# Tagged Questions

The tag has no usage guidance.

7k 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 ...
636 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 ...
561 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 ...
382 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 ...
17k 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 ...
222 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 ...
91 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 ...
200 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 $Z_t$ ...
266 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 ...
104 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 ...
620 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 ...
753 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 ...
99 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), ...
268 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 ...
284 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+...
32 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)). ...
34 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: ...
48 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 ...
49 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 ...
199 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 ...
69 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 ...
82 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 $ln(1) - ln(10) = -230\%$! ...
124 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 ...
29 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 ...
21 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. ...
222 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 ...
19 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 ...
27 views

### Annualized log return for Equity [on hold]

I came across an old question answered here My question is theoretical. I'm not a mathematician/quant professional so please excuse my lack of knowledge. I've read a few papers on forecasting equity ...
34 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 ...
41 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 ...
18 views

### Calculating Portfolio Risk with different assets [duplicate]

I want to calculate the risk of a portfolio (for a certain year) that includes several assets. Therefore, I want to calculate the standard deviation of each specific asset. I will calculate the ...