question archive The logarithmic return for a stock is normal with an annualized mean of 12% and an annualized standard deviation of 50%
The logarithmic return for a stock is normal with an annualized mean of 12% and an annualized standard deviation of 50%
Subject:FinancePrice:2.86 Bought3
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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Annualized Mean = 12% (Mean)
Annualized standard Deviation = 50% (Std Dev)
When you lose money, return = 0% (Observation)
In normal distribution, z statistic is calculated as follows
Z = (Observation- Mean)/Std Dev = (0% -12%)/50% = -0.2400
Now Z(-0.2400) = 1-z(0.2400)
From the probability distribution, we get Z(0.2400) = 0.5948
So, z(-0.2400) = 1- Z(0.2400) = 1-0.5948 = 0.4052
So, Probability of making a loss (i.e. return=0%) = 0.4052 or 40.52%
