Synthetic Option Trading Magic

My last article was called The Level One Blues. It described how to construct option positions in more than one way. This is useful if the option approval level assigned to you by your stockbroker is a low level. You can read more about what option approval levels are and what they mean in the last article. I’ll expand on the idea of synthetic options further here.

Below is today’s chart of QQQ, the exchange-traded fund for the NASDAQ 100 index. With multiple tech stocks having recent bad news, and other issues, the ETF had fallen quickly to around $157. There was an apparent demand zone just below, with a low around $150. Because of recent market price volatility, options were quite expensive.

Let’s say you believed that QQQ was not likely to drop below $150 in the next few weeks, and that you wanted to benefit from the current highly inflated option prices. A common strategy would be to sell (short) a put option at the $150 strike price. The 150 puts expiring in 22 days at that strike could be sold for $2.12 per share, or $212 per contract.

Each put option sold would obligate you to buy 100 shares of QQQ at $150 each, for a total of $15,000. But this obligation is only a contingent one. You would not actually be required to buy the stock unless it was below $150 when the options expired.

If you were correct about the price direction, and QQQ were to recover and remain above $150, then the put would not be exercised and it would be worth nothing when it expired. The $212 that you had received for selling it would be clear profit. On your $15,000 of cash tied up, this would be a profit of 212/15,000 or 1.41% in 22 days. This would be an annualized rate of return of 23.45%.

On the other hand, if the price of QQQ dropped below $150, and remained there at expiration, then you would be obligated to buy the shares of QQQ at $150 each, or $15,000 for the 100 shares. Your net cost per share would then be $150 paid, less the $2.12 received initially for selling the puts. $150 – $2.12 = $147.88 per share. If QQQ were anywhere above that price at expiration, you would have a profit. If not, you would have a loss.

Let’s say you liked these possible returns and decided to place the trade.

But your broker informed you that your brokerage account was only “approved for level 1.” You would not be allowed to place the trade, which requires a higher approval level (level 4 in this case).

This is where the idea of synthetic options comes in. Any option position can be synthesized by substituting a different type of option position.

In last week’s article, I gave the basic equation used when creating synthetic options positions. Quoting from that article:

These are the notations we will be using:

• +S = Long 100 shares of the underlying Stock

• -S = Short 100 shares of the underlying Stock

• +C(x) = One long call option at strike X

• -C(x) = One short call option at strike X

• +P(x) = One long put option at strike X

• -P(x) = One short put option at strike X 

Here is a basic equation:  +S + P(x) = C(x)

This translates to: 100 shares of stock plus one put at strike x equals one call at strike x.

In the above translation, equals means yields the same profit or loss in all conditions.

This equivalence is the result of a property of options that is called Put-Call Parity, as explained in the earlier article.

In today’s QQQ example, we would like to sell a put at the $150 strike. Our desired position, using the above notation, would be:

-P(150)

But we are not allowed to sell short puts. How else can this position be constructed?

We just need to do a little rearranging of the basic equation.

If it is true that: +S + P(x) = C(x)

then: -S -P(x) = -C(x)

Adding +S to both sides of the equation yields: -S +S -P(x) = +S – C(x)

Which simplifies to: -P(x) = +S – C(x)

Fine, but what is the point of all that algebra?

Well, +S -C(x) is a position that is long 100 shares of stock (+S), and also short one call (-C(x)). A position with long stock and a short call is a covered call, which is allowed in a level 1 option account.

In other words, if we buy 100 shares of QQQ at its current market price, and also sell one 150 call, that covered call position would yield the same profit or loss as simply selling a 150 put. In either case, the plan would be to hold the position until the April 20 expiration. At that time the position would be closed for its market value

These were the per-share market prices at the time of the example:

QQQ stock: $157.71

QQQ April 150 put: $2.12

QQQ April 150 call: $9.76

Here is the comparison of the two positions:

Capital Required to enter the position

Covered call: $15,771 to buy stock, less $976 received for the call, a net of $14,795.

Short put: $15,000 security required against the put, less $212 received for the put, net outlay of $14,788.

So, the two positions would require almost exactly the same capital ($14,795 vs $14,788).

Profit/Loss on the position

1. If the stock is flat at $157.71

Covered call: the stock will be called away and you will be paid $15,000. This is a $771 loss from your original stock price. But adding back the $976 originally received for the call, you have a net profit of $976 – 771 = $205.

Short put: The put is worthless. You keep the $212, which is your profit. This is $7.00, or just $.07 per share more than the profit on the covered call.

2. If the stock falls to $150 (or any price between $150 and $157.71)

Covered Call: your shares are not called away. You keep them with a value of $15,000. This is a loss of $771. But adding back the $976 originally received for the call, you have a profit of $976 – 771 = $205. This is the same as if the stock were flat.

Short put: The put is worthless. Again, you keep the $212, which is your profit, same as if the stock were flat.

3. If the stock rises to $160 (or any price above $157.71)

Covered call: the stock will be called away and you will be paid $15,000. This is a $771 loss from your original stock price. Adding back the $976 originally received for the call, you have a profit of $976 – 771 = $205. Same result as if the stock were flat.

Short put: The put is worthless. You keep the $212, which is your profit. Same result as if the stock were flat.

4. If the stock drops to $145 (or any price below $150)

Covered call: the stock will not be called away and you will still own it. Since your original cost was $14,795 and it is now worth $14,500, you have a loss of $295. In any case where the stock is at a price below your $147.95 per share net cost, you will have a commensurate loss.

Short put: The stock will be put to you, meaning that you will have to buy it and pay the $15,000 for it. Subtracting its current value of $14,500, that is a $500 loss. Adding back the $212 you were paid for the put, your net loss is $288. In any case where the stock is at a price below your $147.88 per share net cost, you will have a commensurate loss.

Note that in every case above, the net result of the covered call trade is the same as for the short put trade (except for the insignificant $.07 per share difference). This would be true no matter what the stock does.

So, if your desired position is either a short put or a covered call, they can be freely substituted for each other.

In this example, we wanted to do a short put and substituted a covered call. In other situations, it might be the other way around. For example, we might want to do a covered call on an underlying asset that can’t be owned, like a stock index. In this case, substituting a short put accomplishes the same thing as the desired covered call.

In these two articles, I’ve introduced the idea of synthetic option positions as a way to create desired positions in alternative ways. I hope you find them useful

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