Risk-asymmetry indices in Europe

The objectives of this study are threefold. First, we introduce for the first time a skewness index (SKEW) for each European country. Second, we compute an alternative measure of asymmetry (RAX) based on corridor implied volatilities to assess whether it outperforms the standard skewness index in measuring tail risk. Third, we investigate the properties of the proposed indices by uncovering the contemporaneous linear relationship among skewness, volatility, and returns and the information content of skewness on future returns, which is highly debated in the literature. Last, we propose two aggregate indices of asymmetry to monitor the risk of the EU financial market as a whole. To deal with the limited availability of option-based data for European countries, that represent the main obstacle for the construction of such indices in the EU, we delineate a country-specific procedure. Several results are obtained. First, all the asymmetry indices are on average higher than 100, indicating that the risk-neutral distribution is in general left-skew for the 12 EU countries under investigation. Second, the relation between changes in asymmetry indices and contemporaneous market returns in positive, indicating that asymmetry indices are not able to capture the same fear effect captured by volatility indices. Third, the results for the relationship between asymmetry and volatility (future returns) are mixed both in terms of magnitude and significance and do not allow us to delineate general conclusions. Last, the aggregate asymmetry index based on the RAX methodology is the only one able to forecast future negative returns for all the EU countries in our dataset when it reaches very high levels

Asymmetric correlations and hedging effectiveness of cryptocurrencies for the European stock market

The aim of the paper is twofold: first, to examine the hedging effectiveness of cryptocurrencies and cryptocurrency portfolios for European equities in bearish and bullish market conditions, and second, to contrast cryptocurrencies with gold as a safe haven asset. To this end, daily data from 2018 to 2021 were employed in a linear and nonlinear Autoregressive Distributed Lag (ARDL) framework. The findings have significant implications for investors, financial intermediaries and regulators. First, none of the cryptocurrencies under investigation acts as a safe haven for the European stock market. Second, an asymmetric relationship was found between Bitcoin / Ethereum returns on the one hand and stock market returns on the other, indicating the risk of large joint losses during periods of market turmoil. Third, cryptocurrency portfolios appear to perform better than Bitcoin and Ethereum for diversification purposes. Fourth, among cryptocurrency portfolios, the portfolio made up of the top ten cryptocurrencies appear to be the best in terms of diversification benefits and the risk-return profile. Finally, during the 2020 bear market conditions, not even gold acted as a safe haven for European stocks, highlighting the need to investigate alternative safe haven assets to mitigate portfolio risks

