Safety-first portfolio optimization for US investors in emerging global,Asian and Latin American markets

Risk averse US investors with safety-first objectives in portfolio optimization hold small weights (maximum 10%) in emerging markets when constructing portfolios of the Standard and Poor's 500 (SP), and the Emerging Markets Composite Global (CG), Asia (AS) and Latin American (LA) indexes, respectively. The Composite Global and Asia weights are even smaller than their minimum variance weights. Yet, these optimal safety-first portfolios are dominant in terms of risk and return over the global minimum or higher variance portfolios. In contrast, safety-first optimization for Latin America is hardly different from the minimum variance and not clearly dominant over other mean–variance portfolios. Overall, safety-first limits portfolio losses associated with infrequent catastrophic events and otherwise optimize performance.     

The price of shelter - Downside risk reduction with precious metals

Investor aversion to extreme losses may motivate them to seek out investments perceived to function as a safe haven during times of crisis. In this study, we consider the potential for precious metals to mitigate downside risk when combined with equities, and evaluate the impact on portfolio risk-adjusted returns. Each of gold, silver and platinum are found to contribute to downside risk reduction at short horizons, but diversification into silver and platinum may result in increased long horizon portfolio risk. The price of sheltering an equity portfolio from downside risk is a relative reduction in portfolio risk-adjusted returns. Variance and kurtosis properties of precious metals are identified as marginal contributors to downside risk reduction. Futures markets on precious metals are also shown to present an interesting and viable diversification alternative to physical metals.     

Are gold,USD, and Bitcoin hedge or safe haven against stock? The implication for risk management

This study investigates whether gold, USD, and Bitcoin are hedge and safe haven assets against stock and if they are useful in diversifying downside risk for international stock markets. We propose a combined GO-GARCH-EVT-copula approach to examine the hedge and safe haven properties of gold, USD, and Bitcoin. We then examine the attractiveness of these assets in reducing stock portfolio risk by using downside risk measures estimated by the proposed approach and other competing models. We also evaluate the relative performance of the proposed model in reducing downside risk with the competing models. The findings of the study indicate that the USD is the most valuable hedge and safe haven asset closely followed by gold, while Bitcoin is the least valuable. It is also observed that the proposed combined approach performs best in reducing the portfolio downside risk. The findings of this study are of significance for portfolio managers and individual investors who wish to protect the portfolio value during market turmoil.     

Fund ESG performance and downside risk: Evidence from China

Whether responsible investing reduces portfolio risk remains open to discussion. We study the relationship between ESG performance and downside risk at fund level in the Chinese equity mutual fund market. We find that fund ESG performance is positively associated with fund downside risk during the period between July 2018 and March 2021, and that the positive relationship weakens during the COVID-19 pandemic. We propose three channels through which fund ESG performance could affect fund downside risk: (i) the firm channel in which the risk-mitigation effect of portfolio firms’ good ESG practices could be manifested at fund level, (ii) the diversification channel in which the portfolio concentration of high ESG-rated funds could amplify fund downside risk, and (iii) the flow channel in which funds’ better ESG performance may attract greater investor flows that could reduce fund downside risk. We show evidence that the observed time-varying relationship between fund ESG performance and downside risk is driven by the relative force of the three channels.     

Portfolio choice and equilibrium in capital markets with safety-first investors

This paper develops optimal portfolio choice and market equilibrium when investors behave according to a generalized lexicographic safety-first rule. We show that the mutual fund separation property holds for the optimal portfolio choice of a risk-averse safety-first investor. We also derive an explicit valuation formula for the equilibrium value of assets. The valuation formula reduces to the well-known two-parameter capital asset pricing model (CAPM) when investors approximate the tail of the portfolio distribution using Tchebychev's inequality or when the assets have normal or stable Paretian distributions. This shows the robustness of the CAPM to safety-first investors under traditional distributional assumptions. In addition, we indicate how additional information about the portfolio distribution can be incorporated to the safety-first valuation formula to obtain alternative empirically testable models.     

Portfolio selection with heavy tails

Consider the portfolio problem of choosing the mix between stocks and bonds under a downside risk constraint. Typically stock returns exhibit fatter tails than bonds corresponding to their greater downside risk. Downside risk criteria like the safety first criterion therefore often select corner solutions in the sense of a bonds only portfolio. This is due to a focus on the asymptotically dominating first order Pareto term of the portfolio return distribution. We show that if second order terms are taken into account, a balanced solution emerges. The theory is applied to empirical examples from the literature.     

