Portfolio diversification and value at risk under thick-tailedness†

This paper focuses on the study of portfolio diversification and value at risk analysis under heavy-tailedness. We use a notion of diversification based on majorization theory that will be explained in the text. The paper shows that the stylized fact that portfolio diversification is preferable is reversed for extremely heavy-tailed risks or returns. However, the stylized facts on diversification are robust to heavy-tailedness of risks or returns as long as their distributions are moderately heavy-tailed. Extensions of the results to the case of dependence, including convolutions of α-symmetric distributions and models with common shocks are provided.     

The limits of diversification when losses may be large

Recent results in value at risk analysis show that, for extremely heavy-tailed risks with unbounded distribution support, diversification may increase value at risk, and that generally it is difficult to construct an appropriate risk measure for such distributions. We further analyze the limitations of diversification for heavy-tailed risks. We provide additional insight in two ways. First, we show that similar non-diversification results are valid for a large class of risks with bounded support, as long as the risks are concentrated on a sufficiently large interval. The required length of the support depends on the number of risks available and on the degree of heavy-tailedness. Second, we relate the value at risk approach to more general risk frameworks. We argue that in markets for risky assets where the number of assets is limited compared with the (bounded) distribution support of the risks, unbounded heavy-tailed risks may provide a reasonable approximation. We suggest that this type of analysis may have a role in explaining various types of market failures in markets for assets with possibly large negative outcomes.     

Investigating volatility spillover of energy commodities in the context of the Chinese and European stock markets

This paper investigates spillover from energy commodities to Shanghai stock exchange and European Stock market, and identifies possible risks transmission and portfolio diversification opportunities. The study is conducted on daily spot prices of carbon (CO2) emission, natural gas and crude oil from 16 December 2010 to 29 December 2022, employing Granger causality test, dynamic conditional correlation (DCC), Diebold-Yilmaz (2012) and Barunik-Krehlic (2017) models. Results identify higher volatility and imply greater connectedness in the longer run. Additionally, natural gas is witnessed as the highest contributor of the shocks and crude oil as the highest receiver of the shocks from the network connection. Further results suggest for investment in energy commodities in shorter run rather than long run for efficient portfolio diversification. Results from this study are expected to have practical implications for portfolio managers, investors, and market regulators, given the suggestion of this study to incorporate energy stocks for efficient diversification of risk.     

The Impact of Disability Insurance on a Portfolio of Life Insurances

The aim of this article is to study the impact of disability insurance on an insurer's risk situation for a portfolio that also consists of annuity and term life contracts. We provide a model framework using discrete time nonhomogeneous bivariate Markov renewal processes and in a simulation study focus on diversification benefits as well as potential natural hedging effects (risk-minimizing or risk-immunizing portfolio compositions) that may arise within the portfolio because of the different types of biometric risks. Our analyses emphasize that disability insurances are a less efficient tool to hedge shocks to mortality and that their high sensitivity toward shocks to disability risks cannot be easily counterbalanced by other life insurance products. However, the addition of disability insurance can still considerably lower the overall company risk.     

Optimizing international portfolios with options and forwards

We develop a stochastic programming model to address in a unified manner a number of interrelated decisions in international portfolio management: optimal portfolio diversification and mitigation of market and currency risks. The goal is to control the portfolio’s total risk exposure and attain an effective balance between risk and expected return. By incorporating options and forward contracts in the portfolio optimization model we are able to numerically assess the performance of alternative tactics for mitigating exposure to the primary risks. We find that control of market risk with options has more significant impact on portfolio performance than currency hedging. We demonstrate through extensive empirical tests that incremental benefits, in terms of reducing risk and generating profits, are gained when both the market and currency risks are jointly controlled through appropriate means.     

On the robustness of international portfolio diversification benefits to regime-switching volatility

We examine if the benefits of international portfolio diversification are robust to time-varying asset return volatility. Since diversified portfolios are subject to common cross-country shocks, we focus on the transmission mechanism of such shocks in the presence of regime-switching volatility. Generally, market linkages are stable with little evidence of increased market interdependence in turbulent periods. Furthermore, risk reduction is consistently delivered for the US investor who holds foreign equity.     

Income Risk and Portfolio Choice: An Empirical Study

This paper investigates the relationship between portfolio choice and labor income risk in the National Longitudinal Survey of Youth 1979 Cohort. Permanent income risk (variability of shocks to income that have permanent effect) significantly reduces the share of risky assets in the household's portfolio, while transitory income risk (variability of shocks with no lasting effect) does not. This result provides strong evidence that households' portfolio choices respond to labor income risks in a manner consistent with economic theory.     

Booms,Busts, and Common Risk Exposures

I present a dynamic general equilibrium model in which commonality in bank assets endogenously changes over the business cycle and shapes systemic risk. To reduce individual risks, banks diversify, increasing portfolio overlap and hence the similarity of their exposures to fundamental shocks. Systemic financial crises burst at the end of credit booms when productive investment opportunities are exhausted, banks' diversification incentives are strong, and their portfolios are highly correlated. A calibrated model is able to match key moments related to frequency, severity, and the economy's behavior around systemic crises.     

