying is at strike price – premium received. That said, from a writer perspective, if IV is higher, premium have to be higher to compensate the higher perceived risk from writing insurance.

Say if you are selling OTM calls as secondary positions in a long term strategy, and the underlying price moves up through the sold call strike. Before expiry, to assume that your original underlying will be called away in order to justify doubling your underlying exposure is way risky as nothing is fixed. Yet you also wouldn’t want to cap further upside ‘potential’ profit at the strike. That said, the short call has to be “rolled up” to a higher strike to renew the covered call position with more upside potential. Buying a vertical bull call spread that buyback an equivalent (same strike price and expiry) call sold and, again, sell a call at a higher strike this time with the same duration to expiry.

This adjustment might incur cost, especially so when the underlying had already move up a big magnitude through the strike, resulting in the buyback as an ITM call which is more valuable compared to the time when you sold it as a OTM call. The new call that is sold will be OTM to give more upside potential to the adjusted covered call, and premium earned might not be able to cover the extra cost to buyback an equivalent call that became more valuable. That said, “roll” up is a debiting roll, although one would have earned the return of call. Touch wood, the least favorable scenario would be a drastic change of forecast of bullish to bearish after the adjustments are made.

Alternatively, you have the choice to buy a vertical bull call spread, where the bought call (lower of 2) strike can be higher than the initial covered call strike. This “roll” will cost less as the bought call is less ITM or even OTM than if you were to cover the original call sold. However, for more cost savings, you give up some upside given the gap in strikes, while making your vertical bull call spread forecast more OTM and more bullish. In this case, only the call (of lower strike) bought in the vertical bull call spread should expire the same time as the call sold. This is not an adjustment to a covered call but to extend it with another strategy, a vertical bull call spread.

In order to give more time for the more bullish forecast to materialise, typically the call (of higher strike) sold expires in a further deferred expiration month. This is a diagonal bull call spread known as up and out i.e. up (in strike) out (further in expiration). Besides extending the duration of the covered call strategy, it helps to reduce the “roll” cost since a call with a longer lifespan worth more hence more premium earned on its writing.

Vice versa, if the underlying weakens further and more downside protection is desired besides the premium earned from writing a call, we either “roll” down the strike by selling a vertical bull call spread in the same expiration month, or by selling a diagonal bull call spread known as a down and out. In this case, since buying back an equivalent call sold previously becomes cheaper than the premium earned when it was written because its further OTM, “roll” down is a crediting roll. This increasing income generation will provide further downside protection. Again, the trade off for generating more income by selling a ITM call with further downside protection would cap any price appreciation in the underlying. Writing another call that is more OTM may not be worthwhile if its value will not get any lower for buyback when underlying prices goes down further. A give and take depending on your updated forecast range i.e. if a more bearish outlook is expected, should prioritise income generation (ITM) over a higher cap to capture more price appreciation (OTM).

For crediting roll, a favorable scenario would be a falling IV term structure since it is cheaper to buyback the call sold at an elevated IV. Note that in a typical IV skewed curve, ATM options have lower IV than OTM. A favorable IV shape over strike price is a forward skew. Writing OTM call generates more income for downside protection on top of giving further upside potential and return to call. Ironically, underlying that is crediting over time are crowded with covered call strategy, resulting in reverse skew.

That said, covered call are not “fire-and-forget” trades after earning the premium for writing a call. Adjustments are needed to maintain one’s risk profile as the underlying moves up or down. Less adjustments are needed if the underlying is moving as accordingly to your initial forecast. Here, sideways movement is the best scenario as theta is positive and on expiry, only adjustment would be rewriting a call on an updated forecast. A more timely revision to forecast and an earlier adjustment ensures a more consistent risk profile of the covered call strategy. Suppose you are rolling down the strike, adjusting earlier will generate more credit on the roll than if the adjustment was done later i.e. when call sold becomes more OTM and insensitive to further downside move, and the next call sold will be OTM than if was sold earlier ATM.

Vertical spreads (Limited risk directional strategy)


Directional strategies are designed to:

  • capture a limited-risk bullish or bearish position (unless you expect the price to go INFINITY or ZERO) why? ratio of C:P is 1:1, since only difference is in the strikes,  unlimited risk and return are balanced out
  • reduce capital requirements especially when IV are high and outright purchase of call and put is too expensive
  • combine directional view with IV view
  • generate income

While one can execute a bull call or put vertical spread to express a bullish bias, the payoff is slightly different.

Both buy option with a lower strike, sell option with a higher strike. That is, at higher strike, puts are more valuable than call, hence bull put are crediting whereas bull call are debiting. By default, put vertical spread refer to bear put vertical spread (debiting) and call vertical spread refer to bull call vertical spread (debiting). That said, breakeven price for bull call is lower strike + debit, bull put is higher strike – credit. Why? The upward payoff slope detaches (floor loss) from the long call at the lower strike and detaches (cap profit) from the short put of higher strike. The attachment point is where both options payoff offset (depends on the difference between strikes). That said, maximum loss for a bull call is the debit amount since it detaches at the lower strike call, for bull put is the differences between strikes – credit since its settles by offsetting payoff. Vice versa, maximum profit for bull call is the differences between strikes – debit since its settles by offsetting payoff, for bull put is the credit amount since its attach to the higher strike put.

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  • Detachment means the long option is flooring further loss and both options are OTM e.g. underlying is above both put strikes in a bear put / underlying is below both strikes in a bull call, and capping is achieved from the initial premium differences.
  • Settles by offsetting payoff (Attachment) means both option are ITM e.g. underlying is above both call strikes in a bull call / underlying is below both put strikes in bull put, and capping is achieve when both holder of call of lower strike and writer of call of higher strike exercise and net their payoff.
  • Note: shorting (reversing the legs cash flow) a bull call spread (short nearer the money, long further away from money call) does not change the fact that detachment is always when underlying is higher than both strikes, since they remain as call options!

Using the same principles, for bear call/put vertical spread (sell the lower strike, buy the higher strike)

  • Bear call (crediting) vs Bear put (debiting)
  • Breakeven: Bear call (higher strike – credit) vs Bear put (lower strike + debit)
  • Max loss: Bear call (strikes range – credit) vs Bear put (debit)
  • Max profit: Bear call (credit) vs Bear put (strikes range – debit)

Note: Bull buys the lower strike sells the higher strike (like closing the range), bear sells the lower strike buys the higher strike (like widening the range). So short bull call vertical spread (debit) == long bear call vertical spread (credit) i.e cash flow of payoff is reversed. Later, you see why max profit of bear call (or bull put) is capped at credit, since its equivalent to writing a bull call (bear put).

