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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41
votes
6answers
10k views

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 ...
41
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3answers
29k views

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 ...
37
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2answers
10k views

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 ...
18
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2answers
19k views

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 ...
17
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1answer
1k views

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 ...
17
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2answers
411 views

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
votes
1answer
10k views

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 ...
15
votes
5answers
11k views

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 ...
14
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4answers
10k views

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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1answer
2k views

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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1answer
410 views

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 ...
10
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4answers
4k views

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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1answer
3k views

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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1answer
2k views

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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4answers
1k views

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 ...
9
votes
3answers
1k views

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
votes
3answers
8k views

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. ...
9
votes
3answers
372 views

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
votes
1answer
555 views

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
votes
1answer
7k views

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+...
8
votes
2answers
4k views

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
votes
3answers
2k views

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
votes
2answers
615 views

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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1answer
791 views

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
votes
2answers
676 views

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
votes
3answers
4k views

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
votes
1answer
904 views

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
votes
1answer
435 views

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 ...
7
votes
3answers
5k views

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
votes
1answer
412 views

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
votes
1answer
2k views

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 ...
7
votes
3answers
302 views

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 ...
7
votes
1answer
892 views

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)+\...
6
votes
1answer
6k views

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 ...
6
votes
3answers
1k views

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
votes
1answer
6k views

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
votes
3answers
892 views

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 ...
5
votes
3answers
921 views

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 ...
5
votes
2answers
5k views

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}) - ...
5
votes
2answers
207 views

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-...
5
votes
1answer
794 views

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
votes
4answers
1k views

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
votes
1answer
148 views

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
votes
2answers
287 views

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 ...
5
votes
1answer
3k views

What is a persistent variable?

What is a persistent variable in the context of regression analysis? For example, dividend to price ratio (D/P) is considered to be persistent variable when used to model future returns (Stambaugh ...
5
votes
0answers
178 views

Dividend Index Futures

My question is dealing with the proportionality between Dividend Index Futures prices and Index prices. Indeed, we in the past we used to do a simple regression between these variables and use the ...
4
votes
3answers
34k views

How exactly do I calculate and interpret factors in Fama-French model?

Could anyone explain me how to interpret factors and what kind of regressions I should run? I have already calculated the factor returns as well as 6 Fama-French portfolio returns, the only problem ...
4
votes
3answers
246 views

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\...
4
votes
2answers
5k views

Fama French & Solving for Alpha

This is a question about comparing results from the Fama french 3 factor model. I have not physically done this, but let's assume a Fama French 3 factor regression was performed for Coca-Cola (KO) ...
4
votes
1answer
420 views

Why use square root of companies market cap in the WLS matrix

When doing a regression based performance attribution I see that people normally use WLS. So that both our independent and dependent variables are multiplied by our WLS matrix, which is a diagonal ...

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