³The reason we construct things this way is that we want to be able to consider the consequences of a pure increase in $2 σ𝜀$ that leaves the return the consumer cares about – the arithmetic return – unchanged. That is accomplished by deﬁning the problem’s ‘primitives’ as being the arithmetic return and $2 σ𝜀$ , so that when we increase $2 σ𝜀$ and solve the problem with $2 r = r − σ𝜀∕2$ we will achieve the same expected arithmetic return as before the increase in $2 σ𝜀$ .