We start from a variable (x) over tilde, which has an unspecified (and possibly even infinite-variance) distribution, and we truncate (x) over tilde: from above and below with bounds that may linearly depend on a second variable, (y) over tilde. We investigate how the variance of this truncated variable is affected by a binomial version of the Rotschild-Stiglitz measure of increased riskiness of (x) over tilde or (y) over tilde. We find that, for most unimodel distributions of (x) over tilde, such an increase in the riskiness of (x) over tilde increases the variance of the truncated variable. The effect of changed riskiness in (y) over tilde is ambiguous. (C) 1997 Elsevier Science B.V.