Questions tagged [log-returns]

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2 votes
0 answers
78 views

How to get Annualized Volatility of Log Returns to match or be close to Annual Volatility of Log Returns?

I done 30 Year Rolling Standard Deviation of Annual Log Returns of US Stock Market Data from Robert Shiller 1871-Present (ie I calculate standard deviation of annual returns from Jan 1871-Jan 1901,Feb ...
3 votes
1 answer
311 views

Trading based on the log return series

A common strategy in trading is to use a bollinger band system. Simply put, we bet on reversion to the mean and take the opposite trade to the current movement under the assumption a move is overdone. ...
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How can I estimate value-at-risk of a long/short portfolio without making simplifying assumptions?

I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am ...
0 votes
1 answer
258 views

How to calculate the log return of portfolio?

Suppose that we have five trades each day with these returns ($R_{day,trade}$) and we have 300 days in total: $R_{1,1}$, $R_{1,2}$, $R_{1,3}$, $R_{1,4}$, $R_{1,5}$ $R_{2,1}$, $R_{2,2}$, $R_{2,3}$, $R_{...
2 votes
1 answer
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Dumb question : under the assumption of the normal distribution and using log return stationarity

Under the assumption of the normal distribution, I'm trying to create a single stock mean reversion strategy. I took the log returns because they are stationary, I standardized them and used the ...
0 votes
0 answers
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Should daily log returns be "adjusted" by using the exponent?

For estimating the daily historical/statistical volatility of a financial instrument one can use the following procedure (which makes some assumptions, i.e. log-normal distribution of prices): ...
1 vote
1 answer
179 views

Price vs log returns - stationarity issues

I am trying to analyze the price of Bitcoin versus the number of Reddit posts about Bitcoin and the sentiment of those posts (daily). The price is I(1) while the sentiment and the number of posts are ...
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0 answers
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Compute Sharpe ratio and annualized Sharpe on captured bar returns or trade returns?

I am currently using a vectorized backtester where I have a strategy_returns series which is just a version of the bar-to-bar ...
-3 votes
1 answer
173 views

How to calculate return on a series of long position for each price point

The return between two price points can be calculated as Price(present)/Price(previous) -1 Or, it can be expressed as ...
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Calculation of log returns of a short position with two instruments

The usual method for calculating short log returns would be ln((selling price - fees) / buying price). But how does this apply to a trade with two instruments, e.g., a bond breakeven trade? E.g., the ...
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1 answer
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Derive the price of log contract

I am reading the Neuberger [1999] Log Contract paper and really confused on the log contract. So if the payoff is $\ln(S_T)$, then we can easily solve the price of such derivative: $$f_t^s = e^{-r(T-t)...
6 votes
3 answers
250 views

Do all risky assets have negative expected return over long enough time horizons?

I stumbled across a site that claims "given a long enough forecast horizon H, all assets with positive volatility have an unbiased expected return that is negative". They base this on the ...
1 vote
0 answers
73 views

What are some common methods for calculating short term historical volatility (i.e. look back 5 minute time periods)

I'm interested in quantifying the impact of short term price volatility on a particular strategy I'm running. So far I'm simply calculating the standard deviation of log returns, but I'm a bit unsure ...
-1 votes
1 answer
398 views

Is it possible to calculate logarithmic return for short position? [closed]

In the book "Python for Algorithmic Trading" by Yves Hilpisch, it calculates the logarithmic return by summing up all the log values. When calculates the profit for long position: log(...
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1 answer
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Annualization of discrete returns

There is a well known approach to annualize volatility of log-returns for a given frequency. Let $P(t)$ a price process and define a log return $r_l(t)$ as $$r_l(t) = \ln \left( \frac{P(t)}{P(t-1)} \...
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1 answer
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Combining discontinuous opposing returns into a single continuous function

See the function here. It's my intent to measure the expected log return of the optimal trade with regards to long/short positions in a trading range. The trading range has an equilibrium where the ...
2 votes
0 answers
98 views

How do I calculate the sharpe ratio of a portfolio of stocks?

If I have daily prices for $N$ stocks, how do I calculate the Sharpe ratio for an equal volatility weight portfolio? On each day, I have calculated log returns as: $$ r_{t}^{s} = \ln{price_{t}\over{...
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1 answer
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Non-fixed stationary "conversion"

Dear users of StackExchange, I was wondering why the log returns of a fixed period of time is such a common use in "transforming" a time series into a more stationary one? I thought that ...
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0 answers
147 views

Do I use % return, log return or diff of prices to plot ACF?

I am reading a book on time series. To make a non-stationary series stationary, sometimes we need to difference the series. When it comes to finance, prices are non-stationary. Many authors fit ARMA ...
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weekly returns and the daily returns scaled to weekly

I am new in this blog and first of all I want to apologise for my english. I have to calculate, for a university project, the weekly returns and daily scaled returns to weekly for few stocks For ...
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Log excess returns calculation

I need to calculate log excess returns. I'm given market level monthly total return index, price index and a risk-free rate (from Fama/French 3/5/etc. factors). I'm not sure whether I'm calculating ...
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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 ...
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Converting Euro returns into USD terms

I have a series of log returns calculated on an index that is priced in Euro terms, and I'd like to convert those returns into USD terms. Would it be mathematically correct to calculate log returns on ...
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1 vote
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finding optimal weight using Kelly criterion

Question: Suppose you have two strategies. Strategy 1 gains 8% with probability p, and loses 5% with probability 1-p, where p = 0.53. Strategy 2 gains 8% with probability q, and loses 5% with ...
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1 answer
171 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 ...
1 vote
2 answers
137 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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2 votes
1 answer
250 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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1 answer
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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 ...
0 votes
2 answers
299 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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1 vote
1 answer
271 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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1 answer
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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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3 votes
2 answers
793 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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1 vote
2 answers
368 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 ...
2 votes
1 answer
2k 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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1 vote
2 answers
861 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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2 votes
0 answers
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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 ...
1 vote
0 answers
32 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 (...
1 vote
1 answer
70 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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117 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. ...
1 vote
0 answers
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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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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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2 votes
1 answer
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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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3 votes
2 answers
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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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1 vote
0 answers
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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 ...
8 votes
2 answers
6k 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 ...
0 votes
0 answers
72 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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4 votes
1 answer
6k 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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1 vote
1 answer
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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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1 vote
3 answers
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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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2 answers
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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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