EBI - Risk Assessment
The bottom line: Using EBI, the probability of incurrig a loss in a given year is estimated at 12.7%. Details of the analysis are explained below.
Mean annual return
Confidence intervals for the mean annual return of EBI were estimated as an initial measure of risk. To do so, a probability distribution was created by resampling observations from the group of countries ranked first (the "Top 1" group). More specifically, a new sample was created by randomly replacing a country from the "Top 1" group by other country from the same group. For each new sample a mean annual return was calculated. This operation was repeated 50 thousand times. The distributions were estimated for the retrospective (assuming the "unlucky" scenario) and prospective samples separately.
In the retrospective sample the 95% confidence interval (CI) for the mean annual return is 12% - 57%, while in the prospective sample the CI is 10% - 50%. Although intervals are wide, their lower bounds are fairly high. They indicate that the mean annual return of EBI is higher than 10% with 97.5% confidence.
Annual return and probability of loss
A slightly different question adresses the range of possible annual returns. Knowing the distribution of annual returns enables us to estimate the likelihood of a negative outcome in a given year. As before, we applied bootstrapping to randomly select four quarterly returns from the retrospective and prospective periods, treated separately, and used these to generate annual returns.
Data from the prospective sample indicate that the probability of having a positive return over a four-quarter period is 87.3%. In other words, the probability of incurring a loss in any given year is 12.7% (CI 11.1% - 14.4%).
The figure below shows the annual probability of loss estimated at the end of each quarter since 2020 Q1 (before the Covid-19 pandemic, the estimated probability was close to zero). Since the onset of the pandemic, the probability has moved between 6.6% and 12.7%.
The figure below shows the annual probability of loss estimated at the end of each quarter since 2020 Q1 (before the Covid-19 pandemic, the estimated probability was close to zero). Since the onset of the pandemic, the probability has moved between 6.6% and 12.7%.
A one-year loss probability of 12.7% means that EBI is expected to experience a negative annual return roughly once every 7.9 years. For comparison, over the 2016-2025 period the S&P 500 return in euros recorded negative returns in two years (2018 and 2022) or once every five years; the Stoxx Europe 600 in three years (2018, 2020 and 2022); and the MSCI World index in two years (2018 and 2022). The risk analysis will be updated as additional data become available from the prospective phase.