Left-tail Risk Research Articles

Gold, platinum, and mutual fund flows

Huang and Kilic (2019) demonstrate that gold to platinum price ratio (GP), which proxies for tail risk in the economy, is a priced risk factor in the cross-section of stock returns. We document that GP negatively affects the mutual fund flows of the active equity funds. In cross-sectional regressions, we find that funds with high betas with respect to the change in GP (βΔGP) have larger future fund flows, as such funds provide a hedge against economic distress. Further, βΔGP helps predict the future performance of the fund in the next few quarters. βΔGP also relates negatively to the downside risk of the fund, implying that funds could potentially reduce their left-tail risk by tilting towards securities with above average βΔGP. We also examine the flows to active corporate bond funds and passive funds. While these effects of GP are largely observable for passive funds, they are not as strongly observable for corporate bond funds.

The Left-tail Risk and the Cross-section of Stock Returns: Evidence from China

As a matter of fact, left-tail risk is a common risk in stock market. This study examines the linear correlation considering Value-at-Risk (VaR) and future stock returns within context of the Chinese main board stocks, particularly during periods marked by significant left-tail risk. Processing data from March 2014 to March 2024, this study concentrate to daily and monthly cross-section returns, along with other financial statistics. A suitable Fama-Macbeth regression using in this paper to exam the significance of left-tail risk. The key focus is to investigate the effect of VaR concerning future stock returns under downside market conditions, as indicated by the recent 23% drop in China’s benchmark CSI 300 index. The regression analysis indicates a significant negative correlation between VaR and future stock returns, suggesting that higher potential losses as indicated by VaR correspond with lower future returns. This outcome is contrary to traditional asset pricing theories which posit a positive risk-return relationship. The findings will attract attention of investors to consider extreme risk management of public stocks and contributes to the ongoing discussion on risk assessment in financial markets by highlighting the importance of integrating robust risk management tools like VaR in investment strategies, especially in volatile markets.

Mutual fund illiquidity, selling pressure, and left-tail risk in stocks

We examine whether mutual fund illiquidity introduces fragility into stock prices. The results show that stocks held by more illiquid funds subsequently experience higher left-tail risk and more outflows-induced mutual fund selling. Specifically, this positive effect is almost entirely concentrated during periods of high economic policy uncertainty and bear market. Finally, we confirm that stocks’ liquidity commonality and asymmetric information do not explain our findings. Our research has important implications for fund managers in liquidity management and for regulatory authorities in preventing the risk of investor runs.

Left-tail risk and UK stock return predictability: Underreaction, overreaction, and arbitrage difficulties

Recent studies challenge the standard model risk-return trade-off by showing inverse predictive power of firm-specific left-tail risk for future returns (i.e., left-tail momentum). In this work, we investigate the pricing of left-tail risk in UK stocks. Both the portfolio construction approach and Fama-MacBeth regressions reveal the underperformance of stocks with high left-tail risk. We examine alternative channels behind this pricing anomaly, namely, investor underreaction behaviour, continuous overreaction behaviour, and limits to arbitrage. Our findings suggest that the observed underperformance associated with high left-tail risk is largely a manifestation of investor underreaction to bad performance. However, the results also show that the predictable underperformance of high left-tail risk stocks is manifest in past winners. The empirical investigation reveals that, in addition to underreaction, limits to arbitrage interacts with investor high attention levels to explain part of the anomaly. The empirical findings provided here suggest several important implications for practitioners in the equity market.

Economic policy uncertainty and capital flows' tail risk in China

Since the financial crisis, uncertainty has been a focus of attention in the financial sector. As the two-way opening-up of China's financial market continues to accelerate, special attention must be paid to the risks and challenges arising from cross-border capital flows to maintain financial market stability in China. This study uses predictive quantile regression and skewed t-distribution fitting method to examine the impact of Economic Policy Uncertainty (EPU) on the full probability distribution and tail risks of capital flows. Additionally, we apply the “Capital Flows at Risk (CFaR)” analysis framework from the new paradigm of macroeconomic research to the situation in China, to study the impact of EPU on CFaR. We find that EPU significantly affects the predictive distribution of capital flows. When EPU is rising, the downside risk of capital flows, that is, the left-tail risk of capital flows, will increase; however, when EPU is declining, the upside risk of capital flows, that is, the right-tail risk of capital flows, will increase. In recent years, the scale of China's CFaR has shown a fluctuating upward trend, and EPU has increased the scale of CFaR in the country. This study is significant for stabilizing international capital flows and preventing and defusing the external financial shocks of cross-border capital inflows and outflows.

