Diversfied? Easier Said Than Done

Asset and investment managers have good reasons to say that diversification – reducing risk without affecting returns – is their top priority. Sure, they talk about risk, correlation and efficiency, but we can imagine their job as being a Michelin-starred chef or a Premier League football manager: always on the clock and combining their assets the best possible way. 

Indeed, what sets them apart from their amateur counterparts is not only their superior knowledge but their ability to dynamically adapt and master the right tools to constantly deliver a high-quality performance. As we are going to see, the same applies when we build efficient and well-diversified portfolios. Professionals that aim to achieve long-term and effective diversification, not only know the basics of risk and correlations but are also using AI to better understand their inner dynamics and get an edge. They are moving towards a new approach to portfolio management, taking portfolio construction one step further: a forward-looking approach to diversification to successfully navigate the complexity of financial markets.

Introduction

If we were to explain diversification to our children, we could tell them that having a few different toys to play with is better than just having one. Indeed, even if one broke, they would still be able to play with the remaining ones. To a certain extent, this is what happens when we invest in financial markets, where instead of toys, we have securities like stocks, bonds and derivatives to “play” with. Yet, the same concept holds true: we have to diversify our investments, that is, mitigating the risks of them not delivering the positive performance we expect.

Diversification is indeed a very old and time-tested idea. Formalized during the 19th century, its foundations lie in what we call correlation, that is, the degree and the direction of how a set of variables move with respect to each other. 

In this sense, we are not surprised to see that these concepts have become the cornerstone of the modern approach to portfolio management. Diversification, in this context, is used to mitigate the risk of losing capital during an investment, while correlation, on its side, is how we determine which assets we need to invest in. Simply put, if we select assets that tend to move in opposite directions, the outcome will likely be less risky. However, as one can expect, there are very few instances in which the future turns out to similar to what we have observed in the past, and the same is true for how much securities tend to be correlated with each other. This is why – even though diversification is quite straightforward to understand – making it work in the long run is anything but an easy task. 

This happens because financial markets are a complex, interconnected system in which people buy and sell securities according to their own investment views and needs. Consequently, we can think of price fluctuations – what we consider to determine correlation – to be made of two components: the signal, what is truly informative and useful to make investment decisions, and the noise, not informative and influenced by temporary price misalignments. 

Yet, to cope with the traditional low signal-to-noise ratio of financial data, recently we have observed a massive adoption of artificial intelligence and machine learning techniques in portfolio management. As a result, these extremely powerful tools have paved the way for a deeper and more detailed understanding of correlations, risk and diversification. 

In this regard, they have introduced a new era of how asset and investment managers develop insights and build more robust and efficient portfolios. Thanks to their ability to cut through complexity and adapt to the gradual unfolding of financial markets’ dynamics, they are pushing diversification one step further, beyond the traditional low-correlated portfolio.  As we are going to see, this means building portfolios according to a probabilistic approach to discount possible evolutions and shifts in correlations. Namely, portfolios that are well-positioned to navigate the complexity of financial markets and take advantage of their inner dynamics.

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When the Merchant of Venice Went Bust 

As already pointed out, diversification is far from being a modern concept. Indeed, it forms the cornerstone of financial decision-making to the extent that an imaginary line could be drawn from the famous “don’t put all your eggs in one basket” of Miguel Cervantes’ “Don Quijote” to the Modern Portfolio Theory developed by the Nobel prize winner Harry Markowitz in the early 1950s – which formalized the role of correlations as the driver of diversification in investment decisions. 

Yet, as we often find out when we put theory into practice, there is more than meets the eye in making diversification work. Indeed, just dividing our investments into different “baskets” is not enough to guarantee that our portfolio will be effectively diversified. 

For instance, if all the baskets end up being affected by the same source of risk (i.e. are highly correlated with each other) when one falls apart, the other ones will be affected as well. In other words, factoring in correlations is essential to avoid being left only with the illusion of diversification. 

Again, classical literature offers another great example of why we should not be naive when it comes to diversification. For example, in his famous “The Merchant of Venice” Shakespeare narrates of Antonio, an influential merchant who ends up defaulting on a loan. At the beginning of the play, when he is asked if he is worried about the fate of his ships, Antonio replies:

My ventures are not in one vessel trusted, nor in one place, nor does my wealth depend upon the fortune of this present year. Therefore, my ventures do not make me somber”.

With his statement, Antonio makes a fatal mistake – a clear reference to what we have previously defined as “naive” diversification. By spreading his wealth solely across multiple ships, he fails to see the multi-dimensional profile of diversification. Indeed, even though he does not rely on one single vessel, he does not realize that he is exposed to a single common risk factor, the sea, . The same risk that, years later, Harry Markowitz would call “systematic risk”.

