What does the FIFA 2022 World Cup and investment risk management have in common?
Senior Quantitative Analyst, Saxo Bank
Summary: Brazil and Argentina are favorites to claim the World Cup trophy in Qatar this year, but is it realistic that one of the underdogs surprises? And how does a championship for Australia relate to a loss of more than 70 % in S&P 500? - read more below.
Going into the FIFA 2022 World Cup we see numerous predictions of who will be this year’s winner – with Brazil being the current bookmaker favourite, closely followed by Argentina. But for a quantitative analyst like me, this is actually not the most interesting prediction. Why not look at the surprises we may see at the World Cup – can some of the underdogs run away with the trophy, or is it completely unlikely?
In a separate article, Saxo Strats ‘soccer experts’ present a macro-corrected prediction of who will be the winner of the World Cup.
To be able to quantify the surprising scenarios for the World Cup, we must estimate the probabilities for the different outcomes of a match, given some metrics related to each individual team. For this exercise we rank countries via their Elo rating, which is a relative way of measuring the skill level of teams/players within a certain field such as chess, baseball or soccer. The difference in the ratings has in soccer proven to be a fair predictor for the outcome of a match, with a higher probability of the high Elo rating to win. We have mixed the Elo ratings of the participating world cup teams with betting odds in order to find a mapping from the Elo ratings to the probability outcomes for each world cup match
As an example, Denmark (Elo 1971) will be facing Tunesia (Elo 1707) today. According to our model, Denmark has a 59 % of winning, 25 % of a draw and only 16 % chance of Tunisia winning.
A standard example for predictors of the World Cup winner is to assume that the team with the largest probability to will also be the winner, which in line with the bookmakers predict Brazil as winners:
Bootstrapping to find less-probable scenarios
Instead of going with the most probable scenario, we artificially simulate that the World Cup is played 10,000 times, using these winning probabilities to determine the outcome of every single match. The method is well-known from both science and the financial industry, and the result is 10,000 different equally-probable outcomes for the World Cup. Some of these scenarios will have some of the underdogs as winners, such as this example from the playoff rounds, where Australia turns out as winners:
Only 2 of the 10,000 scenarios have Australia as winner, and as shown above, Australia will need events to go against the odds by beating Netherlands despite an estimated winning chance of 15%.
Combining all 10,000 scenarios, the estimated probability for each country winning the world cup is:
An overview like this reveals that the favourite scenarios with Brazil as winner is only likely in 1/4 of the cases – and that other lower-rated teams like Denmark and Uruguay have decent winning chances.
Tail scenarios in risk management
So how is this identical to investment risk management? Let say you invested in the S&P 500 index five years ago. Assuming that dividends were reinvested, the return would be 66 % on the investment which seems like a brilliant return. But one cannot mention returns without considering the associated risk of the investment. And the return is based on one realized path – but what if the macro events would have been different during the past five years? Would the investment still has been as good?
One way to quantify the risk is by applying bootstrapping to estimate all scenarios – not only the most probable one. Starting five years ago, the return of the S&P 500 index has in most of the weeks been around 0.5 %, and the return in half of the weeks has been between -1.1% and 1.7%:
There are however some rarely occurring weeks with very large losses or gains, exactly like the scenarios where Australia wins the World Cup. In the worst week, the S&P 500 index lost close to 15 % of its value. Thus when doing investment considerations, these so-called tail scenarios can have quite a large impact on the performance and thus cannot be ignored, despite the small probabilities.
A standard way to quantify the impact of these low-probability events is via the bootstrapping method. We do that by simulating 5 years of performance for 10,000 different scenarios. For each scenario we create an artificial path of 5 years performance by drawing weekly return from the histogram above. Thus some of the scenarios will due to the stochasticity contain a lot of the positive weeks, some the very negative events. The latter is exactly what is of importance for investors considering their risk profile. Below we show the 10,000 simulated scenarios which could occur with equal probability, including the actual cumulative performance indicated by the black line.
If we compare to events which (according to this basic model) have the same probability of occurring as the probability of Australia winning the world cup, i.e. 2 in 10,000, the lucky investor would have made 632 %. And the unlucky investor would have lost more than 72 % of the invested value in the worst 2 scenarios out of 10,000.
As for both the World Cup and financial investments, the least probable events are usually the most exciting ones, and bootstrapping is a simple way of quantifying these probabilities. When it comes to wealth management, tail-events can have severe impact on the performance. There are multiple ways of minimizing the impact from these tail events such as having diversified portfolios where the different assets have low correlations. Or by considering options which are far out of the money and only will be triggered in these tail events, although there is a premium associated with buying the option.
Note that the purpose of the bootstrapping exercise above is not to get the mathematical accuracies correct, but it should work as an illustration of how bootstrapping works when quantifying low-probability events. All simulated returns rely on historical data and should not be considered as indications for future returns. The used odds and Elo ratings were updated as of Nov 18, 2022.
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