Monday, 18 August 2014

Portfolio Probabilities

One of the most common ways to play TFA each season has been to follow a number of systems in a portfolio. Until last season, it had been a fairly simple way to make a profit each season and given the large % of systems profitable each season, it was quite difficult to make a loss over the first 3 seasons if using this approach.

Anyone who was reading Steve’s Daily 25 blog will have seen the issues Steve had last season with following a portfolio approach and ultimately, Steve followed 13 systems last season and somehow managed to hit 7 of his 13 systems to be loss making. Given that 35 of the 52 TFA systems live last season were profitable (67%), the odds were obviously in Steve’s favour in terms of randomly selecting a portfolio of systems to follow and being able to make a profit. 

I thought it was worth a very quick blog post to show the probability of making a profit for each season based on the number of systems in your portfolio. Of course, the key thing with this analysis is that the portfolio selection is 100% random and I’m not aware of any TFA subscribers who randomly select a portfolio of systems to follow each Summer. Given these results below, I think it does show that if you follow a small number of systems in a portfolio, you could do a lot worse than randomly selecting the portfolio. Based on the losses that some subscribers suffered last season from following correlated systems in a portfolio, a random selection approach is a much better method than following correlated systems!

2010/11 Season

There were 11 live systems in the first season. All 11 systems were profitable with an average profit of 23.9pts.

Here’s table showing your expected profit and expected probability of your portfolio making a profit based on the number of systems you followed:

Hardly anything too surprising here. No matter how many systems you followed, you were guaranteed to make a profit given every system was profitable.

2011/12 Season

There were 22 live systems and 21 systems made a profit (system 33 made a loss). An average profit of 21.8pts was achieved across all 22 systems.

Here’s the same table as above:

If following 1 system, you had a 95.3% chance of making a profit. If anyone followed system 33 in isolation during this season, they deserve to make a loss! Basically, by the time you get up to following 2 or more systems, you were pretty much guaranteed to make a profit on the season.

2012/13 Season

There were 41 live systems and 8 systems were loss making. All UK systems were profitable but the Euro systems were very poor in their first season. An average profit of 19.6pts was achieved across all 41 systems.

Here’s the same table again for this season:

Starts to get more interesting here and if you only followed one system, you had an 80.5% chance of hitting a profitable system. You needed to be following at least 4 systems to achieve a 90%+ probability of your portfolio being profitable.

2013/14 Season

There were 52 live systems last season and 35 of them made a profit. An average profit of 11pts was achieved across all 52 systems.

Here’s the table again:

If following 1 system, you had a 67% of hitting a profitable system. Even if following 3 systems, you only had an 86.7% chance of hitting a profit.

If we take the example of Steve (Daily 25 blog) from last season, Steve followed 13 systems and based on the numbers above, the chance of Steve making a loss following 13 RANDOM systems last season was less than 1%. However, as I mentioned at the start, Steve’s portfolio was anything but random and was actually heavily correlated. Hence, when one of Steve’s bets lost, it ended up pulling down lots of systems and therefore, his portfolio wasn’t random and therefore, the chances of making a loss were much bigger than outlined in my analysis.

I guess the other trend to pick up is that as I have grown the number of systems season on season, the number of losing systems in a season has grown and therefore, if you were randomly selecting one system to follow, you have more and more chance of hitting a losing season. I saw that last season as I know someone who has followed 7-22 since day one and after 3 profitable seasons, they hit a losing season last season.

However, if you have followed 5 random systems each season since inception, you would have had a 90%+ chance of making a profit each season.

What will 2014/15 season hold for us using a portfolio approach?  Ideally, I’d like to see all 61 systems make a profit next season but then again, I know it’s highly unlikely for this to happen but we’ll see what happens.

Here’s a summary of all 4 seasons below in one table.  Will be interesting to see how season 5 compares next Summer……

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