In portfolio theory, it is well-known that the distributions of stock returns often have non-Gaussian characteristics. Therefore, we need non-symmetric distributions for modeling and accurate analysis of actuarial data. For this purpose and optimal portfolio selection, we use the Tail Mean-Variance (TMV) model, which focuses on the rare risks but high losses and usually happens in the tail of r...

The tail mean–variance model was recently introduced for use in risk management and portfolio choice; it involves a criterion that focuses on the risk of rare but large losses, which is particularly importantwhen losses have heavy-tailed distributions. If returns or losses follow a multivariate elliptical distribution, the use of risk measures that satisfy certain well-known properties is equiv...

In this paper, we analyze momentum strategies that are based on reward-risk stock selection criteria in contrast to ordinary momentum strategies based on a cumulative return criterion. Reward-risk stock selection criteria include the standard Sharpe ratio with variance as a risk measure, and alternative reward-risk ratios with the expected shortfall as a risk measure. We investigate momentum st...

The realized variance (RV) is known to be biased because intraday returns are contaminated with market microstructure noise, in particular if intraday returns are sampled at high frequencies. In this paper, we characterize the bias under a general specification for the market microstructure noise, where the noise may be autocorrelated and need not be independent of the latent price process. Wit...

We consider the problem of estimating a measure of daily volatility from intermittent high-frequency data that are subject to market microstructure effects. We show that a simple Newey-West type modification of the realized variance (RV) yields an unbiased measure of volatility for the ‘open’ part of the day. The modified RV is unbiased even if 1-minute intra-day returns are used. Further, with...