In this paper we show that for a new solution to Nash's bargaining problem, proposed by Lahiri (1988) ("Monotonicity with Respect to the Disagreement Point and a New Solution to Nash's Bargaining Problem", IIM, Ahmedabad, Working Paper No. 724), which satisfies monotonicity with respect to the disagreement point, an increase in risk aversion is to the player's own disadvantage and to the advantage of the opponent in the two person case; to the advantage of all opponents in the multi-person generalization. Thus it parallels results on risk-sensitivity for the Nash and Kalai-Smorodinsky solutions.