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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.

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