La valutazione del rischio di mercato nell'UE

Gli obiettivi di questo studio sono molteplici. Primo, indagare sulle misure di rischio disponibili per il mercato azionario UE e valutare il loro contenuto informativo e le loro proprietà in varie condizioni di mercato e per diversi paesi. Secondo, comprendere la relazione tra la volatilità e l’asimmetria della distribuzione neutrale al rischio, per identificare possibili criticità delle misure esistenti basate sui prezzi delle opzioni e la possibilità di trarre profitto da strategie basate sull’asimmetria implicita. Terzo, studiare il contenuto informativo dell'asimmetria implicita nelle opzioni come misura del rischio di mercato e introdurre, per la prima volta, un indice di asimmetria per 12 paesi europei e per il mercato EU nel suo insieme. Quarto, valutare se il sentiment degli investitori può fornire informazioni preziose agli investitori e ai gestori di fondi per la selezione dei titoli e la gestione del portafoglio. Infine, indagare se il rischio di mercato può essere mitigato attraverso la diversificazione, includendo asset innovativi come le criptovalute in un portafoglio di azioni europee. Alcuni risultati chiave ottenuti della ricerca sono i seguenti. L’indice VSTOXX (attualmente l'unico indice di volatilità implicita che incorpora informazioni provenienti da vari paesi europei) può misurare correttamente il rischio di volatilità solo per Francia e Germania. Al contrario, i risultati dipendono dal periodo in esame per gli altri paesi, soprattutto per quelli periferici. Inoltre, l'indice VSTOXX mostra picchi quando la volatilità di un gruppo di paesi aumenta e rappresenta una media degli indici di volatilità solo durante i periodi di estrema volatilità. Per quanto riguarda la relazione tra volatilità e asimmetria implicite, l’indice di asimmetria basato sulla formula standard agisce come una misura di avidità del mercato anziché di paura, e il suo contenuto informativo non può essere combinato facilmente con quello della volatilità, generando confusione dal lato dell’investitore. Inoltre, l’asimmetria implicita è più ampia in termini assoluti rispetto a quella fisica, generando opportunità di profitto mediante opportune strategie di trading. Per quanto concerne l’utilizzo di indicatori basati sulle opzioni per la misurazione del rischio di mercato, l’indice di aggregato di asimmetria introdotto nello studio (EU-RAX) fornisce informazioni cruciali agli investitori. In particolare, quando l'indice aggregato basato sul metodo RAX raggiunge i suoi massimi livelli, sono attesi rendimenti futuri negativi per tutti i paesi europei oggetto di indagine. Per quanto riguarda l’importanza del sentiment come variabile esplicativa dei rendimenti azionari, i risultati mostrano una forte relazione positiva tra sentiment (misurato dal Bloomberg sentiment index) relativo ai singoli titoli e i rendimenti futuri del mercato. Le azioni con un sentiment alto (basso) mostrano rendimenti alti (bassi) in media. Inoltre, le notizie positive vengono incorporate più lentamente di quelle negative nei prezzi, in particolare per le azioni a bassa capitalizzazione. Al contrario, l'indicatore aggregato di sentiment è inversamente correlato ai rendimenti futuri del mercato: un sentiment alto (basso) prevede rendimenti negativi (positivi) nei mesi successivi. Infine, con riferimento alla possibilità di includere criptovalute in un portafoglio di azioni europee, le singole criptovalute quali Bitcoin ed Ethereum non fungono da bene rifugio, a causa della loro relazione positiva con i rendimenti del mercato, che aumenta durante i periodi di turbolenza e volatilità. Tuttavia, portafogli formati da più criptovalute potrebbero essere almeno utili per la diversificazione poiché mostrano una relazione a breve termine più debole con i rendimenti azionari.The objectives of this study are manifolds. First, to investigate the forward-looking instruments available for the EU market and evaluate their information content and their properties in various market conditions and for different European countries. Second, to better understand the relationships between the volatility and the asymmetry of the risk-neutral distribution, to identify the potential criticalities of the existing option-based risk measures and the possibility of profit from strategies based on option-implied asymmetry. Third, to investigate the information content of option-implied asymmetry as a measure for market risk, and to introduce, for the first time, a skewness index for 12 European countries and for the EU market as a whole. Fourth, to assess whether investor sentiment can provide valuable information to investors and fund managers for stock picking and portfolio selection purposes. Last, to investigate whether market risk could be mitigated through diversification, by including innovative assets such as cryptocurrencies in a portfolio of European stocks. The following are some key findings from the research. The analysis indicates that the VSTOXX index (the only volatility index embedding information from various European countries) can correctly measure the volatility risk only for France and Germany. In contrast, the results depend on the period under investigation for the other countries, especially for peripheral ones. Moreover, the VSTOXX index is intended to spike when the volatility of a few countries increases, and represents an average of the volatility indices only during periods of extreme volatility. Regarding the relationships between the volatility and the asymmetry indices, the skewness index based on the standard skewness formula acts as a measure of market greed, as opposed to market fear, and its information content cannot be easily combined with that of volatility, causing confusion on the side of the investor. Moreover, risk-neutral measure of skewness (i.e., the measure obtained from option prices) is greater in absolute terms than the physical one, creating profitable opportunities for skewness trading strategies. About the information content of option-implied asymmetry as a measure for market risk, the proposed aggregate risk-asymmetry (EU-RAX) index provides crucial information to investors. Specifically, when the aggregate index based on the RAX method reaches its top levels, future negative returns are expected for all the European countries under investigation. As regard the importance of sentiment in explaining stock returns, the results show a strong positive relationship between investor sentiment (proxied by Bloomberg investor sentiment index) on individual stocks and future market returns. Stocks with high (low) sentiment exhibit high (low) returns on average. Moreover, positive news are incorporated slower than negative news in the stock price, especially for stocks with low market capitalization. On the other hand, the aggregate indicator of sentiment is inversely related to future market returns: high (low) sentiment predicts negative (positive) future returns over the following months. Last, regarding the use of cryptocurrencies as a hedge for a portfolio of European stocks, individual cryptocurrencies such as Bitcoin and Ethereum do not act as a safe-haven for the European stock market, due to a positive relationship with market returns that increases during market turmoil periods. However, cryptocurrency portfolios might be useful for investors diversification since they show weaker short-term relationships with market returns

