Market-moving events and their role in portfolio optimization of generations X, Y, and Z

In many studies on life-cycle investing, assets have been divided into risk-free and risky assets. For example, Cohn et al. [1975] and Morin and Suarez [1983] divided different financial and non-financial asset categories into “risky” or “marketable risky” (stocks, mutual funds, derivatives, non-residential real estate) and “risk-free” (treasuries, savings accounts, personal residence, and personal property). In this study, we focus particularly on financial assets and do not include real estate in the portfolio analysis since there are no daily market prices for these types of assets.¹ As Cohn et al. [1975] underscore, it is difficult to find a “riskless” asset because even treasuries – often regarded as such – are still risky, although with low-risk characteristics. Therefore, all assets in our portfolios are treated as “risky” to some extent. Moreover, since we do not use surveys as a data source, riskless assets, such as saving accounts or deposits, are not included; thus, the overall wealth of the investor is not considered. Because new investment opportunities have emerged on the market in recent decades, we go beyond traditional asset classes, such as bonds and stocks, adding a representative of crypto assets – Bitcoin – due to its popularity [Bouri et al., 2017; Guesmi et al., 2019; Shahzad et al., 2019] as an emerging asset class.

Individuals save for various reasons, including precautionary and life-cycle motives [for a comprehensive review, see, e.g., Browning and Lusardi, 1996]. In recent years, the discussion on individuals’ savings preferences (e.g., residential property, deposits, and stocks) from a life-cycle perspective has lost vigor. Ando and Modigliani [1963], based on the pioneering work of Modigliani and Brumberg [1954], emphasized the long-term stability and cyclical variability of the ratio of savings to income while allowing individuals to maintain similar standards of living throughout the life cycle. As their income sources and patterns, as well as risk aversion, change over the life cycle, maintaining similar living standards might thus require shifting the volume and structure of their portfolios. Decreasing risk aversion (usually proxied by the share of risky assets) has been associated with significantly increasing wealth [e.g., Cohn et al., 1975; Riley and Chow, 1992; Wang and Hanna,1997] and with age [Riley and Chow, 1992; DaSilva et al., 2019]. With respect to age, the optimal asset portfolios [see Horneff et al., 2009] should include a large proportion of shares for young investors, which exhibit a downward trend as age increases. In particular, Blake et al. [2014] suggested a high initial share of equities and then a gradual switch to debt instruments as one approaches retirement in the accumulation phase. These studies have not accounted for emerging crypto assets.

In recent years, discussions of differences among generations X, Y, and Z from various perspectives have emerged in many streams of research; however, such discussions have not been particularly popular in the field of finance. Generations are defined based on their year of birth (X – born between 1965 and 1979; Y – 1980-1994, also called “millennials”; and Z – 1995 +). Their overall sociodemographic features have been presented by, e.g., Betz [2019]. All of these generations represent different lifestyles, life-work balances, and education and different scopes and scales of the use of technologies, which are very important from an investment perspective, that is, response time and 24/7 access to trading [e.g., Betz, 2019; Bank of America, 2020]. Generations Y and Z are called “digital natives” [see Betz, 2019]. In particular, generation Z has grown up in a technologically advanced era with easy access to information and its diffusion; they are supposed to be very open to using innovative financial services and types of assets, especially if these instruments are available through mobile applications or online platforms. Therefore, generations Y and Z are more likely to invest in crypto assets [e.g., Fisch et al., 2021], which makes them different from generation X.

Against this background, we identified a research gap related to the lack of studies investigating the investment preferences of various generations. As we rely on market data, instead of microdata from consumer surveys, we do not reflect the actual portfolios of assets, but we predefined their structure to run consecutive simulations.

The literature on portfolio optimization is extensive [for a review, see, e.g., Kolm et al., 2014; Kalayci et al., 2019]. Based on the extant literature, we apply the mean-variance optimization (MVO) procedure and quantify risk based on the actual volatility of portfolio assets. However, the debate in the literature focuses on comparing the performance of various asset allocation methods. A seminal study by DeMiguel et al. [2009] provides evidence that naive allocation – where investors allocate their investment capital evenly across a few different asset classes, without accounting for the individual characteristics of each asset class – mostly outperforms various mean-variance strategies. This may be because the gain from optimal diversification is more than offset by estimation error. Recent studies on longer data find that mean-variance models might be superior to the naive approach for asset allocation, which is primarily because estimation errors are lower for asset classes than for individual assets. Furthermore, in-depth studies show that the basic Bayes-Stein framework cannot offer better out-of-sample performance [Board and Sutcliffe, 1994], but the generalized version, enhanced with the use of machine learning, can offer better out-of-sample performance than the 1/N strategy [Gounopoulos et al., 2022], which is also true for sophisticated portfolio techniques that control for estimation errors.

Achieving portfolio diversification effects requires adding or removing a particular asset class to or from a portfolio. Most research has focused on diversification effects with portfolios consisting of only several components, while we cover seven global asset classes. While there is no single optimal selection of assets, several studies have offered useful guidelines. Ciner et al. [2013] confirmed that the bond market continues to play its traditional role as a hedge for the equity market. Both Khalfaoui et al. [2015] and Khalfaoui et al. [2019] found that investors should hold less stocks than crude oil, with the optimal portfolio weight for oil being close to 20%. This finding was confirmed by many other studies, for example, Belhassine and Karamti [2021], Mensi et al. [2021b], and Kartsonakis-Mademlis and Dritsakis [2021], which provided evidence that indices are good hedges for oil and that oil assets reduce portfolio risk. Moreover, many researchers have also argued that including gold in a portfolio adds to diversification effects since gold acts as a safe haven during turbulent periods [Alkhazali and Zoubi, 2020; Zhang et al., 2021].