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

A smooth non-parametric estimation framework for safety-first portfolio optimization

In this paper, we adopt a smooth non-parametric estimation to explore the safety-first portfolio optimization problem. We obtain a non-parametric estimation calculation formula for loss (truncated) probability using the kernel estimator of the portfolio returns’ cumulative distribution function, and embed it into two types of safety-first portfolio selection models. We numerically and empirically test our non-parametric method to demonstrate its accuracy and efficiency. Cross-validation results show that our non-parametric kernel estimation method outperforms the empirical distribution method. As an empirical application, we simulate optimal portfolios and display return-risk characteristics using China National Social Security Fund strategic stocks and Shanghai Stock Exchange 50 Index components.     

A Note on Risk Aversion,Prudence and Portfolio Insurance

This paper examines some properties of portfolio insurance that are linked to the risk aversion and the prudence of the investor. We provide explicit conditions to measure portfolio sensitivity to downside risk. We also characterize the degree of portfolio insurance by means of the ratio of absolute prudence to absolute risk aversion.     

On the Demand for Portfolio Insurance

While insurers manage underwriting risk with various methods including reinsurance, insurers increasingly manage asset risk with options, futures, and other derivatives. Previous research shows that buyers of portfolio insurance pay considerably for downside protection. We add to this literature by providing the first evidence on the cost of portfolio insurance, the payoff to portfolio insurance, and the relative demand for portfolio insurance across VIX levels. We find that the demand for portfolio insurance is relatively high at low levels of VIX, suggesting purchasers demand more downside protection when this protection is cheap on an absolute basis (but expensive on a relative basis). We also provide the first evidence on the hedging behavior of specific investor classes and show that the demand for portfolio insurance is driven by retail investors (individuals) who buy costly insurance from institutional investors. Results are consistent with other types of paradoxical insurance‐buying behavior.     

Downside Risk in Practice

Although investors associate risk with negative outcomes and downside fluctuations, modern portfolio theory does not. For investors, volatility per se is not necessarily bad; volatility below a benchmark is. A stock that magnifies the market's fluctuations is not necessarily bad; one that magnifies the market's downside swings is. Even Harry Mar‐kowitz, the father of modern portfolio theory, viewed downside risk as a better way to assess risk than the “mean‐variance” framework that he ultimately proposed and that has since become the standard. This article highlights the shortcomings of traditional measures of risk (the standard deviation and beta), introduces the concept of downside risk, and discusses two measures of it—the “semideviation” and “downside beta.” It also discusses the use of such measures in asset pricing models to estimate required returns on equity. Data from a few well‐known companies are used to illustrate that the cost of equity based on downside risk can be substantially different from that based on the CAPM. The article concludes with a brief discussion of risk‐adjusted returns and a comparison of the traditional method of calculating such returns with both the Sharpe ratio and its counterpart in a downside risk framework, the Sortino ratio. The appendix demonstrates how to calculate these risk measures in Excel.     

Conditional extreme risk,black swan hedging,and asset prices

Motivated by the asset pricing theory with safety-first preference, we introduce and operationalize a conditional extreme risk (CER) measure to describe expected stock performance conditional on a small-probability market downturn (black swan). We document a significant CER premium in the cross-section of expected returns. We also demonstrate that CER explains the premia to downside beta, coskewness, and cokurtosis. CER provides distinct information regarding black swan hedging that cannot be captured by co-crash-based tail dependence measures. As we find that the pricing effect is stronger among black swan hedging stocks, this distinction helps explain the absence of premium to tail dependence.     

The effect of downside risk reduction on UK equity portfolios included with Managed Futures Funds

The concept of asymmetric risk estimation has become more widely applied in risk management in recent years with the increased use of Value-at-risk (VaR) methodologies. This paper uses the n-degree lower partial moment (LPM) models, of which VaR is a special case, to empirically analyse the effect of downside risk reduction on UK portfolio diversification and returns. Data on Managed Futures Funds are used to replicate the increasingly popular preference of investors for including hedge funds and fund-of-funds type investments in the UK equity portfolios. The result indicates, however that the potential benefits of fund diversification may deteriorate following reductions in downside risk tolerance levels. These results appear to reinforce the importance of risk (tolerance) perception, particularly downside risk, when making decisions to include Managed Futures Funds in UK equity portfolios as the empirical analysis suggests that this could negatively affect portfolio returns.     

