A ratio strategy is an options strategy with unbalanced sides (different numbers of contracts). Previously, we covered ratio call & put writes and ratio call spreads. This chapter focuses on ratio put spreads, which are put spreads with a heavy side (more contracts) and a light side (fewer contracts).
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 with ratio call spreads, the key to ratio put spread questions is to identify the heavy side and analyze what happens as the market moves.
Here, the investor is short two puts. One short put is effectively hedged by the long put, but the second short put is naked (uncovered). That naked short put creates the main risk: if PDQ falls, losses on the uncovered short put grow as the stock price declines.
In the worst-case scenario, PDQ falls to $0. Even then, the loss is large but limited (because a stock price can’t fall below $0).
The market outlook is similar to a typical short (credit, bull) put spread: the position benefits if the stock stays up. The difference is that the risk and reward are amplified because of the extra short put. In practical terms, the investor is looking for PDQ to rise to (or remain at) $50 or higher by expiration.
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?
Maximum gain = $2,000
First, find the net premium (the cash flow to establish the position):
Net credit = $20 per share ($24 − $4) = $2,000 ($20 × 100).
The maximum gain occurs at $50 or above. At that price, all puts are out of the money and expire worthless, so the investor simply keeps the $2,000 credit.
Maximum loss = $5,000
Because the heavy side is the two short puts, the worst outcome is a large decline in PDQ. The lowest possible stock price is $0, so evaluate the position at $0:
Net exercise result at $0 = −$70 per share (−$100 + $30) = −$7,000.
Now include the initial credit:
Maximum loss = $5,000 (−$7,000 + $2,000).
Breakeven = $40
This position has one breakeven.
The investor starts with a $2,000 credit. At expiration, the long 30 put is out of the money as long as PDQ is above $30, so it contributes $0 intrinsic value at $40.
At $40:
That $2,000 loss offsets the $2,000 credit, so breakeven is $40.
Gain or loss if PDQ rises to $45 = $1,000 gain
At $45:
Net result = initial $2,000 credit − $1,000 = $1,000 gain.
Gain or loss if PDQ falls to $20 = $3,000 loss
Break the position into the long put and the two short puts.
Long 30 put
Two short 50 puts
Net result = $3,600 loss − $600 gain = $3,000 loss.
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?
Maximum gain = $7,200
Start with the net premium:
Net debit = $18 per share ($24 − $6) = $1,800.
The heavy side is the two long puts, so the position benefits most from a decline in XYZ. The lowest possible stock price is $0, so evaluate the position at $0:
Net exercise result at $0 = $16,000 − $7,000 = $9,000 gain.
Now subtract the initial debit:
Maximum gain = $9,000 − $1,800 = $7,200.
Maximum loss = $1,800
The maximum loss occurs when XYZ is at $80 or above at expiration. All puts are out of the money and expire worthless, so the investor loses only the initial $1,800 debit.
Breakeven = $71
This position has one breakeven.
The investor paid $1,800 to establish the spread, so the position must generate $1,800 of intrinsic value at expiration to break even.
At $71:
So breakeven is $71.
Gain or loss if XYZ rises to $75 = $800 loss
At $75:
Net result = $1,000 intrinsic value − $1,800 initial debit = $800 loss.
Gain or loss if XYZ falls to $50 = $2,200 gain
Again, break it into the long puts and the short put.
Two long 80 puts
Short 70 put
Net result = $3,600 − $1,400 = $2,200 gain.
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