Questions tagged [factor-models]

Econometric model that have the purpose to measure the effect of different risk measures on portfolio asset returns.

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How to calculate factor return given a barra model and individual stock returns?

Assuming that we have k factors and n stocks Then Barra provides a k x k factor covariance matrix F, and a k x n factor exposure matrix E. At runtime, we also observed a n x 1 vector r of individual ...
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Why minimum variance portfolio is used to construct factor models

I am reading Tsay's classic "Analysis of Financial Time Series" and I have seen him using minimum variance portfolio Relevant passage on the minimum variance portfolio here (Chapter 9, Page ...
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Clarifying the Fundamental Difference Between Growth and Value Stocks

The more I think about the fundamental difference between growth and value stocks the more confused I am. Both strategies seem to exploit market mispricing: growth investors target underestimated ...
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PCA risk modelling

Been doing loads of reading about PCA, FA and SVD but still fail to understand the fundamentals of how PCA links with factor analysis in the context of risk modelling. Here is where I'm stuck: Given a ...
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Decompose portfolio in factor risk

I am reading the risk chapter of Grinold Active Portfolio Managment. I understand how to calculated specific and factor risk of my portfolio, what I don't understand is how to calculate how much risk ...
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1 vote
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Fama&French models for asset returns applied to European Market

I am trying to use the F&F 3-factor and 5-factor models for the European Market (monthly data frequency). I downloaded the dataset provided by Fama&French and tried to apply the regressions ...
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Interpretation of significant positive Alpha and negative Momentum

I have observed that my portfolios constructed according to positive ESG criteria consistently show negative alphas and positive momentum, while the portfolios with negative ESG criteria show positive ...
1 vote
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Calculating factor attribution to performance from factor exposures?

The process I have followed so far is that I have filtered out the relevant style factors (momentum, growth, value, etc.) for a portfolio using Lasso regression and then done an OLS to calculate the ...
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Regressing on Residuals

I have a time series dataset (Local Gov. bond yields and probable determinants). Due to structural breaks in different exogenous variables in different time points, I have an idea of regressing a set ...
1 vote
137 views

How to create a long-short portfolio on an academic basis

This question may have been asked before, but unfortunately the answers didn't help me very much. It's about how to create long short portfolios. In the papers you often read that they have created ...
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I'm trying to use the methodology proposed in the article "Taming the Factor Zoo: A Test of New Factors" to evaluate whether some new factors can have significant explanatory power on asset ...
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Interpreting Factor Coefficients for an Emerging Markets Fund against the Market and its Benchmark

I ran CAPM, FF3, FF5 and Carhart models for an emerging markets fund against the FF data for emerging markets and against its own benchmark. I am constantly getting negative SMB's which shows relevant ...
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Can factor investing be used for short term trading ? If yes how macroeconomic and style will be different from long term ?
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PCA factors not uncorrelated

I ran into an interesting case recently. I am trying to construct a set of uncorrelated factors for a statistical factor model. I have started with picking a certain amount of assets (indices) which I ...
1 vote
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short-term statistical factor models for equities with different trading hours

I wonder if there are existing theory/literature about estimating a short-term statistical factor models for equities with different trading hours. For example if we are estimating a universe with US ...
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I am wondering about the interpretation of the loading of the SMB factor. Some papers (e.g., here) state that $\beta_{SMB}>0.5$ implies a portfolio is weighted more towards small caps. In other ...
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Multifactor model assignment problem

Consider the following two-factor model for the returns of three stocks:. Assume that the factors and $e_{j}$ have a zero mean, that all the factors have a variance of 0.01 and are uncorrelated, and ...
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How to create custom factors based on an existing factor model?

I'm searching some literatures or books illustrating how to create custom factors based on an existing factor model. For example, given an existing Barra factor risk model, if I want to add some ...
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Analyzing portfolio returns using Fama-French Factors

Here is my problem - I have monthly returns from few portfolios. I also have monthly return from benchmark portfolio. I downloaded F-F 5 factor daily data. Also downloaded Momentum data. Converted ...
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Combination of factors

Let's say I have 10 factors and I want to find a combination (basically sum of exposures) of factors (of any length) from this set which has max sharpe. Is there an easy way to find this out rather ...
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Alphas vs. portfolio rank w.r.t. factors in Fama-French 3-factor model

In the Fama-French 3-factor model, is there a point in looking at the relationship between the estimated alphas for the 25 test portfolios and the size-rank or value-rank of these portfolios? Also, ...
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1 vote
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Multiple factor Hull-While and yield curve deformation

I am currently studying rate models and I understand that the One-Factor model has some incompleteness: The yield-curve can only be shifted. But I don’t understand what parameter controls this shift ( ...
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Why cannot Fama-MacBeth regression identify a zero-mean factor with explanatory power?

