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Here is my understanding from what I’ve gathered, but I want to confirm if this is correct (and/or if there’s something I’m missing).

If a stock becomes hard to borrow, one can create a synthetic short forward position by selling calls and buying puts at the same strike and expiry. This allows a trader to replicate the exposure of a short position without paying the borrow cost. This means that call prices go down due to selling pressure, and put prices go up. This implies the forward price due to PCP goes down due to the hard to borrow nature of the stock.

I haven’t been able to find many resources that say this explicitly, so I’m looking to verify my current understanding.

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  • $\begingroup$ It sounds right (everything you wrote) to me. $\endgroup$
    – KaiSqDist
    Jan 10 at 4:08
  • $\begingroup$ Thanks! @KaiSqDist and to double check the direction of movement, if borrow costs increase, forward prices go down, and call prices go down and puts go up? So in other words, borrow cost increase has the same effect on puts and call prices as an increase in dividend (assuming it is a continuous dividend yield)? $\endgroup$
    – rb612
    Jan 10 at 4:20

1 Answer 1

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As you described, buying a put and selling a call in the hard to borrow stock, you have created a synthetic short future.

Like other equity finance positions, the "difficulty to borrow the stock" will manifest itself in a higher negative carry that must be paid to the "stock lender" to lend the stock. The difficulty in borrowing the stock is manifested in the price of the options through the interest rate input in the options pricing formula.

There are players in the reversal and conversion market ("rev-con"), where participants that own the stock will lend it, by selling the stock and buying the "cheap" synthetic future (sell put, buy call at the same strike and expiry). This is the "cheap" synthetic future that you as the borrower are selling through your long put-short call. The lender effectively earns the carry by being able to buy the stock back cheaper in the future, thereby earning the higher interest rate or carry of hard to borrow stocks.

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  • $\begingroup$ Thank you! Can you please clarify "where participants that own the stock will lend it, by selling the stock and buying the "cheap" synthetic future". When you say "...will lend it by..." here, how is this specifically lending? I see how selling the stock and buying the cheap synthetic earns the carry, but I don't see how it's considered "lending". $\endgroup$
    – rb612
    Jan 10 at 4:53
  • $\begingroup$ By creating a "cheap" synthetic short futures position you are telling the market you are willing to pay for borrowing the stock by willing to sell the stock in the future lower than spot. The cheap synthetic future induces the arbitrager to engage in the rev-con to earn the carry by selling the stock he owns and being able to buy it back cheaper. As the synthetic future seller, if the stock falls below the future price at options expiry, you will earn the difference between where you sell the stock to the synth futures buyer, and where you close your position by buying the stock to sell. $\endgroup$
    – AlRacoon
    Jan 10 at 5:26
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    $\begingroup$ You have effectively borrowed the stock by creating the cheap synthetic future. $\endgroup$
    – AlRacoon
    Jan 10 at 5:29
  • $\begingroup$ Thank you, that makes sense. One final follow-up: I always tend to think of higher cost of carry = higher forward price (e.g. commodity forwards, higher storage cost = higher forward price), but it seems like here we have a higher cost of carry (due to higher borrow costs) but forward price decreases due to PCP. Am I thinking about that right, and if so, how do I reconcile both? $\endgroup$
    – rb612
    Jan 10 at 5:39
  • $\begingroup$ F = S(1+r). If cost of carry is positive, F>S. If r is negative, F<S. When you sold the cheap future, you agreed to sell back the stock lower than today and you are paying the r (negative) $\endgroup$
    – AlRacoon
    Jan 10 at 5:53

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