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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:

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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.

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  • $\begingroup$ 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. $\endgroup$
    – Mild_Thornberry
    May 20, 2021 at 13:05
  • $\begingroup$ So the risk neutral probability is 0.33 as calculated? $\endgroup$
    – Charlie P
    May 20, 2021 at 13:22
  • $\begingroup$ Need 15 chars... yes. $\endgroup$
    – Mild_Thornberry
    May 20, 2021 at 13:46
  • $\begingroup$ Ok, thanks a lot XD $\endgroup$
    – Charlie P
    May 20, 2021 at 14:36

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