The effect of variance on returns

Recently I have been focusing* on minimising Bertie’s variance. The importance of managing variance was brought to attention when I made over £100 on a day where my expected value was something tiny. Not a bad result, but it can go the other way pretty easily. I figured I’d run some quick numbers through my computer to see how bad variance really could be.

Assuming that I have a starting bankroll of £1000 and an expected return of 1% daily, I can test what affect 0 to 10% standard deviation will have on 1 year’s return. To test this, I ran each year as a series of weighted random results and repeated 10000 times for each level of standard deviation.

In this scenario, we would expect the mean to be identical. We can see in the plot below that this holds true. The plot also demonstrates how impactful a 1% daily return is also see what 1% per day really means, and see how wishful this example truly is.

mean return


In the context of variance, I want to know how the spectrum of possibilities stack up. Starting with the median return, I was legitimately surprised by how significantly variance dampened the returns in the graph below.

median return


What about the worst case? As we would probably expect, variance leads to the complete death of my bankroll, but the impact of even 2% standard deviation is quite startling.

min return

What if I am only slightly unlucky? Terrible returns ahead if you choose the volatile path…

25th return

An interesting result to me was the 75th percentile returns, anything with 8% or higher standard deviation still did not return above the mean. Pretty alarming that even if you’re on a mildly lucky random walk you can still be in a worse place than someone who chose no variation in their route.

75th return

The best case with each of the standard deviations? Well it’s almost enough to make it worth rolling the dice…

mean return

Yes, that’s £12 million


*Between work and my home being knocked apart – a picture of the house in its current state is in the title.

** I have assumed a gaussian / normal distribution for these returns.





Bertie: the basics

Bertie has been written in Python and uses a PostgreSQL database. He sits on Betfair’s exchange and offers prices for which punters can bet. Let’s break each of these down.

Python is a programming language. I chose Python due to a combination of its clear syntax, huge selection of libraries built for data analysis and transformation, and the fact that it is open source.

PostgreSQL is a relational database management system which is possibly the most advanced open-source system around. I chose PostgreSQL due to Bertie’s design having multiple simultaneous read-write operations.

The Betfair Exhange operates as a marketplace. This means that Betfair does not get involved in setting a price, and allows users to determine the appropriate price. This may best be explained using the upcoming Ice Hockey match, Boston Bruins vs Ottawa Senators. On Betfair, if you wish to bet on a team to win, you will see something like the below:

Boston Bruins vs Ottawa Senators

The prices in blue are the best prices available to bet on each team. If you believe that Ottawa Senators are going to win this match, you could place a bet on them at a price of 2.22. This means that when you bet £1 you would receive £2.22 back if Ottawa were to win (including your £1) for a net win of £1.22.

Conversely, see the red 2.28 next to Ottawa? This is the price someone else wants to get to bet on Ottawa Senators. If you thought that Ottawa were going to lose, you could accept that person’s bet at 2.28. This means that for every £1 you have accepted, you would have to pay £2.28 (including the £1 the bettor has given you), for a net loss of £1.28.

The numbers you see below the bolded (£310 in blue , £51 in red on Ottawa) shows you the market depth – that is, the amount of money available to bet at those prices. If you wish to bet more money than that, you will have to accept worse odds in order to bet.


What if I want a better price? Let’s say that I want to bet on Ottawa but I do not like the 2.28 price. I can choose to post any price I wish onto the marketplace:

Ottawa Bet

This will place me directly into the exchange, and my bet will appear alongside the others, forming the market as you saw above.

Bertie only operates on the lay side, that is, provides the price for punters to bet on their favourite team winning. Bertie attempts to provide a slightly worse than fair price to the exchange, in the hopes that an equivalent amount is bet on both sides for a guaranteed profit. Bringing it back to the example: what prices did Bertie choose for this market? Turns out he chose to straddle the market lines..

Boston Ottawa Bets

Is this profitable? Well, if I were to have £100 matched at the above prices, I would make 90 pennies. Not exactly an earth shattering amount, but it should be noted that Bertie makes approximately 100 markets a day, so the potential adds up (note, my average return per market is currently approx £0.13).


HMRC and the Alcohol Wholesaler Registration Scheme

I recently had the pleasure of assisting my father in-law with his application to the new HMRC Alcohol Wholesaler Registration Scheme (AWRS). A reasonable policy endeavour – increase the duty receipts on alcoholic beverages through increased transparency on alcohol supply chains.

The application experience has been confusing and stressful for my father in-law. I will spare you all the details, however a combination of a  remarkably complex, one-size-fits-all HMRC Excise Notice alongside HMRC agents who alternate between simply pointing to the excise notice and threatening refusal of the application have him, and others like him, on the verge of early retirement.

To summarise; it looks like there will be fewer players in the off-licence wholesale market in addition to a huge increase in administration. I think there is a decent opportunity for an efficient business to rapidly increase market share over the next year… Might be time to buy a van.

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