Greeks of Bull Call to Bull Put (or Bear Call to Bear Put) are equivalent. Note, only delta is affected by the directional risk profile of a long and short option, other greeks like gamma, vega, theta is are independent from direction. That is where P/L is made for directionless markets.

delta(Bull Vertical Spread) = delta(lower strike) – delta(higher strike)

Delta range  between 0 to 1 and always return to 0 at extreme deviation of strikes from underlying price to reflect the limited risk profile. Delta >0 because it is long the call of lower strike (ITM) and short the call of higher strike (OTM). Vice versa, bull put spread are equivalent since it is long the put of lower strike (OTM) is closer to 0 and short the put of higher strike (ITM) closer to -1. Shorter time to expiry means more sensitive to moneyness.

gamma(Bull Vertical Spread) = gamma(lower strike) + gamma(higher strike)

Rate of change of delta (gamma) is steepest when strike moves from ATM to ITM/OTM, that is, around the strikes, and this gamma sensitivity is amplified for shorter time to expiry. Note gamma is same for Put or Call since their delta is both sloping upwards, just than put is in the range of -1 to 0. In the case of bull vertical spreads, lower strike option will generate positive gamma, higher strike will generate negative gamma. Why? Cause option with the higher strike is shorted, resulting in positive theta, negative gamma (Refer to Greek formulas under Recap section). Vice versa for lower strike. Since ATM options have a higher gamma than ITM/OTM options, gamma peaks (+) when underlying is near the lower strike long option, and troughs (-) when underlying is near the higher strike long option. Likewise to delta, gamma goes to 0 at extreme moneyness, in or out, to reflect limited risk profile.

vega(Bull Vertical Spread) = vega(lower strike) + vega(higher strike)

Since a long option position floors your risk profile, it generates a positive vega i.e. more sensitive to changes in IV. Hence for a bull vertical spread, lower strike option generate positive vega, higher strike option generate negative vega. Since volatility can represent the risk to either upside or downside, vega is symmetrical for both OTM(ITM) call and ITM(OTM) put. That said, an ITM put will have a smaller vega similar to a OTM call of the same strike price. Since ATM options have a higher vega than ITM/OTM options, it have the same peak-trough behaviour as gamma profile. Likewise, since risk profile is 0 at extremes, vega converge to 0. How fast vega converge to 0 depends on its time to expiry. The further away from expiration, the less sensitive vega is to moneyness.

theta(Bull Vertical Spread) = theta(lower strike) + theta(higher strike)

Since writing an option generates upfront credit when the option holder buys from the writer, the floored risk profile in options is supported by the writer who will take unlimited risk. That said, theta will be positive for a option written until the option expires worthless and the writer no longer needs to support the unlimited risk. Theta (sensitivity to the passage of time) unit of measurement is per day, hence moving further away from expiration decreases the sensitivity of theta to moneyness as its averaged over more days. By put-call parity, since value is identical for the same strike and same expiry, theoretically, theta (as option value / days) will be the same. That is, for K=110 when S=100, an ITM put(110) has the same theta as an OTM call(110). Likewise, since bull vertical spread longs the option of lower strike, theta will be most negative when underlying is near the lower strike because theta is largest when it’s ATM.

Image result for theta options
Theta is largest when option is near to expiry and ATM

For bear vertical spreads, the greeks risk profile will be similar except that since the legs are inverse i.e. long the higher strike and short the lower strike. That said, the inverse will happen for theta, gamma, vega gamma, delta profile i.e. the troughs and peaks near the lower or higher strike.

Going through the 1st and 2nd order greeks, we prove that a bull spread, call or put, is synthetically equivalent. Preference over one would depend on the pricing (debit/credit) at the point of execution, as well as whether you desire greater profit potential to be generated by the underlying movement or limited credit that caps your profit potential, vice versa, for limiting the loss to debit.

When should you use a vertical spread?

  • When upside and downside is limited by support or resistance, and you are forecasting a targeted range at a defined period. Or you are expecting a rebound or correction (counter trend with stop loss) as the market position is over crowded, and wish to take a contrarian trade against the trend but also limit your risk if the trend remains strong.
  • When IV is high and outright options purchase are expensive, and when holding the underlying will give excessive delta (delta=1 directional risk) where IV may materialise. To reduce cost of postion, a trade off, you will cap your potential profit by writing another option that limits your delta (directional) and vega (IV) exposure.
  • If you think IV is going to change over the duration till expiry, you can combine your IV view with directional view. Since a long option has a long vega and vega is most positive when underlying is at strike price of long option,
    • Say, if you are bullish with a forecast from 75 now to 85 in 3m, but also expect IV to fall to expiry, you would want the short option leg (higher strike in bull spread) to be at 85, where vega is most negative in a bull spread when underlying is at the higher strike of the shorted option. That is, buy 75/85 call spread or sell 75/85 put spread.

      2018-12-31 21_44_01-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro.png
      Bull Spread Vega
    • Say if you are bearish with a forecast of 40 to 35 in 3m, and expect IV to rise to expiry, you would want the long option leg (higher strike in a bear spread) to be at 40, where vega is most positive in a bear spread when underlying in at the higher strike of the long option. However, since vertical spreads favor a falling IV given the limited risk profile, higher strikes 37.5/42.5 vertical spread would position for a rising IV.

      2018-12-31 22_04_16-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro.png
      Bear Spread Vega
  • Selling OTM vertical spreads that are crediting (synthetic equivalents)
    1. -[+1 -1] short bull call == [-1 +1] long bear call. Both are crediting with a profit capped at the premium earned on writing. That explains why max profit of a bear call is cap since its like writing a bull call!
    2. short bear put = long bull put. Likewise, that explains why max profit of a bull put is cap since its like writing a bear put!
    3. (Opposite to 1) short bear call = long bull call. The max loss of a long bull call is the debit since its floored by the lower strike call, vice versa, its the max profit of a short bear call, that is, the credit from selling a nearer the money call while buying an OTM call.
  • To generate income (theta) by selling vertical spreads that generate credit.
    • Say price gap down from 10 to 13 and you believe 10 will be a strong support in the next 3m. Do you write a bull or bear spread? How does 10 comes into the legging? Since theta is positive for written option and is negative when underlying arrive at strike of the long option, you sell (bear) put spread (initiate crediting bull put spread) with the higher strike at support 10. This is equivalent to a long bull spread, where you are short option with strike 10 so that as underlying is approaching support, you will first receive theta before paying theta if it does break below support to lower strike. Note that since the lower and higher strikes are below underlying, both puts are OTM and we are selling OTM options to generate income (sell OTM puts to generate income from support). Why not sell (bull) call spreads aka bear call spreads since calls are both ITM and hence generating more credit? Because, since theta has a same upward sloping structure as payoff, at higher strike 10, you will have to pay theta first before generating theta. It thus balance out in that while you earn more credit selling bear call spread, you have to pay theta if underlying approaches the higher strike.

      2018-12-31 22_32_08-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro.png
      Bull Spread Theta (Upward sloping, similar to payoff)
    • Say price gap down from 20 to 18 and you believe 20 will be a strong resistance in the next 3m. Similarly, you sell (bull) call spread (initiate crediting bear call spread) with lower strike at 20. This is equivalent to a bear call spread, where you are short option with strike 20 so that as underlying approaches 20, you will first receive theta before paying theta if it does break above resistance to higher strike. 

      2018-12-31 23_04_11-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro.png
      Bear Spread Theta (Downward sloping, similar to payoff)
    • In general, the support or resistance pivot will be the strike of the option you sell to receive theta if it approaches the pivot. If its a resistance, you sell OTM call spread, while if its a support, you sell OTM put spread.

Put or call spread?