Furthermore, in recent years, there has been a proliferation of studies examining the diversification effects of cryptocurrencies, especially Bitcoin. Cryptocurrencies can be incorporated into financial portfolios to provide effective risk management and for optimal dynamic hedging purposes [Hsu et al., 2021]. Nevertheless, there is no fixed consensus on whether Bitcoin can serve investors as a portfolio diversifier, a hedge, or a safe haven [Bakry et al., 2021]. Dyhrberg [2016], Guesmi et al. [2019], and Mensi et al. [2021a] proved that hedging strategies involving Bitcoin considerably reduce a portfolio’s risk relative to a portfolio without it. Including Bitcoin in the portfolio generates substantially higher risk-adjusted returns [Platanakis and Urquhart, 2020]. Huang et al. [2022] show that during uncertain economic environments, such as the post-COVID-19 period, cryptocurrencies provide the same diversification benefits as in more-stable environments. However, Bitcoin’s diversification benefits for investors are counterbalanced by its high volatility [Damianov and Elsayed, 2020] and might be viable mainly for investors with short investment horizons [Corbet et al., 2018] or for risk-seeking investors in non-crisis times [Bakry et al., 2021]. Thus, Damianov and Elsayed [2020] found that Bitcoin’s optimal weight in a minimum variance portfolio is only approximately 1%, while Eisl et al. [2015] suggested 2%–8%. Overall, the safe haven and hedging roles of Bitcoin, gold, and commodities are time varying and differ across horizons and stock market indices [Bouri et al., 2017; Shahzad et al., 2019].

Against this background, we identified a research gap related to the lack of studies showing the portfolio optimization of different generations. The aim of this study is to reduce this gap and stimulate further academic discussion.

All in all, the identified research gaps regarding the investment preferences and the approach to portfolio optimization of various generations (X, Y, and Z) allowed us to formulate the purpose of our investigation, that is, to assess how investors from various generations might adjust their portfolio composition in reaction to important economic and non-economic market-moving events.

Due to the large number of asset types available in global markets, the set of assets selected in particular studies varies significantly [see, e.g., Aït-Sahalia and Xiu, 2016; Tiwari et al., 2018; Kurka, 2019; Le et al., 2021], and there is no widely accepted standard set of assets included in the portfolio. We assume that our investors have access to global markets and prefer highly liquid instruments either of global nature or from developed countries. Such an assumption may be particularly important in the context of this study as some events may lead to liquidity constraints and thus an inability to adjust the investment portfolio. Therefore, American and European stock and T-bond markets are the focus, complemented by global assets, such as gold, Bitcoin, and – in some scenarios – oil as an important type of commodity. Thus, we allow an investor to construct a portfolio using the following assets: the S&P 500 index, the EuroStoxx 600 index, 10-year US and German government bonds, gold, Bitcoin, and Brent crude (a major benchmark for oil prices). Both selected stock market indices account for a significant market capitalization in the US and Europe (approximately 75% in 2021) and thus may be treated as representative of these two markets. In the US and the largest economy in Europe, that is, Germany, T-Bonds and gold are regarded as safe-haven assets [e.g., Tachibana, 2022; Ugolini et al., 2023], reducing the volatilities of the portfolio. Additionally, gold and crude oil provide a hedge against inflation. Bitcoin, being rather speculative in nature, although called “digital gold” [Selmi et al., 2022], represents the largest capitalization of all cryptocurrencies. Moreover, we treat the chosen asset classes as ‘layers’ within which a further selection of specific instruments, which meet certain characteristics, can be introduced. Therefore, the effects of the events analyzed should be understood as those that affect the particular asset class as a whole in a certain way.

Geographically, in turn, the choice is limited to developed markets in Europe and the US, which is constrained both by the location of the events analyzed and by concentration characteristics [e.g., for equities, Europe and the US represent approximately 60% of the global market, Kuvshinov and Zimmermann, 2022]. As government bonds and equities account for around two-thirds of the global market portfolio [Doeswijk et al., 2014], in our study, we use two representatives of these markets, instead of one. Market price data for financial instruments are sourced from Bloomberg.

This choice of different asset classes allows us to include the diverse investor preferences of each generation (see Figure 1). Moreover, since different asset classes should, by definition, exhibit relatively low or opposite correlations [due to internal homogeneity and external heterogeneity; see Kritzman, 1999], such a selection of assets should allow portfolio diversification effects to be achieved. In the long term, correlations between our selected assets are low overall and conform to this approach (a correlation table is available in Appendix 1). We are aware that a relatively small number of assets in a portfolio may raise some concerns about limited diversification benefits. Nevertheless, there is still a body of literature suggesting that a small number of assets is indeed sufficient to achieve a significant diversification effect – for example, approximately 7–10 [e.g., Barber and Odean, 2000; Stotz and Wei, 2014] or 6 for active equity funds included in the funds-of-funds portfolio [Brands and Gallagher, 2005]. This benefit comes with a smaller number of assets, especially when these assets belong to different classes. In effect, the global minimum variance portfolio is considered to be constructed from different sets of 10 assets [Green and Hollifield, 1992]. Obviously, these numbers are determined by a number of factors, including the specifics of the markets, the interrelations between them or current conditions. Nonetheless, limiting the number of asset classes to 7 also makes it easier to identify and understand the relationships. Still, the selected assets give the investor exposure to a number of factors, including economic growth, inflation, interest rates, credit risk, or – albeit indirectly – market uncertainty.

Figure 1.

We do not include alternative investments among the assets available for portfolio optimization for several reasons. The valuation of alternative investments is often problematic, which limits their liquidity and thus dynamic portfolio diversification potential on a daily basis. Furthermore, alternative investments constitute a heterogeneous group of assets, their intrinsic value is often tied to the regional market, and they are not easily understood by a typical investor. Consequently, they are much less likely to be included in the portfolio of a “typical” investor from generation X, Y, or Z.