The effect of margin-trading and short-selling mechanism on left-tail risk: Evidence from a quasi-natural experiment in China

This research investigates the influence of a margin-trading and short-selling pilot program on the left-tail risk of equities, utilizing A-share stock data in China from January 2004 to July 2020 as a sample. By exploiting the staggered implementation of the pilot program within a difference-in-differences framework, we examine the impact of margin-trading and short-selling mechanism on left-tail risks of equities in China. Firstly, we present empirical evidence that the introduction of margin-trading and short-selling mechanism can significantly mitigate the left-tail risk for the designated stocks. In particular, the effect is mainly from short-selling activities. Secondly, the empirical evidence suggests that the presence of information asymmetry among investors plays a mediating role in the mitigating impact. Thirdly, the findings demonstrate that mitigating effect of the mechanism is particularly pronounced during periods characterized by high investor sentiment and high levels of economic policy uncertainty. Additionally, results are robust to DID models when shell value contamination is removed, an alternative time period and measure of left-tail risk are considered, and placebo tests are conducted.

Holding the economy by the tail: analysis of short- and long-run macroeconomic risks

We put forward a macro-financial empirical modeling framework that can examine the tails of distributions of macroeconomic variables and the implied risks. It does so without quantile regression, also allowing for non-normal distributions. The framework offers a number of relevant insights into higher moments of the US output growth distribution, as well as the effects of monetary policy and financial (risk premia) shocks on downside macroeconomic risk. This is not only from the short-run perspective but also from the long-run perspective, which has remained largely unexamined in the existing Macro-at-Risk literature. In particular, we estimate the short-run (conditional) and long-run US output growth distributions and study their evolution. The short-run analysis finds that monetary policy and financial shocks render the conditional output growth distribution asymmetric. As such, they affect downside risk over and above their impact on the conditional mean that policymakers routinely focus on. The long-run analysis indicates that US output growth left-tail risk showed a general downward trend in the two decades preceding the Global Financial Crisis (GFC), but this trend got reversed post-2008. Our examination strongly points to the adopted unconventional monetary policy framework featuring quantitative easing as a potential source of elevated long-run downside tail risk in the post-GFC period.

Technical trading rules, loss avoidance, and the business cycle

We show that simple technical trading rule (TTR) strategies substantially reduce investment left tail risk. An investor following a TTR strategy can also avoid a high percentage of extremely negative returns. This percentage increases substantially during recessions. Interestingly, tail risk reduction does not come at a cost of lower performance – risk adjusted returns of TTR strategies are in fact higher than those of a buy-and-hold strategy. Our findings are robust to changes in trading strategy specifications. They hold in 38 international equity markets, as well as in a large sample of individual US stocks, and survive a reality check bootstrap.

Retail investors and overpricing of left-tail risk: evidence from the Korean stock market

The authors examined whether stocks with higher left-tail risk measures earn higher or lower futures returns. Specifically, the authors estimate the cross-sectional principal component of a battery of left-tail risk measures and analyze future returns on stocks with high principal component values. In contrast to finance theories on the risk–return trade-off relationship, the study results show that high left-tail risk stocks have lower future returns. This finding is robust to various left-tail risk measures and controls for other risk factors. Moreover, the negative relationship between the left-tail risk and returns is more pronounced for stocks that are actively traded by retail investors. This empirical result is consistent with behavioral theory that when investors make decisions based on experience, they tend to underweight the likelihood of rare events.

