An investor with unit wealth maximizes the expected value of the utility function $U(x)=a x-b x^{2} / 2$ and obtains a mean-variance efficient portfolio. A friend of his with wealth $W$ and the same utility function does the same calculation, but gets a different portfolio return. However, changing $b$ to $b^{\prime}$ does yield the same result. What is the value of $b^{\prime}$ ?