I am new to finance, markets and various financial securities. I just started with some Khan Academy Videos and Udemy courses. Our professor introduced the concept of using a Put Option to establish a floor of loss below the underlying. I think that I understand the concept of how a put protects the loss as price falls.

The professor has asked us to simulate a scenario where fractional puts are possible. I am at a total loss as to how buying half a put option would work. Am I insuring only half of the price fall and incurring loss on the other half? That doesn't sound right to me. Any help is greatly appreciated.

  • Look up "mini options contracts". – Ben Voigt Sep 9 '18 at 1:42
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    Can you give more context of the lesson? I suspect that the lesson is on delta-hedging which requires buying odd-numbers of option contracts but it's hard to tell from your question. – D Stanley Sep 9 '18 at 1:49
  • @BenVoigt Based on a quick read, I understood standard Options contract are 100 shares per lot while mini options are 10 shares per lot making it possible to hedge fewer shares. – Shantanu Chopra Sep 9 '18 at 1:56
  • @DStanley Lesson was on simulating and comparing the ETF returns vs Portfolio returns using ETF + Put Option. Task was to evaluate the same when Fractional Put was allowed like 0.5 puts for each share. – Shantanu Chopra Sep 9 '18 at 2:01
  • @Ben Voight - I don't keep up with it but the last that I knew, there were only FIVE mini options created 5-6 years ago and I seem to recall that GOOG minis may have been delisted. There's not much you can do with these unless you're trading in the underlying of these 4 or 5 issues. – Bob Baerker Sep 9 '18 at 13:50

In the US, standard option contracts are for 100 shares. You cannot buy a fraction of a contract.

Long stock has a positive delta (+100 per 100 shares) and a long put has a negative delta. The size of the put's delta depends primarily on its relationship to the price of the underlying (the more in-the-money it is, the higher the delta). Secondary effects would be from implied volatility and proximity to expiration.

In order to meet the requirements of this question, you need a put strategy that maintains a net -50 delta from the underlying's current price down to a price of zero. I know of no such strategy.

The only possibility that I can think of is to buy 200 shares (+200 delta) and buy one at-the-money put (-100 delta) for a net delta of +100 or a delta of +50 per 100 shares (below the strike price). That means that for every point of drop below the strike, the total position will lose 100 delta or $100 which is a 50% hedge. Note that this ignores the cost of the put in the hedge ratio calculation. If an out-of-the-money put was used, for an accurate hedge ratio, you'd also have to include the 'deductible' loss (distance from the underlying's price down to the strike price of the put).

Also note that this is an expiration calculation. Prior to expiration, the net loss will be somewhat greater than 50% until the underlying collapses enough to drive the put's premium to parity (intrinsic value) and its delta to -100.

  • Thanks Bob! So in such a scenario(0.5 puts/share), the losses would not be floored but limited and the average return would be higher than that achieved by 1 put/share (given mean return of underlying is = +x%). I am going to read more on Options and revisit this in a week's time. – Shantanu Chopra Sep 9 '18 at 15:19
  • @Shantanu Chopra - You can slice and dice this a number of ways. With 200 shares and 1 long put, you have 100 shares fully protected ('floored') below the strike price and the other 100 shares completely unprotected. Or you could say that 200 shares are hedged at 50%, also known as the hedge ratio. – Bob Baerker Sep 9 '18 at 15:37
  • @BobBaerker an ATM put has a delta of -0.5 per share, so you would need 2 puts per 100 shares. Also, the delta will change over time, so the position will need to be adjusted accordingly. One put option will put a floor under 100 shares, at maturity, if it expires in the money. – 0xFEE1DEAD Sep 9 '18 at 23:42
  • @0xFEE1DEAD - You're just repeating what I said. If you read my explanation again, you'll note that I stated that the hedge ratio of 50% is on an expiration basis, excluding the cost of the put. It also addresses the fact that before expiration, the hedge ratio will be lower than 50% (hence the loss will be higher than 50%) because the "put has a delta lower than 100". As for the idea of Delta Neutral trading, the OP is a noob at the starting gate and is nowhere near that topic with his question. – Bob Baerker Sep 10 '18 at 1:30
  • @BobBaerker I'm not disagreeing with you, I was just trying to clarify since you wrote "buy one at-the-money put (-100 delta)", which is confusing. – 0xFEE1DEAD Sep 10 '18 at 1:35

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