Is There an Intertemporal Relation between Downside Risk and Expected Returns?

Abstract

This paper examines the intertemporal relation between downside risk and expected stock returns. Value at Risk (VaR), expected shortfall, and tail risk are used as measures of downside risk to determine the existence and significance of a risk-return tradeoff. We find a positive and significant relation between downside risk and the portfolio returns on NYSE/AMEX/Nasdaq stocks. VaR remains a superior measure of risk when compared with the traditional risk measures. These results are robust across different stock market indices, different measures of downside risk, loss probability levels, and after controlling for macroeconomic variables and volatility over different holding periods as originally proposed by Harrison and Zhang (1999).

The Neurobiological Foundations of Valuation in Human Decision Making Under Uncertainty

“…are secondary. See (Bali, Demirtas et al 2006). 4 A few neuroscientists have started to incorporate risk in reinforcement learning.…”

“…The evidence points towards a computational model whereby the brain computes value by separately encoding expected reward and risk, and combining the results. Such a computational model is known to approximate well many types of utility functions (Bali, Demirtas et al 2006) including prospect theory (Agren 2006). …”

“…How does the computational model generate the risk aversion that we may see in choices? Or, in ambiguous situations, how is ambiguity aversion revealed in choices (Hsu, Bhatt et al 2005;Bali, Demirtas et al 2006;Huettel, Stowe et al 2006), and what model underlies it, e.g., alpha-maxmin preferences (Ghirardato, Maccheroni et al 2004), anticipated regret (Segal 1987), or some other.…”

“…The link between the utility models representing actual choice under uncertainty, such as expected utility and prospect theory, on the one hand, and the mean-risk model, on the other hand, is often clarified by means of Taylor series expansions (Bali, Demirtas et al 2006). One of the goals of this chapter is to demonstrate that the logic of a computational model based on a trade-off between expected reward and risk can be extended to choice under ambiguity as well.…”

The Risk Map: A new tool for validating risk models

“…bank B). 4 A solution proposed by Lopez (1999a,b) consists in considering the excess losses over and above the 3 Validation tests are also based on the independence hypothesis (IND), under which VaR violations observed at two di¤erent dates for the same coverage rate must be distributed independently. Formally, the variable I t (B) associated with a VaR violation at time t for a coverage rate B should be independent of the variable I t0k (B), 8k 6 = 0.…”