A **ratio strategy** is an options-based strategy that involves “unbalanced” sides. Previously, we covered ratio call & put writes and ratio call spreads. This chapter will cover **ratio put spreads**, which are put spreads involving a “heavy” side and a “light” side. For example, assume an investor establishes the following positions:

Long 1 PDQ Jan 30 put at $4

Short 2 PDQ Jan 50 puts at $12ABC’s market price = $42

As we did with ratio call spreads, the key to answering ratio put spread questions is focusing on the “heavy” side. The investor writes two puts, one covered by the long put and one naked (uncovered). The biggest takeaway is the risk the investor faces. A short naked put subjects an investor to significant downside risk. The further PDQ’s market price falls, the more they lose on the naked put. In the worst-case scenario, the market price falls to $0, so the loss potential is limited.

The market sentiment is similar to a typical short (credit, bull) put spread, although the risk and return potential is amplified. Essentially, the investor is betting PDQ’s market price rises to or above $50.

Let’s look at some practice questions:

Long 1 PDQ Jan 30 put at $4

Short 2 PDQ Jan 50 puts at $12ABC’s market price = $42

Maximum gain?

Maximum loss?

Breakeven(s)?

Gain or loss if PDQ rises to $45?

Gain or loss if PDQ falls to $20?

Can you figure it out?

(spoiler)

Maximum gain = **$2,000**

First, let’s determine the value of establishing this spread. The investor spends $4 on the long put and obtains $24 to sell the two short puts ($12 x 2). Therefore, the investor receives a total of $20 per share (pay $4, receive $24), or $2,000 overall ($20 x 100 shares) to establish the ratio spread.

The investor will reach their maximum gain at a market price of $50 or above. All the contracts are “out of the money” and will assumptively expire worthless. The investor keeps their initial $2,000 credit with no additional actions taken.

Maximum loss = **$5,000**

Given the short puts represent the “heavy side,” the investor reaches their maximum loss when these positions lose the most. Short puts are bullish strategies, so they lose when PDQ’s market price falls. The furthest the market price can fall is to $0, which is where the investor reaches their maximum loss potential.

Now’s let’s determine what happens if PDQ falls to $0. The long put is $30 “in the money,” which is profit to the investor. The short puts are $50 “in the money,” or $100 overall per share ($50 x 2 contracts) which is loss to the investor. Therefore, the investor experiences a $70 loss per share ($100 short calls loss - $30 long call gain), or $7,000 overall ($70 x 100 shares).

The investor received $2,000 to establish the ratio put spread but loses $7,000 if PDQ falls to $0. Putting it all together, the investor faces a maximum loss of $5,000 ($7,000 - $2,000).

Breakeven = **$40**

This strategy has one breakeven point. As discussed above, the investor receives $2,000 to establish the three positions. At $40, the short calls are “in the money” by $10 and the long call is “out of the money” (and will expire worthless. The combined $2,0000 of intrinsic value losses ($10 intrinsic value x 2 contracts x 100 shares) across the two short calls offsets the $2,000 received upfront.

Gain or loss if PDQ rises to $45 = **$1,000 gain**

The positions provide $2,000 to establish initially. At $45, only the short calls are “in the money.” They maintain $5 of intrinsic value per contract, a $1,000 total loss to the investor ($5 intrinsic value loss x 2 contracts x 100 shares). The long put is “out of the money” and will expire. Therefore, the investor has an overall gain of $1,000 ($2,000 establishment value - $1,000 intrinsic value loss) when PDQ’s market price is at $45.

Gain or loss if PDQ falls to $20 = **$3,000 loss**

An easy way to solve this question is to break down the spread into two separate problems and then add up the numbers. Let’s start with the long put first. The long put costs $4 per share to establish, and at $20 it is $10 “in the money.” Therefore, the long call experiences a $6 gain per share ($10 - $4), or a $600 overall gain ($6 gain x 100 shares).

Let’s now examine the two short calls. The investor receives $12 per share per contract to establish them, and at $20 both contracts are $30 “in the money.” Therefore, the short calls experience an $18 loss per share per contract ($30 - $12), or a $3,600 overall loss ($18 loss x 2 contracts x 100 shares).

Adding up all the numbers, the investor has an overall loss of $3,000 ($3,600 short puts loss - $600 long put gain).

Let’s look at a slightly different ratio put spread:

Short 1 XYZ Jan 70 put at $6

Long 2 XYZ Jan 80 puts at $12XYZ’s market price = $72

Maximum gain?

Maximum loss?

Breakeven(s)?

Gain or loss if XYZ rises to $75?

Gain or loss if XYZ falls to $50?

(spoiler)

Maximum gain = **$7,200**

First, let’s determine the cost of establishing this spread. The investor receives $6 for the short put and pays $24 to buy the two long puts ($12 x 2). Therefore, the investor pays a total of $18 per share (receive $6, pay $24), or $1,800 overall ($18 x 100 shares) to establish the ratio spread.

The investor is “heavy” on the bearish long puts, so the investor will profit when XYZ’s market price falls. The furthest the market price can fall is to $0. At this point, the long puts are $160 “in the money” ($80 ITM per contract x 2 contracts), which provide an overall return of $16,000 ($160 x 100 shares). At $0, the short put is $70 “in the money,” which results in a loss of $7,000 ($70 x 100 shares). Therefore, the investor experiences a net gain of $9,000 ($16,000 long puts gain - $7,000 short put loss) when XYZ’s market price falls to $0.

Putting it all together, the investor has a maximum potential gain of $7,200 ($9,000 maximum exercise gain - $1,800 establishment cost).

Maximum loss = **$1,800**

The investor’s maximum loss is reached when XYZ’s market price is at $80 or above. All contracts are “out of the money” and will assumptively expire worthless. The investor is stuck with their initial $1,800 debit as their maximum loss.

Breakeven = **$71**

This strategy has one breakeven point. The initial net cost to establish the ratio put spread was $1,900. To breakeven, the investor must make back the establishment cost. At $71, the two long puts are $9 “in the money” per contract and the short put is “out of the money” (and will expire worthless). The $9 intrinsic value per contract results in $1,800 of overall gains ($9 intrinsic value x 2 contracts x 100 shares). The $1,800 intrinsic value gain offsets the $1,800 establishment cost, bringing the investor to breakeven.

Gain or loss if XYZ rises to $75 = **$800 loss**

The positions cost $1,800 when initially established. At $75, only the long puts are “in the money.” They maintain $5 of intrinsic value per contract, a $1,000 total gain to the investor ($5 intrinsic value x 2 contracts x 100 shares). The short put is “out of the money” and will expire. Therefore, the investor has an overall loss of $800 ($1,800 establishment cost - $800 intrinsic value) when XYZ’s market price is at $75.

Gain or loss if XYZ falls to $50 = **$2,200 gain**

An easy way to solve this question is to break down the spread into two separate problems and then add up the numbers. Let’s start with the long puts first. The long puts cost $12 per share per contract to establish, and at $50 are $30 “in the money.” Therefore, the long puts experience an $18 gain per share per contract ($30- $12), or a $3,600 overall gain ($18 gain x 2 contracts x 100 shares).

Let’s now examine the short put. The investor receives $6 per share to establish it, and at $50 the contract is $20 “in the money.” Therefore, the short put experiences a $14 loss per share ($30 - $12), or a $1,400 overall loss ($14 loss x 100 shares).

Adding up all the numbers, the investor has an overall gain of $2,200 ($3,600 long puts gain - $1,400 short put loss).

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