# Risk-Neutral Probability in a Binomial Tree

This question is probably very simple and I'm just missing the easy solution but I'm a bit confused so I thought I might as well try ask here.

I've been given this question:

When I tried to calculate $$p$$ I got $$p = 0.33$$ (Let me know if this is incorrect), I obtained this using : $$(e^{r_f} - d)/(u-d)$$ so I had $$(e^0-0.9)/(1.2-0.9)=0.33$$

What I don't understand is the next part of the question, when it asks "is $$p=0.5$$ a risk-neutral probability?". This is confusing me because I've already calculated $$p$$ to be something else, since my $$p$$ is different does that mean that $$p=0.5$$ is not a risk-neutral probability and $$p=0.33$$ is the risk-neutral probability, right? Or have I got this all wrong?

Any help would be really appreciated just to clarify things for me.

• You’re right. Probability .5 implies an effective growth of 5%, and if the risk free rate is 0%, that means your risk premium is 5%. Obviously, if you’re earning a risk premium, you’re not in risk-neutral space. May 20, 2021 at 13:05
• So the risk neutral probability is 0.33 as calculated? May 20, 2021 at 13:22
• Need 15 chars... yes. May 20, 2021 at 13:46
• Ok, thanks a lot XD May 20, 2021 at 14:36