Protecting a Portfolio with Collars. How Many Puts are Required?

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1) I believe you agreed (with caveats) that a portfolio with a beta of .50 and desired maximum loss of 15% can purchase SPX puts 30% OTM (I ignored transaction costs). My confusion: how many contracts to buy.

Assuming I have a $1mm account with a beta of .50 and want to limit losses to 15%. Current S&P is $1,080; the one year 750 put is $36.90.

If I buy 5 at that price wouldn't my portfolio be insured? Say the S&P falls by 35%, the value of my stock & bond portfolio would be $825,000 (given the beta). I would have paid $18,450 for the puts (5*100*36.90) and when I exercise them at 700 I collect $25,000 ((750-700)*100*5).  That gives me a $6,550 gain on the options my portfolio a total value of $831,500 and a loss of a little over 16%.

I ran the numbers at higher loss levels and get the same results – the portfolio loss is limited to roughly 15% with five contracts.  This is troubling to me because your explanation makes sense, but my numbers are giving me the desired insurance.


2) With regard to "the long dated put does not provide the hedge you think", is this because of the following reasons: (1) If you pay up for IV when it is high and IV goes lower the put loses value? This is also why buying longer dated puts and selling shorter dated calls can be risky. (2) The delta is lower given the longer expiration date? (3) If the market moves up, your puts decrease in value and probably no longer provide the desired hedge? 


3) Assuming the above assumptions are correct, if the goal is pure insurance are those points negligible? I believe you outlined this in the post "Q & A. Stretched Collar (LEAPS Puts and Short-Term Calls)". That being said, if IV is high (say like now) then maybe shorter dated puts will prove more beneficial in the long-run.

Again, I want to thank you for your help and hope you can clarify those few questions/statements. 

Our firm is just trying to find a good way to manage risk and insure portfolios. Options seem like the best way (and I loathe structured notes). Thanks so much and keep up the good work. When we start introducing options to our clients your book will certainly be the go to we recommend.



1a) Yes.  SPX is a reasonable proxy for your diversified portfolio, if that portfolio consists primarily of large-cap stocks.  If not, other indexes may be more appropriate.

1b) Yes you can buy 30% OTM puts to suit your scenario of losing no more than 15% (of a 0.50 beta portfolio) in a bear market.  But, this is true only as long as  beta remains near 0.50.

1c) How did you decide to purchase 5 puts? When the strike price is 750, each put gives you the right to sell $75,000 worth of stock.  That equates to $375,000 – and you own a $1mm portfolio.

When buying puts to protect the portfolio, you must use the strike price to determine how much stock you will be able to sell, should it become necessary.  [That statement applies to American style options.  But the math hold true for European options, even though you do not actually sell any shares]  The current index price is not the answer.  Thus buying 5 puts does not give you the right to sell 5 * 1080 *100 worth of shares.

I don't know what you did when you ran the numbers at higher loss levels, but look at this:

If the market is cut in half when expiration arrives, then SPX is 540.  The puts are ITM by 210 points and are worth 21k each, or $105,000.  The portfolio declines by 25% and is worth $500,000. Addendum.  The portfolio is worth $750,000.  Mea culpa. Total value of your assets: $605,000. $855,000  Net loss: 40%. 15%

Assumption: net cost to buy puts and sell calls is essentially zero

Conclusion:  you are not buying enough puts.  Five puts appears to be the correct quantity.


Take it to the (impossible) extreme: SPX goes to zero.  The puts are worth $75,000 each.  How many puts must you own to have $850,000 cash? Five is not sufficient.

1d) You calculated the loss by ignoring the sale of call options, and that's not something to ignore.  Let's assume you collect as much from the calls as you pay for the puts.  That's going to be approximately true, unless you want to take a more bullish stance.


2) Regarding buying long-dated puts and selling short dated calls.  This is important.  I'm pleased that your results are troubling.  They should be. You seem to believe that once the market drops 35%, you no longer lose money on a further decline.

That's true only when you are adequately hedged.  And you believe 5 puts is the correct quantity to buy.  Read on.

a) When the market drops and the calls no longer offer much in the way of downside protection, your position is essentially: Long puts plus long stock.

That is equivalent to being long the long-dated call (same strike price as the put).  Please tell me you understand this – if not, you must pause in your questions and learn about equivalent positions (Chapter 15 in The Rookie's Guide to Options) before going further. 

Thus, you own that synthetic LEAPS call and when the market tanks, what do you expect will happen to the value of your call option?  It's positive delta and you have essentially zero hedge.  Sure, it will pick up a bit of value as IV increases, but the value of the call, and the value of the portfolio decreases.