Diversification and systemic risk

Portfolio diversification makes investors individually safer but creates connections between them through common asset holdings. Such connections create “endogenous covariances” between assets and investors, and enhance systemic risk by propagating shocks swiftly through the system. We provide a theoretical model in which shocks spread through constrained selling from N diversified portfolio investors in a network of asset holdings with home bias, and study the desirability of diversification by comparing the multivariate distribution of implied losses for every level of diversification. There may be a region on the parameter set for which the propagation effect dominates the individually safer one. We derive analytically the general element of the covariance between two assets i and j. We find agents may minimize their exposure to endogenous risk by spreading their wealth across more and more distant assets. The resulting network enhances systemic stability.     

Reducing Risk Through Pooling and Selective Reinsurance Using Simulated Annealing: An Example from Crop Insurance

Agricultural insurance is often faced with the challenge of systemic risk, arising from weather risks that tend to be correlated within a specific region in extreme situations, resulting in large crop losses within the region. However, across many regions, especially if regions are considerable distances apart, weather may be quite different and losses may be much less correlated. The objective of this paper is to improve the diversification of a crop insurance portfolio, through developing a new alternative risk management approach (Model 3) that pools crop risks across all provinces in a country to form a Canada-wide joint insurance pool. This is in contrast to the current approach used in Canada, where crop risks are pooled only within an individual province. Then using a simulated annealing optimization approach, the most suitable combination of the 150 crop types in the portfolio is identified for either retaining in the joint insurance pool or for ceding to reinsurers, such that the variance of the loss coverage ratio of the portfolio is minimized. This model overcomes the problem of insufficient diversification that makes pooling of systemic weather risk challenging. It achieves diversification at a lower cost by using a more efficient combination of pooling and selective reinsurance, resulting in overall higher surplus, higher survival probability, and lower deficit at ruin.     

Correlation Risk and Optimal Portfolio Choice

We develop a new framework for multivariate intertemporal portfolio choice that allows us to derive optimal portfolio implications for economies in which the degree of correlation across industries, countries, or asset classes is stochastic. Optimal portfolios include distinct hedging components against both stochastic volatility and correlation risk. We find that the hedging demand is typically larger than in univariate models, and it includes an economically significant covariance hedging component, which tends to increase with the persistence of variance–covariance shocks, the strength of leverage effects, the dimension of the investment opportunity set, and the presence of portfolio constraints.     

SYMMETRIC VERSUS ASYMMETRIC CONDITIONAL COVARIANCE FORECASTS: DOES IT PAY TO SWITCH?

Volatilities and correlations for equity markets rise more after negative returns shocks than after positive shocks. Allowing for these asymmetries in covariance forecasts decreases mean‐variance portfolio risk and improves investor welfare. We compute optimal weights for international equity portfolios using predictions from asymmetric covariance forecasting models and a spectrum of expected returns. Investors who are moderately risk averse, have longer rebalancing horizons, and hold U.S. equities benefit most and may be willing to pay around 100 basis points annually to switch from symmetric to asymmetric forecasts. Accounting for asymmetry in both variances and correlations significantly lowers realized portfolio risk.     

Modelling optimal asset allocation when households experience health shocks

Health status is an important factor in household portfolio decision-making. We develop a theoretical framework to model how households make optimal asset allocation decisions in response to health risks. Our two- and three-asset models both suggest that the maximum utility is derived when households allocate a majority of their assets to human capital. When households experience acute illness shocks, their welfare and portfolio values reduce, and they need to increase their investment in human capital. When an expensive health catastrophe befalls member(s) of households, the optimal decision for asset-rich households is to undertake medical treatment, whereas for asset-poor households it is to forgo treatment. Asset-poor households in particular require public financial assistance to enable them to invest in human capital.     

Coberturas financieras con derivados y su incidencia en el valor de mercado en empresas colombianas que cotizan en Bolsa

The financial theory (Modigliani & Miller, 1958) rises that risk management was not an issue for companies because shareholders could make their own hedging management through portfolio diversification; however, further studies conflict with that statement and show that corporate financial hedging improves performance and increases the value thereof (Ahmed, Azevedo, & Guney, 2014; Allayannis & Weston, 2001; Allayannis & Ofek, 1998). Efficient management of market risks, which is based on the use of financial derivatives, demands strategic and efficient managers in hedging that adds value to the firm, especially in against shocks and imbalances from a macroeconomic and financial nature. Empirical evidence analyzes the performance of the Q-Tobin as an indicator of the effect of hedging strategies of exchange rate associated to the market value. This paper aims to find evidence in Colombia on the effect of using derivatives in the market value of the firm. Its added value lies in the analysis made by economic sectors, identified by CIIU codes and grouped into 5 sectors (Agricultural, Commercial, Industrial or Manufacturing, Services and Construction). The methodology includes several models estimating regression panel data, using a Pooled regression with estimators of fixed and random effects by maximum likelihood estimator. In general, it was found a premium due to hedging, statistically and financially significant, for companies exposed to exchange rate risks that use derivatives by an average of 6.3% on the market value. Moreover, mixed results were found regarding the analyzed variables in the model.     

