I have persistent, deep problems with the concept of 'risk-neutrality'. To make it more precise, let's look at the following explanation taken from a book:
"In a world where investors are risk neutral, the expected return on all securities is the risk-free rate of interest, r. The reason is that risk-neutral investors do not require a premium to induce them to take risks. It is also true that the present value of any cash flow in a risk-neutral world can be obtained by discounting its expected value [in a risk neutral world] at the risk-free rate.” (Hull-Options, Futures, and Other Derivatives, page 245)
After tens of hours of studying and looking into all books/resources/notes that I could get my hands on, reading countless of explanations (including all relevant ones on this very forum), I must admit that I still seem to not understand the concept of ‘risk-neutrality’. At this point it's become very frustrating. I have masters degree in mathematics so the math isn't the problem; but, trying to get my head around financial math, I keep having problems with the concept of 'risk-neutrality'.
To make it very concrete, regarding the above-mentioned snippet from Hull's book I have the following questions.
It's said: "In a world where investors are risk neutral, the expected return on all securities is the risk-free rate of interest, r." Why is this the case? I can't even tell whether this is true or false, since I lack the understanding of the semantics.
Also it is said: "It is also true that the present value of any cash flow in a risk-neutral world can be obtained by discounting its expected value [in a risk neutral world] at the risk-free rate." Again--why would this be the case?
To me, these are just statements that someone makes; I am unable to verify whether or not this is true, since I am not able to grasp the semantics.
I.e., the core question is: What is a 'risk-neutral world'? Can someone provide me with a definition (or at least an explanation that unveils the semantics), and subsequently prove Hull's claims?
I'd be very grateful if someone had an explanation/perspective on this that could help me. Many thanks in advance!