Portfolio Diversification Effects of Downside Risk

Risk managers use portfolios to diversify away the unpricedrisk of individual securities. In this article we compare thebenefits of portfolio diversification for downside risk in casereturns are normally distributed with the case of fat-taileddistributed returns. The downside risk of a security is decomposedinto a part which is attributable to the market risk, an idiosyncraticpart, and a second independent factor. We show that the fat-tailed-baseddownside risk, measured as value-at-risk (VaR), should declinemore rapidly than the normal-based VaR. This result is confirmedempirically.     

Estimating portfolio risk for tail risk protection strategies

We forecast portfolio risk for managing dynamic tail risk protection strategies, based on extreme value theory, expectile regression, copula‐GARCH and dynamic generalized autoregressive score models. Utilizing a loss function that overcomes the lack of elicitability for expected shortfall, we propose a novel expected shortfall (and value‐at‐risk) forecast combination approach, which dominates simple and sophisticated standalone models as well as a simple average combination approach in modeling the tail of the portfolio return distribution. While the associated dynamic risk targeting or portfolio insurance strategies provide effective downside protection, the latter strategies suffer less from inferior risk forecasts, given the defensive portfolio insurance mechanics.     

OPTIMAL PORTFOLIO SELECTION WITH A SHORTFALL PROBABILITY CONSTRAINT: EVIDENCE FROM ALTERNATIVE DISTRIBUTION FUNCTIONS

We propose a new approach to optimal portfolio selection in a downside risk framework that allocates assets by maximizing expected return subject to a shortfall probability constraint, reflecting the typical desire of a risk-averse investor to limit the maximum likely loss. Our empirical results indicate that the loss-averse portfolio outperforms the widely used mean-variance approach based on the cumulative cash values, geometric mean returns, and average risk-adjusted returns. We also evaluate the relative performance of the loss-averse portfolio with normal, symmetric thin-tailed, symmetric fat-tailed, and skewed fat-tailed return distributions in terms of average return, risk, and average risk-adjusted return.     

Mean-variance versus utility maximization revisited: The case of constant relative risk aversion

We examine if mean-variance (M-V) is a good proxy for portfolios based on the Constant Relative Risk Aversion (CRRA) utility function. M-V portfolios are considered good proxies for portfolios from several utility functions which is why they are routinely used in the portfolio theory literature as the benchmark. Our results clearly show this is not the case. Low risk CRRA portfolios are in many cases very different to M-V portfolios, especially with respect to downside risk. If a risk-free asset is available, in many cases, no M-V portfolio is an adequate proxy for CRRA portfolios. The implications of our findings are that: i) M-V portfolios are a poor proxy for investors with CRRA preferences, ii) CRRA portfolios are more suited to investors who care about downside risk than M-V portfolios, and iii) the efficacy of M-V to proxy for utility maximization should be examined more thoroughly.     

Portfolio risk management in a data-rich environment

We study risk assessment using an optimal portfolio in which the weights are functions of latent factors and firm-specific characteristics (hereafter, diffusion index portfolio). The factors are used to summarize the information contained in a large set of economic data and thus reflect the state of the economy. First, we evaluate the performance of the diffusion index portfolio and compare it to both that of a portfolio in which the weights depend only on firm-specific characteristics and an equally weighted portfolio. We then use value-at-risk, expected shortfall, and downside probability to investigate whether the weights-modeling approach, which is based on factor analysis, helps reduce market risk. Our empirical results clearly indicate that using economic factors together with firm-specific characteristics helps protect investors against market?risk.     

Are cryptocurrencies a safe haven for equity markets? An international perspective from the COVID-19 pandemic

The COVID-19 pandemic provided the first widespread bear market conditions since the inception of cryptocurrencies. We test the widely mooted safe haven properties of Bitcoin, Ethereum and Tether from the perspective of international equity index investors. Bitcoin and Ethereum are not a safe haven for the majority of international equity markets examined, with their inclusion adding to portfolio downside risk. Only investors in the Chinese CSI 300 index realized modest downside risk benefits (contingent on very limited allocations to Bitcoin or Ethereum). As Tether successfully maintained its peg to the US dollar during the COVID-19 turmoil, it acted as a safe haven investment for all of the international indices examined. We caveat the latter findings with a warning that Tether's dollar peg has not always been maintained, with evidence of impaired downside risk hedging properties earlier in our sample.     

An accounting analysis of the risk-return relationship in bull and bear markets

This study provides evidence that accounting beta (earnings and cash flow-based) provides information consistent with the risk-return relationship in up- and down-markets. We are not able, however, to provide similar evidence using market beta. Considering that investors' ability to assess the risk-return trade-off in up- and down-markets is central to efficient portfolio formation, the results suggest that accounting data can provide appropriate measures of portfolio upside and downside risk.