To simulate the optimal portfolios of investors from different generations, we first define these generations by formulating allocation constraints. Such constraints are necessary to construct a portfolio suitable for a particular type of investor – in our case belonging to different generations. We define them using the extant literature [e.g., Eisl et al., 2015; Damianov and Elsayed, 2020] and experts’ judgment. We contacted 10 market practitioners (6 of whom responded), including Certified Financial Analysts (CFA),² with questions about a portfolio structure that they would suggest as adequate for different investor types. This helped us validate our ideas on the portfolio structures. Each respondent provided us with suggested portfolio structures for three generations. Based on the literature review, methodological constraints for the optimization procedure, and expert judgment, we obtained the following average structure of dedicated portfolios for generation X, Y and Z investors (please see Figure 1; detailed data are available in Appendix 2).

The aforementioned portfolio structures reflect some specific characteristics that should be mitigated in our methodology. Specifically, they present a snapshot of a portfolio that is adequate at a given point in time, thus reflecting both the market environment and the preferences and abilities of the generation observed at this point. Moreover, they indicate a fixed portfolio structure over time, which requires frequent rebalancing (to keep the structure stable) and does not allow for temporal adjustments in response to, for example, important events (each adjustment requires an expert assessment). Nevertheless, it also provides some general relations that are worth emphasizing. First, a dominant portion of the portfolios of all generations (amounting to approximately three-quarters) is represented by exposure to two asset classes – fixed income and equity. Thus, when shifting across generations, the majority of adjustment occurs within these asset classes. Second, fixed income is a preferable asset for generation X, while equities are preferable for generations Y and Z. Third, generation X should not be exposed to Bitcoin but to gold instead, while Bitcoin is favored by generation Z, instead of gold. Fourth, exposure to crude oil does not reduce exposure to major assets (fixed income, equities) but is introduced at the expense of gold (gen X) or Bitcoin (gen Z). Importantly, both constraints and optimization adopt the perspective of an asset-only approach in search of the optimal portfolio. We therefore focus solely on the asset side of the investor’s balance sheet and do not model liabilities or goals, which in practice may also have an impact on asset selection and portfolio constraints.

We consider these relations and address them in the form of allocation constraints in our optimization procedure (see Scheme 1). We treat portfolio structures reported by respondents as a reference point for formulating constraints on the portfolio weights. In other words, we use the structure only to tilt the portfolio toward the preferences of each generation and to distinguish them from others. We also want to allow for flexibility and enable the application to past data; therefore, we formulate these constraints only for some of the assets with respect to their minimum or maximum shares in the portfolio (see Figure 1C) while addressing all of the major relations stated before.

For example, we do not assume that generation Z holds Bitcoin as a significant part of their portfolio, as might be suggested by Figure 1A). Instead, we assume that the proportion of Bitcoin in the portfolio cannot be greater than approximately 25%, while the minimum share cannot be lower than 5% (Figure 1C). These limits not only are based on expert judgment but also follow the literature [e.g., Eisl et al., 2015; Damianov and Elsayed, 2020]. Importantly, the constraints imposed must still apply to the group of investors characterized by different perceptions of risk. In particular, the upper-limit constraint is particularly binding for an investor with above-average risk tolerance, while an investor with above-average risk aversion would probably hold a much lower proportion of the portfolio in Bitcoin, despite their generational perceptions. Therefore, a significant part of the portfolio is allocated to Bitcoin only in the case of a specific investor (generation Z with above-average risk tolerance), which in our study is perceived as an investor with the highest possible risk tolerance for whom the risk associated with, for example, equities is not sufficient or, more precisely, that the reward for this risk is too low.

From a formal perspective, we implement a classical MVO procedure. Despite the well-known shortcomings of the model, MVO is often the starting point for making asset allocation decisions. Obviously, the literature offers a range of possible alternatives – from more-sophisticated approaches, including machine learning [which take into consideration higher moments of risk than volatility; see, e.g., DeMiguel et al., 2009] to simpler alternatives (such as the naïve portfolio diversification rule).

In this study, however, while recognizing the drawbacks, we also acknowledge the advantages of MVO. Most notably, it is a simple and easy-to-implement approach that has been widely used in finance for many years. This opens up the possibility of a broad comparison with other results in the literature, a possibility that is not impaired by, for example, the implementation of more-sophisticated and less-popular methods. Most notably, it allows for the identification of not only economic and but also methodological drivers of results. Nevertheless, MVO is flexible enough to be adapted to different investment objectives and constraints and can be combined with other techniques. Ultimately, we prefer to begin with a simple method to more precisely identify possible relations. At the same time, we attempt to minimize the model’s shortcomings, first by selecting assets whose valuations do not include many hard-to-control premiums (e.g., liquidity or extensive credit risk), which need to be managed by higher moments of the return distributions and, second, by our approach to the expected returns.

Our objective is to identify the optimal portfolio on the efficient frontier according to specified criteria. Obviously, this frontier will differ depending on how the risk-free asset is considered. Although we consider long-term government bonds, we do not perceive them as a completely risk-free asset; in fact, we include them in the optimization process. Moreover, we do not allow short selling to mitigate the MVO tendency to produce extreme portfolios combining extreme shorts with extremely long portfolios and to keep the frontier less vulnerable to new information. Therefore, asset weights in the portfolio are described as w ∈ W, where W ≔ {w ϵ ℝ^N|w′1 = 1}. Given the mean (μ_p) and variance σP2$$\left( {\sigma _{\rm{P}}^2} \right)$$ of the portfolio, the mean-variance efficient portfolio maximizes quadratic utility for a selected level of risk tolerance (λ)³: 1w(λ):=maxw∈WμP−12λσP2=maxw∈Ww′μ−12λw′Σw$$w(\lambda ): = \mathop {\max }\limits_{w \in W} {\mu _P} - {1 \over {2\lambda }}\sigma _P^2 = \mathop {\max }\limits_{w \in W} w'\mu - {1 \over {2\lambda }}w'{\rm{\Sigma }}w$$ where X ∈ R N is a vector of asset returns with mean μ and positive-definite covariance matrix Σ.