Imagine a factor perfectly explain the return of all the stocks in a universe, and the factor has a zig-zag shape around zero (as shown by the image). Since the factor perfectly explain the return of ...
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How to calculate Fama French & Momentum factor returns during Covid recession using their data website?

We know that Covid Recession lasted during the months of March & April 2020. Using Fama French data, how do you calculate returns for factors such as ...
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Should I resolve factor collinearity before hedging?

Goal: I want to run a portfolio, daily or weekly rebalanced, with a target idio vol %. Thus I will be market neutral, sector neutral and maintain some style exposure at 70-80% idio overall. Okay, this ...
1 vote
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Return forecasting for portfolio optimization

I have some questions related to forecasting returns and how it's used to generate the inputs for portfolio optimization. First, I want to understand why factor models such as FF- 3-factor model are ...
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1 vote
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Testing one asset pricing model against another a la Cochrane: a counterexample

I am reading section section 14.6 of John Cochrane's lectures notes for the course Business 35150 Advanced Investments. On p. 239-240, he discusses testing one asset pricing model against another. I ...
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How can we simulate daily return based on multi-factor model?

This is an interesting question for simulation. The question is a bit lengthy but I'm trying my best to make it super clear here. Now I have some multi-factor model, say some US barra risk model from ...
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How to formalize and validate models of fundamental factors involved price changes?

Suppose you have some stock X, and its price can be considered a time series. You believe that real-world number Y, like industry or government statistics, which is also time series, influences stock ...
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1 vote
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How can I show that these assets do not satisfy a 1-factor model?

Suppose these two assets satisfy a 1-factor model: $$R_1= E(R_1) + F + ε_1 \\ R_2= E(R_2) - F + ε_2 \\$$ where:  E(F)=E(ε_1)=E(ε_2)=0 \\ Var(F)=1, Cov(F,ε_1)=Cov(F,ε_2)=Cov(ε_1,ε_2)=0 \\ Var(ε_1)=...
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French and Fama - Alpha vs Residuals (Error)

When running a regression to empirically test models like CAPM or the Fama and French Model, why do we test the statistical significance of the intercept? Do we ignore the residual error? Why not ...
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Shanken's correction for Fama-MacBeth (1973) generalization of the CAPM

Fama & MacBeth (1973) tested the CAPM against an alternative that the dependence between the expected excess return $E(r_{i,t}^∗)$ and the relative systematic risk $\beta_𝑖$ is nonlinear (namely, ...
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Minimizing variance of market neutral portfolio given factor covariance matrix and stock return predictions

If I am given a return prediction and factor exposures for say 50 stocks, as well as the factor covariance matrix, what is the process to determine the weightings of the minimum variance portfolio, ...
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Fama / French 3 Factor Data Not Giving Expected Results

I'm toying around w/ the Fama-French 3 factor data, and I'm having a hard time getting results that approximate what was covered in their paper here: https://www.bauer.uh.edu/rsusmel/phd/Fama-...
119 views

What is the definition of aggregate volatility, and how to compute it?

I am quoting the following sentence from Andrew Ang's paper "The Cross-Section of Volatility and Expected Returns". Can someone explain how aggregate volatility is defined and how to compute ...
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Seeking Research on Comprehensive Approaches to Defining the 'Quality Factor' in Financial Analysis

I have noticed that the definition of the "Quality Factor" in financial research seems to be somewhat fragmented, with many studies focusing primarily on individual financial metrics such as ...
88 views

How to get Fama-French Factors for current month

I have developed a strategy based, among other things, on the Fama-French model. For the backtest I used the factors from Ken French web side. But there are only historical factors calculated until ...
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Normalize positive distributed time series data without window parameters

I have a piece of daily volume and a piece of daily trades data, now I divide them and I get volume/trades as a factor. This factor has positive value and I want it to be normalized to predict the ...
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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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How are the risk premiums (SMB, HML) calculated for the Fama-French factor model

The question is assuming a Fama-French model, how should we calculate the expected return of an asset? To do this according to arbitrage pricing theory requires the risk premiums of the 3 factors, but ...
286 views

Why can I use equilibrium asset pricing models to predict future returns?

This is a general question that applies to the CAPM and any version of the APT (e.g. the Fama & French three factor model). Speaking in terms of the APT: Assuming a simple one-index version of the ...
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How to Maximize Portfolio Sharpe Ratio using Lagrange Multipliers in a Factor Model

I've come across the notes of the 2003 lecture "Advanced Lecture on Mathematical Science and Information Science I: Optimization in Finance" by Reha H. Tutuncu. It describes on page 62 in ...
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Fama-French factor model: why mimicking portfolios?

I am trying to understand the Fama-French factor model, or any kind of CAPM extensions really. What is really puzzling me is the use of mimicking portfolios. Fama and French create mimicking ...
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