11 votes
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 ...
demully's user avatar
  • 5,071
10 votes
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: $r = log(R+1)$
amdopt's user avatar
  • 4,738
9 votes
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Black Scholes and the Log Normal Distribution

The Black-Scholes-Merton (1973) model implies that the prices of the underlying asset at maturity $S_T$ are log-normally distributed $$ln(S_T)\sim N\big[ln(S_0)+(\mu-\frac{\sigma^2}{2})T,\;\sigma^2T\...
jthg's user avatar
  • 445
8 votes

Do stock returns show positive skewness?

I think most people agree that aggregate (index) stock returns have negative skewness. However, this does not appear to be the case for individual stock returns. These two papers find that average ...
fes's user avatar
  • 1,717
7 votes
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Stock Prices are Lognormal - Formal Definition

In reality, neither are stock prices log-normally distributed nor are returns normally distributed. More sophisticated models drop this assumption. For instance, returns are more peaked and have ...
Kevin's user avatar
  • 15.7k
6 votes
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Returns vs log returns formula

Let $R$ denote the arithmetic return and $r$ the log returns. $$R=\frac{V_f-V_i}{V_i} \textrm { and } r=\ln\left(\frac{V_f}{V_i}\right)$$ Arithmetic and log returns are connected as: $$R=\frac{V_f-...
alexbougias's user avatar
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5 votes
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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 ...
Alex C's user avatar
  • 9,372
5 votes

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 ...
Orvar Korvar's user avatar
5 votes

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 ...
Gogo78's user avatar
  • 636
5 votes
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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 ...
Kevin's user avatar
  • 15.7k
5 votes
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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 (...
Kevin's user avatar
  • 15.7k
5 votes
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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 ...
Richard Hardy's user avatar
4 votes

How to interpret negative log return more than -100%?

Large? ? The relationship between normal and log returns is $$(normal return) = exp(log return)-1$$ Therefore log-returns can be from $-\infty$ to $+\...
Kiwiakos's user avatar
  • 4,317
4 votes
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Intuition behind log return of portfolio = weighted sum of log returns

The above relation really only approximately. If you consider arithmetic retunrs then it is exact. For the approximation you just need to look at the Taylor series of the exponential: $$ e^x = 1 + x +...
Richi Wa's user avatar
  • 13.7k
4 votes

What is, here, the relationship between "compound" and "arithmetic return" and "volatility"?

There is no possibility to convert any two of your mentioned variables into the remaining one. For the compound and arithmetic return you can derive an inequality, but that's the best you can do. The ...
skoestlmeier's user avatar
  • 2,916
4 votes

Returns and logreturns differences

It happens because the log function is concave around 1, which means it returns "more negative" numbers for values less than 1 than the positive values it returns for numbers the same distance greater ...
D Stanley's user avatar
  • 1,321
4 votes

Normality or Log-Normality of Regular Returns

The return $R_i$ as expressed in $$R_{i+1,i}=\frac{S_{i+1}-S_i}{S_i}=\mu \Delta t + \sigma \Delta W(t_{i+1},t_i)$$ is not possible. To see this, let's get the returns over two small time steps of $\...
stackoverblown's user avatar
4 votes
Accepted

Trading based on the log return series

Firstly, distributions don't have to be symmetrical to have a standard deviation. In addition, I think you mean that financial instruments (stocks, futures, ect.) have FAT tails not long tails. This ...
Max van Leeuwen's user avatar
3 votes

Black Scholes and the Log Normal Distribution

BS assumes prices NOT returns are log-normally distributed. Why making that assumption? 1.log-normal is not perfect but OK to fit potential prices distribution. 2.The nature of log-normal distribution ...
Hui's user avatar
  • 402
3 votes
Accepted

Should log returns be used in multilinear regressions?

As you pointed out, not necessarily: I know that Fama-French have developed their 3 factor model using only simple returns That's because of a very common misconception: and, after all, the ...
madilyn's user avatar
  • 5,230
3 votes
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Calculating intraday returns from imperfect data in R

Create a new price series that has a value for every minute, e.g. by carrying the last observation forward. Then compute returns from this new price series. (There are simpler approaches for this ...
Enrico Schumann's user avatar
3 votes

Geometric means, standard deviation, and sharpe ratios

The geometric mean of quantities $\{a_1, \dots, a_n\}$ is $$ \bar{a}_g = \left( \prod_{i=1}^n a_i \right)^{1/n} $$ Taking the logarithm of both sides gives $$ \log \bar{a}_g = \frac{1}{n} \sum_{i=1}^n ...
Chris Taylor's user avatar
  • 5,901
3 votes
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Log daily returns of multiple securities for multiple time period in R

Well, it wasn't easy because you didn't mentioned how your data is formatted. I create my own data.frame() basing on data you provided. You can skip this part if ...
KryptonLC's user avatar
3 votes
Accepted

Why can we assume that asset return rates are normally (or lognormally) distributed?

In the colloquial sense of the word "justified," it is not justified. I will describe why it is justified mathematically and under what circumstances and in what case it is not justified. ...
Dave Harris's user avatar
  • 4,369
3 votes
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How To Understand the Drift of ln(S) if S Follows Geometric Brownian Motion

Because $\mathbb{E}\left(e^{\sigma W_t}\right) = e^{\frac{1}{2}\sigma^2T} > 1$, you need that correction to ensure that your asset grows on average at rate $\mu$ (or $r$ in the risk-neutral measure)...
siou0107's user avatar
  • 2,620
3 votes

The use of volatility from log returns and raw return

There is no right or wrong, just those 2 conventions are different, each one with its pros/cons. In general what is more important is to be clear about conventions used to avoid miscommunication and ...
Ezy's user avatar
  • 2,187
3 votes

How to calculate the log return of portfolio?

Now this is a farily basic question, but since I see professionals having trouble with this all the time, let us go through it Simple returns aggregate nicely (linearly) across trades but not time, ...
Pontus Hultkrantz's user avatar
3 votes

GARCH on returns or on log-returns?

I would not use anything but log returns in finance. The reasons logs are used so frequently are summarised here. Commonly used textbooks like Ruey Tsay, Analysis of Financial Time Series always ...
AKdemy's user avatar
  • 9,059
3 votes
Accepted

Effect of back-transforming forecasted mean of log returns to get forecasted mean of price

Assume the stock index is given by $S_t$ and you form a forecasting model for the log-returns $r_{t+1}=\log(S_{t+1}/S_{t})$. You are then interested in the expected next period stock index level $$\...
fes's user avatar
  • 1,717
3 votes
Accepted

Difference between statistical properties of log returns and simple returns

I try to translate your code to random variables, then things might be clear. Assume $X$ is normal with $X\sim N(\mu,\sigma^2)$. This is your log-return. Then $Y = \exp(X)$ is lognormal with ...
Richi Wa's user avatar
  • 13.7k

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