Questions tagged [regression]
Techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables.
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Machine Learning vs Regression and/or Why still use the latter?
I come from a different field (Machine learning/AI/data science), but aim to ask a philosophical question with the utmost respect:
Why do quantitative financial analysts (analysts/traders/etc.) prefer ...
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3
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How to build a factor model?
Factor models such as Fama-French or the other ones that are partially summarized here work on the cross-section of asset returns.
How are the factors built, how are sensitivities/coefficients ...
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3
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Which approach to estimating fundamental factor models is better, cross-sectional (unobservable) factors or time-series (observable) factors?
There are many approaches to estimating fundamental factor equity models. I would like to focus on two traditional methods:
The time-series regression approach of Fama and French. Factors are ...
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Fama-Macbeth second step confusion
I am confused on how to run the second step of the Fama Macbeth (1973) two step procedure.
I have monthly stock returns and monthly Fama-French factors, for around 10,000 stocks. This creates an ...
18
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1
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Testing Valuation, Size and Momentum (proprietary factors) from 1988-2013: No evidence of driving cross-sectional returns
I am currently testing whether three proprietary factors - Valuation, Size and Momentum - explain cross-sectional returns. A sample of 3000 securities was tested using Fama-MacBeth two-pass ...
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Regression model when samples are small and not correlated
I received this question during an onsite interview for a quant job and I'm still scratching my head on how to solve this problem. Any help would be appreciated.
Mr Quant thinks that there is a ...
16
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1
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Time Series Regression with Overlapping Data
I am seeing a regression model which is regressing Year-on-Year stock index returns on lagged (12 months) Year-on-Year returns of the same stock index, credit spread (difference between monthly mean ...
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Using linear regression on (lagged) returns of one stock to predict returns of another
Suppose I want to build a linear regression to see if returns of one stock can predict returns of another. For example, let's say I want to see if the VIX return on day X is predictive of the S&P ...
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R: Fast and efficient way of running a multivariate regression across a (really) large panel (First pass of Fama MacBeth)
I am attempting to run a rolling multivariate regression (14 explanatory variables) across a panel of 5000 stocks:
For each of the 5000 stocks, I run 284 regressions (by rolling over my sample period)...
14
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1
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How do I reproduce the cross-sectional regression in "Intraday Patterns in the Cross-section of Stock Returns"?
Recently I was trying to reproduce the results of "Intraday Patterns in the Cross-section of Stock Returns" (published in the Journal of Finance 2010). The authors used cross-sectional regression to ...
12
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Regression in liquidity risk model of Jarrow/Protter
In the paper "Liquidity Risk and Risk Measure Computation" authors describe a linear supply curve model for liquidity risks in presence of market
impact, i.e. impact-affected asset price $S(t,x)$ is ...
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How to perform risk factor calculation?
I am studying Arbitrage Pricing Theory (APT) and I have a question about calculating factor exposures.
Assume:
\begin{equation}
r = \beta_1r_1 + \beta_2r_2 + ... + \beta_kr_k + r_e
\end{equation}
...
10
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What's the meaning of the intercept in asset pricing model?
I would like to understand the role of alpha (intercept) in the regression-based asset pricing model or $n$-factor models; one of the most famous of those one is the Fama-French 3-factor model.
...
10
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1
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What are the steps to perform properly a risk factor analysis on a portfolio?
I have been asked to perform a factor analysis on a given portfolio, assume it's a Swiss portfolio in CHF.
First step, I chose which factors I would like to see in my analysis.
The first factors I ...
10
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1
answer
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Expected return from a multiple linear regression?
How can I compute the predicted return from a linear regression that includes a number of different terms. For instance, suppose my equation is:
$r_{future} = \alpha + \beta_1 r_{history} + \beta_2 ...
10
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4
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Hedge Fund risk management on a daily basis
Since Hedge Funds/Fund of Funds report on a monthly basis usually within 10 days after the month end, monitoring and managing (hedging) potential risks is quite a difficult task. Having done some ...
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Does Kalman filter always improve over linear regression?