That's the reason why collars are a slightly bullish play.  You earn a limited profit on the upside, but lose on the downside.  The purpose of a collar is to limit, not eliminate, those losses. When you own a call (or a synthetic call as you do in this scenario), loss is limited.  But make no mistake, you have a loss.

By selling the long dated call instead of the short-term call, you collect MUCH more premium.  You still lose on the downside, but the loss is less.  If the market punches through the put strike price (of your collar), then you have ultimate protection.  But you still lose (in your scenario, that's 15%).

b) If the market surges and moves through the call strike price, then the call delta moves quickly to 100 and the put delta moves slowly towards zero.  This is the reason why selling short-term options is so dangerous – high negative gamma.  The long-term options you buy have a much smaller gamma and the option delta does not approach 100 quickly.  The delta moves slowly. 

That means your put loses significant value on the upside while your covered call portion (yes: the long stock plus short call is a covered call) of the position gains, it gains much less quickly than the put loses.  Two reasons:  the put value gets crushed by an IV decrease and it contains far more time value  than remains in the call.

The profit potential of a covered call that has already moved significantly into the money is merely the time premium (not its full price) in the call.  And that is going to be far less than that of the long-term put.

Mixed month collars are risky and you do not want to trade them for clients who are using collars for safety.  Mixed month collars are NOT safe positions.


3) Yes.  In my opinion long-term options (when planning to hold for a long time) should only be purchased when you believe IV is relatively low. 

Yes, shorter-term puts are better when IV is high.  The definition of 'high' is highly subjective.  And short-term puts are FAR more effective when the market tanks?  Why?  They have a much higher positive gamma.  The delta moves to 100 quickly.  There is far less time premium to lose when they move deep into the money.

But the bottom line is that you do not want to own mixed month (stretched) collars.  Just too risky for you and your clients.  For aggressive clients, that's another story.  But clients who use collars for safety should not be subjected to this risk.

ZA: If your firm feels some consultation would be beneficial, my rates are truly a bargain, and you get to ask all the questions you feel like asking.  With immediate replies.


"I thoroughly enjoyed your book “The Rookies
Guide to Options”.  The book has paid for itself many times
over.  Thank you."  VR


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5 Responses to Protecting a Portfolio with Collars. How Many Puts are Required?

  1. ZA 06/04/2010 at 8:20 AM #

    Here is how I got to the 5 puts: ($1m portfolio * .50 beta) / (1080 current SP level * 100 multiplier), rounded up.
    In the extreme example the S&P 500 goes to zero and the puts are worth $375,000, which I agree does not adequately hedge. However, if Beta holds the portfolio should be worth $500,000, so the total portfolio would be worth $875,000 and providing the desired hedge. Now if the S&P did actually go to zero I have no doubt the beta of my portfolio would probably be closer to .95, but for these examples I am assuming beta holds.
    Also, in the other example if the market is halved the portfolio would be worth $750k ($1m * (1+(-.50 decline * .50 beta)). If you add the $105k in out value the hedge holds.
    I think you did not take into account the movement of the portfolio, if beta holds, will not be 1. I hope this clears up my math.
    I am going to talk to the partners in my firm and see if consultation is something we should look at. How should I contact you?

  2. Mark Wolfinger 06/04/2010 at 8:34 AM #

    Thanks for correcting my error.
    Apparently 5 puts are sufficient.
    I sent contact info via email

  3. simon 06/04/2010 at 8:43 PM #

    Tried opening AUG & SEP ICs on strikes with wide bid/ask, low volume and little open interest but could’nt get filled anywhere near the mid price. Even as the volatility increased and prices moved closer I still had no luck. Whats your take on this?

  4. Mark Wolfinger 06/05/2010 at 9:08 AM #

    When the market makers have no interest, there’s not much you can do. Low trading volume precludes trading with other individual investors.
    My suggestion: Decide how much premium you want to collect, and ask that amount (starting higher and moving to your level). If you cannot get your price, so be it. I am not concerned how much below the midpoint I have to move when the markets are so wide.
    Alternative: Move one strike closer to get your price. But do be aware that the probability of profit is slightly lower when the strike is closer to being ATM.
    Clarification: I am only willing to make these concessions at a time when IV is relatively high. Under those conditions, I am already collecting a higher premium than I can collect under most market condition,s so feel I have room to be flexible.
    I do recognize that IV is high for a reason, but when planning to hold a trade for almost three months, another dime is not the deciding factor for me.

  5. simon 06/05/2010 at 11:11 AM #

    welcome your response, much appreciated Mark. It gives me something to think about.