Defining Q≔ Σ⁻¹ − (1′Σ⁻¹1)⁻¹ Σ⁻¹ 11′Σ^-1, w(λ) has the solution w(λ) = w_GMV + λQμ, where wGMV:=Σ−111′Σ−11,$${w_{GMV}}: = {{{{\rm{\Sigma }}^{ - 1}}1} \over {1'{{\rm{\Sigma }}^{ - 1}}1}},$$ and Σ denotes the positive-definite covariance matrix. With respect to the above, λ = 0 corresponds to the global minimum-variance (GMV) portfolio, while λ = ∞ corresponds to the maximum mean return portfolio. Empirically, most investors’ risk aversion is consistent, with λ between 1 and 10, and λ = 4 can represent a moderately risk-averse investor [Ang, 2014]. Therefore, in our study, we introduce two levels of that parameter: above-average risk aversion (λ = 2) and below-average risk aversion (λ = 7). Importantly, in our study, we assume that these parameter values are common to investors of all generations. We do not impose different risk tolerance levels for different generations as we believe that in a ‘conservative’ generation, there may be individuals with a higher risk tolerance, and vice versa. Furthermore, to the best of our knowledge, the literature has not defined lambda parameters with reference to investors belonging to different generations.

One of the most important inputs in MVO is the vector of expected returns, partly because of the model’s significant sensitivity to estimation errors of the input parameters [see, e.g., Kan and Zhou, 2007; Kuhn et al., 2009]. Simultaneously, the literature confirms that the accurate estimation of expected returns is difficult and sensitive to the chosen methodology and, particularly, that historical returns are confirmed to be a poor predictor of expected returns [e.g., Ledoit and Wolf, 2003]. The selection of assets for analysis mentioned previously gives us the comfort of deriving the market perspective of expected returns, rather than relying on estimates. Since for all assets – except Bitcoin – an investor can easily access the range of derivative financial instruments, instead of attempting to improve the quality of moment estimates, this study uses forward-looking moments of return distributions that can be derived from option pricing. The market probability distribution derived at a given point in time is, in our view, a good proxy for market expectations at a given horizon. In this approach, we follow Martin [2017] and do not rely on the assumption of any particular return distribution. By introducing such an approach to expected returns, we believe we can control the typically high sensitivity of the composition of efficient portfolios to estimates of expected returns and overcome the drawbacks of the MVO technique as a relatively simple method.

With respect to the expected return of Bitcoin, which can be seen as a specific case of the aforementioned approach, we mirror the approach of Foley et al. [2022] and share the range of characteristics obtained. In particular, the expected return of Bitcoin is several times higher than, for example, that of the stock market, which was at its highest in early 2018 and has gradually declined in recent years. In particular, this is in line with the general perception of Bitcoin as a high-risk asset that should be rewarded accordingly. However, derivative markets for Bitcoin were not developed during its early years of operation. Therefore, for the analysis of investment portfolio structure in the years of 2012–2017, we assumed that the expected returns of Bitcoin in this specific period are proxied by its historical performance. For the remaining sample, as for other financial instruments, the expected returns are implied from the derivatives. We consider the potential risks outlined earlier and associated with this approach to be relatively mitigated as we allow only a small portion of the portfolio to be allocated to Bitcoin.

Since we believe that the interrelations across assets and their risk-to-return characteristics evolve over time, we rely on a dynamic approach to find an optimal portfolio structure. To do so, we estimate the model presented previously in a rolling window for two investment perspectives. We consider a short-term portfolio, in which the decision-making process considers only the last three years and a long-term portfolio formulated based on the last 10 years. Additionally, given that the assets included in this study are relatively widely available at low cost, we assumed the transaction cost to be fixed and to account for 0.1%. Such an approach simply indicates higher transaction costs for more-diversified and/or more-frequently adjusted portfolios. In our opinion, a more in-depth approach to transaction costs – additionally considering, for example, liquidity differentiation across asset classes – falls beyond the scope of this study.

The main objective of this study, in fact, is not to propose a perfect portfolio structure for the aforementioned investors. Instead, we assess whether short-term events can affect the strategic portfolio structure. On the one hand, such a structure should, by definition, be based on at least a medium-term perspective of the market and thus not be affected by short-term episodes. On the other hand, if events are significant enough, they may be reflected in asset characteristics – such as expected return or volatility – and hence in the structure of the optimal portfolio. The literature tends to independently examine whether the events in question can affect the expected return, the volatility of the assets, or the interrelations between them. In this study, however, we want to consider their ‘combined’ effect, assessed from the perspective of holdings in the optimal portfolio. Such a combined effect may indicate that although a specific event affects both the expected return and risk of an asset, the overall effect on the portfolio may be negligible. Therefore, we attempt to analyze whether the magnitude or direction of these adjustments was common within the category of events. In our view, this may be useful since it allows us to identify which categories of events may affect financial markets only in the short term (around the time of their occurrence) and may have longer-term consequences as a result of the rebalancing of investment portfolios that they trigger. In addition, it enables verifying to what extent the portfolio – in order to remain optimal – is affected by a specific category of undivorceable risk that arises purely from unpredictable events.

