This paper proposes two concepts of changes in risk which are the subsets of first-degree stochastic dominance (FSD) changes called an ‘FSD shift with respect to a point k’(k-FSD shift) and a ‘monotone probability ratio FSD shift with respect to a point k’(k-MPR shift). These shifts can be applied to the specific economic model such as the standard portfolio model or the coinsurance model which is linear in both the decision and the random variable. In the standard portfolio model or the coinsurance problem, the point k can be the sure interest rate or the insurance premium, respectively. This paper explores that the MPR shift in Eeckhoudt and Gollier (1995) is the subset of the k-MPR shift and any k-MPR shift can be decomposed into two FSD shifts, one k-FSD and the other MPR. When we restrict the payoff function to be linear in the random variable and limit our analysis to risk-averse decision makers, we obtain the interesting comparative statics results for these two shifts. Compared with the result for the MPR shift, the comparative statics result for the k-MPR one, there is a trade-off between the restrictions on the set of changes in cumulative distribution function (CDF) and the structure of the concerned payoff function.