I started writing yet another article trying to convince risk managers to grow their quant competencies, to integrate risk analysis into decision-making processes and to use ranges instead of single point planning… but then I thought… why bother… why not show how risk analysis helps make better risk based decisions instead?
After all, this is what Nassim Taleb teaches us. Skin in the game.
So I sent a message to the Russian risk management community asking who wants to join me to build a risk model for a typical life decision? 13 people responded, including some of the best risk managers in the country, and we set out to work.
We decided to solve an age-old problem – win the lottery. With the help from David Vose and his free ModelRisk we set out to make history (not really, been done before, still fun though).
Here is some context:
- lotteries are an excellent field for risk analysis since the probabilities and range of consequences are known
- in Russia, as in most countries of the world, lotteries are strictly regulated
There is a rule when a large amount accumulates, several times a year it is divided among all the winners. This is called roll-down.
- if no one takes the jackpot before or during the roll-down, then the whole super prize is divided between all other winners
- so the probability of winning is the same as usual, but the winnings for each combination can be significantly higher if no one wins the jackpot.
And so we set out to test our risk management skills in a game of chance.
Whatsup group created. Started collecting data from past games. Some of the best risk managers in the country joined the team, 15 in total: head of risk of a sovereign fund, head of risk of one of the largest mining company, head of corporate finance from a O&G company, risk manager from a huge O&G company, head of risk of one of the largest telecoms and many others.
Placing small bets to do some empirical testing.
First draft model is ready…
Created red team and blue team to simultaneously model potential strategies using 2 different approaches. Second model is created…
Testing if the lottery is fair, just in case we can game the system without much math. Yes, some numbers are more frequent than others and there appears to be some correlation between different ball sets but not sufficient to make a betting strategy out of it. The conclusion – the lottery appears to be fair, so we will need to model various strategies.
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Constantly updating red and blue models as we investigate and find more information about prize calculation, payment, tax implications and so on. The team is now genuinely excited. Running numerous simulations using free ModelRisk.
Did nothing, because all have to do actual work.
After running multiple simulations we selected a low risk good return strategy. Dozen more simulations later here are the preliminary results:
- used very conservative assumptions
- probability of loss 9.8%, worse case scenario we lose 60% of the money invested
- probability of winning 90.2%, 80% of the time winning would be between 50% and 100% of the amount invested, after taxes (this means there is a high possibility to double invested cash at relatively low risk)
- potential upside significantly higher than downside
Red and blue team models produced comparable results.
Started fundraising. If we manage to collect more than necessary, we decided to make 2 bets: one risk management bet (above) and one speculative bet with much higher upside and possible downside.
To be continued. I will keep you posted on the developments.
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P.P.S. Good luck solving this puzzle with a heatmap :))