# Questions tagged [log-returns]

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106 views

### Do all risky assets have negative expected return over long enough time horizons?

I stumbled across a site that claims "given a long enough forecast horizon H, all assets with positive volatility have an unbiased expected return that is negative". They base this on the ...
66 views

### What are some common methods for calculating short term historical volatility (i.e. look back 5 minute time periods)

I'm interested in quantifying the impact of short term price volatility on a particular strategy I'm running. So far I'm simply calculating the standard deviation of log returns, but I'm a bit unsure ...
156 views

### Is it possible to calculate logarithmic return for short position? [closed]

In the book "Python for Algorithmic Trading" by Yves Hilpisch, it calculates the logarithmic return by summing up all the log values. When calculates the profit for long position: log(...
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### Log Returns or Simple Returns for Portfolio Performance Analysis

Simple question but one thats stumping me slightly. I am doing a study analysing historical portfolio performance related to portfolios constructed with separate factors in mind. I realise simple ...
50 views

### Why is the approximate entropy of (some) stock returns zero?

I downloaded some prices for TSLA and AMZN from yahoo finance to try and see if I could measure the entropy on a rolling basis with the intention being maybe returns have lower entropy (are more ...
53 views

### Non-fixed stationary "conversion"

Dear users of StackExchange, I was wondering why the log returns of a fixed period of time is such a common use in "transforming" a time series into a more stationary one? I thought that ...
60 views

### Do I use % return, log return or diff of prices to plot ACF?

I am reading a book on time series. To make a non-stationary series stationary, sometimes we need to difference the series. When it comes to finance, prices are non-stationary. Many authors fit ARMA ...
26 views

### open-close intraday demeaned log return calculation

open-close return is basically what I feed into the realized kernel volatility and recently I noticed the realized kernel covariance/variance is generating negative value so I had to retrace my ...
78 views

### weekly returns and the daily returns scaled to weekly

I am new in this blog and first of all I want to apologise for my english. I have to calculate, for a university project, the weekly returns and daily scaled returns to weekly for few stocks For ...
361 views

### Log excess returns calculation

I need to calculate log excess returns. I'm given market level monthly total return index, price index and a risk-free rate (from Fama/French 3/5/etc. factors). I'm not sure whether I'm calculating ...
111 views

### Variance of Log Returns

Consider an asset held for $n$ time periods with weakly stationary log-returns $r_t$, $1≤t≤n$. Show that $var(r_1 +r_2 +r_3 +r_4)=var(r_1 +r_2 +r_3)+var(r_1)(1+2ρ_3 +2ρ_2 +2ρ_1)$, where $ρ_k$ is the ...
43 views

### LogNormal VaR Formula Risk Metrics

https://web.mst.edu/~huwen/teaching_VaR_Weiqian_Li.pdf On page 6, the paper above mentions RiskMetrics would use the following VaR formula: ...
56 views

### Converting Euro returns into USD terms

I have a series of log returns calculated on an index that is priced in Euro terms, and I'd like to convert those returns into USD terms. Would it be mathematically correct to calculate log returns on ...
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### Forecasting returns and volatility using ARIMA-GARCH model in R

I am using rugarch package in R to forecast returns and volatility of a stock. I train an ARIMA (p ,d q) + GARCH(s, r) model on ...
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### finding optimal weight using Kelly criterion

Question: Suppose you have two strategies. Strategy 1 gains 8% with probability p, and loses 5% with probability 1-p, where p = 0.53. Strategy 2 gains 8% with probability q, and loses 5% with ...
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### Using Taylor formula with logarithmic returns

I would like to calculate PnL scenarios for an FX portfolio using Taylor series approximation: \begin{align} \text{PnL} \approx \delta \Delta r + \frac{1}{2} (\Delta r)^2 \Gamma \end{align} I ...
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### Industry or academic standard frequency to report the return, standard deviation, and Sharpe ratio?

Everyone (funds, banks, academics, financial information sites etc.) reports the annualized return, standard deviation, and Sharpe ratio. Yet we never get to know what the basis of their computation ...
213 views

### Do stock returns show positive skewness?

Do highly liquid (blue chip) stocks exhibit positive skewness more than negative skewness? If so, would positive, rather than negative, skewness be an appropriate and intuitive prior when modeling ...
139 views

### How to exclude N/A while calculating daily log returns

I have daily price data of hundreds of companies from 2010-01-01 to 2020-08-21, there are many missing values in my data frame. if I use na.omit, it deletes all my data. I try to use ROC(), but it ...
168 views

### Calculating excess returns with 3M T-Bill

I have to calculate weekly log excess returns using the 3-month T-bill. However I am not really sure if I am doing this correctly. This is what I did: first I calculated the returns with ln(price/...
208 views

### Why do cumulative returns have a bimodal distribution?

Regular returns (log-differenced prices) have statistical distributions that are bell-shaped and unimodal (one mode/peak) despite being non-normal and fat-tailed. Cumulative returns, on the other hand,...
149 views

### Predict Log Stock Return Direction and Trading Strategy

The $k$ period log return is defined as $$r_{t}(k)=log(S_{t}/S_{t-k}),$$ Where $S_{t}$ is the stock closing price at time $t$. For argument sake, assume that by time I mean a stock trading day and ...
485 views

### Normality or Log-Normality of Regular Returns

Another old question on this site (How to simulate stock prices with a Geometric Brownian Motion?) inspired me to ask the following question: if we assume that regular returns could be normally ...
147 views

### About the log return in the Black&Scholes model

I'm currently studying the Black&Scholes model and I'm not sure about the following thing: the log return, say r, doesn't evolve in time? I mean, dr/dt = 0, its derivative is zero? Does only its ...
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### The use of volatility from log returns and raw return

As far as I know, we usually use log returns( $ln\frac{p_{t+1}}{p_{t}}$ ) in quantitative finance. For example, let's say we have lots of monthly log returns data, $R_m$. Then, we can get the mean ...
430 views

### Campbell Shiller log linear relation

I am trying to derive the campbell shiller log linear relation, and i got stuck with something (i believe) quite simple. Before we are using the first-order tayler expansion is where i got stuck, ...
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### What benefits do using log returns for model training provide?

I came across a paper that uses Support Vector Machines to classify a buy/sell/hold decision each hour at the $\pm$0.5% threshold. The paper can bee seen here. The ...
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### Lognormal asymmetry implication on Value at Risk

To examine the Value at Risk implications for a portfolio consisting of a spot and futures time series I have generated a 1-day monte carlo simulation. I was long in the spot and short in the future (...
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### arithmetic mean of log returns that starts and ends with the same price in a time series

quick question: arithmetic mean of log returns that starts and ends with the same price in a time series say a stock time series starts at t0 price 100 fluctuates in between the time series and ends ...
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### Fitting a non-stationary GARCH model

I'm very new to financial time series. I have a dataset containing the daily simple returns of the Dow Jones Industrial Average and I want to model a (univariate) GARCH model for the daily logreturns. ...
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### Expected value and variance of the stock log-returns under Local Volatility framework

I want to calculate the expected value and the variance of the stock process log-returns in the Local Volatility setting (and the realized/terminal correlation but let us begin in the one-dimentional ...
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### Sharpe ratio of annualized log returns

I have returns from the last 12 months on a portfolio, and i have risk free rate for the latest year, on daily basis. I have annualized the risk free rate, and i am using log returns for the period. ...
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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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### Stock Prices are Lognormal - Formal Definition

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 ...
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### 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 ...
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### 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 ...
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### 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 ...
3k 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 ...
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### 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 ...
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### 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 ...