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.     

Strong Increases in Downside Risk Aversion

A ranking of risk preferences is of economic interest insofar as it leads to unambiguous comparative statics predictions, and for this to be the case, the ranking must be a strict partial ordering. The ranking by greater risk aversion meets this demand at the second order, and yields a variety of well-known predictions concerning the effect of greater risk aversion on demands for insurance and risky assets, among many other applications. There has been less success at the third order, where ranking preferences by aversion to downside risk has not produced a strict partial ordering. The problem is that account has not been taken of the fact that an increase in downside risk aversion must induce changes in risk aversion as well. We propose a definition of stronger downside risk aversion that does yield a strict partial ordering by requiring a nested increase in both second- and third-order risk aversion, so that v is more strongly downside risk averse than u if v is more risk averse and more downside risk averse than u. We demonstrate that v being more strongly downside risk averse than u is characterized by v never liking any change in the probability distribution for y that induces a third-order stochastic dominance deterioration in the distribution for u(y). We apply the definition to obtain intuitive comparative statics predictions in the precautionary saving problem, and relate the definition to alternatives proposed in the literature.     

Tail risk measurement in crypto-asset markets

The paper examines the relationships among market assets during stressful times, using two recently proposed econometric modeling techniques for tail risk measurement: the extreme downside hedge (EDH) and the extreme downside correlation (EDC). We extend both measures taking into account the sensitivity of asset's return to innovations not only from the overall market index, but also from its components, by means of network modeling. Applying our proposal to the cryptocurrencies market, we find that crypto-assets can be clustered in two groups: speculative assets, such as Bitcoin, which are mainly “givers” of tail contagion; and technical assets, such as Ethereum, which are mainly “receivers” of contagion.     

Delayed Expected Loss Recognition and the Risk Profile of Banks

This paper investigates the extent to which delayed expected loan loss recognition (DELR) is associated with greater vulnerability of banks to three distinct dimensions of risk: (1) stock market liquidity risk, (2) downside tail risk of individual banks, and (3) codependence of downside tail risk among banks. We hypothesize that DELR increases vulnerability to downside risk by creating expected loss overhangs that threaten future capital adequacy and by degrading bank transparency, which increases financing frictions and opportunities for risk‐shifting. We find that DELR is associated with higher correlations between bank‐level illiquidity and both aggregate banking sector illiquidity and market returns (i.e., higher liquidity risks) during recessions, suggesting that high DELR banks as a group may simultaneously face elevated financing frictions and enhanced opportunities for risk‐shifting behavior in crisis periods. With respect to downside risk, we find that during recessions DELR is associated with significantly higher risk of individual banks suffering severe drops in their equity values, where this association is magnified for banks with low capital levels. Consistent with increased systemic risk, we find that DELR is associated with significantly higher codependence between downside risk of individual banks and downside risk of the banking sector. We theorize that downside risk vulnerability at the individual bank level can translate into systemic risk by virtue of DELR creating a common source of risk vulnerability across high DELR banks simultaneously, which leads to risk codependence among banks and systemic effects from banks acting as part of a herd.     

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.     

Conventional and downside CAPM: The case of London stock exchange

Many studies on asset pricing have highlighted the importance of downside risk, in line with the actual losses of investors. In addition, the capital asset pricing model (CAPM), although presented as a universal theory, may provide significantly different rates of return in bull and bear markets. Using the CAPM under different conditions could be regarded as an alternative measurement and valuation approach to downside risk. This paper investigates conventional and downside approaches to risk taking into account different measures of downside beta coefficients. A further contribution of this research is the development of an alternative approach to testing the CAPM relationship. For this purpose, conditional relationships of the CAPM are proposed in which risk premiums are set separately in bull and bear periods. Using equity data and portfolios from the United Kingdom, we obtained positive and statistically significant downside risk premiums. We observed a slight advantage of downside measures over conventional beta measures. Conditional models provide evidence of a positive risk premium in rising markets and a negative risk premium in falling markets. The robustness analysis in subperiods indicates that these findings are largely unchanged for downside beta coefficients, which is not fulfilled by the model in a variance approach.     

Testing macroprudential stress tests: The risk of regulatory risk weights

We compare the capital shortfall measured by regulatory stress tests, to that of a benchmark methodology — the “V-Lab stress test” — that employs only publicly available market data. We find that when capital shortfalls are measured relative to risk-weighted assets, the ranking of financial institutions is not well correlated to the ranking of the V-Lab stress test, whereas rank correlations increase when required capitalization is a function of total assets. We show that the risk measures used in risk-weighted assets are cross-sectionally uncorrelated with market measures of risk, as they do not account for the “risk that risk will change.” Furthermore, the banks that appeared to be best capitalized relative to risk-weighted assets were no better than the rest when the European economy deteriorated into the sovereign debt crisis in 2011.     

