The chances of winning big on the lottery are slim, and every ticket is likely to return much less than you paid for it. But would you really be better off investing rather than buying lottery tickets? Sometimes a simulation can be illuminating, even when the answer seems obvious.
What we will do is assume that we either invest £26 a month for 25 years in a fund or spend it on lottery tickets. I chose £26 a month because it’s an amount just above the minimum regular contribution threshold for a few ISAs, and spending this amount on the lottery does not sound outlandish. Plus 25 years might be the period over which someone saves for retirement.
Let’s play the (simulated) lottery
Using numbers drawn from the National Lottery website, matching five numbers and the bonus ball pays £1,000,000 on average, matching five numbers gets you £1,750, four wins £140, three pays £30, and two nets you just £2. Matching all six numbers will pay an average jackpot of £5,000,000.
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I randomly generated 300 lottery results and 13 lucky dip ticket numbers for each draw to simulate 25 years of monthly play, for which the player would be £7,800 down if they won nothing. This was done 1,000 times, so we have a range of simulated winnings (or losses). None of these players would have been celebrating.
Our lottery players lost £5,105 on average, with £5,846 being the worst loss recorded and being £2,838 down the best performance. No life-changing amounts were won.
Smart investors?
What we will simulate investing in is the iShares Edge MSCI Europe Minimum Volatility ETF offered by Blackrock. This will track the performance of a European, large-cap equities benchmark, and returns 0.78% per month on average after fees, with a standard deviation of 2.76%.
How did our 1000 investors do? They invested £26 every month for 25 years and received a monthly return (randomly generated from a normal distribution based on our fund’s monthly mean return and standard deviation) on whatever they had invested at the time. They did much better than the lottery players.
The simulated investors ended up with £30,390 on average with one lucky investor walking away with £105,842. Even the worst performance of £9,664 was far better than the luckiest lottery player and beats stuffing £26 a month under the mattress.
The winning ticket
Past performance is not a guide to future performance, and yes, the fund results are based on historical numbers and investing is not without risk. If I had simulated 10,000 or 100,000 lottery players we may have had a jackpot winner, and maybe the average winnings do not represent the true range of prizes given now or in the future.
But I think the assumptions are reasonable, and the difference in fortunes is so stark that we can say with confidence that wealth is more likely to be built by investing in this single fund (and do not forget the many others that are out there) compared with playing the lottery. Of course, in the real world, a portfolio should be appropriately diversified and reflect the investor’s risk and return preferences.
If someone enjoyed playing the lottery, perhaps for the chance to dream about winning, I would not say they must stop. But I would suggest that they invest what they can afford first, and then buy lottery tickets.
