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Questions tagged [log-returns]

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1answer
59 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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0answers
38 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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1answer
66 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_{...
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1answer
71 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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0answers
35 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
178 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
63 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
172 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
129 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
121 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
278 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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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
2k 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
111 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
211 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
123 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
198 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
102 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
129 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
2k 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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0answers
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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
224 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
456 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 ...
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1answer
42 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 ...
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1answer
381 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(...
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1answer
514 views

Intuition behind log return of portfolio = weighted sum of log returns

Suppose we have $n$ assets, each of which has weight $w_i$ in the portfolio. The log return of asset $i$ is denoted by $r_i$. What's the intuition why this holds approximately: $$ ln \left( \sum_i ...
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1answer
355 views

z-score versus log standardisation of stock prices for calculating correlation; which to use (in ML clustering, distance measure)?

I need to compare (get correlation between) different financial instruments (stocks). The problem is that different stocks will have different price scales. I was thinking of using z-score ...
0
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1answer
88 views

How did Dimson, Marsh and Staunton (2002) computed the equity index annual real return?

I was trying to read the triumph of the optimist, but it was almost impossible to see a well-written formula to show how the returns have been computed. In a simple sense, I do not know how the annual ...
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1answer
102 views

Adjusting a daily log return for a cash inflow/outflow [closed]

If I had a portfolio with one stock with an initial value of 100 and the next day the stock gained 5 and I added 50 too, would I adjust the log return this way: ln [(155-50)/100]?
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1answer
146 views

Finance beta: normally distributed?

If we assume normally distributed return (or normally distributed log Returns) for an asset and the market, can be then also say that the betas derived by this are also normally distributed? How ...
0
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1answer
2k 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?
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1answer
847 views

Annualized Log Returns

I backtested an investment strategy over ten years (521 weeks to be specific) and calculated the weekly return using log returns. The sum of all weekly returns added up to 145%. How do I annualize ...
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0answers
617 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 ...
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2answers
2k views

Transforming log return volatility into standard return volatility

If I have a forecasted volatility of the log returns of say, 0.03, this is obviously transformed relative to the log I took of the returns. It strikes me that I should raise ...
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2answers
262 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), ...
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0answers
361 views

R:log return calculation for panel data structure

I have a long form panel for hourly prices of stocks. I want to do log return calculation for this panel data structure. This is sample data: ...
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1answer
55 views

logarithm and absolut value in returns of stocks [closed]

Well, i'm interested in model a GARCH for a serie. The original serie is $y_t$ (price index of a Stock Market), which has a unit root. So i create the returns: $x_t = ln(y_t) - ln(y_{t-1})$. Now, i'm ...
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0answers
522 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 ...
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1answer
1k 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 mean(ln(1+rt)) and exp(mean(ln(1+...
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1answer
256 views

Creating the histogram for the distribution of the portfolio returns

Given log returns for some stocks $A$ and $B$, which are the constituents of our hypothetical portfolio in equal weights, how does one actually come up with a distribution of the log returns of the ...
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3answers
2k 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 $ln(1) - ln(10) = -230\%$! ...
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1answer
2k 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 ...
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1answer
2k views

How to compute simple and log portfolio returns?

I am looking for more details to perform simple and log returns for an entire portfolio. However, I've only been able to find the following semi-reliable source (see Page 9 and Page 19): Here are my ...
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2answers
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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 ...
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2answers
6k 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 ...
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1answer
32 views

Raw (level) variable is significant while log return is not significant

I know this might be an "amateur" question, but I am pretty surprised to see the following fact: I have a dependent variable, let's call it Y. Then I have an independent variable, let's call it X. ...
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1answer
237 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)). ...
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1answer
2k views

When measuring autocorrelation should you use log returns or prices?

Let's say you want to measure intra day autocorrelation from 9:30 am to 1pm using 5-minute prices should you calculate the autocorrelation using raw prices or log returns (i.e. diff(log(prices)))? Can ...
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0answers
523 views

Monte Carlo simulation returns not normal distributed

I am generating 100,000 paths of SPX out to 1 year using Euler discretization. I look at how S is distributed for 100,000 paths at the 1 year point and I find it is lognormally distributed. I look at ...
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0answers
92 views

Calculating Asset Returns

The question pertains to a simple phenomenon. There is gold futures listed on Exchange A and Exchange B. Exchange A and Exchange B overlap times with A and B starting 8 hours later and A and B ...