That said, note that in the above, for income generation, I kept translating a written bear spread as equivalent to long bull spread. I tried to avoid using put or call when referring to spreads, while keeping them simple as either bull or spread spread. But when should we favor call over put in a bull or bear spread? Does that fact that bull put is always superior over bull call since it generates a credit that can earn interest, while debit doesn’t’? Remember that option pricing model, such as Black-Scholes or binomial tree backwards derivation model does take into account discounting the time value of money, that is, option prices are discounted to compensate for the cost of financing the position (debiting spreads), and the buyer will pay slightly pass premium to compensate his debit balance, while the seller of the option will receive less premium correspondingly given that he can receive interest on his credit balance. Think FVA (Financing value Adjustment). This discounting of option price tends to remove any advantage associated with a credit vs a debit trade of synthetically equivalent positions. 

To illustrate this, consider a box spread market-neutral structure that compose a bull call vertical spread and a bear put vertical spread (same strikes, same expiration), where both are debiting and synthetically equivalent positions to separate out the interest rate component that accounts for the difference in pricing between a bull call spread and a bull put spread. This is similar to a long jelly roll which explains the difference in the pricing between call and put time spread. Market neutral means no delta, no gamma, no vega, no theta.

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Long box spread = bull call spread – bull put spread (Both are debiting and synthetically equivalent) = bull call spread + bear put spread

Image result for box spread options payoff

At expiration, the maturity value of a box spread is the difference in higher and lower strikes (K2 – K1). Image result for box spread options payoff

Any time before expiration, box spread will trade at a discounted PV to compensate for carrying costs. 2018-12-31 00_24_53-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro.png

  1. Bull call value (debit) + Bear put value (debit) = box spread value (credit at maturity). Relative advantage available if this equation does not balance.
  2. Bull call debit – PV(Box) = Bull put credit
  3. (-2) Bear call credit + PV(Box) =  Bear put debit

(2) shows that bull put credit < bull call debit. (3) shows that bear call credit < bear put debit. That is, difference in put or call is explained by PV(Box).

Referring to the detachment points where both options become OTM, for a bull spread, its the long (market order at ask) call of lower strike in bull call spread vs. the short (market order at bid) put of higher strike in bull put spread. That said, we compare the sum of these detachment points (call ask + put bid) against the box spread value. Likewise, for bear spread, focus points are call bid + put ask.

Say, 50/55 box is 4.95, (bull) call spread 2.5 bid – 2.6 ask, (bear) put spread 2.45 bid – 2.55 ask. By default, call spread is bull spread, put spread is bear spread.

Since put spread bid + call spread ask = 5.05 is more expensive than box value = 4.95, we sell (bear) put spread aka bull put spread.

  • Bull Spread Rules
    • If call spread ask + put spread bid > PV(Box), sell put spread
    • If call spread ask + put spread bid < PV(Box), buy call spread
  • Bear Spread Rules
    • If call spread bid + put spread ask > PV(Box), sell call spread
    • If call spread bid + put spread ask < PV(Box), buy put spread

While vertical spreads are lower cost and have limited risk, it is still good to have a plan on how to manage and adjust the positions if forecast if correct or incorrect.

  • Most efficient way to take P/L? Cost and Liqudity factors to decide.
  • What to do if underlying reaches target range ahead of schedule? What to do if underestimated the magnitude of the move? Roll the strikes… 
  • What to do if completely wrong on forecast direction? Exit! Unlike covered call strategy that needs long term execution consistency, “rolling” the strike against forecast direction to not admit your mistake is not recommended. 
  • What to do if other non-directional forecast like IV turn out incorrect?

“One mistake that is consistently made by options traders is staying too long in a position or making too many modifications when their market view changes from the initial forecast. The simplest and most effective rule in risk management is this: If the trader is wrong, he should get out! This means that if any of the assumptions that went into a market forecast turn out to be wrong, the investor should get out of the position. There is no room for hoping or praying!

Exit strategy is either to liquidate using the original position or net with a synthetic equivalent. Cost and liquidity are factors to consider when choosing either.

Say if its a bull call spread and its ITM at its attachment point, that is, for individual calls of both strikes, they are ITM. That said, market makers typically widen their bid-ask spread of ITM options to compensate for a larger hedging risk, since as options move ITM, they acquire a larger delta and is more sensitive to underlying. This behaviour will pass on to a wider bid-ask spread for the (bull) call spread since its individual legs are ITM. Wider bid-ask spread reflects a lower liquidity. Vice versa, OTM options acquire a lower delta and poses less hedging risk to market makers which result in narrower bid-ask spreads for each individual OTM legs in a vertical spread i.e. if a bull spread at maximum profit (credit) was a put. And this pass on to a narrower bid-ask spread on a vertical spread at detachment point where both legs are OTM. That said, a vertical spread at attachment point comprising of ITM options will have a wider bid-ask spread than a vertical spread at detachment point comprising of OTM options. This moneyness effect, especially on deep ITM options, on market maker quoting behaviour make a strong case to favor using synthetically equivalent positions to exit a vertical spread, since an ITM (bull) call spread has a synthetically equivalent OTM (bear) put spread, and an ITM (bear) put spread has a synthetically equivalent OTM (bull) call spread. Likewise, a bear call spread at maximum profit at detachment point where both calls are OTM will favor buying a (bull) call spread since its more liquid with a narrower bid-ask spread. Do note that exiting with a synthetically equivalent results in a residual box spread position.

That said, you can use the box spread rules to determine which is more cost efficient to liquidate the position. In the scenario of liquidating the bear call spread, if market quotes are showing call spread bid + put spread ask > PV(Box), that is, bull call spread (is more expensive than) > bull put spread, then it follows that it is cheaper to sell put spreads (initiating a bull put spread) over buying an OTM (bull) call spread, although moneyness effect may suggest otherwise. market quotes suggest that using a synthetically equivalent to liquidate and hold a residual box spread is cheaper.

Say if the forecast direction is still on track but the magnitude of the move is underestimated, the trader would adjust and roll the strike further towards the forecast direction to continue participating in further price movement of the underlying. Note that you need a vertical spread (2 legs) to roll a covered call (1 leg).  Here we need a butterfly (3 legs) to roll a vertical spread (2 legs). As illustrated below, what it actually does is liquidate the original positions and then initiating a new vertical spread where the lower strike becomes the higher strike (rolling down), vice versa. That is, such adjustment is expensive as it requires initiating 4 times the number of options. Again, the liquidation process is same as the exit strategy where a synthetically equivalent spread can be used to liquidate the original position, and the choice of whether to use call or put spread to roll the spread further in forecast direction depends on the box spread value and liquidity. 2018-12-31 23_50_45-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro2018-12-31 23_50_30-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro

Collars and Risk-Reversals (Equidistant OTM options)


An unhedged collar is quite similar to bull vertical spreads where you buy the option of lower strike, sell the option of higher strike, both of the same expiration cycle, except that the lower strike option is a put and the higher strike is a call. That said, if underlying is in between both strikes, both put and call are OTM. An unhedged collar is a bearish spread where, unlike bear vertical spreads that limits the risk at extreme upside and downside risk, it limits the risk around the underlying price and has unlimited risk. Breakeven are put (lower) strike – credit or call (higher) strike + debit.

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Unhedged Collar (bearish)

Typically, unhedged collars are structured so that the total cost of the spread is near zero. That is, the two options are approximately (ideally) equidistant from current underlying price so that they carry approximately the same premium. However, factors such as a backwardation forward curve (equity dividends, positive FX swap rate) will favor calls over put as strikes are adjusted lower corresponding to the underlying, or a reverse IV skew that results in OTM put being more expensive than equidistant OTM call.