If I have a simple linear regression that has statistical signification but I would like to improve the overall prediction results. Will a Kalman filter be always an improvement or as least achieve ...
9
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3
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How to improve the consistency of explained variance statistics in a linear equity model?
I have an intraday equity returns linear model that, overall, shows good values in terms of $R^2$, p-value and other explained variance statistics. Around 70% of the stocks show consistent R-squared (...
9
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1
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Is Least Median Squares (LMS) regression commonly used in Finance?
Least Median Squares is often argued to give more stable results than does OLS. Whereas in OLS one minimises the mean of squared residuals, in LMS, one instead minimises the median of squared ...
8
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1
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Interpreting the coefficients of Fama-MacBeth regression
According to Fama & MacBeth (1973) two-step regression, you start with estimating the beta factors. When applying the Fama-French 3-Factor model, you first run the linear regression
$$r_{i,t}=α_i+...
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1
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How to use factor models for prediction?
I was looking at this thread here, reading about how to run regressions and thereby construct factor models.
Assuming these factor models are properly specified, I am trying to better understand how ...
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Using cross-sectional factor model (BARRA type) returns in a time series factor model (Fama-French type)?
This may be seen as a follow up question for the previous discussion on time-series vs cross-sectional factor models: Which approach to estimating fundamental factor models is better, cross-sectional (...
8
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1
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From $AR(p)$ to SDE
Let the Vasicek model to be
$$\Delta r_{t}=k(\theta - r_{t-1})\Delta t+\sigma\Delta z_{t}$$
Due to the fact that
$$\Delta r_{t}=r_{t}-r_{t-1}$$
if you let $\Delta t=1$, it is easy to see by ...
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Using rolling returns in a multivariate linear regression?
I am trying to use fundamental factors such as PE, BV, & CFO in a multivariate linear regression with the response variable being the rolling 1 month returns. But this approach seems flawed as the ...
8
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2
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Efficiency vs. Robustness - To use a constant or not in single factor time-series regression?
Arbitrage pricing theory states that expected returns for a security are linear combination of exposures to risk factors and the returns on these risk factors. Betas, or the exposures of the security ...
8
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3
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Return Attribution: Possible remedies for multicollinearity
Let's say I have the following regression setup, which I am using for portfolio return attribution:
$R = 1*\beta(1) + A*\beta(2) + B*\beta(3) + C*\beta(4) + \epsilon $
where A is dummy matrix of ...
8
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1
answer
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How to run an asset replication regression?
I am doing extensive research on portfolio replication and was hoping to get some help with some problems I am encountering.
I am running a regression between 2 assets that I believe replicate ...
7
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1
answer
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Fama Mac-Beth (1973) vs Fixed effect
Currently testing if monthly fund characteristics (size, capital flows, age, risk, persistence,...) explain funds abnormal returns.
My data is set as a panel with 1000 equity mutual funds over the ...
7
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2
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Why are regressors squared and not ^1.5 or ^2.2 or ^2.5?
When a researcher in economics or finance wants to apply a linear regression model but suspects a non-linear relationship between one of the regressors and the dependent variable, it is typical to ...
7
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1
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What drives the idiosyncratic volatility puzzle?
I am currently analyzing the idiosyncratic volatility (IVOL) puzzle. (Ang, Hodrick, Xing, & Zhang (2006) found that idiosyncratic volatility (IVOL) and next-month cross-sectional returns are ...
7
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CAPM model as a regression
The CAPM model states that the returns of a stock are-
$r_s=r_f+\beta (r_m-r_f)+\varepsilon_s$
The $\beta$ defined above is then calculated as $\frac{cov(r_s,r_m)}{var(r_m)}$. My question is ...
7
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3
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How to interpret the French-Fama SMB factor?
I regressed ten portfolios on the Fama French factors and get significant loadings on the SMB factor. However, if I look at the actual average market cap of these portfolios, the portfolios with the ...
7
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1
answer
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Filtering out AR(1) effects before using stochastic volatility model
I wonder if I first filter out AR(1) (autoregressive model with lag 1) effects from univariate time series and then fit stochastic volatility model does above procedure introduce any bias at first or ...
