Collars and Deltas

A collar is composed of  an outright position, a out-of-the-money option write at your profit objective collecting time premium and a purchased out-of-the-money option to define your risk, with both the written and purchased option having the same expiration (see Figure 1, below). For example

105 call write, collect 2
100 long position
95 put purchase, pay 2

The collar’s long put acts as a hedge for the long position, and the short call finances the long put. The short call also caps the potential profit of the long position. The collar’s max loss occurs if the position price is below the strike price of the long put at expiration. The max profit occurs if the position’s price is at or above the strike price of the short call at expiration.


FIGURE 1: Dynamic Collar. When you put on a collar, you’re buying long stock, shorting
an out-of-the-money call, and buying an out-of-the-money put. Costs can add up. For
illustrative purposes only.

Traditionally, you might place a collar over your long stock, and let it go to expiration without adjusting it. But the nature of collars gives them flexibility, not only when putting them on, but also after time passes and the stock price moves. In fact, larger investment managers use this flexibility to build a bigger stock position by using a strategy known as the “dynamic collar.”

Delta Is More Than Change

Technically, the collar is a bullish strategy that has positive deltas—meaning it benefits from the long stock moving higher. But where do those deltas come from?

The long stock has 100 positive deltas for each 100 shares. Both the long put and short calls have negative deltas, but how much depends on their strikes. The further OTM the long put or short call, the fewer negative deltas they have, and so the more positive deltas the collar has. If the long put and short calls are closer to the current stock price, they have larger negative deltas, and offset more of the long stock’s positive deltas.

Let’s say the stock price is $50, the 52-strike calls have a 0.40 delta, and the 48-strike puts have a -0.40 delta. A collar with those calls and puts has +20 deltas. Why?

One hundred shares of stock = +100 deltas
The short 52 calls = -40 deltas
The long 48 puts = -40 deltas.

100 + -40 + -40 = +20

Now, suppose the 55-strike calls have a 0.20 delta, and the 45-strike puts have a 0.25 delta. A collar with those calls and puts would have +55 deltas (-20 + -25 + 100). That’s why choosing the strikes for the calls and puts determines how bullish you want the strategy to be. But it also means the delta of the collared stock position can change if the stock price moves down toward the long put strike, or up toward the short call strike.

In the collar example with the 48 put and 52 call, if the stock moves from $50 down to $48, let’s assume the 48 put now has a -0.50 delta and the 52 call now has a 0.15 delta. That would take the delta of the collar from +20 to +15.

Now, let’s say the stock moves from $50 to $54. Let’s further assume the 48 put has a -0.10 delta and the 52 call has an 0.80 delta. That would take the delta of the collar from +20 to +10.

These numbers are hypothetical, but they illustrate that when the stock price nears either strike, or moves beyond them, the delta of the collar becomes less positive. When the stock price is between the strikes, the delta of the collar becomes more positive. It’s that changing delta that can make the collar “dynamic.”

Think Collars, Think Flexible

The dynamic collar originated with institutional investors and money managers who were looking to establish large positions in a stock over time, but wanted a hedge against market corrections.

Let’s start a new hypothetical with, say, buying 1,000 shares of stock, buying 10 out-of-the-money (OTM) puts as a hedge, then selling 10 OTM calls to off-set the cost of the puts. If the price of the stock drops, the long puts and short calls should theoretically be profitable because the have negative delta.

Assume you sell the long puts, buy back the short calls, and use the profit to buy more shares of the stock. Suppose that’s enough to buy 100 more shares. That would make the stock position 1,100 shares, so you would now buy 11 new OTM puts and sell 11 new OTM calls. The larger position could create more positive deltas. So, you’re get- ting longer deltas (i.e., buying more stock) after the price drops, but still retaining the hedge.

Now, when the stock price drops, it doesn’t mean the whole dynamic collar is profitable. But that’s not the point. Remember, the collar is, after all, a bullish strategy. And you’re building a position in the stock based on the dynamic fluctuation in the stock price. The loss on the long stock is usually greater than the profit on the long OTM put and short OTM call. To build your position, the idea is to establish a larger delta position in the stock at the lower price via the dynamic collar.

If the stock rallies, the collar could have an overall profit if the long stock has a higher profit than the losses on the long put and short call. In that case, you could take the profit and move on to the next trade, or “roll” the long put into a higher strike closer to the new stock price, and the short call to a higher strike further from the new stock price. This allows you to capture some prof- it without exiting the position, and begin a new collar at the higher stock price.

Rolling usually costs money, so this could cut into some of the long stock’s profit. But it could help you maintain roughly the same delta as when the collar was established, if you continue to be bullish on the stock.

Deep Pockets Help

The dynamic collar gets more positive deltas in two ways with a lower stock price.

