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The variance risk premium defined as the difference between risk neutral variance and physical variance is one of the most crucial information recovered from option prices. It does not, however, reflect the asymmetry in upside and downside movements of underlying asset returns, and also has limitation in reflecting asymmetric preference of investors over gains and losses. In this sense, this paper decomposes variance risk premium into downside - and upside-variance risk premium, and then derives the skewness risk premium and examines its effectiveness in predicting future underlying asset returns. Using KOSPI200 option prices, we obtained the following results. First, we found out that the estimated skewness risk premium has meaningful forecasting power for future stock returns, while the estimated variance risk premium has little forecasting power. Second, by utilizing our results of skewness risk premium, we developed a profitable investment strategy, which verifies the effectiveness of skewness risk premium in predicting future stock returns. In conclusion, the empirical results of this paper can contribute to the literature in that it helps us understand why variance risk premium, in most global markets except the US market, has not been successful in forecasting future stock returns. In addition, our results showing the profitability of investment strategies based on skewness risk premium can also give important implications to practitioners.

This study examines whether the variance risk is a priced risk factor in Korea using the over-the-counter variance swap quotes and realized variance data. We also study the term structure of variance risk premium. The empirical results show that the model with 2 stochastic variance risk factors with jumps in return is required to fit the variance swap and realized variance data. The analyses with the estimated models suggest that the variance risk premium in Korea are highly negative and the size of the premium increase with the maturities, meaning that risk averse investors in Korea are willing to pay a premium to hedge variance risk.

In asset management, what if clients want to purchase protection from risk factors, under the form of variance risk premia. This paper aims to address this topic by developing a portfolio optimization framework based on the criterion of the minimum variance risk premium (VRP) for any investor selecting stocks with an expected target return while minimizing the risk aversion associated to the portfolio according to “good” and “bad” times.

To accomplish this portfolio selection problem, the authors compute variance risk-premium as the difference from high-frequencies' realized volatility and options' implied volatility stemming from 19 stock markets, estimate a 2-state Markov-switching model on the variance risk-premia and optimize variance risk-premia portfolios across non-overlapping regions. The period goes from March 16, 2011, to March 28, 2018.

The authors find that optimized portfolios based on variance-covariance matrices stemming from VRP do not consistently outperform the benchmark based on daily returns. Several robustness checks are investigated by minimizing historical, realized or implicit variances, with/without regime switching. In a boundary case, accounting for the realized variance risk factor in portfolio decisions can be seen as a promising alternative from a portfolio performance perspective.

As a new management “style”, the realized volatility approach can, therefore, bring incremental value to construct the conditional covariance matrix estimates.

The authors assess the portfolio performance determined by the variance-covariance matrices that are derived by four models: “naive” (Markowitz returns benchmark), non-switching VRP, maximum likelihood regime-switching VRP and Bayesian regime switching VRP. The authors examine the best return-risk combination through the calculation of the Sharpe ratio. They also assess another different portfolio strategy: the risk parity approach.

With the presence of pricing errors, the authors consider statistical inference on the variance risk premium (VRP) and the associated implied variance, constructed from the option prices and the historic returns.

The authors propose a nonparametric kernel smoothing approach that removes the adverse effects of pricing errors and leads to consistent estimation for both the implied variance and the VRP. The asymptotic distributions of the proposed VRP estimator are developed under three asymptotic regimes regarding the relative sample sizes between the option data and historic return data.

This study reveals that existing methods for estimating the implied variance are adversely affected by pricing errors in the option prices, which causes the estimators for VRP statistically inconsistent. By analyzing the S&P 500 option and return data, it demonstrates that, compared with other implied variance and VRP estimators, the proposed implied variance and VRP estimators are more significant variables in explaining variations in the excess S&P 500 returns, and the proposed VRP estimates have the smallest out-of-sample forecasting root mean squared error.

This study contributes to the estimation of the implied variance and the VRP and helps in the predictions of future realized variance and equity premium.

