Questions tagged [log-returns]

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finding log returns for multiple stocks using R [closed]

Consider a portfolio with four stocks Google(GOOG), 3M(MMM), Microsoft (MSFT), and IBM(IBM). We are interested in monthly return (log return between 22 business days) of the portfolio elements from 01/...
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1answer
49 views

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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2answers
56 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 ...
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1answer
167 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 ...
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1answer
64 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 ...
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2answers
43 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/...
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1answer
150 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,...
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1answer
75 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 ...
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2answers
206 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 ...
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2answers
69 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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1answer
142 views

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 ...
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2answers
80 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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0answers
48 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 ...
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0answers
23 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 (...
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1answer
39 views

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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55 views

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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0answers
89 views

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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52 views

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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1answer
112 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, $d(lnS)=(r-0.5*σ^2)dt+σdW(t)$, ...
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2answers
913 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 ...
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71 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 ...
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2answers
552 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 ...
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35 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 ...
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1answer
375 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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1answer
74 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 ...
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2answers
159 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 ...
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1answer
97 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 ...
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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{\...
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142 views

Applying portfolio variance weight based on logarithmic returns?

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 ...
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2answers
182 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})$ $y_t∼logN(log(y_{t-1})+μ_{daily},σ^2_{daily}))$ ...
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1answer
206 views

Simulated Sharpe Ratio Calculation for Leveraged Portfolio

I've written some VBA code to simulate the effect of borrowing money, investing it, and repaying the loan daily. PseduoCode: Start with a portfolio value of P = 1 Each day borrow P, invest 2*P, ...
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42 views

Log likelihood function, GARCH(1,1) with asymmetric term

I am modelling a GARCH(1,1) and a GARCH(1,1) with an asymmetric term. $$h(t)=\omega+\alpha\varepsilon(t-1)^2+\beta\sigma(t-1)^2$$ and $$h(t)=\omega+\alpha u(t-1)^2+\beta\sigma(t-1)^2 + \gamma (u(...
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1answer
755 views

Why should we use log returns? Log normality

According to this link, there are some reasons we have to use log returns. But I can not understand the first reason provided in the link: First, log-normality: if we assume that prices are ...
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1answer
138 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 ...
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1answer
1k views

Log returns of individual assets and calculating portfolio returns

I am researching optimal asset allocations and am wondering if I am making mistake(s) in calculating the portfolio return. I have three assets, of which I have monthly return data. I have calculated ...
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1answer
443 views

Are Kenneth French Research Returns log-Returns?

Does anyone know if Kenneth French's return data on his website is log returns?
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2answers
273 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, ...
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1answer
2k 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 $R = log(\frac{V_f}{V_i} -1)$?
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1answer
109 views

Which method would you use to compare if a time series of financial returns has more “clusterized volatility” than another?

It is known that the historical series of financial returns are characterized by the so-called volatility clustering. Suppose we approximate the number of two-type clusters, namely the high and low ...
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2answers
6k 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??
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1answer
549 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 ...
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1answer
300 views

Calculating intraday returns from imperfect data in R [closed]

The aim is to calculate minute returns in R. Given is minute price data in a tbl_df. A row was only added if there actually were trades. ...
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0answers
193 views

How can I compute a realized variance for raw instead of log returns?

Whenever I read about calculating realized variance, people are using log returns. However, I was asking myself whether it is possible to calculate realized variance also for simple, raw returns. ...
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1answer
381 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, ...
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2answers
124 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 ...
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1answer
250 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: ...
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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 ...
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101 views

Elobaration on: Discrete returns versus log returns of assets

I read Discrete returns versus log returns of assets and it is very helpful. However, if log-returns are easier for time-aggregation, then why do economists work with discrete returns e.g. in GDP ...
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2answers
303 views

Log normal price simulation

I'm trying to figure out a spreadsheet I have which simulates 50000 returns in excel using the following function: LOGNORM.INV(RAND(),0,0.35)-1 Question: How ...
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1answer
510 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 ...