As stated before, given the estimated portfolio weights, we attempt to assess whether their evolutions might arise from events. To capture this possibility, we specify a regression model for asset weights in the portfolio (w_i) in which we control the overall market risk: 2qτwi∣Ωt=ατ+βτDt+γτRISKt$${q_\tau }\left( {{{\rm{w}}_{\rm{i}}}\mid {{\rm{\Omega }}_{\rm{t}}}} \right) = {\alpha _\tau } + {\beta _\tau }{D_t} + {\gamma _\tau }{\rm{RIS}}{{\rm{K}}_{\rm{t}}}$$ where q_τ(·) is the conditional quantile function evaluated at the τth quantile, Ω_t is the information set available at time t, and α_τ, β_τ, and γ_τ are the parameters to be estimated at the τth quantile. The dummy variable D_t takes the value of 1 during the periods corresponding to the events and 0 otherwise. The variable RISK_t should be viewed as a measure of overall market systematic risk and is constructed using a statistical technique, principal component analysis (PCA), with aims to reduce the idiosyncratic nature of a set of measures and capture only the common element of market risk. Specifically, the RISK_t measure is the first component (of a set of components extracted from the PCA) for a group of indicators describing investor sentiment in stock markets (VIX index), currency markets (JPM G7 implied volatility index), and bond markets (MOVE index), as well as the overall economic uncertainty (TED spread), global market liquidity squeeze (USD basis swap premium), and credit risk (US IG-HY spread). Therefore, the RISK variable allows us to control for widely understood market risk separately from the volatility risk specific to the asset category that was already introduced into the optimization procedure. The outcome of this part of the analysis is presented in Section 4.2.

To assess the impact of events on the optimal portfolio structure, we use the further refined and updated event database from Iwanicz-Drozdowska et al. [2021]. The database covers more than 300 individual events classified on a daily basis from January 1, 2000, to June 30, 2021. In contrast to the original version, we organized events into 11 categories (by, e.g., merging the monetary policy categories). We included (separately for the US and Euroarea) restrictive and expansive monetary policy,⁴ prudential policy in the banking sector,⁵ and major problems of multinational banks.⁶ Non-economic events are classified into key geopolitical events of international importance, major terrorist attacks, and information about the outbreak and spread of a virus.⁷ We believe that this approach covers the main types of potential market-moving events and allows us to generate findings, rather than analyzing each event separately. Of course, each may differ to some extent, but within one category, they share a number of similarities – including, most importantly, their nature and channels of potential impact.

As a next step, finally, we investigate whether an investor can enhance the portfolio return (with respect to the optimal return) by introducing tactical overweighting in reaction to the events. The motivation behind this approach is as follows. Since the events analyzed can be interpreted as having short-term, rather than structural, effects, they may not be reflected in the estimates of expected returns and hence in the optimal portfolio structure. However, an investor may wish to capitalize on such events. Thus, we simulate a decision-making process that allows us to overweight one selected asset on the day of the event occurrence (while proportionally decreasing the weighting of other assets in the portfolio).

This tactical deviation is introduced with the rule-based approach, that is, a general rule that applies in a similar way to all assets and events analyzed. Specifically, assuming that, on the day before an event occurred, the share of asset i in the portfolio amounted to w_i (in percent terms), the investor reacts to the event by increasing the allocation to that asset by wi.$$\sqrt {{w_i}} .$$ Theoretically, such reaction scaling leaves space for tactical overweighting ranging from 1 percentage point (when the original share was close to 1%) to 10 percentage points (if the portfolio consists of a single asset). It is a simple rule, but it ensures that the decision to deviate is strictly linked to the initial structure of the portfolio. This is particularly important because the initial structure represents the strategic view of the investor and is constructed with the aim of being consistent with the investment profile and risk tolerance characteristics. Therefore, as a tactical deviation, the investors cannot completely rebalance their portfolio structure but must remain within the strategic view. In addition, a strict rule reduces emotionally driven decisions. In this sense, the proposed rule helps maintain long-term goals and avoid impulsive decisions. This may be particularly important in the context of this study as we intend to analyze a number of market events. These events, in fact, may cause or contribute to market instability and volatility, and the temptation to profit from them can lead to the portfolio being shaped by emotional biases. In this context, a simple rule reduces this risk. As a result, short-term market fluctuations are introduced into the portfolio in a consistent manner. Ultimately, we are not suggesting that the aforementioned rule is the best way to react to various events, and most likely it is not. Rather, the purpose of this exercise is to test whether a one-size-fits-all reaction function can benefit the investor who reacts when a particular event occurs.

The simulation is conducted separately for each analyzed asset. This means that if we have five assets in the portfolio, we allow the investor to make five independent decisions to overweight each asset. The aim is to compare and contrast all the possible outcomes and identify the asset that benefits the investor the most. More importantly, the aim is to see whether the similar response to each type of event produces a similar outcome and whether a pattern that worked once can be repeated. The findings of this exercise are reported in Section 4.3.

In the first step, a broad picture of the portfolio structure – that is, an outcome of rolling estimation given exogenous constraints – should be provided. Such an approach results in a dynamic structure for this portfolio that can be analyzed from several perspectives – across investment horizons, generations, and risk tolerances and with respect to the significance of asset exposure (see Figure 2). It should be noted that the evolution of the portfolio structure might not be associated with a particular event, but rather reflects the broad environment that affects market pricing. Therefore, an assessment of portfolio evolution that arises around particular events is undertaken in the following section.

Figure 2.

First, addressing the investment horizon, we confirm that the long-term perspective (Figure 2B) is characterized by a visibly smaller frequency of shifts in the portfolio structure. Over this horizon, a similar asset composition of a portfolio persists for years, while in the short term, it evolves many times even during a single year (Figure 2A). This process results – to some extent – from our assumptions, that is, the length of the observation window, which is considered when the investor decides on the adjustment of the portfolio structure. However, a greater tendency of short-term portfolios toward rapid and frequent shifts is not an obvious characteristic since it is evidenced only in the most recent years. In particular, until 2012, the implied structure of the short-term portfolio was characterized by significantly greater stability, which was evidenced for all generations and both risk tolerance levels. We believe that this structure might be the result of the start of the sovereign debt crisis in several Euroarea (EA) countries, which rattled financial markets thereafter (and, e.g., increased demand for safe assets such as 10Y Bunds). In this way, we confirm the findings of Bratis et al. [2020] that financial spillovers strengthened in the postcrisis period.