This study is the first to propose consistent estimations for the implied variance and the VRP with the presence of option pricing errors.

This paper aims to examine whether the crypto-currencies’ market returns are symmetric or asymmetric informative, through analysing the daily logarithmic returns of bitcoin currency over the period of 2011-2017.

In doing so, the symmetric informative analysis is estimated by applying the generalised auto-regressive conditional heteroscedasticity (GARCH) (1,1) model, whereas asymmetric informative or leverage effects analysis is estimated by exponential GARCH (1,1), asymmetric power ARCH (1,1) and threshold GARCH (1,1) models. In addition, the generalized autoregressive conditional heteroskedasticity in mean (GARCH-M (1,1)) was applied to examine whether the risk-return trade-off phenomenon was persistent in crypto-currencies market.

The main findings indicate that bitcoin market return or volatility is symmetric informative and has a long memory to persist in the future. Furthermore, the sympatric volatility is found to be more sensitive to its past values (lagged) than to the new shock of the market values. However, asymmetric informative response of volatility to the negative and the positive shocks do not exist in the bitcoin market or, in other words, there is no leverage effect. This suggests that the bitcoin market is in harmony with the efficient market hypothesis (EMH) with respect to the asymmetric information and violated the EMH with regard to the symmetric information. Hence, the market price or return of bitcoin currency could not be predicted by simply exercising such past market information in the short-run investment. In addition, the estimated coefficient of conditional variance or risk premium (λ) in the mean equation of CHARCH–M (1,1) model is positive however, statistically insignificant. This indicates the absence of risk-return trade-off, in which case the higher market risk will not essentially lead to higher market returns. This paper has proposed that an investment in the crypto-currency market is more appropriate for risk-averse investors than risk takers.

The findings of the study will provide investors with necessary information about the bitcoin market price efficiency, hedging effectiveness and risk management.

This study aims to examine the return predictability of variance risk premium, which is defined as the difference between risk-neutral variance and expected realized variance, on KOSPI 200 index returns. Although extant literature shows that variance risk premium estimated from U.S. index options has a predictive power on underlying returns, little study has been conducted in KOSPI 200 index returns. In addition, there is no conclusion for the predictive power of variance risk premium in other financial markets. In this paper, we can find the predictive power of S&P500 variance risk premium on KOSPI200 index returns as well as on S&P500 index returns, but cannot find the predictive power of KOSPI200 variance risk premium on both indices. These results are consistent to Londono (2012) and Bollerslev et al. (2013). The poor performance of KOSPI200 variance risk premium is explained by the assumption that U.S. economy is a leader economy, while Korea economy is a follower economy. To support this conclusion, we conduct Vector Auto-Regression (VAR) using two variance risk premiums. Two premiums have bi-directional lead-lag relationship but S&P500 variance risk premium is informationally superior to KOSPI200 variance risk premium regarding return predictions.

This paper aims to examine the relationship between the conditional variance of the factors from the Fama–French three‐factor model and macroeconomic risk, where macroeconomic risk is proxied by the conditional variance for a default risk premium and real gross domestic product (GDP) growth.

A generalised autoregressive conditional heteroscedastic model is used to generate the conditional volatilities and bivariate Granger causality tests are used to examine the empirical relationship between the risk measures.

Past values of the conditional variance for a default risk premium have information that is precedent to the conditional volatility for value premium and the small stock risk premium, and the conditional variance for the market risk premium has information about the future volatility of macroeconomic risk, as proxied by the conditional variance for GDP growth.

The implications are that conditional volatility associated with default is related to current and future volatility in value premium; however, volatility associated with the market risk premium appears to be a predictor of future macroeconomic risk. A caveat is that the results are dependent on the proxies used for macroeconomic risk and more refined measures of macroeconomic risk may yield different results.

