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In Python, simple geometric returns: import numpy as np import pandas as pd sp500 = pd.io.data.DataReader('^GSPC', 'yahoo')['Close'] simple_ret = sp500.pct_change() (1+simple_ret).cumprod()[-1] -1 0.74751768460019963 Log-returns: log_ret = np.log(1+simple_ret) np.exp(log_ret.cumsum()[-1]) -1 0.74751768460020074 In ...

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When doing series like this in Python, I usually just add 1 to each return, then multiply across these sums for cumulative returns. Such as, if my returns over three days were -5.2%, 2.1% & 4.8%, then the values I would store would be: 1 + (-0.052) = 0.948 1 + (0.021) = 1.021 1 + (0.048) = 1.048 Then, to calculate my cumulative returns, I ...

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The log likelihood function is indeed rather flat in the $\mu$-direction, for small time horizons (you used $T = 1$ it looks like). As you may have noticed, increasing the number of observations but keeping the time horizon the same DOES NOT IMPROVE the accuracy of the estimate of $\mu$ - this is a bit counterintuitive, if you ask me. But, increasing the ...

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In practice, when you encounter a relationship between historical financial variables that looks good on levels but not on returns, the model you get from it essentially always fails to be predictive. I generally think of this as being due to the historical relationship arising from some confounding third (plus fourth and fifth...) variable effects that ...

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If you are short you need to use log((entryprice-fees)/exitprice). It is the same logic as in log long return case. You just need to change your entryprice and exitprice inputs. In this case, entryprice is the selling operation and exitprice will be the buying operation (just the opposite).

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