Questions tagged [log-returns]

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4
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1answer
106 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 ...
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66 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 ...
-2
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1answer
156 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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1answer
74 views

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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56 views

Inputs to Min-Var Portfolio

Although I always use daily data, I am wondering if a Min-Var portfolio based on weekly bar data would be more stable (less noise) than using daily bar data as inputs? [I have no interest in the ...
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59 views

How to arrive at excess real log return? (Conflicting answers on the web)

I am finding many conflicting takes on how to arrive at the excess real return. My understanding is we take log nominal return - log inflation to find real log return. Then we take log nominal risk ...
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37 views

What details must be considered when assessing an asset’s inflation beta?

The inflation beta of an asset is described as: $$ r_{i,t}-r_f = \alpha_i + \beta_\pi^i \epsilon_{\pi, t} + u_{i,t} $$ For shorthand, I will use “return” to mean excess return. In academic literature ...
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1answer
31 views

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
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0answers
46 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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37 views

Log Returns or Simple Returns for Portfolio Performance Analysis

Simple question but one thats stumping me slightly. I am doing a study analysing historical portfolio performance related to portfolios constructed with separate factors in mind. I realise simple ...
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50 views

Why is the approximate entropy of (some) stock returns zero?

I downloaded some prices for TSLA and AMZN from yahoo finance to try and see if I could measure the entropy on a rolling basis with the intention being maybe returns have lower entropy (are more ...
0
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1answer
53 views

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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0answers
60 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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0answers
26 views

open-close intraday demeaned log return calculation

open-close return is basically what I feed into the realized kernel volatility and recently I noticed the realized kernel covariance/variance is generating negative value so I had to retrace my ...
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0answers
78 views

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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361 views

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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0answers
111 views

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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43 views

LogNormal VaR Formula Risk Metrics

https://web.mst.edu/~huwen/teaching_VaR_Weiqian_Li.pdf On page 6, the paper above mentions RiskMetrics would use the following VaR formula: ...
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56 views

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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0answers
78 views

Forecasting returns and volatility using ARIMA-GARCH model in R

I am using rugarch package in R to forecast returns and volatility of a stock. I train an ARIMA (p ,d q) + GARCH(s, r) model on ...
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0answers
50 views

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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1answer
93 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
87 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 ...
2
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1answer
213 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 ...
0
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1answer
139 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
168 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/...
1
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1answer
208 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,...
0
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1answer
149 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 ...
3
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2answers
485 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
147 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
772 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
430 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
124 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
28 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
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1answer
46 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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0answers
90 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
238 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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0answers
142 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. ...
2
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1answer
130 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
1k 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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0answers
136 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 ...
3
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2answers
4k 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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0answers
40 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 ...
4
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1answer
3k 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 ...
1
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1answer
93 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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3answers
325 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 ...
0
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2answers
168 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 ...
1
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1answer
65 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
180 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 ...
3
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2answers
270 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})$ $y_t∼logN(log(y_{t-1})+μ_{daily},σ^2_{daily}))$ ...