This paper suggests that examination of the relationship between the volatility of macroeconomic factors and the explanatory factors in asset‐pricing models will help to further understanding of the relationship between risk and expected return.

This paper focuses directly on the links between risk associated with the Fama–French factors and macroeconomic risk. This added knowledge is beneficial to practitioners and academics whose interest lies in asset price modelling.

Using data from the stock markets of Japan, the UK and the US, this paper examines the time series properties of a price index derived from a zero net investment strategy of buying value stocks and short selling growth stocks. We use the results of this analysis to consider implications for the validity of competing hypotheses on the source of the value premium. Overall, the results from this study indicate that the US value premium displays different characteristics to the value premiums for the UK and Japan. This has farreaching implications for financial modelling and for the success, or otherwise, of investment strategies based on the existence of a value premium.

The purpose of this paper is to study the variance risk premium in corn and soybean markets, where the variance risk premium is defined as the difference between the historical realized variance and the corresponding risk-neutral expected variance.

The authors compute variance risk premiums using historical derivatives data. The authors use regression analysis and time series econometrics methods, including EGARCH and the Kalman filter, to analyze variance risk premiums.

There are moderate commonalities in variance within the agricultural sector, but fairly weak commonalities between the agricultural and the equity sectors. Corn and soybean variance risk premia in dollar terms are time-varying and correlated with the risk-neutral expected variance. In contrast, agricultural commodity variance risk premia in log return terms are more likely to be constant and less correlated with the log risk-neutral expected variance. Variance and price (return) risk premia in agricultural markets are weakly correlated, and the correlation depends on the sign of the returns in the underlying commodity.

Commodity variance (i.e. volatility) risk cannot be hedged using futures markets. The results have practical implications for US crop insurance programs because the implied volatilities from the relevant options markets are used to estimate the price volatility factors used to generate premia for revenue insurance products such as “Revenue Protection” and “Revenue Protection with Harvest Price Exclusion.” The variance risk premia found implies that revenue insurance premia are overpriced.

The empirical results suggest that the implied volatilities in corn and soybean futures market overestimate true expected volatility by approximately 15 percent. This has implications for derivative products, such as revenue insurance, that use these implied volatilities to calculate fair premia.

Risk aversion is considered as an important factor in predicting asset prices. Many studies have proved that there exists important price information spillover among crude oil, precious metals and agricultural markets. Then there naturally follows the question: Is the risk aversion of investors in crude oil market predictable for the returns of precious metals and agricultural products? The purpose of this paper is to answer this question. For this reason, the authors explore the directional predictability and the cross-quantile dependence between risk aversion of crude oil market investors and returns of precious metals and agricultural products.

To better describe the risk aversion of investors, this paper uses high-frequency data and model-free calculation method to obtain variance risk premium of crude oil. Then, this paper uses the cross-quantilogram method to investigate the directional predictability and cross-quantile dependence between risk aversion of crude oil market investors and returns of precious metals and agricultural products. Meanwhile, it employs the partial cross-quantilogram (PCQ) method to test the impact of control variables on the empirical results.

Firstly, risk aversion of crude oil market investors has directional predictability for returns of precious metals and agricultural products. Secondly, different degrees of risk aversion of crude oil market investors have different impacts on returns of precious metals and agricultural products. A low (high) degree of crude oil market investors' risk aversion has negative (positive) predictability for returns of precious metals and agricultural products. Finally, during the sample period, the returns of precious metals are more affected by risk aversion of crude oil market investors than returns of agricultural products.

First of all, this paper studies the impact of risk aversion of crude oil market investors on returns of precious metals and agricultural products. It updates previous relevant studies on the factors influencing the prices of precious metals and agricultural products, and provides a new idea for the forecast of those commodity returns. Secondly, this paper provides the evidence that different degrees of risk aversion of investors have different effects on the returns of commodities, and expands the research on the topic of commodity returns prediction. Finally, high-frequency data are employed in this paper to better capture the risk aversion of investors than commonly used daily data.