Questions tagged [log-returns]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
23
votes
2answers
18k views

Discrete returns versus log returns of assets

There have been similar posts here already but nevertheless I find the question worth posting: why do some people claim that log returns of assets are more suitable for statistics than discrete ...
14
votes
3answers
13k views

Why do we usually model returns and not prices?

I think this is a quite similar question for most of you, however it is not completely understandable for me at the moment: Why do we usually use returns and not prices to model financial data in ...
7
votes
2answers
3k views

How to annualise the volatility of non-iid returns?

I have a series of monthly log-returns; let's assume the log-returns are normally distributed, but exhibit significant serial correlation. In the case of normal, i.i.d. returns, I can annualize the ...
5
votes
2answers
2k views

Risk-adjusted performance measurement: Log returns vs. simple returns and geometric vs. arithmetic mean return

I have just simulated 49 weeks of correlated returns on 5 different stocks, assuming returns being lognormally distributed. Next, I am supposed to assume that the simulated 49 weeks of returns ...
5
votes
0answers
1k views

Fitting Student t-distributions to log-returns

It seems that some tail-risk centric groups are bent on using Paretian and t-distributions to account for tail risk when fitting log-returns. It has been observed, however, that with and without ...
5
votes
0answers
323 views

Estimation of ranks of log-returns via copula

I have successfully chosen and estimate a copula for the ranks of the log-returns of my actions. My question is, since I have worked with the ranks instead of directly the log-returns (in order to be ...
4
votes
2answers
32k views

How to calculate equally weighted market portfolio

There's two studies that test the same thing in different markets (i.e. they apply the identical methodology). They state: 1) "$R_{mt}$ is the equally weighted average stock return in the dual-listed ...
4
votes
1answer
488 views

Modelling returns in the real world measure with or without drift

What I would like to discuss is the following. I don't think that this is a pure duplicate, so I would be happy about comments: On one hand it is reasonable to model log-returns as Gaussian: $$ \log(...
4
votes
0answers
973 views

Variance of a portfolio based on log-returns

Modern Portfolio Theory Optimization Problem is based on expected linear returns and covariances of linear returns. That's said, variance and expected return of a portfolio based on linear returns r ...
3
votes
2answers
1k views

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 ...
3
votes
2answers
336 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 ...
3
votes
2answers
3k 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 ...
3
votes
1answer
290 views

What is the relationship between arithmetic versus geometric averages and simple versus logarithmic prices?

I know that the geometric mean is used in order to make percentage returns across time comparable. Similarly, I know that log prices make percentage returns comparable for example when prices are ...
3
votes
1answer
2k 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 ...
3
votes
2answers
219 views

Distribution of simple returns vs logreturns

I understand that stock prices are conditionally modeled using a log normal distribution by the relationship $ y_t/y_{t−1}∼logN(μ_{daily},σ^2_{daily})$ $y_t∼logN(log(y_{t-1})+μ_{daily},σ^2_{daily}))$ ...
3
votes
2answers
689 views

How to get around flat likelihood function when calibrating GBM parameters?

I want to calibrate jointly the drift mu and volatility sigma of a geometric brownian motion, $$\log(S_t) = \log(S_{t-1}) + (\mu - 0.5*\sigma^2) \Delta t + \sigma*\sqrt{\Delta t}*Z_t$$ where $Z_t$ ...
3
votes
1answer
467 views

Log returns: volatility, outperformance, Sharpe/information ratios

I have developed the habit of simply stating that a 21% return compared to a 10% benchmark return means that the outperformance was 10% (not 11%). So, treating the whole thing in a multiplicative way, ...
3
votes
0answers
677 views

Modelling log-returns and calculating the portfolio return

I know this might be a trivial question, however, I would be grateful for some clarification. I am working on weekly log-return data, doing volatility-foracasting using GARCH models and then using ...
2
votes
1answer
186 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 ...
2
votes
3answers
4k views

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

I'm doing some analysis on log returns and I notice that returns can exceed 100%. For example, if a security's close price \$1 today and \$10 yesterday, the log return is $ln(1) - ln(10) = -230\%$! ...
2
votes
1answer
313 views

Geometric Return & Performance Results for Quarterly Rebalancing

I have a Portfolio that is rebalanced every 3-months. The portfolio is made up of assets that have daily log-returns. I am a bit confused when charting the results using ...
2
votes
1answer
121 views

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, $d(lnS)=(r-0.5*σ^2)dt+σdW(t)$, ...
2
votes
1answer
59 views

Aggregation to MSCI world return from subindicies

I have Bloomberg Data PX_LAST for the MSCI world (MXWO Index). I also have Bloomberg Data PX_LAST for all subindices for the ...
2
votes
1answer
2k views