Extreme downside risk and market turbulence

We investigate the dynamics of the relationship between returns and extreme downside risk in different states of the market by combining the framework of Bali et al. [Is there an intertemporal relation between downside risk and expected returns? Journal of Financial and Quantitative Analysis, 2009, 44, 883–909] with a Markov switching mechanism. We show that the risk-return relationship identified by Bali et al. (2009) is highly significant in the low volatility state but disappears during periods of market turbulence. This is puzzling since it is during such periods that downside risk should be most prominent. We show that the absence of the risk-return relationship in the high volatility state is due to leverage and volatility feedback effects arising from increased persistence in volatility. To better filter out these effects, we propose a simple modification that yields a positive tail risk-return relationship in all states of market volatility.     

Downside beta and the cross section of equity returns: A decade later

This study reexamines the relation between downside beta and equity returns in the United States. First, we replicate the 2006 work of Ang, Chen, and Xing who find a positive relation between downside beta and future equity returns for equal‐weighted portfolios of NYSE stocks. We show that this relation doesn't hold after using value‐weighted returns or controlling for various return determinants. We also extend the original sample, add AMEX/NASDAQ stocks or utilize alternative downside beta measures and still find no downside risk premium. We focus on factor analysis results, persistence of downside beta, and various subsamples to understand the economic reasons behind the findings.     

Beyond cash-additive risk measures: when changing the numéraire fails

We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on cash-additive risk measures, for which the eligible asset is a risk-free bond, on the grounds that the general case can be reduced to the cash-additive case by a change of numéraire. However, discounting does not work in all financially relevant situations, especially when the eligible asset is a defaultable bond. In this paper, we fill this gap by allowing general eligible assets. We provide a variety of finiteness and continuity results for the corresponding risk measures and apply them to risk measures based on value-at-risk and tail value-at-risk on L ^p spaces, as well as to shortfall risk measures on Orlicz spaces. We pay special attention to the property of cash subadditivity, which has been recently proposed as an alternative to cash additivity to deal with defaultable bonds. For important examples, we provide characterizations of cash subadditivity and show that when the eligible asset is a defaultable bond, cash subadditivity is the exception rather than the rule. Finally, we consider the situation where the eligible asset is not liquidly traded and the pricing rule is no longer linear. We establish when the resulting risk measures are quasiconvex and show that cash subadditivity is only compatible with continuous pricing rules.     

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.     

Omega performance measure and portfolio insurance

We analyze the performance of the two main portfolio insurance methods, the OBPI and CPPI strategies, using downside risk measures. For this purpose, we introduce Kappa performance measures and especially the Omega measure. These measures take account of the entire return distribution. We show that the CPPI method performs better than the OBPI. As a-by-product, we determine the set of threshold values for these risk/reward performance measures.     

Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions

Financial returns typically display heavy tails and some degree of skewness, and conditional variance models with these features often outperform more limited models. The difference in performance may be especially important in estimating quantities that depend on tail features, including risk measures such as the expected shortfall. Here, using recent generalizations of the asymmetric Student-t and exponential power distributions to allow separate parameters to control skewness and the thickness of each tail, we fit daily financial return volatility and forecast expected shortfall for the S&P 500 index and a number of individual company stocks; the generalized distributions are used for the standardized innovations in a nonlinear, asymmetric GARCH-type model. The results provide evidence for the usefulness of the general distributions in improving fit and prediction of downside market risk of financial assets. Constrained versions, corresponding with distributions used in the previous literature, are also estimated in order to provide a comparison of the performance of different conditional distributions.     

Asymmetric Volatility,Skewness, and Downside Risk in Different Asset Classes: Evidence from Futures Markets

This study examines the cross‐sectional variation of futures returns from different asset classes. The monthly returns are positively correlated with downside risk and negatively correlated with coskewness. The asymmetric volatility effect generates negatively skewed returns. Assets with high coskewness and low downside betas provide hedges against market downside risk and offer low returns. The high returns offered by assets with low coskewness and high downside betas are a risk premium for bearing downside risk. The asset pricing model that incorporates downside risk partially explains the futures returns. The results indicate a unified risk perspective to jointly price different asset classes.     