Second, regarding the differences between generations, at the short-term investment horizon, variability in the portfolio structure intensifies as the generation becomes younger. Therefore, the frequency of portfolio adjustment does not solely arise from the length of horizons considered in the decision process (as might be supposed when comparing short- and long-term horizons) but also results from the investment preferences and risk tolerance of a given generation. In summary, the portfolio structure is more stable in the case of (i) a long-term investment horizon (in contrast to a more-volatile short-term horizon); (ii) older generations (as opposed to younger ones); and (iii) portfolios with greater risk aversion (than risk-seeking ones).

Third, the younger the generation is and/or as the risk aversion relaxes, a broader range of asset classes is introduced into the portfolio with a significant share. On the one hand, the investor seeks returns and thus introduces assets with greater return-generating characteristics into the portfolio at the cost of higher portfolio volatility. On the other hand, however, this broader range of asset classes allows investors to benefit from diversification effects, which might be particularly important given the diverse impacts of particular event types on the risk-to-return ratio for different asset classes. Therefore, although the risk-averse portfolios with “safe assets” might experience lower volatility, they might also expose an investor to the concentration of event risk. In this light, more-diversified portfolios might compensate for event risk through diversification effects. Nevertheless, diversification benefits are likely to be lower during periods of financial market stress [Ming-Yuan, 2007; Bratis et al., 2020].

Fourth, with respect to exposure to particular asset classes, in the majority of optimal portfolios, fixed income instruments dominate, most notably before 2012 (see Figure 2). Thus, this dominant asset class transmits impulses to the portfolio and reflects investors’ perceptions of the past environment, and it acts as a hedge for the equity market [Ciner et al., 2013]. Therefore, it is simultaneously expected to be the class that will reflect the reaction to a variety of events the most. Since equities were ex ante allocated a relatively small share (even for the above-average risk tolerance portfolio), they are the most likely source of improvement in portfolio returns. Bitcoin’s share, in turn, is driven to a great extent by the constraints. The optimization procedure suggests allocating a prominent share of portfolios to this asset class, despite its substantial volatility. This share in the majority of the analyzed period is then limited by exogenous constraints. Thus, our results subscribe to the mixed impact of Bitcoin on portfolio volatility or its returns [Dyhrberg, 2016; Guesmi et al., 2019; Damianov and Elsayed, 2020; Bakry et al., 2021].

Against this background, gold plays a significant role, particularly in long-term portfolios. At this investment horizon, exposure to gold becomes significant for all analyzed generations (in some periods accounting for even half of the portfolio), while most of the short-term portfolios allocate only a meagre share to it. The post-global financial crisis (GFC) environment resulted in short-term portfolios being skewed toward equity exposure and long-term portfolios toward gold. Moreover, the short- and long-term perspectives introduce gold in different periods. Interestingly, portfolios with above-average risk aversion – for both investment horizons – do not allow for any significant exposure to gold. This aversion is evidenced even regardless of gold being recognized as a safe haven asset under some circumstances [in line with the results of Baur and McDermott, 2016; Nguyen et al., 2016; Alkhazali and Zoubi, 2020; Zhang et al., 2021]. According to our analysis, gold as a commodity – albeit a specific one – is characterized by greater price volatility than particularly fixed income. Since our optimization procedure employs this measure as a main risk component, it penalizes the allocation toward gold for an investor who is characterized by above-average risk aversion, that is, below-average volatility. The role of this characteristic in the optimization procedure was particularly strengthened by the market environment, namely, the medium-term underperformance of gold since 2011.

Next, we assess the extent to which events drive the evolution of the optimal portfolio structure. Hence, we analyze shifts in the optimal portfolios of different generations in response to economic and non-economic events from short- and long-term perspectives.

From a short-term perspective (Figure 3A), the youngest generation might be more reactive to events to maintain the optimal portfolio structure. For more risk-averse investors from generations X and Y, reactions to various events focus mainly on slight shifts in exposure to treasuries, regardless of the type of event, while generation Z is expected to introduce more adjustments. The increased focus on US treasuries can be attributed to the role that prudential measures play in the economy, that is, they show the implied risk reduction in the financial industry through, for example, deleveraging. The most significant changes in the portfolio structure for generation Z are also induced by restrictive monetary policy measures (in the US and Eurozone) and the EA’s prudential events and defaults.

Figure 3.

From a short-term perspective but for less risk-tolerant investors (i.e., below-average risk aversion; see Figure 3, bottom-left panel), the optimal portfolios require more adjustments in response to various events than in the case of more risk-averse investors. As in the previous case, the portfolios of generation Z are the most reactive; thus, we comment on them.

From the short-term perspective, the most significant (±10 p.p.) shifts in the portfolios of generation Z are mostly caused by two non-economic events (terror and virus) and prudential and monetary policy events (mostly in the US). These non-economic events cause a shift from US stocks to European stocks. The impact of prudential events reduces the share of US stocks in return for increased exposure to gold. Moreover, EA prudential actions result in a decrease in US treasuries. Regarding monetary policy measures, for US events, portfolio adjustments are focused on the European market (decreasing stakes), while restrictive policy in the EA shifts portfolios to higher exposures to US treasuries. In this context, the portfolios of generations X and Y are less reactive. In general, while generation Y might shift its portfolio structure to a lesser degree (±5 p.p.) than generation Z, for generation X, only a few events result in significant changes. For treasuries, shifts in generation Y’s portfolios should follow economic events, US prudential steps, and EA defaults.