First, the options’ deltas and stock combine to give the collar a lower positive delta when the stock price drops closer to the OTM put. Second, you can increase the position size with the options’ profit, or available capital. If the stock price keeps dropping, the dynamic collar could be losing less money on bigger positions compared to unprotected stock. That’s why the strategy is often employed by money managers with the capital to withstand large losses on long-term investments.

In exchange for the risk of expanding losses, the dynamic collar can be more prof- itable if the stock price rallies back. Because the strategy often creates more positive deltas as the stock rallies, the strategy could possibly break even, or be profitable, with a smaller rally in the stock price. Be sure to keep careful records as you track all the adjustments to a dynamic collar. Make sure you know the new breakeven stock price for the strategy after all adjustments are in place.

Mirror Images

You might notice that the collar is synthetically equivalent to a long call vertical spread. In other words, the long put plus long stock has the same risk profile as a long call with the same strike as the long put. Look at the profit and loss graph below.


FIGURE 2: Dynamic Twin. The risk profile of the call vertical spread above is nearly identical
to the collar, and much less capital intensive. For illustrative purposes only.

Because the long put is OTM, that synthetic long call is ITM. Combine the synthetic long ITM call with the short OTM call, and you have a long call vertical. The collar with the long 48 put and short 52 call is synthetically the long 48/52 call vertical. In fact, the collar and the long vertical could have the same max profit and max loss numbers. Also, the collar could have higher commissions than a vertical because the collar is stock plus two options, while the vertical is just two options.

So why don’t investment managers just buy call verticals if they’re synthetically the same as collars? Simple: voting rights. Owning stock shares gives you a voice in a company’s business such as board elections, mergers and acquisitions, and stock splits. Options, on the other hand, don’t confer voting rights. Because the collar strategy is built around owning shares, the manager preserves voting rights.

The dynamic collar strategy can also rack up commissions because of increased trade frequency and increased position size. If you employ the strategy, make sure the potential profits are large enough to cover commissions.

Are Dynamic Collars For You?

What if you don’t buy 1,000 shares of stock? Maybe 100 shares are more appropriate for your account. Do dynamic collars still make sense?

In a scenario where the stock price drops and the profit from a long put and short call is used to buy more shares, the profit might not be enough to buy 100 shares. Although it’s possible to trade odd lots of stock, there could be a mismatch between the options’ contract size and the number of shares.

For example, if the collar profits composed of 100 stock shares, long one put, and short one call are enough to buy 10 shares of stock, the position will have 110 shares. But each stock option has a contract size of 100 shares. There aren’t standard equity options with a contract size of 110 shares. One long put and one short call hedge only 100 shares. But two long puts and two short calls might be too much of a hedge.

Sometimes Fake Is More

If the collar is too rich of an investment for your capital, you might be better off with the collar’s synthetic equivalent, the long call vertical spread mentioned on page 23 (Figure 2, above). However, in the absence of long stock, the way to make it dynamic is with deltas. How many positive deltas does the long call vertical have, and how many deltas do you want when the stock price drops?

Using our 48/52 collar example with the stock at $50, the synthetically equivalent call vertical would simply be long one 48 call and short one 52 call, with a delta of +20. No stock and no put here.

Now, suppose the stock price drops to $48, and the 48/52 call vertical has lost $40. Our collar would also lose the same $40, but that would be made up of a $200 loss on the stock and a $160 profit on the long 48 put and short 52 call. Once the collar is closed, you could use the $160 to buy three and one-third shares of stock at $48 (not subtracting transaction costs). But instead of buying three shares, the long call vertical could in- crease its deltas by a little over 3.3%, which is the equivalent of adding three and one-third shares to a 100-share position.

Further, if the delta of the 48/52 call vertical is +35 when the stock is $48, making it a “dynamic vertical” could increase the delta by 3.3% to +36.2. You might do that by rolling the short 52 call up to the 53 strike, or even roll the long 48 call to a further expiration depending on those options’ deltas.

That said, adjusting the position for 0.01 deltas is tough, and you may want to wait for a larger theoretical profit before you adjust. And like the dynamic collar, trading long verticals in this way can result in high commission charges.

You could also tweak the vertical strike to make it even more dynamic than the collar. Selling an OTM call in a closer expiration against an ITM call in a further expiration is still a hedged position. But the short front-month call theoretically decays faster than a further expiration call, all things being equal.

And that’s how some pros build a bigger position without spending extra capital using dynamic collars. Though the strategy requires a fundamental grasp of delta that may seem complex at first, it’s worth taking a close look at a strategy the pros have been running with for years.

If you’d like to review this and/or other programs/markets schedule an online review using this link, we’ll answers your questions and provide you with all supporting links for additional information and/or  verification.

Peter Knight Advisor



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