chat icon
Camille Van Vyve

Camille Van Vyve

14 Feb 2024
Share on Linkedin Share on Facebook Share on Twitter Share on Twitter

Investment insights from a simple coin toss

Nothing is easier to understand than a game of heads or tails: a bet in its most basic form. But behind this apparent simplicity lie numerous concepts and mechanisms that can help us better understand investment. Ready to bet? Let's see if you can come out on top!

Tossing a coin can learn you a bit about investment.

Heads or tails: zero returns in the long run

In a heads or tails game, with a 50% chance of winning and a 50% chance of losing, the expected long-term return is zero. You probably wouldn't bet your savings on such a game.

Leveraging information advantage

Now, imagine a rigged heads or tails game: with each toss, there's a 60% chance the coin will land on heads. If you have this information, you undoubtedly have an advantage over other players, and your expected return should be positive. By investing your capital in such a game, you could potentially achieve a handsome long-term return.

Take the test!

Let's see if you can take advantage of this edge. If you have a few minutes, click on this link and try it out. You start the game with €25 in hand. There's a rigged coin in front of you with a 60% chance of landing on heads. You can bet any fraction of your portfolio on each toss. If your prediction is correct, you win the amount bet; if it's wrong, you lose that amount.

Not so simple...

So? Without prejudging your investment skills, it appears that in a large-scale study, 33% of participants end the experience either bankrupt or at a loss. Only 22% of participants manage to reach a capital of €200 or more!

The Kelly Criterion

The main challenge of the game lies in the amount wagered. Betting too much risks bankruptcy, while too little leads to poor returns. The Kelly Criterion precisely calculates the optimum amount of a bet to maximize the long-term growth of your capital. This formula is based on the probability of winning (60% in our case) and suggests an optimum of 20%. In other words, in this game, by consistently betting 20% of your portfolio, you maximize the growth of your capital in the long term.

Balancing risk and reward

Let's play another type of heads or tails. The coin isn't rigged, so it has a 50% chance of landing on heads and a 50% chance of landing on tails. But a correct prediction wins you 50% of your portfolio, while an incorrect one only loses you 40% of your portfolio. You have €100 in hand: would you play such a game?

Positive average trend

Intuitively, you might say yes... With a 50% chance of winning €50 and a 50% chance of losing €40, the expected value of each toss is €25-€20=€5. In the long run, the trend must be positive, and that's indeed what we observe when simulating a series of 60 tosses a million times.

Cumulative effect of losses

But this average hides a much sadder reality: in this game, the vast majority of players end up bankrupt because the cumulative effect of losses is devastating. Imagine starting by losing 40% of your initial €100; you're left with €60. In the next round, a 50% gain won't even be enough to offset this loss, as it will only bring you to €90! While the average trend is positive in this game, it's due to a few lucky individuals who end up with huge gains.

The Kelly Criterion revisited

The problem here is that you have to bet your entire portfolio each time. Once again, by modifying the rule to bet only 20% of your portfolio on each toss, the chances of achieving a positive long-term return are maximized—a parameterized model of this kind yields a total portfolio of €232.437 for a participant after 1000 tosses!

Volatility has a greater effect than average return

Betting your entire fortune on heads or tails is equivalent to investing your entire capital in a single stock or a highly concentrated portfolio. As shown by the above experiments, even with a positive expected return, the volatility is too high and will most likely lead you to ruin.

Volatility management in investments

To achieve the optimal level of volatility and maximize long-term returns, there are three rules to follow in investing: diversify your portfolio to the maximum, rebalance it regularly, and smooth your investments over time. Note that in heads or tails, the only diversification option is cash—fortunately, markets offer other, more profitable options!

Maximize returns with Easyvest

With Easyvest's index portfolios, invested through ETFs in global stocks and eurozone bonds, you diversify your portfolio to the maximum. To ensure an allocation always in line with your profile, we rebalance it once a year. And finally, thanks to the automatic fund addition feature of our app, you can invest regularly, effortlessly. Explore our site, simulate your portfolio, and start your online investment journey today!

Share on Linkedin Share on Facebook Share on Twitter Share on Twitter
Easyvest is a brand of EASYVEST NV/SA, with company number 0631.809.696, authorized and regulated by the Belgian Authority for Financial Services and Markets (FSMA) as a portfolio management company and as a broker in insurances, with registered office at Rue de Praetere 2/4, 1000 Brussels, Belgium. Copyright 2024 EASYVEST NV/SA. Past performance is no guarantee of future results. Any historical returns, expected returns, or probability projections may not reflect actual future performance. All securities involve risk and may result in loss.