Category Archives: Seasonal

Day of month effect on rebalancing a portfolio

In this post we will:

  1. Take a look at a simple, momentum based, monthly rebalanced Equity/Bond portfolio consisting of two ETFs: SPY and TLT.
  2. Search for what has been the optimal dates in the month to rebalance such a portfolio.

Each month we allocate to SPY and TLT.

If SPY has outperformed  TLT we rebalance to 60% SPY – 40% TLT.

If TLT has outperformed  SPY we rebalance to 20% SPY – 80% TLT.

For the first run we will re-balance on the first of the month and close at the last day of the month.

Rebalancing portfolio 1st day

Now will try different combinations of entry and exit days.

Continue reading Day of month effect on rebalancing a portfolio

Seasonals – SP500, Euro

Here’s the strategy:
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.



Mr. Francois is the oldest employee of the Royale and has been there since the very beginning. His job is to record the history of those machines. How many times each paid off and how much. 
Mr. X and Francois are buddies. So Mr. X has access to Francois’ notes. 
Francois keeps telling Mr. X, that past does not guarantee the future: If machine #3 paid off 100% of the times it was played, does not mean that it will pay off the next one.
But if it did, if the winning rates and payoffs were “stable”, ie, we expected future statistics to be similar to past statistics, which machine should Mr. X choose and how much should he bet?
The answer to both is the Kelly criterion: f=(bp-q)/b

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.

The bigger the probability of winning and the bigger the money paid per $1 bet, the bigger Kelly becomes. . Which only makes sense since we want to play games with big winning percentages and large payoffs. So we can use Kelly as an “indicator” to tell us what would be our “best” bet.

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



For December here are the stats:

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

So now that we got all that out of the way, here’s a longer term chart for the SP500 (^GSPC) with data since 1960:
Here you can visually see where the “sell in May and go away” saying comes from. Again, this is historical stats. Doesn’t mean they predict the future.
Probably all this is known to you: The best months to have invested on the SPY are November and December and the worst are May to October. 
And why am I posting this now? It’s already the end of December…
So here’s another seasonal for my European friends that have lost much of their purchasing power over the last 2 years.
This is the Euro (using the Futures prices, since 1995). Keep in mind that the Euro has had a bullish bias through most of it’s history. But look at January:

Approximate continuous “averaged” EURO graph Jan. to Dec

Past returns may not be indicative of  future returns.

Best Day to buy Bovespa – Part 2

If you bought Bovespa on Thursday and sold on Friday every week since 2003, you would be rich (if you compounded). We know this. If one was to follow such a strategy, in real-time, would it make money?

In the following strategy an investor would buy at the Close of the “optimal” day that performed best in the 5 past years. She would buy on this day (sell on the next close) for 6 months. At the end of 6 months she would re-optimize, find the “optimal” day of the past 5 years from the current date and follow it for another 6 months. So here is a walk-forward back-test that shows how she would do.

Results are NOT compounded (hence the huge difference).
Initial Capital:   $100,000 – Profit:  $127,438.7




Begin
End No. Net Profit Net % Profit day of week Profit $$
34820 34826 1 3809.68 3.81 1
34826 35186 1 9849.84 9.85 4 13659.52
35186 35192 1 15842.02 15.84 4 29501.54
35192 35551 1 6754.01 6.75 4 36255.55
35551 35557 1 12394.78 12.39 4 48650.33
35557 35916 1 -19902.37 -19.9 4 28747.96
35916 35922 1 10016.43 10.02 1 38764.39
35922 36281 1 22435.88 22.44 1 61200.27
36281 36287 1 -16342.55 -16.34 1 44857.72
36287 36647 1 15916.31 15.92 4 60774.03
36647 36653 1 4610.77 4.61 4 65384.8
36653 37012 1 7781.22 7.78 4 73166.02
37012 37018 1 -10523.76 -10.52 4 62642.26
37018 37377 1 -12518.35 -12.52 1 50123.91
37377 37383 1 -3076.38 -3.08 4 47047.53
37383 37742 1 4480.75 4.48 4 51528.28
37742 37748 1 9594.63 9.59 4 61122.91
37748 38108 1 3838.22 3.84 4 64961.13
38108 38114 1 21109.48 21.11 4 86070.61
38114 38473 1 8833.46 8.83 4 94904.07
38473 38479 1 3687.74 3.69 4 98591.81
38479 38838 1 8690.9 8.69 4 107282.71
38838 38844 1 8881.05 8.88 4 116163.76
38844 39203 1 -4282.91 -4.28 4 111880.85
39203 39209 1 12311.72 12.31 4 124192.57
39209 39569 1 -767.54 -0.77 4 123425.03
39569 39575 1 -2413.08 -2.41 4 121011.95
39575 39934 1 -9401.48 -9.4 4 111610.47
39934 39940 1 14681.36 14.68 4 126291.83
39940 40299 1 3449.71 3.45 4 129741.54
40299 40305 1 -3704.01 -3.7 4 126037.53
40305 40664 1 1401.17 1.4 4 127438.7

Bovespa- Best day to Buy Brazil

Best Day to Buy Brazil Index :Thursday
Worst Day to Buy Brazil Index :Friday

1993-2011 –  Buy on Close of Day. Sell on Close next day.
Commissions =Slippage=0.

Buying On Thursday  Sell next Day. $1,000 growth.

——————————————

Buying on Friday. Sell next Day $ 10,000  growth.

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Note to myself:
Best EOM buy Days: Monday or Tuesday.