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33 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 ...
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), ...
28 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 ...
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: ...
47 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 ...
283 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+...
48 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 ...
123 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 ...
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 ...
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 $ln(1) - ln(10) = -230\%$! ...
264 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 ...
198 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 ...
266 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 ...
198 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 $Z_t$ ...
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. ...
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)). ...
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 ...
221 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 ...
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 ...
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 ...
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 ...
629 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 ...
559 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 ...
103 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 ...
79 views

Log returns vs Relativizing to Portfolio size of \$1

In a current empirical research project, I am tracking a non-parametric measure of a transaction cost. To this extent, I track this cost in two ways Cost in terms of log returns Cost in terms of ...
379 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 ...
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 ...
619 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 ...