# Questions tagged [log-returns]

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### How To Understand the Drift of ln(S) if S Follows Geometric Brownian Motion

As we know, if an asset S follows geometric Brownian motion, under risk neutral measure, it can be expressed as $\frac{dS}{S}=rdt+\sigma dW$, by applying Ito's lemma, $d(lnS)=(r-0.5*σ^2)dt+σdW(t)$, ...
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I'm struggling with what the exact meaning of "stock prices are lognormal" (and its use to show normality of returns). My assumption was that given ${S_t}$ are stock prices and returns are defined as $... 0answers 60 views ### Log returns vs normal returns with weekly prices I am constructing equity factors and I am given weekly prices for several thousand stocks. Every year the portfolio should be rebalanced, so I am always calculating the returns for a single year. Now ... 2answers 125 views ### Returns and logreturns differences I have a time series of stock prices and I tried to calculate simple returns and log returns. However, I end up that simple returns has positive mean, but log returns has negative mean. Is it possible ... 0answers 33 views ### Turning a spread always-positive for profit calculations? I have a strange problem. I am running a backtest on a strategy whose signal is based on a spread. Naturally, a spread can go negative or positive. If I try to calculate the log return of a difference ... 1answer 38 views ### Convert arithmetic returns to log returns [closed] I have a series of arithmetic returns and I need log returns. I do not have the underlying prices. How do I convert? All the posts I have found explain why using one versus the other is appropriate ... 1answer 66 views ### Portfolio & Asset Returns across Multiple Periods The stocks of CK Tan's, Robertson's, and Tamashimaya are held by the hedge fund SSK. They hold an equally weighted portfolio. The end-of month prices of the stock during five months this year is given ... 0answers 86 views ### Fractional derivative returns on a VWAP series? In Marcos Lopez De Prado's book, Advances in Financial Machine Learning, the author explains the method of fractional differentiation as an alternative to calculate returns. The method basically ... 2answers 108 views ### Why can we assume that asset return rates are normally (or lognormally) distributed? In many theories of financial mathematics it is assumed that asset return rates are normally distributed (e.g. VaR models) or lognormally distributed (e.g. Black-Scholes model). In practice, asset ... 1answer 60 views ### Calculate return for a set of securities downloaded using quantmod I downloaded adjusted closing price using quantmod for a set of securities. I want to calculate daily/weekly/monthly return for all securities. Usual dailyReturn, weeklyReturn etc not working. What do ... 1answer 62 views ### Which are the practical implications that the continuously compounded rate of return can be smaller than the expected rate of return? I'm reading Hull's Options, Futures and other Derivatives and it intrigues me that the distribution of the continuously compounded rate of return x is:$x \sim \phi(\mu - \frac{\sigma^2}{2}, \frac{\...
The expected logarithmic return of a portfolio is calculated as : $$𝐸_p = \log\left(\sum_i w_i e^{R_i}\right)$$ Therefore, I was wondering that how can I apply weight to use with the variance based ...