Geometric means, standard deviation, and sharpe ratios

I have 3 related questions: a) I've seen formulas for GM and GS which eithier do, or do not, involve taking the exponent. Which is right? i.e. for GM I've seen both $\text{mean}(\ln(1+r_{t}))$ and $\...
2
votes
2answers
353 views

Cumulative Return on Futures

In my current backtesting, I am using log returns as a proxy for simple returns via the relationship $\ln(1 + r) \approx r$ for small enough r. This gives me wonderful properties like time additivity, ...
2
votes
1answer
291 views

Simple Compounding vs Continuous Compounding in return series

I'm creating a log price series in MATLAB. This is fairly easy to do using standard functions. Given a price series prices: ...
2
votes
1answer
530 views

Distributional assumptions in PRIIPs

And yet another question to discuss the assumptions in PRIIPs. It is remarkable that in these legal documents a Cornish-Fisher expansion including skewness and kurtosis is used. Looking at the very ...
2
votes
3answers
1k views

Logarithmic returns for realized variance?

I am wondering which method makes more sense when computing log returns. I am trying to compute log returns for realized variance, and I have the opening and closing prices for every minute. Since ...
2
votes
0answers
105 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 ...
2
votes
0answers
81 views

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 ...
2
votes
1answer
1k views

Continuous returns for negative roll-adjusted futures data

I've generated roll adjusted notional futures data by adding a roll adjustment to the settlement price then multiplying by contract multiplier through time. For example, for crude oil CL, on 15 March ...
1
vote
3answers
276 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 ...
1
vote
2answers
8k views

Black Scholes and the Log Normal Distribution

Why does the Black Scholes Equation imply the returns are log-normally distributed?? How can we tell that the returns of the underlying asset wouldnt be normally distributed??
1
vote
1answer
3k views

Returns vs log returns formula [closed]

Probably something very simple I'm missing, but if returns is: $R = \frac{V_f}{V_i} -1$ Then why is log returns $R = log(\frac{V_f}{V_i})$ instead of $R = log(\frac{V_f}{V_i} -1)$?
1
vote
2answers
9k views

Calculating log-returns across multiple securities and time

I've been getting very confused on the topic of calculating returns. To get cumulative returns in time, log-returns are used, but apparently log-returns aren't used across different securities at a ...
1
vote
1answer
4k views

What is the difference between overlapping and non overlapping returns [closed]

My prof asked me to make an Variance-Ratio test for overlapping as well as for non-overlapping returns. What is the difference between overlapping and non-overlapping?
1
vote
2answers
72 views

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 ...
1
vote
2answers
116 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 ...
1
vote
1answer
165 views

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

I'm trying to find the exact (ie, not an approximate) relation between the "Compound Return", "Arithmetic Return", and the "Annualised Volatility" as given the assumptions below, and from there the ...
1
vote
1answer
795 views

Should log returns be used in multilinear regressions?

As the title already says, should log returns, instead of simple returns, be used in regression analysis? In this case, I want to analyse the impact of specific factors (Dividend yield etc.) on the ...
1
vote
2answers
139 views

Does forecasting asset returns by default assumes non-stationarity of asset returns?

If we assume the assets returns are stationary then the best forecast can only be the mean of the distribution. But if we assume non-stationarity we are forecasting the mean parameter (assuming ...
1
vote
1answer
3k views

Log daily returns of multiple securities for multiple time period in R

I have dataset containing daily closing prices of 5413 companies from 2000 to 2014. I want to calculate daily log returns for the stocks as according to dates as log(Price today/Price yesterday). I ...
1
vote
1answer
188 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,...
1
vote
2answers
433 views

How to simulate 3 correlated stock processes following a GBM?

Suppose we have 3 stocks following GBMs. We are given the distribution of the daily log returns which is multivariate normal. Suppose I want to sample the stock price tomorrow ($\Delta t = 1$ day), ...
1
vote
1answer
84 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 ...
1
vote
1answer
64 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{\...
1
vote
1answer
664 views

Are Kenneth French Research Returns log-Returns?

Does anyone know if Kenneth French's return data on his website is log returns?
1
vote
1answer
3k views

Definition of log return of an asset [closed]

What is the general usage of the term daily log returns $Y_t$ of an asset? (1) or (2)? $$(1) \text{ } Y_t = log (\frac{p_t}{p_{t-1}})$$ OR $$(2) \text{ } Y_t = log (\frac{p_t-p_{t-1}}{p_{t-1}})$$ for ...
1
vote
1answer
378 views

Calculate short log return including fees

log long return is log((exitprice-fees)/entryprice) without leverage. log short return is the negative long return. So, from the above I would get short return = log(entryprice/(exitprice-fees)). ...
1
vote
0answers
26 views

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 (...