  This paper discusses an alternative explanation for the empirical findings
contradicting the positive relationship between risk (variance) and reward
(expected return). We show that these contradicting results might be due to the
false definition of risk-perception, which we correct by introducing Expected
Downside Risk (EDR). The EDR parameter, similar to the Expected Shortfall or
Conditional Value-at-Risk, measures the tail risk, however, fits and better
explains the utility perception of investors. Our results indicate that when
using the EDR as risk measure, both the positive and negative relationship
between expected return and risk can be derived under standard conditions (e.g.
expected utility theory and positive risk-aversion). Therefore, no alternative
psychological explanation or additional boundary condition on utility theory is
required to explain the phenomenon. Furthermore, we show empirically that it is
a more precise linear predictor of expected return than volatility, both for
individual assets and portfolios.