Likewise, an unhedged reverse-collar is quite similar to a bear vertical spread, except it sell a lower strike OTM put and buy a higher strike OTM call, resulting in a bullish spread.

Its popularity over simply outright buying or selling the underlying or one option is because:

  1. it’s structured to minimise the IV risk and time decay risk so that the timing of a forecast bullish or bearish move need not be precise (Later, netting of greeks will explain why)
  2. they can be used to address any anomalies in the existing structure of IV at the time of the trade i.e. when IV is unusually high against its historical benchmark or is exhibiting an extreme “smirk” defying put-call parity
  3. wrapping a (bearish) collar around an existing long underlying position will transform the risk/reward payoff into that of a limited risk (synthetic) bull vertical spread. Vice versa, wrapping a (bullish) reverse-collar around an existing short underlying position transforms it into a limited risk (bullish) (synthetic) bear vertical spread. This allows traders to modify their outright long and short positions as market conditions evolve, modifying from unlimited risk/reward to limited risk/reward profile with little cost. This happens because of synthetic equivalence i.e. S + P = C +PV(strike) of cash.

    2019-01-01 16_57_09-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro
    Wrapping a Collar around a long underlying position = Bull Call Vertical Spread
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Wrapping a Reverse-Collar around a short underlying position = Bear Call Vertical Spread

Greeks of collar and reverse-collar spreads

On the far downside, a collar becomes a long put as the call sold expires worthless. On the far upside, a collar becomes a short call as the put bought expires worthless. However, the behaviour of the Greeks in between the strikes, ranges of IV or over time is interesting.

The dreaded “double whammy” of poor timing is that an outright long option position is subject to negative time decay and a positive IV risk and if the trader is off on his timing for the forecast move to happen, or if underlying slips into a consolidation where IV falls before the move, it costs money as each day pass and the option loses value on a lowered IV. That said, comparing against vertical spreads that consist of 2 legs of either both calls or both puts, the benefit of using a put and a call is that the either one can be sold to offset time decay (since short option generates positive theta) and offset IV risk (since short option has negative vega) so that you can stay with the position longer without a “double whammy” as he waits for the forecast directional move to occur. In other words, selling a put instead of a call in a reverse collar allows you to capture the upside risk with the long call as the delta of a short put is positive rather than negative (if short call), while the other greeks (theta, vega) remains unchanged for a short option. So if you are forecasting a strong upside directional movement in the underlying, but concerned that timing may be off and do not wish to incur paying the cost of an outright call option, you will still long a call at a higher strike (resistance where breakout occurs) but also, sell a put at an equidistant lower strike to mitigate the cost of buying an option and an off timing issue. That said, for this to work, you should also be confident that the underlying will never go below the (lower) put strike (support) of the reverse-collar such that the writing the option is only to your favor. Likewise, buyer of a collar should be expecting a strong downside directional movement below the (lower) put strike.

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Forecast suitable for reverse-collar

Since underlying only has delta=1 and no other greeks, a hedged position (long underlying + collar) will have a delta that peaks at 50 delta (-50 delta if unhedged) when underlying is in between strike, and fall to 0 delta (-100 delta if unhedged) when price moves below the lower strike or above the higher strike such that one option leg becomes ITM with one delta. Sensitivity to underlying is soften if there is a greater time to expiration. Resulting delta profile is similar to a bull vertical spread.

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Collar hedged long underlying delta profile (Same as bull vertical spread)

An ATM option with a longer time left to expiration will have a higher gamma. Gamma is same for call and put, but positive for a long option (inverse to negative theta) since delta converges faster to 100 delta when option is increasingly ITM. Gamma profile is similar to bull vertical spread where since its a long (put) option at lower strike and short (call) option at higher strike. That is, gamma peaks at lower strike, troughs at higher strike (since short option and highest when ATM). Same profile for vega since a long option have positive gamma and positive vega, while inverse profile for theta. Vice versa for a reverse-collar, where greek profiles are similar to a bear vertical spread since its a short (put) option at lower strike and long (call) option at higher strike.

Below figures are the greeks profile. Darker line is least time to expiration.

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Collar hedged long underlying gamma (same as bull vertical spread gamma)
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Collar vega hedged long underlying (same as bull vertical spread vega)
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Collar theta hedged long underlying (same as bull vertical spread theta)

When should you use a (reverse) collar?

  • When you are expecting a large directional move but is unsure of the exact timing for the big move to occur.
  • When there is clear support and resistance (pivot) levels to trigger the strategy. That is, to sell an OTM put at support and buy an OTM call at resistance when you expect a large upside move when it breaks resistance (or buy an OTM put at support, sell an OTM call at resistance when you expect a large downside move when it breaks support)
  • When (reverse) collar are structured to allow some sloppiness in timing, the chosen expiration for construction of the (reverse) collar needs to have enough time with a couple of extra weeks to cover the time horizon when the big move would be taking place. Say on historical average, the longest consolidation takes around 15 business days and existing options are expiring in 28 and 60 calendar days, you would need the additional margin of error and favor structuring with the 60 calendar days options.
  • Base level of IV is high and outright purchase of options are expensive. Here, base level refers to current ATM options IV against its historical benchmark of ATM options IV. If base IV is expensive compared to its history, collars are preferred for their smaller net vega and theta exposure and lower netted cost of positioning. Vice versa, if base IV is cheap, an outright long call favored over reverse-collar or long put over collar.
  • Besides base level of IV (of ATM options), since collar involve OTM options, abnormal IV skew against strike price will favor collar strategies over outright purchase of option. For instance, when the IV reverse skew is unusually extreme, and you are expecting a large upside move, you would prefer a reverse collar that buys a cheap OTM call while selling an expensive OTM put, over buying an ATM or OTM call outright, since you can generate upfront credit. Vice versa, if IV forward skew is unusually flat, where for higher strikes IV is higher too, if you are expecting a large downside move, you will favor a collar that buys a cheap OTM put while selling an expensive OTM call over purchasing an outright put. Remember that since reverse skew happens when downside risk is of more paramount concern, that said, for this preference to play out, you are positioning as a contrarian. Not only would you earn a credit for initiating this contrarian position, you would earn more than just from the directional move because the IV skew may, while not necessarily always the case, invert to its norms and the option you bought cheap would be more valuable when its IV increases. Say you bought a 50/60 reverse-collar and the underlying had moved up from 55 to 65, the put sold at strike 50 becomes worthless, the call bought at 60 becomes ITM. Preference for buying OTM put as protection on their long underlying falter or remain unchanged, nevertheless, the supply of ITM call would falter while demand picks up as covered call writers would either roll up their strike and buy back the calls they sold around 60. This would result in pricier or higher IV calls(60).

Note that Risk Reversal is a reverse-collar (short OTM put, long OTM call), and RR quotes are σ(25-delta call) – σ(25-delta put. 25-delta put means a put option that has -0.25 delta. That is, a positive 25-delta RR implies a reverse volatility skew and greater demand for OTM put or more supply for OTM call i.e. risk is to the downside. It is cheaper to long a reverse-collar when 25-delta RR is negative and if you think that the reverse volatility skew is overly extreme and would revert to a less skewed smile. In other words, if the market is overly concerned of a downside risk, the risk is then reversed to the upside, since upside is unlimited and the downside or the cost of OTM calls is diminished, resulting in a higher return-to-risk favoring the upside. Vice versa, a positive 25-delta RR favors a long collar position.

