Textbook

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

Long 1 ABC Jan 50 call at $9

Short 2 ABC Jan 60 calls at $4ABC’s market price = $51

The key to answering ratio strategy questions is focusing on the “heavy” side. The investor writes two calls, one covered by long call and one naked (uncovered). The most significant takeaway is the risk the investor faces. Maintaining a short naked call will always subject an investor to unlimited risk. The further ABC’s market price rises, the more they lose on the naked call.

The market sentiment is somewhat similar to a typical long (debit, bull) call spread, although there are some differences, plus the risk and return potential is amplified. Essentially, the investor is betting ABC’s market price rises to $60 and stops.

Let’s look at some practice questions:

Long 1 ABC Jan 50 call at $9

Short 2 ABC Jan 60 calls at $4ABC’s market price = $51

Maximum gain?

Maximum loss?

Breakeven(s)?

Gain or loss if ABC rises to $75?

Gain or loss if ABC rises to $55?

Can you figure it out?

(spoiler)

Maximum gain = **$900**

First, let’s determine the cost of establishing this spread. The investor spends $9 on the long call and receives $8 to sell the two short calls ($4 x 2). Therefore, the investor must pay a total of $1 per share (pay $9, receive $8), or $100 overall ($1 x 100 shares) to establish the ratio spread.

The investor will reach their maximum gain at a market price of $60. At this market price, the long call is $10 “in the money,” while both short calls are “at the money,” have no intrinsic value, and will expire. The long call can be exercised, resulting in 100 shares being purchased at $50 that are worth $60, ending in a $10 gain per share at exercise, or $1,000 overall ($10 x 100 shares).

Putting it all together, the investor paid $100 to establish the spread and gained $1,000 at exercise, resulting in an overall maximum gain of $900.

Maximum loss = **Unlimited**

Although one of the short calls is covered, the other is naked. If ABC’s market price rises above $60, all three calls are “in the money.” The long call offsets the losses incurred on the short covered call. However, the short naked call continues to result in losses the further ABC’s market price rises. Therefore, the investor is subject to unlimited loss potential.

Breakevens = **$51 and $69**

This strategy has two breakeven points. As discussed above, it costs $100 to establish the three positions. At $51, the long call is “in the money” by $1, allowing the investor to buy 100 ABC shares at $50 when they’re worth $51. The option has $100 of intrinsic value ($1 x 100 shares), which offsets the spread’s $100 initial cost.

We established this spread reaches its maximum gain of $900 at a market price of $60. When ABC stock rises above this point, the naked call incurs additional losses (the other short call and long call offset each other). Once the market price reaches $69, the naked call experiences $900 in losses ($9 “in the money” x 100 shares), which offsets the $900 gain when ABC was at $60.

Gain or loss if ABC rises to $75 = **$600 loss**

There are two reasonable ways to determine the answer. First, let’s start with the $69 breakeven discovered above. At $69, there is no gain or loss. As the market price rises above $69, the short naked call continues to result in additional losses. At $75, the uncovered option loses an additional $6 per share, or $600 overall ($6 x 100 shares).

The other way involves breaking down the spread into two separate problems and then adding up the numbers. Let’s start with the long call first. The long call costs $9 per share to establish, and at $75 it is $25 “in the money.” Therefore, the long call experiences a $16 gain per share ($25 - $9), or a $1,600 overall gain ($16 gain x 100 shares).

Let’s now examine the two short calls. The investor receives $4 per share per contract to establish them, and at $75 both contracts are $15 “in the money.” Therefore, the short calls experience an $11 loss per share per contract ($15 - $4), or a $2,200 overall loss ($11 loss x 100 shares x 2 contracts).

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

Gain or loss if ABC rises to $55 = **$400 gain**

The positions cost $100 to establish initially. At $55, only the long call is “in the money.” It maintains $5 of intrinsic value, a gain to the investor. The two short calls are “out of the money” and will expire. Therefore, the investor has an overall gain of $400 ($500 intrinsic value - $100 initial cost).

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

Short 1 MNO Jan 85 call at $16

Long 2 MNO Jan 100 calls at $7MNO’s market price = $95

Maximum gain?

Maximum loss?

Breakeven(s)?

Gain or loss if MNO falls to $90?

Gain or loss if MNO rises to $120?

Can you figure it out?

(spoiler)

Maximum gain = **Unlimited**

First, let’s determine the value of establishing this spread. The investor obtains $16 for the short call and pays $14 to buy the two long calls ($7 x 2). Therefore, the investor receives a total of $2 per share (receive $16, pay $14), or $200 overall ($2 x 100 shares) to establish the ratio spread.

The investor profits in one of two scenarios. First, the investor keeps the initial $200 credit if all options expire. This would occur if MNO’s market price falls below $85, resulting in all legs being “out of the money” and a $200 overall gain as all contracts expire.

The other way to profit is if MNO rises significantly. Once the market price rises above $100, all contracts are “in the money.” Above $100, the short call’s losses offset the gains of one of the long calls. The other long call continues to gain more the further MNO’s market price rises above $100. Therefore, the investor has unlimited gain potential.

Maximum loss = **$1,300**

The investor’s maximum loss is reached when MNO’s market price is at $100. At this price, the short call is “in the money,” by $15 and both long calls are “at the money.” Neither long call has intrinsic value, so they will not provide a return to the investor. Netting the $2 received to establish the positions up front against the $15 short call intrinsic value loss results in a $13 per share maximum loss, or $1,300 overall ($13 x 100 shares).

Breakevens = **$87 and $113**

This strategy has two breakeven points. As discussed above, establishing the three positions costs $200 overall. At $87, the short call is “in the money” by $2, which is $200 of overall intrinsic value* ($2 x 100 shares). The $200 intrinsic value loss offsets the spread’s $200 initial establishment value.

**Remember, intrinsic value is a loss for a short contract.*

We already know this spread reaches its maximum loss of $1,300 at a market price of $100. When MNO stock rises above this point, the extra long call continues to make gains (the other long call and short call offset each other). Once MNO’s market price reaches $113, the extra long call experiences $1,300 in gains ($13 “in the money” x 100 shares), which offsets the $1,300 loss when MNO was at $100.

Gain or loss if MNO falls to $90 = **$300 loss**

The positions provide $200 to the investor when initially established. At $90, only the short call is “in the money.” It maintains $5 of intrinsic value, a loss to the investor. The two long calls are “out of the money” and will expire. Therefore, the investor has an overall loss of $300 ($500 intrinsic value loss - $200 establishment value).

Gain or loss if MNO rises to $120 = **$700 gain**

There are two reasonable ways to determine the answer. First, let’s start with the $113 breakeven discovered above. At $113, there is no gain or loss. As the market price rises above $113, the extra long call continues to make additional gains (the short call’s losses offset the other long call’s gains). At $120, the extra long call gains an additional $7 per share, or $700 overall ($7 x 100 shares).

The other way involves breaking down the spread into two separate problems and then adding up the numbers. Let’s start with the short call first. The short call pays $16 to establish, and at a market price of $120 is $35 “in the money.” Therefore, the short call experiences a net $19 loss per share ($35 intrinsic value loss - $16 establishment value), or a $1,900 overall loss ($19 loss x 100 shares).

Let’s now examine the two long calls. The investor pays $7 per contract to establish them, and at $120 both contracts are $20 “in the money.” Therefore, the short calls experience a $13 gain per share per contract ($20 intrinsic value - $7 establishment cost), or a $2,600 overall gain ($13 gain x 100 shares x 2 contracts).

Adding up all the numbers, the investor has an overall gain of $700 ($2,600 long calls gain - $1,900 short call loss).

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