Risk Taking Under Semivariance

Downside deviation, semivariance, or the second lower partial moment are different names for the same risk measure, proposed in the literature for capturing the downside risk of investment decisions. This paper analyzes multiperiod decision making under such a risk measure, and finds that a V-shaped decision rule in wealth is prevalent for the most common assumptions on the distribution of uncertainty. Given that a V-shaped rule is acceptable nor desirable in practice, the use of semivariance needs a reconsideration in terms of its plausibility for guiding actual decision making in investment and elsewhere.