Flawed Foundations: Why Traditional Statistical Methods are Not Ideal for Financial Advice.

Most in the Industry laugh at the concept of efficient markets and the idea that there is no alpha to be had. Most accept the risk profiling process, asset allocation, portfolio construction process, client modelling and the capital markets assumptions used without question.

We aren't discussing the utility theory underpinning the Chicago school's extensions of Modern Portfolio Theory in this article. We are discussing the reliance on traditional statistical methods to form the most significant aspects of advice.

When the Advice industry is dependent on the concept of portfolio diversification and as a consequence, the use of assumptions, uncertainties and blind spots which are inherent in the statistical models used to form the most significant underpinnings of advice do we accept these tools when other areas have long since adjusted their approaches.

Ben Walsh, Head of Research at Padua Solutions speaks to this reliance and how it gives rise to the following limitations.

Overreliance on Normal Distribution

Traditional statistical models, including those used in portfolio diversification, often assume a normal distribution of returns. This assumption implies that most observations fall near the average, with fewer extreme events occurring. However, financial markets are known to exhibit fat-tailed distributions, meaning that extreme events occur more frequently than predicted by the normal distribution. Relying solely on the normal distribution underestimates the risks associated with rare occasions and fails to account for their potential impact on portfolios.?I am yet to find a find an Advice Firm that even look at the parametric nature of the assets they are using in their statistical models. That is no one looks for fat tails.

Figure 1, below shows how normal distributions can vary. Each bell shape has a different tail shape. This reality applies to securities, asset classes, currencies, etc. The shape of the tails is critical in evaluating risk, both upside & downside.

Ignoring Tail Risks

The statistical models used in portfolio diversification tend to overlook tail risks—rare, unpredictable events that can have significant consequences. These events, often referred to as "black swans," can result in large losses that traditional statistical measures fail to capture. Tail risks are more prevalent than commonly assumed and can severely impact investment portfolios. Neglecting the potential for extreme events can lead to inadequate risk management and an overreliance on historical data, which may not adequately capture the accurate distribution of future returns. Figure 2, illustrates the variation difference between "normal" risk cost and "black swan" risk cost.

Tail events can also represent lost opportunity as Figure 3 below shows. This is an important consideration for modelling as it shows Clients the limits of the positive effects of an optimal portfolio diversification strategy.

Sensitivity to Model Assumptions

Statistical models used in portfolio diversification rely on various assumptions, such as constant correlations, stationarity (the assumption that statistical properties remain the same over time), and independence of observations. However, these assumptions may not hold in real-world financial markets.

Markets are dynamic and subject to changing conditions, invalidating assumptions of stability and independence. The sensitivity of statistical models to such assumptions can lead to inaccurate results and ineffective risk management.

The classic example of this is the change in correlation for bonds in recent history as it relates to equities. Figure 4 below shows the outcome of this in the 2021/22 column.

Incomplete Understanding of Complex Systems

Financial markets are complex systems influenced by numerous interconnected factors, including human behaviour, economic variables, and geopolitical events. Statistical models often oversimplify these complexities, reducing the multidimensional nature of market dynamics to a few variables. This simplification overlooks the interdependencies and nonlinearities present in markets, limiting the ability of statistical models to capture the full range of potential outcomes accurately.

Figure 5 illustrates some of the factors that need to be considered but usually are not when utilising existing statistical models.

Black Swan Fallacy

The use of historical data and statistical models to predict the occurrence of black swan events can be problematic. These events, by definition, are highly unlikely and have significant impacts. Placing undue confidence in statistical models that assume a known distribution of risks can lead to complacency and vulnerability to extreme events.?The 1997 Asian Financial Crisis is an example of this. Figure 6 illustrates the characteristics of a black swan event.

Conclusion

These criticisms highlight the limitations of statistical models in capturing the complexity and uncertainty of financial markets. Our view would be to advocate for a more robust risk management approach that embraces the potential for rare events, incorporates a broader range of possible outcomes, and implements strategies that can withstand extreme shocks. In addition, that risk model needs to produce a single dollar expression of the risk cost. This empowers Advisers and Clients to make informed decisions and adds significant value to your advice.

This perspective challenges the conventional reliance on statistical models and encourages investors to adopt a more resilient and adaptive approach to portfolio diversification.?This is a new way of thinking way beyond the ridiculousness of “growth” & “defensive” or “standard risk measures”.? All these existing methods are dated and not useful.

Want to deliver more value to your clients think beyond return and think in terms of “Preservation”.?With higher long-term interest rates and as a consequence lower profits & higher discount rates, returns will be lower and risk greater.?This means managing risk first. Consider the validity of using risk budgets, a strategy used by institutions.

Our next article will outline what we believe is the sensible approach to resolving the issues raised in this article.

Want To Know More?

Nassim Taleb is an acknowledged thought leader on “Black Swans” and developed the ingenious “Antifragile”.?? I have attached a video of Nassim speaking about Black Swans. His insights around this issue are very valuable and relevant to our discussion.