Similarly, oftentimes investors rely on simplistic investment strategies based on a partial – yet incomplete – understanding of diversification, as we often see with the traditional “60-40” stock-bond portfolio. It is clear that, although combining equity and fixed income has been historically a good idea, the real degree of the diversification benefit is determined by what we expect their correlation to be in the future, not in the past.

Eventually, as we start putting together all the pieces of the diversification puzzle, it appears that the more we dig, the more we need to understand the real informational content financial correlations bring, and how can we harness their incredible potential to improve our investment decision-making. This calls for a step back, as we ask ourselves: what is truly correlation?

Exhibit 1 — Woodcut drawing of 16th Century British merchant vessels 

Landing on Correlation Island

Let’s imagine being on an airplane slowly approaching an island. Initially, we would only see only its contour but, as soon as we get closer and closer to the landing strip, we would notice countless details that went previously unnoticed. In this sense, in the span of minutes, we would be able to gather a lot more information only by changing our perspective – or better, the scale at which we see the same object. 

To a certain extent, we experience the same when we look at financial data. Indeed, similarly to what happens with our airplane example, the more we zoom in and out of financial markets, the more we can understand how all elements (e.g financial securities) fit together and get a more realistic picture of what is going on at an aggregate level (e.g. investment portfolios).

For this reason, correctly interpreting the information provided by financial markets is fundamental to efficiently manage risk and build well-diversified portfolios. In this sense, we are going to explore three elements of correlations that provide useful insights to investors: how they move, why they are useful allies and what are the hidden risks that we must avoid. 

Correlation 101

Often times, when financial professionals talk about correlation, they refer to what statisticians call “linear correlation”, an index that measures the direction and the intensity of the average co-movements between the returns of two securities. So, for example, saying that Apple and Microsoft stocks have a correlation of +0.85 means that the two stocks move very similarly, that is, are highly correlated. On the contrary, saying that stocks and bonds usually have a low (or negative) correlation, means that on average their movements go in opposite directions.

In this sense, Exhibit 2 can help us grasp what correlation means from a graphical point of view. At a higher level, a positive correlation indicates that both assets tend to move together in the same direction: when one rises, the other rises as well. The closer correlation is to +1, the more similar their movements will be. A negative correlation means the opposite. If the correlation coefficient of two assets is close to zero, it means that there is a weak, random – or even absent – relationship between the two.

Exhibit 2 — Correlation can have different magnitudes, from -1 (negative) to +1 (positive)

Opposites do Attract

As Markowitz noted, by selecting uncorrelated (or low correlated) assets, it is possible to reduce the overall risk of the portfolio. Logically, when two instruments move in independent or opposite directions, the losses recorded by one can be smoothed out by the gains of the other, resulting in a more stable line of performance.

In particular, the diversification benefit – the reduction in portfolio volatility – tends to increase as soon as we add more uncorrelated assets into our portfolio. In this sense, Exhibit 3 can help us frame two important characteristics. The first one is that generally portfolio volatility (measured on the y-axis) decreases as soon as we add more assets (measured on the x-axis) for every level of correlation. The second one is that the amount of the reduction grows more significantly as the average correlation among assets decreases. For instance, if we consider a portfolio of just 10 assets, a portfolio with an average correlation of 0.8 (i.e. the light blue line) only achieves a reduction of about 20%, while the portfolio with the lowest average correlation (i.e the green line) is able to get a reduction of about 80%, four times more.

Exhibit 3 — Diversification benefit for different levels of correlation

Yet, as we immediately grasp the potential benefit of investing in low correlated assets, it also appears to be far from being the magic formula of investing. On the contrary, as we are going to see, investors need to pay attention to how they interpret correlations, and avoid biases and estimation errors that can lead to poor investment decision making.

Complex Simplicity

In this sense, although powerful, naively apply correlation analysis may contribute to make the wrong investment decisions. Indeed, as they tend to vary over time, so does the amount of their diversification benefit. From this standpoint, Exhibit 4 shows the dispersion of the correlation that different asset classes had with the US stock market during the last 20 years. For example, if we take US Long Term Treasuries, historically they moved from a minimum of about -0.6 to a maximum of about 0.2 with an average (and current correlation) of about -0.25 with the S&P 500 Index.

  

Exhibit 4 — Distribution of the rolling 5-year correlations with the S&P 500 for different asset classes 1999-2020

Yet, not only does correlation vary over time, but additional instability comes from the arbitrariness of how we choose the sampling frequency and the time horizon – something known as time period bias. Indeed, as correlation can be measured on daily, monthly or annual returns, they will provide different results. Moreover, also the length of the analysis period, how much we go back in time to measure it (i.e. six months, a year), is another factor that adds volatility to our estimates. Evidently, there are thousands of different combinations to consider before being confident with correlation estimates.

Eventually, there is no doubt that correlations provide an important piece of information about what to expect from future price movements. Yet, this information is hidden behind a curtain of noise that makes it difficult to grasp immediately. Indeed, if you think about it, correlation depends on asset prices and returns, and if they provide a low signal-to-noise ratio as we mentioned earlier, so will our correlation estimates.