Moment risk premia and the cross-section of stock returns in the European stock market

This article investigates whether volatility, skewness, and kurtosis risks are priced in the European stock market and assess the signs and the magnitudes of the corresponding risk premia. To this end, we adopt two approaches: a model-free approach based on swap contracts, and a model-based approach built on portfolio-sorting techniques. A number of results are obtained. First, stocks with high exposure to innovations in implied market volatility (skewness) exhibit low (high) returns on average. Second, the estimated premium for bearing market volatility (skewness) risk is negative (positive), robust to the two approaches employed, and statistically and economically significant. Third, in contrast with studies on the US stock market, we identify the existence of a size premium in the European stock market: small capitalization stocks earn higher returns than high capitalization stocks

The Information Content of Corridor Volatility Measures During Calm and Turmoil Periods

Measurement of volatility is of paramount importance in finance because of the effects on risk measurement and risk management. Corridor implied volatility measures allow us to disentangle the volatility of positive returns from that of negative returns, providing investors with additional information beyond standard market volatility. The aim of the paper is twofold. First, to propose different types of corridor implied volatility and some combinations of them as risk indicators, in order to provide useful information about investors’ sentiment and future market returns. Second, to investigate their usefulness in prediction of market returns under different market conditions (with a particular focus on the subprime crisis and the European debt crisis). The data set consists of daily index options traded on the Italian market and covers the 2005–2014 period. We find that upside corridor implied volatility measure embeds the highest information content about contemporaneous market returns, claiming the superiority of call options in measuring current sentiment in the market. Moreover, both upside and downside volatilities can be considered as barometers of investors’ fear. The volatility measures proposed have forecasting power on future returns only during high volatility periods and in particular during the European debt crisis. The explanatory power on future market returns improves when two of the proposed volatility measures are combined together in the same model

Towards a Fuzzy Volatility Index for the Italian Market

The measurement of volatility is of fundamental importance in finance. The standard market practice adopted for the computation of a volatility index imposes to discard some option prices quoted in the market, resulting in a considerable loss of information. To overcome this drawback, we propose to resort to fuzzy regression methods in order to include all the available information and obtain an informative volatility index for the Italian stock market

Option implied moments obtained through fuzzy regression

The aim of this paper is to investigate the potential of fuzzy regression methods for computing more reliable estimates of higher-order moments of the risk-neutral distribution. We improve upon the formula of Bakshi et al. (RFS 16(1):101\u2013143, 2003), which is used for the computation ofmarket volatility and skewness indices (such as the VIX and the SKEW indices traded on the Chicago Board Options Exchange), through the use of fuzzy regression methods. In particular, we use the possibilistic regression method of Tanaka, Uejima and Asai, the least squares fuzzy regression method of Savic and Pedrycz and the hybrid method of Ishibuchi and Nii.We compare the fuzzy moments with those obtained by the standard methodology, based on the Bakshi et al. (2003) formula, which relies on an ex-ante choice of the option prices to be used and cubic spline interpolation.We evaluate the quality of the obtained moments by assessing their forecasting power on future realized moments. We compare the competing forecasts by using both the Model Confidence Set and Mincer\u2013Zarnowitz regressions. We find that the forecasts for skewness and kurtosis obtained using fuzzy regression methods are closer to the subsequently realized moments than those provided by the standard methodology. In particular, the lower bound of the fuzzy moments obtained using the Savic and Pedrycz method is the best ones. The results are important for investors and policy makers who can rely on fuzzy regression methods to get a more reliable forecast for skewness and kurtosis

INDICES FOR FINANCIAL MARKET VOLATILITY OBTAINED THROUGH FUZZY REGRESSION

The measurement of volatility is of fundamental importance in finance. Standard market practice adopted for volatility estimation from option prices leads to a considerable loss of information and the introduction of an element of arbitrariness in the volatility index computation. We propose to resort to fuzzy regression methods in order to include all the available information from option prices and obtain an informative volatility index. In fact, the obtained fuzzy volatility indices do not only offer a most possible value, but also a lower and an upper bound for the interval of possible values, providing investors with an additional source of information. We also propose a defuzzification procedure in order to select a representative value within this interval. Moreover, we investigate the occurrence of truncation and discretization errors in the volatility index computation by resorting to an interpolation-extrapolation method. We also test the forecasting power of each volatility index on future realized volatility