*Each month we buy at the Open of the first day of the month and sell at the close of the last day of the month.*Here’s the average profit loss for the S&P500 Etfs, SPY (yahoo:SPY). Data from 1993.

This chart shows that for example if we bought every December @ the open and sold at the end of the month @the Close, we would average a 1.97% profit.

But is average profit, alone, a good indication of profit loss potential?

One way to look at this is his:

Mr. X., a french expat and a bon viveur, wakes up and just feels like gambling. He takes a trip to the nearby casino. We ‘ll call it the Casino “Royale”. He enters the lobby and is presented with 12 different slot machines.

where:

f* is the fraction of the current bankroll to wager;

b is the net odds received on the wager (“b to 1”); i.e., if you play $1, how much do I win/loose.

p is the probability of winning;

q is the probability of losing, which is 1 − p.

So again, here’s the SPY chart using Kelly instead of Average Profit.

#### NumOfwins[12]: 14 – i.e., 14 Decembers were wins

NumOfloss[12]: 6 – i.e., 6 Decembers were losers

AvgWin[12]: 2.6075

AvgLoss[12]: -2.02946

Certainty[12]: 70 – i.e. 14 winning Dec’s out of 20 = 70% winning prob.

EXPECT[12]: 1.21641

KELLY[12]: 0.466505

*Approximate continuous “averaged” EURO graph Jan. to Dec*

*Past returns may not be indicative of future returns.*

Aidan O'Mahony has coded a simple strategy based on this post and the SP500 seasonal month statistics. It's written in Python, using the Quantopian free backtester:

https://www.quantopian.com/posts/buy-and-hold-of-spy-on-profitable-months