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A log returns distribution with median zero

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Alexandra 2015 年 5 月 5 日
終了済み: MATLAB Answer Bot 2021 年 8 月 20 日
I have a time series of monthly log returns, to which I subtracted the median, so that they have zero median. I did this because I want the price distribution (kernel) for each month to have median X. So that for the first month P = X*exp(ln), such that the median of P is X. And for the second P'=X*exp(ln)*exp(ln'). I do this for twelve months.
The problem is that although the time series of returns have median zero, when I fit ksdensity and run 500.000 iterations, the median is not zero and so after 12 months P'''''''''''' is very different from X. Anyone knows what can I do?
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Alexandra 2015 年 7 月 28 日
Hi Michael,
No, I am not related with the other question. The thing is, I want to simulate a random distribution of some price P. I use log returns ln(p1/P0). But I want the distribution of P do have median X. So I start from X*exp(ln(p1/p0)) with many returns from historical data. P does not have median X. I tried to make sure historical returns have median 0, but the random return simulated do not have median zero. Was I clear? many thanks,

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