Is co-skewness a better measure of risk in the downside than downside beta?: Evidence in emerging market data

We define three measure of systematic co-skewness risk in a downside framework by extending three downside beta risk measures in the literature. In pricing models in a downside framework it may be sufficient to include a risk measure that accounts for co-semi-variance or co-semi-skewness and not both. Downside risk is appropriate when returns distribution is skewed—a common feature in emerging markets. A cross-sectional analysis provides evidence that downside co-skewness is a better explanatory variable of emerging market monthly returns than downside beta. Our conclusions remain largely unchanged when the analysis is subjected to various robustness checks.     

基于时间序列极值理论的跳跃风险研究

金融资产的跳跃行为作为对极端事件的刻画,为研究极端事件风险提供了良好工具。基于时间序列下的极值理论,在放松独立同分布假设下,构造了金融资产收益率序列尾部中跳跃动态特征的极值模型。通过对上证综指大跨度、高频度的实证研究,剖析了投资者结构、投资者行为与收益尾部分布之间的相互作用机制,进一步对金融资产收益尾部的跳跃风险进行了有效测度。结果表明,极端跳跃风险的分布特征在频率与尾部方向上呈现很强的不对称状态。     

Accounting-based downside risk,cost of capital,and the macroeconomy

We hypothesize that earnings downside risk, capturing the expectation for future downward operating performance, contains distinct information about firm risk and varies with cost of capital in the cross section of firms. Consistent with the validity of the earnings downside risk measure, we find that, relative to low earnings downside risk firms, high earnings downside risk firms experience more negative operating performance over the subsequent period, are more sensitive to downward macroeconomic states, and are more strongly linked to earnings attributes and other risk-related measures from prior research. In line with our prediction, we also find that earnings downside risk explains variation in firms’ cost of capital, and that this link between earnings downside risk and cost of capital is incremental to several earnings attributes, accounting and risk factor betas, return downside risk, default risk, earnings volatility, and firm fundamentals. Overall, this study contributes to accounting research by demonstrating the key valuation and risk assessment roles of earnings downside risk derived from firms’ financial statements, also shedding new light on the link between accounting and the macroeconomy.     

Time Diversification,Safety-First and Risk

The purpose of this article is to demonstrate the effect of investment time horizon on the choice of risky assets in a portfolio when the investor in question is optimizing a Safety-First (downside risk-aversion) utility function. It is shown, under standard assumptions, that although shortfall risk decreases exponentially with investment time horizon, the portfolio asset allocation proportions remain invariant. In fact, in some instances, the optimal allocation will not even depend on the drift of the underlying assets. Thus, we extend the classical results of Samuelson and Merton, derived under conventional utility assumptions, to an individual optimizing an A.D. Roy Safety-First objective; a discontinuous utility function that has been extolled as conforming to observed investor behaviour. A numerical example is provided.     

Accounting-based downside risk and expected stock returns: Evidence from China

We document that earnings downside risk contains information on firms' future operating performance and is positively associated with expected stock returns in Chinese stock markets, and the return predictability of earning downside risk mainly comes from its accrual downside risk component. The pricing of earnings downside risk is especially evident among firms with more transparent information environment and stronger governance efficacy, such as large firms, non-high-tech firms, old firms, and firms with high analyst coverage. Lastly, we show that aggregated earnings downside risk and its components at the market level are all significantly and positively associated with subsequent stock market returns, which is consistent with the notion that the accounting-based downside risk measures contain information about future macroeconomic conditions.     

What Do FAS 157 “Fair Values” Really Measure: Value Or Risk?

FAS 157, the U.S. accounting standard that prescribes how fair values of assets and liabilities are to be measured when other U.S. GAAP standards require fair valuation, stipulates that fair values be measured as the exit values of assets and liabilities—the proceeds for assets hypothetically sold on the date of the financial report, and, correspondingly, the amount required to settle liabilities on the date of the financial report. This conceptual article argues that exit values do not reflect the value of the net assets of the firm to shareholders, which is best reflected by discounted cash flows to maturity. Moreover, exit values—biasing fair values downward when markets are illiquid—have a pernicious, systemic risk effect; specifically, they give rise to write‐downs that in turn cause contagion: prices of equities and other financial instruments of peers react negatively, leading to further write‐downs by those peers. This may have aggravated the recent financial crisis. However, while exit values are not proper measures of value to shareholders, they are useful measures of downside risk when prospects turn sour for a firm. Thus, both exit values and discounted cash flows should be presented in financial statements.