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In my question, as stated in the title, I aim to understand when the strategy of the CBOE Put Protection Index (PPUT) makes profit; particularly during which market conditions.

Given the description of CBOE: that the PPUT index holds a long position indexed to the SP500 and buys a monthly 5% OTM-Put option as hedge, what does that mean in terms of making profit? How does it make the profit?

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    $\begingroup$ If I got it right from CBOE description: You make profit as long as SP500 monthly increase is higher than the option premium. In exchange your worst loss is %5 + option premium. $\endgroup$ – berkorbay Nov 1 '17 at 12:57
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The PPUT strategy is an example of a "tail protection strategy". The objective is to have a return somewhat similar to the return of the S&P 500 but with better performance during "crashes" (sharp down moves in the S&P). The strategy buys puts, which cost money (i.e. detract from returns) but are helpful when the SP drops more than 5% (improving the return in that case, i.e cushioning the fall).

As berkobay said, the strategy makes money as long as the rise in S&P exceeds the cost of the puts. As we will see later the average cost of the puts is about 10 or 20 basis points per month (although it can be much higher at times, such a after a crash), so for example when the S&P is up 3% in a month the PPUT might be up 2.8%, if the S&P is unchanged, the PPUT return might be -0.20% and so on.

Let's use the > 30 years of data provided by the CBOE, and look at returns during each "option-month", where an "option-month" goes from the 3d Friday of a calendar month to the 3d Friday of the next month. For example "option-September 2017" goes from 2017/08/18 to 2017/09/15.

Here are basic statistics for the monthly returns for the PPUT strategy and for the SPX index (recall that the SPX index does not include dividends):

    PPUT                         SPX
         Monthly Annualized           Monthly Annualized
N            374   31.17     N            374   31.17
Avg     0.006327  0.075919   Avg     0.007394  0.088724
Stdev    0.03595  0.124533   Stdev   0.045541  0.157759
Frac>=0 0.596257             Frac>=0 0.625668
Max     0.125122             Max     0.139962
95%tile 0.065314             95%tile 0.072122
Min     -0.07937             Min     -0.25061
5% tile -0.05982             5% tile -0.06378

As you can see the PPUT has lower returns per year (7.59% vs 8.87%) but with lower volatility (12.45% per year vs 15.78%). PPUT is less risky, as we can more clearly see by comparing the worst (i.e. tail) outcomes. For example the worst monthly return for SPX during this period was -25% (during the option-month from September 19, 2008 to October 17, 2008), while the worst possible outcome for PPUT was "only" -7.9).

To answer your first question the PPUT makes money a decent percentage of the time (59% of months) but the SPX makes money 62% of he time.

Finally a chart of the PPUT and SPX cumulative returns visually confirms these statistics: a better return for the SPX, but a smoother ride for the PPUT.

enter image description here

Many more statistics could be computed, of course: I leave those up to you.

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