Expectation vs Variance in Economics

Question

When deciding between two projects available, where E[ReturnB] > E[ReturnA] but Var[B] > Var[A], why would this not be a clear case and rather look at the principle of maximization of expected return?

I have trouble understanding the concept of choosing projects based on expectation and return. For example which project (A vs B) would be preferable in the case that:

E[ReturnB] > E[ReturnA] but Var[B] < Var[A]

and why?

Thank You!!!!

Answer 1

Let me ask you this. Suppose you have two kinds of stocks: $A$ and $B$. Moreover, suppose they have the same price right now. What would happen one year from now? Suppose you have some sort of super power so that you could know the probability density function of stock price of $A$ and $B$, so that you could compute $E(A),E(B),Var(A), Var(B)$. And here's what you got:

$E(A)=400,E(B)=500$.

"Wow, I'll go with stock $B$. But since I have this super power, I'll compute the variance as well.

$Var(A)=5, Var(B)=300$.

Now you tell me, which one would you choose and why?