What if the open ended risk from the option sold materialise when the strong pivot levels you position yourself fail to hold? You would need stop-loss orders to mitigate the unlimited risk of the short option leg. Trade management for hedging (wrapping collar on underlying position) and directional strategy (collar only) are of different motivation and should be handled differently. 

Directional Strategy Trade Management

When the collar strategy is successful, you actively manage the long option component (directional strategy) to squeeze the maximum profit out. while closing out the residual risky short option component that is now further OTM. Rolling the long option position that is “going your way” allows you to maintain the exposure in the direction of the breakout to profit from further movement, while taking money off the table. Options have a asymmetrical floored payoff and that means profit taken off the table is taken off. Only downside is the execution cost to sell the vertical spread in order to lock in profit but in return, gives you more holding power.

Say you are bearish with a collar and the long put is ITM. Underlying broke below support (put strike). You roll down the ITM long put strike by selling a (bear) pull vertical spread with the higher strike at the long put (lower) strike. Close residual open ended risky short call given its further OTM. For example, if you think 95 is the next support level where price will consolidate before the next breakdown, 95 will be the lower strike of the put vertical spread.

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Collar Rolling Points in a breakdown
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Collar Put Roll

Say you are bullish with a reverse collar and the long call is ITM. You roll up the ITM long call strike by selling a (bull) call vertical spread with the lower strike at the long call (higher) strike. Close residual open ended risky short put given its further OTM. For example, if you think 100 is the next resistance level where price will consolidate before the next breakout, 100 will be the higher strike of the call vertical spread.

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Reverse-Collar Rolling Points in a breakout
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Reverse=Collar Call Roll

When the collar strategy is unsuccessful, you actively manage the short option component (hedge). Typically, such risk management is done before entering the trade. You would place a stop order right below the key support (put strike in a reverse collar) or right above the key resistance (call strike in a collar). This level is an additional stop to reduce your open ended risk in the event that your forecast direction turn out wrong. In the event of holidays occuring before expiration of strategy, if there are major news on the day of the holiday, gapping through stop loss level mean that stop orders are not executed. Depending on whether if there is any value left for the long option, you can either hold it as a lottery ticket or close it to salvage any value remaining.

Say you hold a 100/105 collar and underlying does not breakdown below 100 by expiration. If you think you need more time for the breakdown to happen and wish to roll the collar into a further expiration cycle, you will close the original collar legs along with reopening a collar with a further expiration by buying the 100 put calendar spread (long calendar spread = long further expiration + short nearer expiration) and selling 105 call calendar spread. Vice versa, to extend more time to a reverse collar, you would want the further expiration legs of the calendar spreads to be long call, short put, where put is always of the lower strike. That is, sell put calendar spread of lower strike, buy call calendar spread of higher strike.

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Example: Extending a collar strategy

Hedging Strategy Trade Management

Since wrapping a collar around a long underlying transforms position into a synthetic bull call vertical spread, it also needs management as underlying price changes. The collar (lower) put strike will be the lower strike of the call vertical spread. That said, if underlying is near 100, a key resistance, and you think underlying will correct to 92.5, you will buy a 92.5/100 collar to transform it into a 92.5/100 bull vertical spread. When underlying falls to 92.5, you would unwind the collar near support. That is, the put bought at 92.5 become more valuable since it is nearer the money now, and  the call sold at 100 become further OTM for you to buyback. Yes, it is counterintuitive against the expectation of a breakdown below collar put strike since you are long the underlying, and it transforms the position into a bull vertical near the higher strike, and liquidates the collar to transform back to underlying only when it falls near the lower strike – that is, counterintuitively being bullish near the resistance and capping further upside at resistance so as to earn more credit.

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Hedging a long position with a collar

Vice versa, you wrap a reverse-collar around a short underlying transforms position into a synthetic bear call vertical spread when underlying is near its support and unwinding the reverse-collar when underlying rebounds back to resistance – that is, sell a put with strike at support, buy a call at resistance, then closing these options at a better valuation when underlying rebound. To simplify, since a collar structure is bearish, you buy collar when underlying tops and sell the collar when underlying falls, or you sell collar (bullish) when underlying bottoms and buyback the collar when underlying rises. That is, it sells nearer the money synthetic call vertical spread, then buys them back when vertical is further from the money. The counterintuitive part is that collar is initiated when collar is close to being OTM and unwind before collar becomes ITM. 

Straddles and Strangles (Non-Directional, Large Magnitude Strategies)


Long straddles or strangles are used when the trader is forecasting a large magnitude move in the underlying in either direction (intrinsic value of options moving ITM due to a change in underlying price) or an overall increase in IV base levels (rise in extrinsic value of options bought). Vice versa, short straddles or strangles are used when the trader is forecasting little to no directional movement in the underlying and seeks to profit from a decrease in the overall value of the position due to time decay or falling IV which will lead to a decline in extrinsic value of options sold.

Long strangle is a 2 leg spread that simultaneously buys both a call and a put at the same strike price, typically both at 50 delta (ATM) since the trader does not have a clue on the direction. If both expires in March and strike at 80, its a “long March 80 straddle”. Maximum loss is fixed on execution and it’s the debit to buy both call and put. Maximum profit is unlimited to the upside with a symmetrical payoff that results in profit regardless of direction. That said, there are 2 breakeven points at either put strike – max loss, or call strike + max loss.

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Long Straddle P/L diagram

Long strangle is a 2 leg spread that simultaneously buy a call and a put but of different strikes, where typically, both are OTM and equidistant from current underlying price since the trader wants to be delta neutral e.g. delta 25. Strangle is preferred over straddle sometimes to be cheaper to execute since ATM options are way expensive to initiate the straddle i.e. both strategies are delta neutral, but straddle at delta 50 has highest gamma, vega, most negative theta. For example, if current underlying is 1000, it could be a “long March 950/1050 strangle”. Payoff structure is similar to a straddle, except that its maximum loss or upfront debit to initiate the strategy is cheaper, but it has a larger range where it does not breakeven since put strike is lower, call strike is higher.

Vice versa, since payoff is symmetrical, for the writers who simultaneously write these options, will inherit the maximum loss of buyers as maximum profit (credit for taking his bi-directional risk) while taking unlimited maximum loss (floored at underlying price at 0 if its not a derivative). Breakeven price range is the same as it inherits as a counterparty to the buyer.

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Short Strangle P/L diagram

Why straddle at the same strike or strangle at strikes equidistant from the delta 50? So that the call would be +0.5 or +0.25 and put be -0.5 and -0.25 respectively, so that the structure delta would negate to delta=0 (delta neutral). Delta ranges from -100 to 100 with a higher gamma (steeper delta slope) between breakeven prices and highest (positive) gamma when at strike. Similar with all options, with more time to expiration, the sensitivity of greeks over strikes will be smooth out over time as more possibilities could happen. Likewise, buying 2x options will have 2x negative theta given the 2x debit paid on initiating and theta is most negative when underlying is at the strike. That’s the price to pay to be positioned long when the market goes up, and short when the market goes down. With 2 OTM strikes, strangles have slightly different greek profiles than straddle, where their delta is flatter between strikes, corresponding to a dip in gamma between strikes, gamma and vega peaks at each options’ strike (troughs for theta), and this greek profile is accentuated for short time to expiry. Vice versa, selling these strategies will have a direct opposite greeks profile.