As a result, instability poses a significant threat for investors because, from a practical point of view, it can lead to changes in terms of asset allocation, or better, how each security (or asset class) is weighted and contributes to the final performance of the portfolio. In this sense, it becomes clear why asset and portfolio managers are increasingly moving towards the new techniques offered by AI and machine learning models, as they allow to dynamically adapt to the gradual unfolding of the financial markets and build more stable and efficient portfolios.

AI: The Lifebelt in the Financial Ocean 

As we have seen, despite correlations being the cornerstone of the modern approach to portfolio management, naively relying on them can be extremely dangerous. In fact, as they tend to vary over time, investors risk misinterpreting noise as signal and consequently make wrong decisions. 

Yet, in the last few years, understanding correlations has gone through several breakthroughs. As a matter of fact, new techniques, such as AI and Machine Learning, are helping investors not only to stay afloat but also to navigate today’s complex markets with confidence.  

First, AI models can process huge amounts of data both in time and across different dimensions. This means that they can take into consideration several probabilistic scenarios of possible evolutions and shifts in correlations, allowing investment managers to rapidly adapt to shifting market dynamics.

Secondly, AI, machine learning and neural networks can help investors with the above-mentioned time period bias. If you remember the airplane example from the previous chapter, you know the usefulness of zooming in and out of financial markets. Indeed, these new technologies enable us to expand the depth of our analyses and evaluate thousands of different sampling parameters, finding the one the offers the most consistent investment signal.

Lastly, AI can cut through the complexity of financial markets to extract valuable information. For instance, it can explore relationships and dynamics taking a vast universe of securities to find the most effective diversifying opportunity, rather than focusing on a single relation between two assets. As a result, asset and portfolio managers can expand their understanding of the market and really explore the entirety of correlation determinants under different layers, considering not only asset classes, but also sectors, geographical areas, and others. 

Eventually, there are plenty of reasons why the finance industry is increasingly leveraging the power of AI. In fact, investors are now able to develop better estimations of correlation coefficients and expand the dimensions in which their portfolios can be considered diversified. Consequently, they can steadily reduce their volatility and control their risk premia exposure, in the end achieving more stable performances.

Taking Diversification One Step Further

On top of all the things we have said, AI brings to the table another interesting benefit worth exploring: positioning, the ability of a portfolio to efficiently withstand the possible evolutions of financial markets. In this sense, positioning represents a precious advantage that AI brings for asset and portfolio managers, that emerges out of all the improvements discussed before.

Once again, it can be useful to imagine ourselves in that airplane slowly approaching an island, this time making a different yet important consideration. For aircraft pilots, it is incredibly hard to foresee when they will encounter turbulence. However, we as passengers remain relatively calm knowing that airplanes are engineered and built to withstand air turmoil.

In finance, AI is increasingly giving investors a similar feeling of tranquillity. Indeed, despite the complexity and unpredictability of financial markets, managers using AI to support their investment strategies know that they can promptly adapt to unforeseen shifts.

As we have seen, AI sifts through a vast amount of data in search of hidden relationships. This allows AI to dig deeper than simplistic correlation analyses, extrapolating more information than a static “low correlation” coefficient. This eventually leads to the identification of more effective diversifying opportunities – at multiple levels. 

Moreover, thanks to its continuous learning – a never-ending process of feedback generation and integration – AI is capable of dynamically adjusting to sudden changes in market conditions. As a result, investment managers can reach a new, more robust level of diversification: portfolios not reliant anymore on static, historical low correlations, but solidly built on probabilistic scenarios to discount any possible evolution of the market.

This translates into a forward-looking, more accurate approach to correlation analysis that helps investment managers avoid decisional and operational biases, leading to more solid performances. 

Looking from The Vantage Point

The key to a well-diversified portfolio lies in how the portfolio is built or, in other words, in the structure of its correlations. In particular, by combining low correlated assets, it is possible to achieve a stable investment appreciation while reducing portfolio risk. 

Due to the increasing complexity of financial markets, these concepts are more important today than ever before. Indeed, a naive approach to diversification can pose a great danger for investors.

As a matter of fact, correlation coefficients can often change over time and be easily influenced by sampling biases. Additionally, investors are finding more difficulty in extrapolating valuable information from correlation analyses due to the growing noise of the markets.

As a result, the finance industry is continuously exploiting the power of Artificial Intelligence and Machine Learning techniques to overcome these issues. By exploring correlation dynamics under hundreds of thousands of probabilistic scenarios, AI can extrapolate significantly more information about the interconnections among securities. 

Eventually, investors can create more robust positions on the market, building portfolios that offer reduced volatility and increased efficiency, discounted across an infinity of different scenarios. In this sense, AI allows investors to have a holistic view of the financial market, cut through its complexity and adapt to the gradual unfolding of its dynamics.

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