Honest: Equivalent Positions are Equivalent

Hi Mark,

I've been thinking about the equivalence of some option strategies, and how to determine which position would be better.

Take for instance a put debit spread:
Buy XYZ Jan 60 Put
Sell XYZ Jan 50 Put

and a call credit spread:
Buy XYZ Jan 60 Call
Sell XYZ Jan 50 Call

If both the above have the same profit & loss potential, how do you evaluate which is the better position? With the debit spread, time decay would chip away at it, while the credit spread would increase in value. 



You are trying to turn something very simple into something that is more complex.

1)If the positions are equivalent, neither one is better. Time decay is the same for each spread.

They provide, by definition, equal profit/loss pictures. That 'equal profits' takes into considerations dividends, if any, and interest costs – which make a different when interest rates are high. What is not included are trading costs.  

2) One is better than the other – when it is priced out of line. That does happen on occasion, but not frequently. 

One is better than the other if trading costs are reduced (think naked put vs. covered call).

One is better than the other if it is easier to exit the spread – if you elect not to hold to expiration (again naked put much better than covered call).

Look at your example. If you buy the put spread, your best result (XYZ < 50) makes the put spread worth 10. If you sell the call spread, your best result occurs when XYZ < 50, and the spread is zero. Thus, each makes the maximum profit in the same price range.

Similarly, XYZ > 60 gives you the maximum loss. The put spread is zero and the call spread is 10.

3) At every possible price, the sum of the two positions is 10. Thus, if you pay 10-x for the put spread, it's the same trade as selling the call spread for x.

If you pay $7.10 for the put spread, then selling the call spread and collecting $2.90 provides the same payoff.

Which is better? Neither. But there are reasons why selling is better than buying. If you buy the put spread, you pay interest on that cash. Today that may be essentially zero, but that's not always the case.

If you sell the call spread, you collect interest on $290. To the extent that interest is above zero, you always want to collect the cash rather than pay. Unless the spread prices account for that difference in interest costs.

But if you can buy the put spread @ $700 instead of $710, then that's the better deal (assuming that the call spread can still be sold @ $2.90. It's not a better deal if the call spread can be sold @ $3.00). 

For traders with very small accounts, selling may result in a problem if assigned prior to expiration.  Buying eliminates that risk (if assigned, just exercise) – and to prevent a margin call, buying may be preferred.

One final consideration. You buy the put spread because you are bearish. If you are correct and both options are ITM at expiration, most brokers charge two exercise/assignment fees. If you sell the call spread, both options expire worthless and the broker is paid nothing. So once again, selling is better than buying.


13 Responses to Honest: Equivalent Positions are Equivalent

  1. Bram 01/24/2010 at 5:22 AM #

    Small, nit-picking comment:
    I don’t think that there is any option market maker who uses a bid/ask on their risk-free rate. As a result, nothing is to be gained from receiving money rather than paying upfront as long as you can borrow/lend against the risk-free rate.
    Now obviously this won’t be the case and retail saving/deposit rates often provide a rate > risk free rate. So in that sense receiving money rather than paying money (lending rates close to the risk free rate aren’t available to retail investors as well) is better, but this has nothing to do with that there is an “arb” in rates used for option pricing, but rather because there is an arb between rates used for option pricing versus retail savings/deposit rates. Moreover, this “arb” isn’t a real arb after crossing the IV bid/ask in almost all cases I would guess.

  2. Jason 01/24/2010 at 8:21 AM #

    I have done covered calls for a while. Looking to increase returns without taking on much more risk. Wondering about a covered spread approach where I own the stock, short OTM calls, short OTM puts, and enter a stop sell order to automatically liquidate shares if stock hits my put strike price to cover situation where stock could be put to me. This seems like a no brainer to enhance returns without anymore risk but wondering if I’ve overlooked anything. Thoughts?

