Variable Ratio Write Explained

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Variable Ratio Write

The variable ratio write is a variant of the ratio write strategy in which the options trader owns a holding of the underlying stock and sells more calls than shares owned.

Variable Ratio Write Construction
Long 100 Shares
Sell 1 ITM Call
Sell 1 OTM Call

Like the ratio write, it is a limited profit, unlimited risk options trading strategy that is taken when the options trader thinks that the underlying stock price will experience little volatility in the near term.

Unlike the 2:1 ratio call write, which involves writing two at-the-money calls, the 2:1 variable ratio write involves writing one out-of-the-money call and one in-the-money call. As such, the variable ratio write has a lower profit potential but the profit zone is wider.

Limited Profit Potential

Maximum gain for the variable ratio write is limited and is made when the underlying stock price at expiration is anywhere between the strike prices of the options sold. At this price range, the higher striking short call expires worthless while the lower striking short call expires in the money.

Any loss resulting from the gain in the intrinsic value of the short call is offset by the premiums earned for selling this call while any profit from the drop in intrinsic value of this short call is completely negated by the corresponding depreciation of the long stock position. As a result, the options trader gets to keep as profit the time value of the premiums received when putting on the trade.

The formula for calculating maximum profit is given below:

  • Max Profit = Net Premium Received + Strike Price of Lower Strike Short Call – Purchase Price of Underlying – Commissions Paid
  • Max Profit Achieved When Price of Underlying is in between the Strike Prices of the Short Calls

Unlimited Risk Potential

Loss occurs for the variable ratio write when the stock price makes a strong move to the upside or downside beyond the upper and lower breakeven points. There is no limit to the maximum possible loss.

The formula for calculating loss is given below:

  • Maximum Loss = Unlimited
  • Loss Occurs When Price of Underlying Strike Price of Higher Strike Short Call + Max Profit
  • Loss = Price of Underlying – Strike Price of Higher Strike Short Call – Max Profit OR Strike Price of Lower Strike Short Call – Price of Underlying – Max Profit + Commissions Paid

Breakeven Point(s)

There are 2 break-even points for the variable ratio write position. The breakeven points can be calculated using the following formulae.

  • Upper Breakeven Point = Strike Price of Higher Strike Short Call + Points of Maximum Profit
  • Lower Breakeven Point = Strike Price of Lower Strike Short Call – Points of Maximum Profit

Referring to the graph shown above, since the maximum profit is $400, points of maximum profit is therefore equals to 4. Therefore, upper breakeven is at $54 while lower breakeven is at $36.

Example

Suppose XYZ stock is trading at $45 in June. An options trader executes a 2:1 variable ratio write by buying 100 shares of XYZ stock for $4500, selling one in-the-money JUL 40 call for $700 and selling another out-of-the-money JUL 50 call for $200. The total premiums received for putting on the trade is $900.

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On expiration in July, if XYZ stock is still trading at $45, the long stock position is still worth $4500, the JUL 50 call expires worthless while the JUL 40 call expires in the money with $500 in intrinsic value. With $900 in premiums earned, buying back the short JUL 40 call for $500 still results in a $400 profit. This is the maximum profit and can be made when XYZ stock price is anywhere between $40 and $50.

If XYZ stock rallies and is trading at $54 on expiration in July, all the call options will expire in the money. The JUL 40 call is now worth $1400 while the JUL 50 call is worth $400. This $1800 loss is completely offset by the $900 appreciation of his long stock position and the $900 in premiums he received earlier. Therefore, he achieves breakeven at $54.

Beyond $54 though, there will be no limit to the loss possible. For example, at $70, the written JUL 40 call will be worth $3000 while the JUL 50 call will be valued at $2000, resulting in a combined loss of $5000 on the short position. Meanwhile, his long stock position has only appreciated by $2500 and together with the $900 in premium received, the options trader still need to come up with another $1600 to close the position.

Using the formula for computing the breakeven point, we calculated the lower breakeven point to be $36. At $36, all the call options expire worthless. However, his long stock position also suffers a loss of $900 in value but this loss is offset by the $900 in premiums earned. Therefore, there is breakeven at $36.

Below $36 however, there is no limit to the potential loss. For example, if the stock price is trading at $20 on expiration, while all the call options expire worthless, the long stock position suffers a $2500 drop in value. Even with the $900 in premiums to offset the loss, the options trader still suffers a $1600 loss.

Note: While we have covered the use of this strategy with reference to stock options, the variable ratio write is equally applicable using ETF options, index options as well as options on futures.

Commissions

For ease of understanding, the calculations depicted in the above examples did not take into account commission charges as they are relatively small amounts (typically around $10 to $20) and varies across option brokerages.

However, for active traders, commissions can eat up a sizable portion of their profits in the long run. If you trade options actively, it is wise to look for a low commissions broker. Traders who trade large number of contracts in each trade should check out OptionsHouse.com as they offer a low fee of only $0.15 per contract (+$4.95 per trade).