Dynamic volatility spillovers and investment strategies between the Chinese stock market and commodity markets

Building on the increased interest in the volatility spillover effects between Chinese stock market and commodity markets, this paper investigates the dynamic volatility spillovers of Chinese stock market and Chinese commodity markets based on the volatility spillover index under the framework of TVP-VAR. The result shows that there is a highly dependent relationship between the stock market and commodity markets. On average, the Chinese stock market is the net recipient of spillover, non-ferrous metals and chemical industry have a very obvious spillover impact on the stock market. The degree of total volatility spillover is different in different periods. After major crisis events, the volatility correlation between markets increases. Since the outbreak of COVID-19, the spillover effect of the stock market on the commodity market has been significantly enhanced. Then optimal portfolio weights and hedge ratios are calculated for portfolio diversification and risk management. The result shows that the ability of most commodities to hedge against risks is significantly reduced when the crisis occurs; NMFI (precious metals) and CRFI (grain) still have good hedging ability after the crisis, but the effectiveness of hedging risk is relatively low. Besides, the combination of CRFI and SHCI (the Shanghai composite index) is the most effective for risk reduction.     

Cross‐region and cross‐sector asset allocation with regimes

Cross‐region and cross‐sector asset allocation decisions are one of the most fundamental issues in international equity portfolio management. Equity returns exhibit higher volatilities and correlations, and lower expected returns, in bear markets compared to bull markets. However, static mean–variance analysis fails to capture this salient feature of equity returns. We accommodate the nonlinearity of returns using a regime switching model across both regions and sectors. The regime‐dependent asset allocation potentially adds value to the traditional static mean–variance allocation. In addition, optimal allocation across sectors provide greater benefits compared to international diversification, which is characterized by higher returns, lower risks, lower correlations with the world market and a higher Sharpe ratio.     

Do ETFs provide effective international diversification?

Global investments have been a hot issue for years. Investors can diversify risks and obtain benefits from foreign markets by investing directly in the foreign security market or indirectly in Exchange-Trade Funds (ETFs). Because direct investments are not always feasible, we investigate whether indirect investments can replace direct investments. We create different regional optimal portfolios containing ETFs and ensure optimal asset portfolio allocation. In addition to mean-variance approach, the Sharpe index, we also adopt the Campbell et al. (2001) method to have the efficient frontier under control risks, the Value at Risk. We apply both normal and non-normal distributions for comparisons and find that different assumptions of return distributions affect the results of efficient frontier. The results show that international diversification is a reasonable strategy. In addition, when comparing ETFs and target market index portfolios, ETFs have higher Sharpe measures than target market indices especially in the emerging markets. However, there are no significant performance differences between direct and indirect methods even if we use different performance measures. We also find that the diversification benefits are the same before and after the Subprime crisis. We conclude that it is effective for investors to use indirect methods to create internationally diversified portfolios.     

Equity fund ownership and the cross-regional diversification of household risk

We explore the link between portfolio home bias and consumption risk sharing among Italian regions using household-level information on consumption, income and portfolio holdings. Since equity funds are typically diversified at the national or international level, we use data on equity fund ownership to proxy for regional home bias. Cross-regional patterns of equity fund ownership are qualitatively consistent with simple portfolio theory: regions with more asymmetric business cycles are more diversified because they have higher fund participation rates (the extensive margin of diversification) and higher average holdings of equity funds (diversification’s intensive margin). Also, fund holdings increase with the exposure of non-tradable income components (such as labor or entrepreneurial income) to regional shocks. Finally, interregional consumption risk sharing increases with fund holdings and this effect seems strongest when participation is widespread. Increased equity market participation could substantially improve interregional risk sharing.     

Using Four‐Moment Tail Risk to Examine Financial and Commodity Instrument Diversification

We consider the effect of higher moments on diversification, since most assets possess a potential for tail losses. In particular, we examine higher‐moment Value‐at‐Risk measures for individual instruments and diversified portfolios. We find that a naïve futures portfolio is consistently superior to common stock indexes. As few as ten randomly chosen instruments diversify away 85% of the unsystematic four‐moment tail risk. We also compare the two‐ and four‐moment tail risks for different size portfolios. Finally, the tail risk for naïve portfolios varies much less over time than other portfolios.     

Two-sided coherent risk measures and their application in realistic portfolio optimization

By using a different derivation scheme, a new class of two-sided coherent risk measures is constructed in this paper. Different from existing coherent risk measures, both positive and negative deviations from the expected return are considered in the new measure simultaneously but differently. This innovation makes it easy to reasonably describe and control the asymmetry and fat-tail characteristics of the loss distribution and to properly reflect the investor’s risk attitude. With its easy computation of the new risk measure, a realistic portfolio selection model is established by taking into account typical market frictions such as taxes, transaction costs, and value constraints. Empirical results demonstrate that our new portfolio selection model can not only suitably reflect the impact of different trading constraints, but find more robust optimal portfolios, which are better than the optimal portfolio obtained under the conditional value-at-risk measure in terms of diversification and typical performance ratios.