Left-tail momentum and tail properties of return distributions: A case of Korea

This study documents the importance of considering the cross-sectional differences in the tail properties of stocks' return distributions when analyzing the left-tail momentum (LTM) phenomenon. This phenomenon is verified in the Korean stock markets, which shows that stocks showing large losses in the past tend to continue to perform poorly in the future. However, when tail fatness (TF), measured using standardized return distributions, is considered, the LTM phenomenon is significant only in the low-TF stock group. This means that investors underestimate the persistence of left-tail risk only for stocks with a low frequency of large losses, and not for all stocks that show large losses. The results of the measurement of tail risk (TR) reaffirm the positive relationship with expected returns, which shows that the existence of LTM is verified only in the low-TR stock group, suggesting a need for caution in interpreting the LTM phenomenon with low TR as a market anomaly.

Will a boom be followed by crash? A new systemic risk measure based on right-tail risk.

In this study, we demonstrate that high short-term gains on the A-share market may lead to significant losses in the future and potentially cause a market catastrophe. To study the accumulation, outbreak, and cross-sector spillover process of systemic risk in the Chinese stock market, we define right-tail risk as a large rally process that may lead to left-tail losses in the future and construct a tail volatility spillover network by distinguishing between left-tail and right-tail risk. In the risk accumulation process, the market expectation bias of common shocks considerably magnifies heterogeneity risk, and in the risk outbreak and spillover processes, the greatest systemically important and systemically susceptible sectors are banking and information technology, respectively. In addition, the level of risk spillover is extremely sensitive to tail shocks and increases as tail shocks intensify. Moreover, right-tail risk has more forward-looking predictive power for left-tail risk. Apart from achieving immediate regulatory objectives, Chinese authorities must consider market expectation bias when implementing rules. Additionally, authorities want to be wary of right-tail risk, which has the potential to create serious and pervasive damage in the future if the market is allowed to be unregulated during short-term spikes.

Patented Innovation and Left-Tail Risk: Evidence from China

Patented Innovation and Left-Tail Risk: Evidence from China

Government Put: What Options Market Imply about the Volatility and Left-tail Risk of Indian Public versus Private Banks

Government Put: What Options Market Imply about the Volatility and Left-tail Risk of Indian Public versus Private Banks

Carry and Conditional Value at Risk Trend: Capturing the Short-, Intermediate-, and Long-term Trends of Left-tail Risk Forecasts

Carry and Conditional Value at Risk Trend: Capturing the Short-, Intermediate-, and Long-term Trends of Left-tail Risk Forecasts

Left-Tail Momentum of Korean Stock Markets

This study examines the relationship between left-tail risk and stock return in the Korean stock markets and ascertains whether there is a left-tail momentum phenomenon in which stocks with high left-tail risk have lower investment performance than those with low left-tail risk (Atilgan et al., 2020). The results reveal that left-tail risk has a significant negative relationship with stock returns for future holding periods and that the left-tail momentum is strongly observed in the Korean stock markets. The excess return of the Fama-French 3-factor model of the decile portfolio-based (H-L) zero-cost investment strategy using left-tail risk has a significant value of -0.67% to -0.73% per month on average. These results are robust even after controlling for changes in the left-tail risk measures or key related variables that could affect the left-tail momentum. In addition, the left-tail momentum has explanatory power regarding the fluctuations of stock returns independent of Fama-French 3-factors.

Carry and conditional value at risk trend: Capturing the short-, intermediate-, and long-term trends of left-tail risk forecasts

Given the empirical evidence that investors underreact to bad news, we examine the ability of changes in the Conditional Value at Risk (CVaR) to predict the cross-section of currency excess returns. Therefore, we introduce a variable CVaR-Trend to capture the short-, intermediate- and long-term trends of CVaR forecasts. We find that the relationship between CVaR-Trend and expected G-10 currency excess returns depends on conditioning on different regimes of FX forward discount. Our results imply a novel long-short currency trading strategy, named CVaR-Trend trade, that generates high excess returns that cannot be explained by exposure to the most common currency risk factors in both funding and investment markets.

Tail risks, firm characteristics, and stock returns

We focus on the left-tail (right-tail) risk of stocks, that is, the huge losses (gains) of financial assets with a small probability. The empirical results mainly reveal that both the left and the right tail risks of stocks in the Chinese market are negatively related to their one-month-ahead returns and Chinese investor is prone to chase winners. Moreover, the tail risk effect is more pronounced in stocks with more retail investors, less investor attention, and more transparency. Finally, we show that prospect theory and salience theory fail to capture the left tail effect, while the right tail effect is consistent with these theories.