  3. Mark Wolfinger 01/24/2010 at 8:24 AM #

    Nits are ripe, and it’s fine to pick them.
    I wasn’t so much making the case for always taking in the cash rather than spending it. I’m trying to convince readers that equivalent positions are equivalent and neither is ‘better.’
    Sure, there can be an advantage when one of the positions is cheaper to execute the trades or carry (due to the time value of money) the position, but there is no need to worry about which is ‘better.’
    I agree completely that an ‘arb’ opportunity is not going to be available (or not remain available for more than a few seconds) and it does not pay to spend the time searching. However, I have occasionally found that a tighter bid/ask spread that results from a customer bidding or offering a few contracts, can make one of the two equivalent positions a better ‘do’ for a very limited time.

  4. Mark Wolfinger 01/24/2010 at 8:44 AM #

    This is not a no-brainer. It is riskier than you think.
    I have lots of thoughts on this issue.
    I hope you can wait – I’d like to reply at length as a separate post.

  5. Roger 01/24/2010 at 12:36 PM #

    Apologies for the dumb question here: When you say “The put spread is zero and the call spread is 10” or “The call spread is zero”, in what sense is a spread zero?

  6. Mark Wolfinger 01/24/2010 at 12:40 PM #

    The only ‘dumb’ quetion is the one you don’t ask.
    In the sense that both options that comprise the spread are out of the money, expiration has arrived, and the options are, for forever will be, worthless.

  7. Rob 01/24/2010 at 1:56 PM #

    Hi Mark,
    I have a question unrelated to the current thread. You’ve mentioned that a rolling adjustment is often used by traders when perhaps it shouldn’t be. Would you be willing to elaborate on conditions that make rolling a good/viable adjustment choice?
    I ask because I recently rolled my puts on an OEX condor and used the following rationale:
    1. I originally received $1.30 for my 4-lot Mar 485P/495P. During this downdraft OEX was within 15 points of my short, and my comfort zone was breached.
    2. By rolling to 460P/470P I took a loss of $375 on the original spread, and collected $1.15 for the new 4-lot spread. This resulted in a position that I like–it’s delta neutral and theta is still good. I considered rolling the calls down to finance rolling the puts, but decided it wasn’t worth the additional risk.
    3. With more than 50 days to expiration, there is still time to make money in this trade. It has a $795 profit potential, though I won’t be staying long enough to collect all of that. By this I mean that I’m not flirting with rolling adjustments the week before expiration in a desperate attempt to eek out a “win”.
    4. I can still get out of the trade and keep losses down to a reasonable size if it continues to lose. This rolling adjustment seemed like a reasonable balance between staying in the trade (and perhaps profiting) and managing risk to prevent a losing trade from losing too much.
    I’d be curious to hear your thoughts on rolling, and of course any other ideas you have about this situation. While the market moves over the past few days haven’t been huge by historical standards, they are larger than I’ve had to deal with so far!
    Kind Regards, Rob

  8. Mark Wolfinger 01/24/2010 at 2:56 PM #

    You know the answers. your reply tells me that.
    1)A roll is a good, viable choice when two conditions are met:
    a) You want to exit the current position
    b) You WANT to own the new position.
    That’s it.
    2) OEX is the wrong underlying asset for iron condors – unless you never allow short options to move too far ITM. There is a serious risk associated with early exercise when trading AMERICAN style, cash-settled options. OEX is the only one that exists.
    3)Point #3 above is 100% irrelevant – at least to me. The old position is gone. Forget it. the new position is what you own. My advice is: manage it for risk – don’t manage it for profits.
    If you eke out a win or exit for safety and eke out a loss does not matter in the long run. If you manage positions well, you will survive. If you feel the need to have as many wins as possible, your future is going to depend on how lucky you get.
    4) Point #4 above sums it up. You are in good shape and have a winning mindset. That bodes well.
    5) These moves are nothing compared with recent events (2008/early 2009)