7
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1
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How to determine ratios for mean-reverting basket
Suppose I have a basket of 3 securities A, B, and C. I believe that the basket is cointegrated and I want to create a mean-reverting trade. I fit the model:
$\log(A)=\beta_b*\log(B)+\beta_c*\log(C)+\...
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Why and when we should use the log variable?
Normally, I see finance papers use the real ratios but log regarding non-ratio variables. For example, some papers used log(asset) or log(1+firm age) or log GDP, but regarding the ratio, they use the ...
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Calculating alpha and its meaning
According to wikipedia, CAPM model is described by:
$E(R_{i})=R_{f}+\beta _{{i}}(E(R_{m})-R_{f})$
And according to website such as http://investexcel.net/jensens-alpha-excel/,
$\alpha = E(R_{i}) - ...
6
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3
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Modelling and forecasting mixed frequency financial data
I was wondering if someone could provide some guidance to me. I would like to
Combine various financial data of mixed frequencies (some daily,
weekly, some quarterly) to a composite index. I have ...
6
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1
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How to use Newey West covariance corrector?
I have implemented the following model:
daily_vol(t+1) = A*daily_vol(t) + B*weekly_vol(t) + C*monthly_vol(t) + error
where vol means volatility, and A, B, C are ...
6
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3
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Testing the validity of a factor model for stock returns
Consider the following m regression equation system:
$$r^i = X^i \beta^i + \epsilon^i \;\;\; \text{for} \;i=1,2,3,..,n$$
where $r^i$ is a $(T\times 1)$ vector of the T observations of the dependent ...
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Newey-West standard errors in Fama-MacBeth regressions
I noticed that during the recent decade most of papers, which use Fama-MacBeth regressions compute Newey-West standard errors. I tried to find detailed description of this procedure in the books on ...
6
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GMM time-series regression factor model with factors that are not returns
Factor models with factors that are not returns are usually estimated and tested by cross-sectional regressions. However, there is a way to use time-series regression to estimate and test the model. ...
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Definitions of Beta
Definition of Beta
It is generally understood that the beta of an asset $i$ is given by coefficient of the linear regression of the asset returns on market ($m$) returns, i.e.
$$\beta_i = \frac{\rho\...
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1
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What is the textbook answer to dealing with multicollinearity?
I have recently struggled in interviews, for two quantitative trading positions, by producing weak answers to effectively the same (fairly basic) question. I would like to understand, from a quant ...
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2
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How does the number of free dimensions of a model affect its required size of sample?
Adding more variables to a model usually increases its accuracy. However, without adequate analysis it could also lead to curve fitting.
Another question (How much data is needed to validate a short-...
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How to do Fama French (1993) cross sectional regressions? A few questions
I am still relatively new to asset pricing factor models and have a few questions about my current empirical study. I would be very pleased if you could help me.
I have created a new factor which I ...
5
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1
answer
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Hansen and Jagannathan distance
Hansen and Jagannathan distance, or HJ-distance for time-series regression of excess test assets return on excess factor return reads:
$HJ = \sqrt{\alpha'(E[RR']^{-1})\alpha}$
However, I am little ...
5
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2
answers
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Model is economically significant, but has negative $R^2$?
I'm reading a paper by Rama Cont that says (Page 25):
We remark that negative R^2 values do not imply that the forecasts are economically meaningless. To emphasize this point, we will incorporate ...
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Regressor: Nominal return, continuous return or first difference?
Suppose the application is linear models in financial econometrics. If we want to analyze stocks, the standard approach is to take the continuous/log return: $\ln{ \frac{P_t}{P_{t-1}} }$. Suppose, ...
5
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1
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Fama and French 1997 Cost of Equity
Dear Quantitative Finance Members,
I was wondering if you can clarify me the following issue. I am trying to estimate the cost of equity following "Industry costs of equity" (Fama and French, 1997). ...
5
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2
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Regression coefficient and basic trading strategy
This question might be very basic but still I couldn't really find a satisfying answer anywhere.
I want to analyse the effect of a repeated event (data release) on the price of a specific asset (I ...