# Derivatives - Own Underlying, Bear Put Spread

Probably getting too far into the minutiae here but I also weirdly enjoy derivatives. There was an answer to question 2-C on the Actual 2014 AM exam that had the following answer:

Greene could combine her purchase of put options with the sale of put options that have a lower strike price and the same maturity as the long puts (put spread). A disadvantage of this strategy is that Greene would lose downside protection if the stock price moves below the strike price of the short put.

I understand how this would be cheaper as the premium income would be gained from selling the lower put would offset purchasing the higher put but methodically how would this work? Say I owned the underlying which is currently at \$50 and I bought a put at \$45 and sold a put at \$40. What would happen once the stock went to \$45 and I exercised the put? Also, what would happen when the stock continued to fall to \$40? Would I be on the hook for the rest of the downside from \$40 to \$0?

If the stock dropped to \$45 you would lose \$5 on the stock itself. This loss of the entire position would be increased by the premium you paid for the protective put at 45 (your insurance premium per se) but the loss would be decreased a bit by the premium received from the \$40 put you sold.

So basically your stock position can only lose you \$5 plus the net premiums.

You lose downside protection because you’re now essentially left with a naked/uncovered put at \$40. You’ve entered into a contract to buy someone else’s shares for \$40 regardless of how low the stock drops. For example, if the stock drops to \$25 and the option expires or is exercised, you’d have to pay \$40 to buy a stock that has a market value of \$25. A loss of \$15 per share to you. So yes you’d be on the hook for the downside all the way to the bottom if you kept the entire position unchanged. If at some point you wanted to sell your shares but keep both options open, you’d be protected against any significant loss because your long put value would more than offset your short put liability since its exercise price is \$5 more in the money.

Let’s say Spot = 47 and you bought the Put 45 for 1\$ and sold the P40 for 0.3, your net hedging cost is 0.7.

If the price goes to 40, you lose \$7 on your stock position, you make 5 on your long put, and the short put 40 is worthless.

Net PnL = - 7 + 5 - 0 - 0.7 = -2.7

If spot falls below 40, the short and long puts cancel each other out. Your hedge stops working.

The general idea of combining a bear put spread and a long stock position is to get some downside protection to a certain level and pay less cash upfront. For example, one can setup a bear put spread on SPY by buying a 5% downside strike from the current level and selling a 20% downside strike both expiring on the same date in three months.

There is no protection in the first 5% drop, but the SPY position is hedged from -5% down to -20%. After dropping 20%, the protection is gone. The last time there was more than a 20% drop in a quarter was back in 2008-2009 period. By implementing a bear put spread, the initial cost is smaller than buying a put.

On a side note, managers may implement a covered call (ie selling 5% upside in a quarter) in addition to the put spread to mitigate the cost of the downside protection. The combo is like a cheaper and imperfect collar on a stock position.