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Long Strangle (long C+P with OTM strikes) – Delta flat between strikes
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Long Strangle (long C+P with OTM strikes) – Theta troughs at C and P strikes

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Long Strangle – Vega is much higher and less accentuated at OTM strikes with longer days to expiration

Since straddles and strangles are spreads that capitalize on large movement (or lack thereof for writers) in the underlying stock or index, volatility is key to the success or failure of these strategies. That is, these strategies have large positive vega (or negative if writing these strategies). Remember that vega is very sensitive to time until expiration of the options and vega is greater when there is more time to expiration. If the structure has a vega = +0.33 means the price of the structure increases by ~0.33 for every 1% rise in IV. Here, IV are in annualised terms like VIX.

However, given the fact that if it has became a common knowledge to the market that on a specific day, there is a large binary outcome event that will affect the underlying price in a large magnitude in either direction, and market is not pricing any baseline scenario into the underlying to a large extend going into the event, then the base IV on that day for both calls and puts will be elevated to an abnormal level, resulting in a “kink” at the future specified date in the IV term structure. That said, how early the kink appears at the event depends on the market coverage on the issue and the experience of the market to come out with a baseline scenario for the event. If it’s a sudden binary risk event that pops out such as a Brexit election date being announced, and market have no experience in handling the outcome, and if the market thinks the event is firm and will proceed as planned, the IV kink will start rising correspondingly from the date of announcement till a point where the cost of options far outweigh the possible magnitude of the move against their positions. Of course, strangles are sought after as cheaper alternatives to straddles when the base IV is elevated, resulting in higher IV across strikes. And since calendar spreads is an alternative strategy to trade a rising IV view around a specified period, the IV surrounding the specified date will rise accordingly, resulting in a smoother kink in the term structure.

While the pivot level (strikes) for a future risk event need not be the current underlying strike price since going into the event, unforeseen circumstances would cause the flexible market to favor a particular direction, it does affect your cost of initiating the strategy since if strike is not delta-neutral, that is, one option has to be ITM and such that you would be ITM on entry, and that would add to the cost of initiation. That said, you are paying ITM option premium to be ITM on entry, but you are positioning yourself to make more profit only if your delta bias on initiation is correct, otherwise, your profit could be returned to less than the cost of initiation and be unable to breakeven. Why start climbing from the middle of a mountain when you can start from ground and have the flexibility of choosing which mountains i.e. long when underlying appreciates, short when underlying depreciates in value? If you have a directional forecast, then straddle is perhaps not the best execution plan. That said, being delta neutral from the initiation of a straddle strategy has a higher probability of profitability in the face of a binary risk either way, and do not place your positions in any delta bias. As for a strangle, you have the choice to not follow an equidistant strike from underlying price, and choose a call strike that is closer to ATM than the put strike that is further OTM to favor an upside over downside biases on the underlying.

Regardless of where the strike is placed in between the strikes, the investment objective of initiating a straddle or straddle is for a large magnitude move or a rise in base level of IV. Since a straddle’s theta is doubly negative, that can only be achieved by timing the the breakout from a consolidation in market pricing. Why consolidation? It means market is equally clueless and have no agreement on a delta bias on the outlook of the underlying pricing as well, and that means there will be a mispricing gap when reality hits the market which appears as a breakout. Say if the breakout isn’t coming from a “wait-and-see” stance, then it means that the market is holding onto a baseline scenario in which they are pricing. That said, if market is positive delta bias and pushing price upward to fair value ahead of time, then the risk would be to the downside, since the risk is that they have pushed the bar too far from the scenario that is not their baseline scenario. That said, there is actually a delta risk that the market can speculate, and a straddle strategy is not suitable when the market is pricing delta bias since the risk is one-sided. Here, the magnitude of the risk against current market biases to their expected endgame depends on how far the bar they set is from the actual scenario. As the saying goes, “setting the bar too high can only lead to failure”. motivational_poster_expectations.jpg (416×247)

Besides a rise in intrinsic value of the straddle, one can have a view on the other greeks involved in an option pricing (vega). Theta is fixed with time and the debit on initiation. Delta and gamma depends on the underlying that is intrinsic. Rho is negligible as options trading is not a suitable instrument to express a view on rates. A higher base IV could be due to a expectations of higher underlying (implied) volatility at the expiration such that at the game point (expiry), the writer needs to be compensated with more premium (quoted in terms of $). Or it could be that the actual (historical) volatility of the underlying price have been on the rise. Note that it follows that the underlying price experiencing a large move would have a high actual volatility, but a high implied volatility does not necessarily ensue a large movement. However, that doesn’t mean a rise in intrinsic value due to a breakout would lead to a higher extrinsic value of options as well, since vega is highest ATM but becomes dominated by delta when the option is ITM or OTM. From the charts below, a breakout with follow through is different from a higher volatility regime without follow through but is filled with no agreement, lack of commitment and whipsaws.

Likewise, if you have an opposite view to what market expects and you expect the consolidation to be extended and stay as such for a longer period of time, then you would sell such strategies with an expiration to reflect that extension. That is, it will remain with a low or lowered volatility without any breakout follow through. This could be a result of a postponed meeting or bypassed meeting of no firm conclusions. In other words, favor selling straddle as high income generating strategies if time is at your side, else if movement is at your side, pay for these expensive strategies.

Trade Management for long straddle

Say if the breakout does happen on the upside, then you would squeeze the maximum profit out from the ITM call, while deciding whether to liquidate the OTM put if there is any value, or keep it as downside protection if there is any downside risk. As mentioned, rolling the long call up the strikes by selling (bull) call spreads, or rolling the long put down the strikes by selling (bear) put spreads, is the best way to generate extra income by selling spreads (a positive carry increases the “holding power” to be more tolerant of drawdown), to secure partial profit that is between the old strike and the new roll strike, while maintaining exposure in the direction of the breakout, a win-win-win scenario. 

Say if breakout does not happen, you would need a price stop-loss and a time stop-loss i.e. a cutoff time where you will not carry the negative theta position any further.

Trade Management for short straddle

While you can hold a short straddle as IV is rising before expiration, you have to actively manage the call and put sold when a breakout you least expected happened, given your maximum loss is unlimited. In this case, note that it is debiting to widen the breakeven range of underlying prices by buying vertical spreads to roll down the put strike or roll up the call strike. A price stop-loss immediately below the put strike and above the call strike manages that so that it will not eat into the credit you earned on writing this strategy.

