1. Using a long data set, the authors find that "over the long run, stock portfolios with lesser variance in monthly returns have experienced greater average returns than their "riskier" counterparts;find that the risk-return relation strongly depends on the sample period and whether the sample period is dominated by a bull or bear regime,1975
2. in turn necessitating an immediate stock-price decline to allow for higher returns. Therefore, the causality underlying the volatility feedback effect runs from volatility to prices, as opposed to the leverage effect that hinges on the reverse causal relationship" (see also Campbell and Hentschel;Bollerslev;) describe the volatility feedback effect as: "If volatility is priced, an anticipated increase in volatility would raise the required rate of return,1987
3. More formally, from ? t 1 � ? t it follows w t 1 ? target {? t 1 ? target {? t w t , i.e. an increase in volatility induces a decrease in the weight of the risky asset. Due to this relation;Harvey;The volatility feedback effect is reflected by the construction of the target volatility weighting given in Equation,2018
4. On the coherence of expected shortfall;C Acerbi;Journal of Banking & Finance,2002