# 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
Variable Ratio Write Payoff Diagram

## 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 Lower Strike Short Call - Max Profit OR 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.

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.

Short Strangle (Sell Strangle)
Short Guts

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