spx put selling strategy

Is Naïve Put-Selling Superior to Put-Selling in Coordination With the S&P 500 Model?

Mechanically selling an at-the-money put on the S&P 500 every month for the past 50 years would have been a net profitable strategy. Would this strategy have been improved if it had been used in coordination with the S&P 500 model incorporating seasonality, interest rates, and valuation? The answer is, not really.

Using the November, 2001, actual premiums about 2.6% for a 0.5% out-of-the-money put and 3.2% for an at-the-money call:

	Naive:	Model:
$10 becomes:	1,381,981	120,146
Average:	25.4%	19.6%
Maximum monthly loss:	-18.7%	-5.0%
Standard Deviation (annual):	10.39%	8.67%
Maximum 12 month loss:	-9.6%	0.1%

It is unclear what value is added from the model per se. A naïve, mechanical approach, which has the advantage of not trying to second-guess the market, generates a 25.4% return per year from 1950-April, 2002, versus 19.6% for the model. The main advantage of using the model seems to be a lower standard deviation (8.67% versus 10.39%) and maximum loss (-9.6% versus 0.1%). Note that the model never had a losing 12-month period!

Note how this compares to buy and hold with reinvested dividends over the same time period:

	S&P 500:	Naive:	Model:
$10 becomes:	4,478	1,381,981	120,146
Average:	12.4%	25.4%	19.6%
Maximum monthly loss:	-21.5%	-18.7%	-5.0%
Standard Deviation (annual):	14.39%	10.39%	8.67%
Maximum 12 month loss:	-38.8%	-9.6%	0.1%

If you tweak the number of put contracts sold, however, the model does add quite a bit of value:

Model proportion invested:	Sell puts to equal exposure of:
0	0.5
0.5	1
1	1.5
1.5	2

Gives the following results:

	Naive:	Model:
$10 becomes:	1,381,981	11,032,377
Average:	25.4%	30.4%
Standard deviation:	10.39%	13.30%
Maximum loss:	-9.6%	-4.2%

Note that the return improves dramatically with only a marginal maximum 12-month loss increase (to -4.2%, still better than naïve put-selling's -9.6%, and far better than buy and hold's -38.8%).

Straddle-writing (at-the-money call and put) led to even more profitability:

	Naive:	Model:
$10 becomes:	203,063,192	463,795,082
Average:	37.9%	40.1%
Standard deviation:	15.74%	17.50%
Maximum loss:	-12.5%	-3.0%

However, the model was hampered because it tended to sell more puts and calls during very bullish months; instead it should switch to a put selling only mode during these months:

p inv:	puts sold:	calls sold:
0	0	1
0.5	1	1
1	1.5	1
1.5	2	0

Note that calls are always sold except during extremely bullish periods. Puts are sold only for moderately bullish or better periods. The results of this strategy are staggering with no 12-month losses:

	Naive:	Model:
$10 becomes:	203,063,192	1,130,372,916
Average:	37.9%	42.5%
Standard deviation:	15.74%	14.23%
Maximum loss:	-12.5%	0.0%