  9. Rob 01/24/2010 at 3:29 PM #

    Thanks for the feedback Mark.
    Regarding OEX, I understand the issue with the American-style exercise. I prefer the European-style XEO and have traded it a couple of times, but really had difficulty getting filled. I tried OEX and got filled at mid prices almost immediately, though I can’t always expect that.
    Perhaps RUT and OEX/XEO are too closely correlated to provide any diversification. They share similar behavior… except when they don’t! I’m trying to find my way here, and have been thinking that trading a condor on one underlying and a d. diag on another underlying is a good way to to be reasonably delta and vega neutral.
    Lots to think about! (Mildly understated…)
    Thanks, Rob

  10. TR 01/24/2010 at 7:39 PM #

    Hi Mark
    Your suggestion that an IC trader should be removing cash (from the post on Jan 22nd : Size Mattes) from their trading account on a regular basis (as opposed to continuously compounding earnings) triggered a question in my mind.
    Is there a certain percentage of total savings/investment portfolio that you think an IC trader should dedicate towards this strategy? I was hoping you could elaborate a liitle bit of how you think through this issue.
    In my own trading my “money at risk” in my IC portfolio represents about roughly 10% of my total investment portfolio (the other 90% is in index ETF’s based on an asset allocation approach). My game plan was to increase my IC exposure slowly over time as I become more comfortable with the strategy. That being said, I haven’t given much thought to what the maximum amount (or %) I should allocate to IC’s.
    I would imagine that if you are willing to spend money on isurance then you would likely be more comfortable allocating a larger portion of your portfolio to IC’s.

  11. Mark Wolfinger 01/24/2010 at 8:16 PM #

    If you are using 10% of your total investment portfolio for one strategy, that feels very reasonable to me.
    If you are successful and this percentage grows, you should consider a limit on how far it can grow. That affords protection from over-confidence.
    There is a psychological barrier to overcome. If you do well and double your account value in an unspecified period of time, the temptation is to continue ‘doing what you are doing.’
    To a point that’s a smart decision. But, to do that you must be certain that you have ‘mastered’ your trading and that good luck played no role in your success. Most traders will fall into the trap of believing they are much better traders than they are.
    I suggest you set a limit on how much you want this account to grow and then take about 75% of all earnings above that level and place it elsewhere. That leaves 25% for continued growth.
    After your first withdrawal, take money out (75% of the new profits) whenever those profits reach $X. That may be as little as $1,000 for a small account. But I’d suggest that a 10% increase calls for another withdrawal in larger accounts.
    The numbers are not important. It’s following the principle.
    The safer your portfolio, the more you can allow the portfolio to grow. But disasters can happen when not careful. Your other 90% is allocated rather conservatively. That does not make me think you would be comfortable taking big chances on losing a bundle.
    Just be certain that whatever amount to elect to leave with this strategy that your comfort zone is not violated.

  12. Bram 01/26/2010 at 4:54 PM #

    Got another nit 🙂 For the point you were trying to convey, it actually doesn’t matter, but for other strategies it might as well as that it might provide some further insight to some:
    Honest: Equivalent positions aren’t equivalent. Epsilon (sensitivity) to dividend yield, is different for a call and a put. So in that sense, there is a real difference, between being having written a covered call and having written a put! Example: if a company pays a higher dividend than implied from option prices, the position of long the stock + short the call is profits whereasthe written put loses.

  13. Mark Wolfinger 01/26/2010 at 6:47 PM #

    You are right that they are not equivalent down to a whole bunch of decimal places, but the real cash difference is small, and I’d rather save commission on the naked put than write the covered call.
    Of course if the company pays a higher dividend than implied by the options, then there is an arbitrage opportunity. That would tend to move the options back to implying the correct dividend
    I don’t want to provide any mis-information in this blog, but remember that much of my writing is directed to the options rookie. I truly believe that that the CC and NP are ‘equal enough’ for most purposes. I’m talking about monetary outcomes, and am not teaching a graduate level finance class.
    Appreciate the comments, but I really don’t want to get into the higher level math in this blog.