# Ratio Spreads Part III. Break-even

I believe it's best to trade positions based on current risk and to ignore prices at which your trade becomes a break-even proposition.

Nevertheless, I recognize that most traders are always interested in break-even prices for their positions.  With that in mind, Let's look at ratio spreads and discover how to calculate those break even prices.  This post is primarily for option rookies, especially those who have avoided the temptation to sell extra (naked short) options.

The ratio spread (Part I, Part II) is designed to earn a good profit when the underlying trades within a price range, and it's advantageous when the underlying moves somewhat higher or lower. However, there's always a limit to how far the underlying can move before a profitable situation becomes risky to hold.  A continued move turns the position into a monetary loser.  The worst part of trading these positions is defending against the essentially unlimited losses that are possible. [To eliminate the chance for incurring large losses, the broken-wing butterfly spread can come to the rescue.  That's the topic for part IV in this series]

Break-even for 'non-risky side' of the trade

When you trade a call ratio spread, the position contains one or more naked call options.  Risk is to the upside and there is essentially no downside risk.

When you trade a put ratio spread, the position contains one or more naked put options. Risk is to the downside and there is essentially no upside risk.

When the initial position is established, there are three possibilities:

• A cash credit is collected
• The trade is made at 'even -money'.' and no cash is required to make the trade
• A cash debit is paid

When cash is collected, there is no chance to lose money when the stock moves to the 'non-risky' side.  Here is an example.

XYZ is trading near \$92 per share

Buy 5 XYZ Jan 95 calls @ \$4.00

Sell 9 XYX Jan 100 calls @ \$2.30  (Note: the long/short ratio does not have to be an integer)

Net cash:  Collect \$70

Risk:

• Downside: No matter how far XYZ falls, there is no risk of loss.  The options eventually become worthless, but that \$70 premium is yours to keep
• NOTE: When a cash debit is paid to open the ratio spread, that debit represents the maximum possible loss when the stock moves to the 'non-risky side.'  Most traders prefer to collect a cash credit for ratio spreads – and the idea of a guaranteed profit when the underlying moves in one direction is the rationale behind that strategy.

Break-even for risky side of the trade

• Upside:  Because you are short four extra calls, there is an expiration price at which this position begins to lose money.
•  The position shows a real loss at a much lower price prior to expiration because the nine short options carry more  time premium than the five long options.  Clarification:  As the stock rises, the nine Jan 100 calls collectively increase in value more quickly than the five Jan 95 calls (the total position is short delta).  This only happens when you are net short calls.  Individually, the Jan 100 calls never increase more rapidly than the Jan 95 calls.  But when short extras, there is upside risk.

Recognizing that there is an upside price beyond which this ratio spread loses money, the objective is to calculate that price.  NOTE:  This discussion involves finding the break-even price at expiration.

Method A (I find this method to be much easier)

You own 5 XYZ Jan 95/100 call spreads.  Above 100, these are worth \$500 apiece, or \$2,500.

You collected \$70 cash to open the trade

Thus, you have a profit of \$2,570 when XYZ is \$100 at expiration.

You are short four extra calls

You lose money at the rate of \$400 per point when XYZ moves above \$100

Divide the meximum profit (\$2,570) by \$400.  Result: \$6.425

That tells you how far the stock can rise (beyond \$100) to reach the break-even point.

Result:  Upside break-even point for this trade (ignoring commissions) is \$106.425

Method B (Algebra)

For the trade to be a break-even, the value of the longs and shorts must be the same.

Let X = the option value that represents the break-even price.  At that price, each of your long calls is worth \$500 more than each of the short calls.

5*(X+500) +70 = 9X
5X + 2,500 +70 = 9X
2,570 = 4X
X = 642.5

The option 'value' above \$100 is \$642.50, or \$6.425 per share.

B/E = \$106.425

I understand how important it is for most traders to recognize the break-even prices for a position such as the ratio spread.  However, by focusing on these price points, it's easy for a trader to fall into the trap of believing that as long as the stock trades within those prices (in this example that's between 0 and \$106.42) that all is well and that the trade is under control.

That is false security.  There is no risk on a market decline (when it's a ratio call spread that generated a cash credit), but there is upside risk that comes into play well before the expiration break-even price is reached.  Just think of the risk when XYZ is trading near \$106.00 two weeks before expiration.  It's more important to manage current risk and to be certain your comfort zone boundaries are not violated than to ignore risk and gain comfort that the position is still below the break-even price..

Ratio spreads work well in the hands of traders who understand how to limit damage when the underlying moves too far.  Concentrating on expiation break even is exactly the same as looking at naked short options, hoping they expire worthless.  In this example, the strike price of the extra options is \$106.42.  Losses accrue well below that price prior to expiration.  It's just as risky to 'hope' XYZ finishes below that price as it is to hope that short options expire worthless.

If the potential losses of ratio spreads are of concern (they should be), next time we'll look at methods for capping those losses at acceptable levels. [It must be acceptable by definition because you get to choose the maximum potential loss.]

to be continued…

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