From a long-term perspective (Figure 3B), we consider generations X and Y since, for generation Z, the investment perspective is too short. Generation Z includes investors born typically in early 2000s; thus, their investment activities would have started much later than in case of generations X and Y. Accordingly, given the fact that our sample ends on 2021H1, practical investment experience of generation X is likely no more than several years, which cannot be considered as a long-term perspective on par with generations X and Y. In the case of more risk-averse investors, one can observe only slight shifts in treasuries, confirming that from a long-term perspective, the given event types are of lower importance.

This presentation relied on an average reaction to a specific type of event. Importantly, however, a relatively high level of ambiguity of each selected event within a category was observed. For the sake of consistency, we present here results and comments only for more risky investors from generation X (Figure 4). The remaining results are presented in Appendixes 3 (short-term) and 4 (long-term).

Figure 4.

Although for Euro Stoxx and Bitcoin, the changes are rather concentrated (approximately ±1–5 p.p.), this is not the case for other assets, the reactions of which to events can differ significantly (by more than ±10 p.p.). A question arises: Which of the events causes the most significant changes? For example, the outbreak of the COVID-19 pandemic shifted portfolios toward gold. Terrorist attacks in Europe (Nice and Berlin in 2016 and London and Manchester in 2017) resulted in other shifts. Among geopolitical events, the most striking are social unrest in Turkey (June 2013) and presidential elections in the US (November 2016). They resulted in shifts between German and US treasuries.

Regarding economic events, the bailout measures approved for Banca Monte dei Paschi di Siena, for example, coincided with expansionary US policy measures, resulting in significant shifts between German (increase) and US treasuries (decrease). Individual events could result in a significant change in the portfolio structure, although, on average, they range between ±10 p.p.

Overall, in the short run, events originating in the US are more important for shifts in the portfolios. Events from the Eurozone cause a change in investors’ interest in US assets and gold.

This exercise led us to two key findings: (i) For the majority of event categories, the response of the optimal portfolio structure is rather muted, in particular for long-term portfolios; (ii) a relatively high level of ambiguity was observed for each selected event within a category.

These findings are, in our view, consistent with a general characteristic of most of the events mentioned. As these events are not structural in nature, their market effects tend to diminish relatively quickly. Therefore, they may not have a significant impact on the estimates of asset characteristics (such as expected return or covariance). For equities, estimates of expected returns can be affected to a greater extent by, for example, earnings data [Lamont, 1998], investments [Cochrane, 1991], or aggregate consumption or wealth [Lettau and Ludvigson, 2002]. The common element of these factors is that they capture at least the medium term, whereas the range of events we are analyzing is more short term in nature. Therefore, their natural characteristic is that they tend to diminish sooner or later. The events may not be expected to change the perception of expected return or covariance, or the impact may not be worth acting upon. However, even if the events do not affect the expected return, they are reflected in the pricing through the abnormal returns.

The purpose of this section is to analyze a general rule for the event category that is purely exogenous in terms of the magnitude of portfolio weighting adjustments. The analysis presented in this section is intended to give the reader an idea of how such a rule (by deviating from the optimal state) has actually worked in the past. The aim is to be able to select an asset class to overweight when a particular event occurs, regardless of whether the event affects expected return estimates.

This step of the analysis is intended to assess whether a deviation from the optimal portfolio, based on the exogenous decisions of an investor, can bring an additional return to the portfolio or – in other words – whether the investor is able to capitalize on the short-term nature of the events. Therefore, we simulated a reaction to an event independent of the estimated optimal portfolio structure and assessed whether it could bring an additional return to the portfolio over that implied by the optimal portfolio. The simulation assumes that the investor chooses one specific asset class and overweights its share in the portfolio when a specific event occurs. Which asset type to select in reaction to which type of events is evaluated through the incremental return that the portfolio should earn in comparison to the optimal structure discussed previously.

This part of the analysis provides additional insights, which are presented in a complex way in Figure 5. Their interpretation can be summarized using a simple example: the red triangle within the EA restrictive monetary policy in the top left-hand panel of Figure 5. The interpretation of this point can be formulated as follows: “The decision to overweight gold in response to a restrictive monetary policy decision adds ~1 p.p. of additional annual return to the portfolio of the generation X investor, who is characterised by above-average risk aversion.”

Figure 5.

Considering the broad picture, we found that, first, an exogenous change in exposure in response to a specific event could affect the return profile across all of the generations and for both the short- and long-term perspectives (see Figure 5). In other words, the reactions to all categories of events can bring an additional return to a portfolio; however, an inappropriate selection of assets might also result in incremental loss in the portfolio across all categories. This outcome in particular means that none of the events creates an extraordinary opportunity to generate profit, regardless of the asset selected for the portfolio.

Second, the return-generating ability of a selected portfolio adjustment generally seems to be consistent across many original portfolios. Most notably, as long as the structure of the portfolio remains within a given investment style, the exogenous decision to overweight one selected asset seems to benefit the portfolios across types and investment horizons.

Third, the incremental portfolio returns are relatively moderate since they usually do not exceed ±4 percentage points. With a decrease in risk aversion (hence an increase in risk tolerance), the additional gain/loss in response to an event usually increases. Most notably, different types of events call for different adjustments to the portfolio structure to generate incremental gain. Thus, the selection of an asset that should be overweighted in comparison to the optimal portfolio should rely on the type of event at hand.

Nevertheless, comparing this step with the previous one (Section 4.2), exogenous portfolio adjustments reduce the ambiguity of the reactions to events within each category. As stated previously, the optimal portfolio in some cases requires different responses for similar events in each category. This step, however, assumes that within each group of events, investors’ reaction is fully coherent. Such decision-making “comfort”, in fact, results in incremental returns being relatively muted.