Similar Strategies

The following strategies are similar to the variable ratio write in that they are also low volatility strategies that have limited profit potential and unlimited risk.

Variable Ratio Write Definition

What Is the Variable Ratio Write?

The variable ratio write is an options strategy defined by an investor or trader holding a long position in the underlying asset while simultaneously writing multiple call options at varying strike prices. It is essentially a ratio buy-write strategy.

Variable ratio writes have limited profit potential because the trader is only looking to capture the premiums paid for the call options. This strategy is best used on stocks with little expected volatility, particularly in the near term.

Variable Ratio Writes Explained

In ratio call writing, the ratio represents the number of options sold for every 100 shares owned in the underlying stock. This strategy is similar to a ratio call write, but instead of writing at-the-money calls, the trader will write both in the money and out of the money calls. For example, in a 2:1 variable ratio write, the trader will be long 100 shares of the underlying stock. Two calls are written: one is out of the money and one is in the money. The payoff in a variable ratio write resembles that of a reverse strangle.

As an investment strategy, the variable ratio write technique should be avoided by inexperienced options traders as this strategy has unlimited risk potential. Because losses begin when stock price makes a strong move to the upside or downside beyond the upper and lower breakeven points, there is no limit to the maximum possible loss on a variable ratio write position. Although the strategy appears to present significant risks, the variable ratio write technique does offer a fair amount of flexibility with managed market risk, while providing attractive income for an experienced trader.

There are two breakeven points for a variable ratio write position. These breakeven points can be found as follows:

Real World Example of a Variable Ratio Write

Take as a hypothetical example an investor who believes XYZ stock (which is trading at $100) is unlikely to move very much over the next two months. As an investor, he is unlikely to add or reduce his stock position, where he owns 1,000 XYZ shares. However, he can still generate a positive return if his prediction is correct by initiating a variable ratio write by selling 30 of the 110 strike calls on XYZ that are due to expire in two month’s time. The options premium on the 110 calls are $0.25, and so our investor will collect $750 from selling the options.

After two months, if XYZ shares indeed remain below $110, then the investor will book the entire $750 premium as profit, since the calls will expire worthless. If the shares rise above the breakeven $110.25, however, the gains on the long stock position will be more than offset by losses by the short calls, for which he has sold more (representing 3,000 shares of XYZ) than he owns.

Variable Ratio Schedules: Examples & Definition

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Variable Ratio Schedules of Reinforcement

Like all schedules of reinforcement, variable ratio schedules of reinforcement are an important aspect of operant conditioning. A variety of schedules of reinforcement can be used to reinforce behavior, all possessing their own unique properties. In addition to variable ratio schedules, variable interval, fixed ratio, and fixed interval schedules of reinforcement exist and are used to reinforce behavior.

The easiest way to understand the meaning of variable ratio schedules of reinforcement is to understand the individual words that comprise the concept: variable, ratio, schedule, and reinforcement. These four words individually can have many meanings, but when used together, they have a very specific meaning within the context of operant conditioning.

Variable refers to reinforcement being delivered following an average number of responses. In the world of operant conditioning, schedule refers to how often the reinforcement is provided. Reinforcement refers to a reward for engaging in some specific behavior.

So, a certain behavior is exhibited when a reinforcer is presented. The concept of reinforcement says that the reinforcer should provide motivation for the behavior to be repeated. A pretty basic example of a schedule of reinforcement would be giving a child a prize of candy every time he cleans his room. This is referred to as a continuous schedule of reinforcement because the reward is provided every time the behavior occurs.

Ratio refers to the fact that the reinforcement is delivered following a specific set of behavioral responses. It does not matter how much time has passed; that is what interval schedules of reinforcement are for. When it comes to ratio schedules of reinforcement, the only thing that matters is that the behavior occurs a specific number of times.

So, a variable ratio schedule of reinforcement is a schedule of reinforcement wherein a reinforcer is provided following a pre-determined average number of responses. For example, a variable ratio schedule that is set up to deliver a reinforcer based on an average of 5 responses might deliver reinforcement after the 2nd, 3rd, and 10th responses (5 is the average of 2, 3, and 10). To the responder, it can be mysterious as to what the reinforcement schedule actually is, but as we will see from two examples, not knowing when the reinforcer is coming can still be quite reinforcing.

Everyday Examples

Let’s look at a couple of examples of variable ratio schedules of reinforcement in everyday life.

It’s pretty safe to say that slot machines can be used to successfully alter human behavior. Go into any casino across the U.S., and you will see people repeatedly pulling the handle or pushing the button over and over again, believing that the next pull or button push could result in a big payout. Thanks to variable ratio schedules of reinforcement, people will continue to put money in the machine even if they don’t initially get rewarded.

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