Disclaimer (no free lunch!): Straddles and strangles can be very seductive trading vehicles. Traders with a weakness for the “long shot” can easily be blinded by the potential of long straddles and strangles—they give the appearance of making money in every direction and have unlimited profit potential. These traders tend to fall in love with their delta and gamma numbers and usually overlook the fact that they have to pay time decay and are exposed to declines in implied volatility. After some time passes and their forecasts are proven incorrect, they are left wondering where the money went. Traders looking for a “sure thing” can become addicted to short straddles and strangles. Short straddles and strangles profit from time decay, and what could be more certain than time passing? These traders tend to fall in love with their theta numbers and overlook the negative gamma or the unlimited risk aspects of their positions. They count their time decay income day after day only to see it all vanish when a large move takes place or implied volatility rises. The bottom line is that there is no free lunch with straddles and strangles. For every upside there is a downside, and the risks have to be understood, factored into the forecast, and properly managed in a disciplined fashion if one is to be successful trading straddles and strangles (or using any other strategy).

Butterflies and Condors (Directionless strategies)


Similar to selling straddles/strangles, long butterflies and condors are directionless strategies that is not having a particular directional forecast but instead, forecasting little or no directional movement, or bound by a trading range or consolidating. Differences from straddles is that when underlying moves far away from strikes, loss is capped rather  than unlimited. Hence, butterflies and condors is preferred over selling straddles. Likewise, selling flys/condors as a strategy to capture large bidirectional moves is limited as the maximum profit is capped, however, since it involves selling 2 ATM options for buying 1x OTM option and 1x ITM option, the cost of initiation is much cheaper.

Notice that leggings in trade is fungible. Started of with single options to hedge underlying position, then to vertical spreads, which are then usable to roll strikes in any option strategy, vertical spreads or collars, or if more time needed, a diagonal spread. Likewise, a long call fly that shorts 2x ATM call and longs 1x OTM call and 1x ITM call actually contains an embedded synthetic equivalent short straddle wrapped by a (wider) long strangle. A long call condor that shorts 1x less ITM call and 1x less OTM call, and longs 1x more OTM call and 1x more ITM call actually contains an embedded synthetic equivalent short strangle wrapped by a (wider) long strangle. This wrapping of a wider strangle structure around the primary position is a hedge that limits the risk in the structure and appeals to risk-adverse, directionless strategy traders. The use of synthetic equivalent led to the “iron” equivalent that consists of a mixture of puts and calls. The result is cost savings, since buying puts at lower strike price is cheaper, lowering the cost of initiating the structure. In fact, it transforms a debiting condor or fly to a crediting iron condor and iron fly respectively! Why? Because iron actually is a synthetic equivalent of selling a (bull) call spread and sell a (bear) put spread! Note that buying a call fly means buying ITM call at lower strike, and buying a put fly means buying ITM put at higher strike. For an iron fly, it has neither of those challenges as it buys OTM put at lower strike and buys OTM call at lower strike!

2019-01-12 17_12_24-book1 - excel (product activation failed)
Synthetic Equivalence of a butterfly and condor leads to derivation of “Iron” standard

A tradeoff between condor vs fly: while a condor stretches the “body” of the structure over 2 strikes “wings”, giving it a higher chance of profitability since it allows the underlying to move within a wider price range, a condor is typically more expensive than a fly given the extra premium spent on buying a wider price range of profitability. That is,  the P/L payoff is shifted down by the extra premium spent i.e. a  decreased maximum profitability (capped at credit received on initiation.. less credit earned since more spent), and an increased maximum loss. From the table above, an iron condor sells OTM call and OTM put to generate income. When the strike is expanded and options sold are further OTM, the structure generates less premium on initiation. On the other hand, an iron fly that sells both options ATM (select strikes equal to underlying price) generates more credit since ATM options have higher vega and theta.

Condors and flys main objective is to profit from time decay and declining implied volatility. Since it does not forecast underlying price to move above a call strike or below a put strike, it does not profit from change in intrinsic value (the option value when it is ITM, delta=1). It seeks to profit from selling not-ITM options with high extrinsic value, coming from a high uncertainty about the option’s possible value, that is, given a longer time to expiration and a higher implied volatility before expiry (other extrinsic factors beside underlying price). Since only the intrinsic value is settled on maturity, any extrinsic value priced in on buying will decay over time as option approaches expiry. Vice versa, option sellers will gain money every day from time decay (theta>0) and declining IV (vega<0) i.e. extrinsic value decay. That said, while time to expiry only gets shorter over time, a long option extrinsic value can increase if the rise in IV (vega=+0.3 means option value +-.3 per +1% IV) more than offset the time decay. Note that for a long ATM option, while theta is negative and gets more negative closer to expiry (corresponding to an accelerating fall in option (extrinsic) value nearing expiry), vega is positive and gets less positive closer to expiry. That is, a near dated expiry option extrinsic value will be dominated by time decay and less sensitive to changes in IV.

Remember that since theta is most positive when underlying is hovering around the strike, hence strike placement is crucial. Ideally, on initiation, the middle strike should be ATM or the price where underlying will spend the most time at so that there is no directional bias (delta-neutral without climbing delta hills) and generates the most credit (upfront premium) given the higher theta when option strike is ATM. That is, it’s more favorable to initiate a fly/condor structure when the underlying is at the middle of the consolidation range or where underlying will spend the most time, so that theta is most positive, time decay is fastest, vega is most negative and fall in extrinsic value is fastest per +1% IV.

Greeks of fly/condor (Same for call/put/iron since synthetic equivalent)

As mentioned, greeks are peaking/bottoming when underlying is close or at the strike of options, and for other options at other strikes that are ITM or OTM, their greeks (vega, theta, gamma) will be faded since they are not ATM. Hence the greek profile will be dominated by the option whose strike is closest to the underlying price. Hence for a fly or condor, you desire a short option risk profile with time decay and negative vega (generates extrinsic value on falling IV), that is, you desire the underlying price to stay close to the short options strike, to stay within the “body” perimeter by the 2 strikes.

With its synthetic equivalent vertical spreads, we simplify the overal greek exposure by taking an example of 95/100/105 fly as a combination of short 95/100 put spread and short 95/100 call spread. When underlying is at 100, the middle strike, it is approximately delta neutral. When it is below the middle strike, it have a positive delta since its equivalent to a bull pull spread, peaking when underlying is at 95. When it is above the middle strike, it have a negative delta since its equivalent to a bear call spread, bottoming when underlying is at 105.

2019-01-12 22_11_51-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro.png
Delta of a Long Butterfly

To recap, the delta of a bull (call or put) vertical spread looks like this. Remember the theta of a bear vertical spread? It looks the delta above because it is short the lower strike option (theta resembles the delta below) and long the higher strike option. In other words, its is equivalent to combining the greek profile of each legs of the structure like a fractal of a bigger fractal (a structure with more legs).

2019-01-12 22_15_12-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro.png
Delta of a Bull Vertical Spread

As the fly structure involves selling 2x ATM option (where theta is highest) and long 1x OTM call of higher strike and long 1x OTM put at lower strike, where OTM options theta is much lower because the intrinsic value is close to 0 (delta is linear, gamma is small, so is theta), a fly’s theta is dominated by the ATM options sold.

2019-01-12 23_41_21-option spread strategies trading up, down, and sideways markets.pdf - adobe acro
Butterfly Theta

Note that when options are deep ITM or OTM, delta becomes linear, and gamma N'(d1) diminishes. Call delta is N(d1), Put delta is N(d1)-1. Refer to Theta formula, where Gamma N'(d1) is a component inverse to Theta. Since gamma becomes more linear when underlying is further away from strike, so does Theta. That is, nearing expiry, only theta will grow larger when strike is ATM, whereas it fades smaller when strike is away from the underlying price. 