Multi-Period Mean Expected-Shortfall Strategies: ‘Cut Your Losses and Ride Your Gains’

Dynamic mean-variance (MV) optimal strategies are inherently contrarian. Following periods of strong equity returns, there is a tendency to de-risk the portfolio by shifting into risk-free investments. On the other hand, if the portfolio still has some equity exposure, the weight on equities will increase following stretches of poor equity returns. This is essentially due to using variance as a risk measure, which penalizes both upside and downside deviations relative to a satiation point. As an alternative, we propose a dynamic trading strategy based on an expected wealth (EW), expected shortfall (ES) objective function. ES is defined as the mean of the worst β fraction of the outcomes, hence the EW-ES objective directly targets left tail risk. We use stochastic control methods to determine the optimal trading strategy. Our numerical method allows us to impose realistic constraints: no leverage, no shorting, infrequent rebalancing. For 5 year investment horizons, this strategy generates an annualized alpha of 180 bps compared to a 60:40 stock-bond constant weight policy. Bootstrap resampling with historical data shows that these results are robust to parametric model misspecification. The optimal EW-ES strategy is generally a momentum-type policy, in contrast to the contrarian MV optimal strategy.

The Predictive Power of Past Left Tail Risk in the Estimation of Left Tail Risk in Future

بازده غیرعادی کم (زیاد) سهام­هایی با ریسک دنباله چپ بالا (پایین) یکی از ناهنجاری­های مالی مطالعه‌شده در پژوهش­های تجربی قیمت­گذاری دارایی­های سرمایه­ای است. علت ایجاد این ناهنجاری وقوع رویدادهای نامطلوب و غیرمنتظره­ای است که باعث ایجاد ضررهای شدید برای سرمایه­گذاران می­شود و این زیان دارای ویژگی استمرارپذیری در دوره آتی است. از آنجایی که پیش­بینی ریسک دنباله چپ می­تواند در تدوین راهبرد معاملاتی مناسب مفید باشد، هدف پژوهش حاضر پیش­بینی ریسک دنباله چپ به وسیله اطلاعات گذشته این ریسک است. در پژوهش حاضر از تجزیه و تحلیل پرتفوی و همچنین رگرسیون فاما و مکبث (1973) استفاده شده است. بدین منظور از داده­های 307 شرکت­ بورس اوراق بهادار تهران و فرابورس ایران طی سال­های 1384 تا 1398 استفاده شده است. نتاج پژوهش حاضر نشان‌دهنده توانایی پیش­بینی ریسک دنباله چپ به وسیله اطلاعات گذشته این ریسک در نمونه پژوهش است. کنکاش بیشتر به وسیله تحلیل­های اضافی مبتنی بر تجزیه و تحلیل پرتفوی حاکی از این مهم است که قدرت پیش­بینی ریسک دنباله چپ آتی توسط اطلاعات گذشته ریسک دنباله چپ در بین سهام­های با ویژگی اندازه کوچک و نوسان­پذیری غیرسیستماتیک بالا بیشتر است، اما تنها سهم کوچکی از بازار به سهام با ویژگی­های مذکور اختصاص داده شده است.

Portfolio Optimization on Multivariate Regime-Switching GARCH Model with Normal Tempered Stable Innovation

This paper uses simulation-based portfolio optimization to mitigate the left tail risk of the portfolio. The contribution is twofold. (i) We propose the Markov regime-switching GARCH model with multivariate normal tempered stable innovation (MRS-MNTS-GARCH) to accommodate fat tails, volatility clustering and regime switch. The volatility of each asset independently follows the regime-switch GARCH model, while the correlation of joint innovation of the GARCH models follows the Hidden Markov Model. (ii) We use tail risk measures, namely conditional value-at-risk (CVaR) and conditional drawdown-at-risk (CDaR), in the portfolio optimization. The optimization is performed with the sample paths simulated by the MRS-MNTS-GARCH model. We conduct an empirical study on the performance of optimal portfolios. Out-of-sample tests show that the optimal portfolios with tail measures outperform the optimal portfolio with standard deviation measure and the equally weighted portfolio in various performance measures. The out-of-sample performance of the optimal portfolios is also more robust to suboptimality on the efficient frontier.