We find that expansionary monetary policy generates the greatest potential for incremental returns across all of the analyzed events and for all investor profiles. This finding is likely a consequence of significant global spillovers caused by monetary policy decisions [Georgiadis, 2016; Georgiadis and Gräb, 2016]. The return is typically introduced into the portfolio by overweighting the equity market. In the case of defensive portfolios (i.e., those for above-average risk aversion), this additional exposure to equity is relatively small since the portfolio must be kept consistent with the investor’s profile. However, the incremental return over the optimal portfolio that such an action generates is relatively comparable to that originating from a similar action undertaken in the aggressive portfolios (which by definition need a greater change in equity exposure).

In response to the restrictive monetary policy shock, rising exposure to gold usually brings the greatest incremental return for all types of investors. Moreover, as in the previous case, equities can also be perceived as enhancing portfolio returns in restrictive monetary policy environments, although to a relatively smaller extent. This finding might seem to be counterintuitive since restrictive monetary policy results in rising real interest rates and should exert downward pressure on gold (as demand for inflation hedge weakens) and equities (throughout higher marginal cost of market funding). In line with this expectation, we confirm that the optimal portfolio reacts by lowering exposure to these two assets in a restrictive monetary policy environment (see, e.g., Figure 4). In this section, however, we find that reversing this action throughout a tactical deviation from the optimal portfolio can, in fact, enhance the portfolio return. Empirical studies have confirmed that the relation of gold and interest rates is strong only in the recessionary phase [e.g., Apergis et al., 2019] and that gold loses its inflation hedging characteristics during periods of low inflation [Zhu et al., 2018], which is the case for the period in our study. In this context, we claim that restrictive monetary policy can be seen as an opportunity to build up exposure to gold without introducing drawdown risk into the portfolio. Obviously, this outcome might be only a period-specific effect since expansionary monetary policy significantly dominated our sample; thus, the effects of restrictive monetary action might be understated.

Given this scenario, the return that arises from the fixed-income part of the portfolio and its adjustment to events should also be analyzed with respect to the role of the investment horizon. Since the market reaction to events is usually relatively short- to medium-lived, an investor in the fixed-income market remains in the space when the pricing effect of interest rate changes outweighs the cash flow effect. Therefore, the short-term portfolio usually generates a loss while increasing exposure to the fixed-income market in response to restrictive monetary policy. However, our study confirms that as the horizon changes from a short to long term or as risk aversion decreases, the incremental loss also originates from increased exposure to fixed income in response to expansionary monetary policy. Notably, the aforementioned findings for monetary policy events are comparable for both the US and EA in terms of structure. When considering the incremental size of return/loss due to the action, however, it is greater in the latter case. This finding might not necessarily mean that the monetary policy of the ECB has a greater impact on markets and thus affects the analyzed portfolios to a greater extent. This outcome might partly arise from US monetary policy being accorded greater consideration at the level of the optimal portfolio. Consequently, the tactical deviation from this structure does not result in significant incremental returns.

Addressing the second subset of economic events – namely, the micro- and macroprudential policies, as well as defaults – we find that their return-generating ability calls for a comparable response to that of expansionary and restrictive monetary policy, respectively. Specifically, to generate incremental returns in response to a prudential action – similar to expansionary monetary policy – the equity market should be overweighted in the portfolio. Moreover, this view is consistent for the short- and long-term investment horizons. However, at both horizons, such an action in response to US prudential events enhances portfolio returns to a greater extent than in the case of responses to EA prudential events. When considering default, return enhancement characteristics can be introduced by overweighting gold, particularly over the long-term investment horizon (EA market) or fixed income (US market). Unlike the prudential action, the response to default episodes allows us to enhance portfolio returns to a greater extent when originating from the EA market.

In contrast to this, both the incremental gains and losses that arise due to the reaction to non-economic events are relatively small compared to economic ones. In particular, increased exposure to fixed income and/or gold protects against the effects of geopolitical events since these assets add some incremental return to the portfolio, while overweighting equities results in a loss for all investor types. The smallest incremental return in this case can arise from the investment approach itself. First, an optimal portfolio should mitigate the return effect of such types of events; second, the market reaction to them, particularly that of major asset classes, could be relatively short-lived with a strong tendency to be reversed, which is derivative of the minor and short-lived impacts that terror attacks, for example, exert on the stock market [Markoulis and Katsikides, 2020]. As a result, the overall value added in such an environment is meagre.

The perspectives of incremental returns due to changes in asset exposure for short- and long-term portfolios share a range of similarities. However, the introduction of crude oil into the portfolio (see the results in Appendix 5) starts to significantly differentiate the incremental returns of these two types of investing. Such a strong differentiation was not evidenced earlier, that is, for a comparable portfolio structure that did not include this commodity. From the short-term perspective, the presence of crude oil in the portfolio significantly reduces the return opportunity that can be generated due to the reaction to events in most cases, with the strongest effect being observed in the portfolio of generation Y. In other words, if crude oil is introduced into the portfolio, overweighting any other asset class in response to events results in weaker incremental returns (generations X and Z) or even incremental losses (generation Y) compared with portfolios without this commodity. In certain cases, crude oil generates an opportunity to realize greater gains; however, this opportunity is relatively rare (evidenced only for two types of events, e.g., prudential action and US expansionary monetary policy). Therefore, crude oil can be perceived as an asset class that introduces more event risk than opportunities into the portfolio due to the reactions to some episodes. We thus concur with the findings of Raza et al. [2016] that oil volatilities have a negative impact on stock markets in both the short and long terms. However, we stand partly in contrast to Martín-Barragán et al. [2015], who showed the diversification benefits of oil in non-crisis times, and El Hedi Arouri et al. [2011], who argued that oil is a dynamic and valuable asset class that helps improve risk-adjusted performance.