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The logarithmic return for a stock is normal with an annualized mean of 12% and an annualized standard deviation of 50%. Assume you were thinking

The logarithmic return for a stock is normal with an annualized mean of 12% and an annualized standard deviation of 50%.

Assume you were thinking of buying the stock. What is the probability that in six months time you will lose money? Show each step of your calculation.

If the analysis took place in a risk neutral economy, what would be the estimated probability of losing money? Show each step of your calculation.

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