# An Interview Question

#### Yike Lu

##### Finder of biased coins.
You guys make good points, but at an interview what I would actually do is to clarify the purpose of the question if objections are raised to my martingale assumption/answer. Without knowing the purpose of the question, it is impossible to determine whose answer would be "accepted", although again DStahl and Diego both make valid poitns.

$$\beta=\frac{Cov(r, r_m)}{Var(r_m)}=\rho\frac{\sigma}{\sigma_m}$$

Therefore,

$$\sigma=\frac{\sigma_m}{\rho}$$

And the median stock price is above 20 iff

$$\mu-\frac{1}{2}\frac{\sigma_m^2}{\rho^2}>0$$

So the stock price is more likely to go up for a higher correlation and less likely for higher market volatility. We are not talking about risk-neutral drift here, so it is really a question about what mu is. I would probably say it is more likely to go up, since stocks go up on average in the long run.

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