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490_lecture4_2011 - Lecture 4 Distribution of Returns...

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Lecture 4 Lognormal Distributional of Gross Returns Informational Efficiency Technical Trading Distribution of Returns Recall that p t+1 =R t+1 p t , where R t+1 is the gross return. Typical assumption: R t are independent and lognormally distributed. We get ln(R t+1 )=ln(p t+1 )-ln(p t ). Then ln(R t+1 ) must be normally distributed. Log-normal Distribution X is log-normally distributed if ln(X) is normally distributed. Let μ and ! denote the mean and standard deviation of ln(X). And let F μ, ! (x) be cdf of a normal distribution with mean μ and standard deviation ! . Then the cdf of X is F μ, ! (ln(x)). Log-normal Distribution How do we compute F μ, ! (ln(x))? In Excel we use the function normdist to compute F μ, ! (x) Usage: normdist(x,μ, ! ,true) For lognormal: normdist(???,μ, ! ,true)
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Log-normal Distribution How do we compute F μ, ! (ln(x))? In Excel we use the function normdist to compute F μ, ! (x) Usage: normdist(x,μ, ! ,true) For lognormal: normdist(ln(x),μ, ! ,true) Log-normal Distribution The cdf is F μ, ! (ln(x)). Determine the pdf for the log-normal distribution: Log-normal Distribution The cdf is F μ, ! (ln(x)). Determine the pdf for the log-normal distribution: ! F μ , " (ln( x )) ! x = ?????
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