I’ve bought insurance against major market falls over the next six months

​On Thursday I bought put options on the Dow Jones Industry Average Index.  The exercise price is 180 and this right to exercise expires on the third Friday in December.   I’ll explain.
Let’s start with what a put option is: a right, but not an obligation, to sell the underlying at a fixed price at some point in the future or over a period of time.
Applying that to the Dow: when I bought on Thursday the underlying, i.e. the DJIA stood at 26,000.  A put option gives me the right to sell the Dow at a set price in December.
A slight complication: instead of the straightforward Dow the DJIA number is divided by 100 for the option contract.
Thus if the real Dow is at 26,000 the option that is “at the money” is expressed as 260 (an at the money option has an exercise price the same as the current market price).
Each of those points is worth $100.
I’ll illustrate with the put that I purchased on Thursday: I bought the right but not the obligation to sell at 180.
If I was to go ahead and exercise my right I would be selling 180 x $100 = $18,000.
But, with index options I do not have to sell the underlying because these are what is called “cash settled”.
That is, only the difference between 180 and the value at expiry is paid over in cash (I don’t sell the 30 different company shares making up the Dow).
Obviously, I would not want to exercise the right to sell at 180 when the market is at 260. This means that the option does not have intrinsic value (it is “out of the money”).
If I had bought a 270 put option instead I would have the right to sell at 270 x $100 = $27,000. And I could buy that index at 260 x $100 = £26,000 to offset. Overall a profit.
This put option has intrinsic value of 10 points or $1,000 (it is “in the money”).
But such an option costs a lot more than the heavily out of the money one I did buy. I paid 3.90 points for the right to sell at 180.
Those 180 points are worth 180 x $100 = $18,000, whereas my option cost 3.90 x $100 = $390, which is 2% of the underlying.
I have between now and the third Friday in December for my option to gain some intrinsic value.   It will not do so if the Dow stays above 18,000.
So, if the underlying fell to 170 (that is 17,000 on the real Dow) I would have the right to sell at 180 while being able to “buy” at 170. The market organiser (CBOE in Chicago) will cash settle with me for 10 points per contract (180 – 170), each point worth $100, thus sending me $1,000 in December.
Thus, I have a highly geared position on the Dow. For a large range of Dow values in December I receive nothing, but when (or, rather, IF) the Dow falls below 18,000 I start to gain quite high percentages.  If the Dow falls all the way to 14,000, off about 46% from its current level, then the amount I receive is 9 times the amount I put down as a premium – see table.
Real Dow in DecemberDow for the purpose of option pricingI can sell atNumber of points differenceValue of optionPercentage change for the 3.90 points x $100 = $390 paid for each option
26,000260180negativeExpires worthless – all option premium lost-100%
18,0001801800Expires worthless – all option premium lost-100%
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