As the fly structure involves selling 2x ATM option (where theta is highest) and long 1x OTM call of higher strike and long 1x OTM put at lower strike, where OTM options theta is much lower because the intrinsic value is close to 0 (delta is linear, gamma is small, so is theta), a fly’s theta is dominated by the ATM options sold. ote that when options are deep ITM or OTM, delta becomes linear, and gamma N'(d1) diminishes. Call delta is N(d1), Put delta is N(d1)-1. Refer to Theta formula, where Gamma N'(d1) is a component inverse to Theta. Since gamma becomes more linear when underlying is further away from strike, so does Theta linearise. That is, nearing expiry, only theta will grow larger when strike is ATM, whereas it fades smaller when strike is away from the underlying price.

theta moneyness over time
Theta Extrinsic Value: OTM (linear) < ITM (linear) < ATM (exponential time decay when approaching expiry)
theta-itm-otm.png
Theta goes higher approaching expiry for ATM, but falls  for OTM and ITM options

As with a short option position, a positive theta have an inverse negative gamma. Negative gamma positions always move against the trader. Say gamma is -0.1. In other words, if the underlying moved up by 1 point, the position would become 0.1 delta shorter, and if the underlying moved down by 1 point, the position would become 0.1 delta longer. When underlying is moves away from the body or middle strike into the area of the long option wings of the outer strikes, theta reverses to negative and gamma to positive. Gamma is softer with more time to expiry.

2019-01-13 00_12_09-OPTION SPREAD STRATEGIES Trading Up, Down, and Sideways Markets.pdf - Adobe Acro.png
Butterfly Gamma

Similar to gamma, vega is large negative when the long butterfly is ATM and reverse to a small positive vega when underlying moves away from the body to the  long wing strikes. Vega increases with more time to expiry.

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Butterfly Vega

A long condor has an almost similar greek profile as the long butterfly, except that the short body is fatter at 2 strikes wrapped with a wider long wings. This widens the underlying price range where vega stays negative and theta stays positive.

Strategy Selection

Regardless of how one arrives at a view of a directionless market (validated support and resistance levels, critical policy handles like bands or pegs, trendlines, mixed-fundamentals at inflexion points, wait-and-see sentiment on inexperience or beyond appetite risk), the following information is key to structure a butterfly or condor strategy.

  1. Support and resistance price levels (long options wing strikes to wrap around the middle strike)  – If they are often invalidated and broken with a bull/bear trap before reversion, then a condor with a stretched wings strike provides an extra safety of margin.
  2. Mean-reversion price area – the price area where the underlying tends to return to as it meanders in its trading range (middle strike selection) so time decay is fastest and the long fly/condor position will be ITM faster to withstand any possible drawdown, giving it more “holding power”. If it reverts to a particular price, a fly fits the bill. If it reverts within a price range, a condor would do the job.
  3. Projected time in the trading range before a directional trend returns – If forecasted consolidation will persist for 30 days time, then options that expire before that time is preferred. If consolidation is expected to persist for a much longer period of time, then a blend of expirations occuring in that time period is favored. Shorter-dated options bear fruits quickly than their longer-dated cousins, but they are more risky as they cost more?
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Long Butterfly Strike Selections
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Long Condor Strike Selections

Managing the trade

As with all carry trades, while you theoretically increase your position value by theta or $0.10 worth of time decay per day, you might lose $3.00 worth of accumulated profits when the underlying breaks out and goes on a directional tear. Hence, watching the market action and making a judgement if market is actually going accordingly to your plan and forecast is a way to validate your initial strike selections and time given for consolidation, before you think of carrying for “one more day”. When the underlying will be or starts behaving differently, given new information, position should be exited.

Since its limited risk structure based on the wings strikes, and the profit is limited on initiation, the structure earns over time as time decays or IV declines. If underlying have managed to stay on track at or within the body for a long period with the fastest time decay and you now have grounds to believe its not going to continue that way, or IV have declined to a level considered low by historical benchmark, you can scale out by taking partial profit e.g. liquidating 3/10 long flys, while leaving 7/10 remaining positions to hold till expiry.

Say that based on some grounds, market has changed and volatility will pick up. A clever way to jump strategy, from harvesting profits from a ranging, declining IV, to positioning for a bi-directional, large magnitude breakout in underlying price, would be to cover the body or inner strikes that is synthetically equivalent to a short straddle. Buying back the inner strikes straddle (on a butterfly) or the inner strikes strangle (on a condor) results in a residual synthetic long (wings) strangle positions. Clever because instead of closing 4 legs and opening 2 new legs, netting 2 legs would do the job. Note that since iron/cut/put fly are synthetic equivalent, buying a straddle at inner strikes will result in the same residual position, that is a long strangle

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Transforming long Butterfly to long Strangle

Suppose the underlying did remain directionless as the initial forecast but the strikes chosen are wrong as the underlying happens to be wider or narrower than initial forecast. You can purchase an additional butterfly to “roll” your long butterfly into a long condor with additional range coverage i.e. stretching the body also stretches the wings. 

For example, if existing fly short strike is at 100, but underlying seems to be trading between 100-105, you are not getting the fastest time decay and thus you stretch the body from 100 to 100-105. Buying an additional butterfly with its middle strike at the bottom strike of existing fly will transform existing long butterfly to a long condor with the body (and wings) strikes widen to the downside range. Likewise, with the middle strike at the upper strike of existing fly, the body (and wings) strikes are widen to the upside range. Illustration below uses call/iron butterfly to transform call/iron/put butterfly into condors with body (and wings) stretched upwards to higher strikes. Note that synthetic equivalence allows any fly added to any existing fly to transform it to the any condor, regardless of call/put/iron. Iron is typically preferred as its purchase is always crediting!

2019-01-13 15_02_18-execution - flys condor synthetic equivalent - Excel (Product Activation Failed).pngAdding call fly to existing long call/iron/put fly at upper strike, residual long condor with wider upside range

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Adding iron fly to existing long call/iron/put fly at upper strike, residual long condor with wider upside range

For example, if existing fly short strikes are at 100 and 105, but underlying seems to be homing in on 100 strike, you could get a faster time decay if short strikes are focus at 100 and thus you shrink the body from 100-105 to 100. Selling an additional butterfly with its middle strike at the body’s bottom strike of existing condor will transform a long condor to a long butterfly with the wings narrowed to the upside range. Likewise, with the middle strike at the condor’s body upper strike, the wings are narrowed to the downside range. Note that synthetic equivalence allows any fly subtracted from any existing condor to transform it to the any butterfly, regardless of call/put/iron. Iron is typically avoided as its sales is always debiting!

2019-01-13 15_13_04-execution - flys condor synthetic equivalent - excel (product activation failed)
Selling iron fly on existing long call/iron/put condor at upper strike of body, residual long fly with narrowed upside range
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Selling call fly on existing long call/iron/put condor at upper strike of body, residual long fly with narrowed upside range

 

The thread have extended to a pretty long post, and I have decided to split it. Stay tune for Ideas are cheap, execution is everything – Part II for more elaboration on the other vanilla option strategies (calendar, backspread, ratio) as well as digital, double digital (like vertical spread), touch, and KO options.

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