# Tag Info

Accepted

### Returns and logreturns differences

OK, this need have nothing to do with any single sample of data. It's an inherent difference between the behaviour of linear vs logarithmic numbers. Which is what make up your respective simple and ...
• 5,071
Accepted

### Convert arithmetic returns to log returns

Transmuting one to the other is pretty straightforward without the underlying sequence of prices. To go from log to simple: $R = exp(r) - 1$ To go from simple to log: $r = log(R+1)$
• 4,738
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• 1,416
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### What is the difference between overlapping and non overlapping returns

An example of non-overlapping one month returns: the return in January, the return in February, the return in March, etc. An example of overlapping 30 day returns: the return from January 1 to ...
• 9,372

### Discrete returns versus log returns of assets

To fill in the details of what "John" just explained above: Say that you have stock portfolio for several years: $t_0, t_1, \ldots, t_m$. Say that you have $n$ stocks, so that stock $i$ has ...
• 265

### Stock Prices are Lognormal - Formal Definition

Stock prices cannot be negative which means that they are not normally distributed due to the fact they cannot be negative as result of this stock prices behave similarly to exponential functions. To ...
• 636
Accepted

### Campbell Shiller log linear relation

You can simply start with the definition of gross returns \begin{align*} R_{t+1}&=\frac{D_{t+1}+P_{t+1}}{P_t} \\ &=\frac{1+P_{t+1}/D_{t+1}}{P_t/D_t}\frac{D_{t+1}}{D_t}, \end{align*} where the ...
• 15.7k
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### Normality or Log-Normality of Regular Returns

You're right but a GBM doesn't assume that percentage returns are normally distributed. It's about log-returns. If the log-return $r_t=\ln\left(\frac{S_{t+dt}}{S_t}\right)$ is normally distributed (...
• 15.7k
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### GARCH on returns or on log-returns?

What is usually used in practice to forecast volatility? I believe it is log-returns. Is it more appropriate, in general, to fit a GARCH on returns or on log-returns to estimate volatility? The ...
• 3,031