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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 ...
Georgi B's user avatar
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1 answer
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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 ...
Anonymous's user avatar
2 votes
1 answer
92 views

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 ...
Shawn Hsueh's user avatar
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0 answers
62 views

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 ...
Arjun P.'s user avatar
2 votes
1 answer
423 views

Factor loadings in Nelson-Siegel model

The Nelson-Siegel model has the following form $y(\tau)={}_{1}X+{}_{2}X\frac{1-e^{-\lambda{\tau}}}{{\lambda{\tau}}}+{}_{3}X\left ( \frac{1-e^{-\lambda{\tau}}}{{\lambda{\tau}}}-e^{-\lambda{\tau}} \...
Martin N.'s user avatar
3 votes
0 answers
81 views

Aggregation of (cross-sectional) Factor model

Suppose I have a large factor model for security returns, i.e. I have a vector $\mathbf{Y}(t) \in \mathbb{R}^{P}$, with factor loadings $\mathbf{\beta} \in \mathbb{R}^{P \times K}$ over a set of $K$ ...
bfg's user avatar
  • 31
0 votes
2 answers
433 views

Question on effective days of an exponentially weighted moving average model

I have been reading the book "RiskMetrics —Technical Document" by Longerstaey (J.P.Morgan) and Spencer (Reuters) (4th Edition, 1996). I am wondering what the effective days of the ...
user avatar
4 votes
0 answers
158 views

Fama French Model; 5 Factors yield higher alpha than 3 Factors [closed]

I am currently running some Fama French regressions for a number of specified portfolios, consisting of US stocks (for a university level course). The regressions are conducted in R, using the lm ...
14896236842145's user avatar
0 votes
1 answer
933 views

Marginal Risk Contribution under Factor structure

Given the factor structure below with K factors, the return for N assets is given by (under matrix notation): $R =\alpha + \beta F + \epsilon$ where $F$ is matrix of K factor returns and $\beta$ is ...
frederico's user avatar
1 vote
0 answers
46 views

Should I include factor loadings as explanatory variables for regression of abnormal and raw returns?

My research is to explain stock returns in a regression model. My dependent variable is raw returns and abnormal returns calculated from 3-factor model (Fama and French). Besides regressing against my ...
Grisha's user avatar
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1 answer
280 views

factor evaluating methodology with factor return and factor exposure

studying with a factor model, I get confused more and more as I think about factor exposure and factor return The concept (or mechanism) I get used to is evaluating a factor's Long Short Return(Q1-Q5) ...
geonhwa's user avatar
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Index Tracking Problem

I have set up a mean variance optimization problem, $$min:{W}^{\prime}{\Sigma_{\varepsilon}{W}}$$ $$s.t:{W}^{\prime}{\alpha}=R_B\;,\;\;W^{\prime}l={1},\;\;W'\beta=0,\;\;W'Z=\beta_p$$ where, $W$ is an (...
Market Maker's user avatar
1 vote
0 answers
124 views

factor hedging erodes portfolio alpha

I am hedging a long-short equity portfolio for statistical factors, and finding an improvement in sharpe but not surprisingly an erosion of portfolio alpha (ex ante and ex post). No one factor is ...
Henry's user avatar
  • 111
2 votes
1 answer
74 views

structural model - exposure estimation

The following example is from the book Active Portfolio Management by Grinold and Kahn. Suppose we have the factor returns and want to estimate the exposures/factor loadings. Say the factor returns ...
Xiaohuolong's user avatar
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400 views

How to implement a factor model from scratch?

Imagine we have price-volume data set and fundamental data set which gives us all the info we need (e.g,. OHLC, earnings, dividends etc.) for stocks listed in a market for long time period. I.e., you ...
Validus Oculus's user avatar
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Could anyone please help me in understanding how the authors calculated "SMB-hedged with QMJ" at page number 489 of the paper?

Link for the paper: https://www.sciencedirect.com/science/article/pii/S0304405X18301326. "Size matters if you control your junk" by Asness et al. (2018) It's Figure 1.
Biv's user avatar
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1 answer
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PCA on returns gives negative loadings on market short

I have run a PCA on some returns to get a set of factors. All is good except that the first PC seems to be the short of the market, it has a correlation of -0.9 with the S&P500 but all the ...
Simon Nicholls's user avatar
1 vote
1 answer
301 views

PCA and K-means clustering on returns

I am running a PCA on a set of returns and I would like to cluster the results of the output to group stocks that have similar factor exposures. However when I run the PCA on the covariance of the ...
Simon Nicholls's user avatar
1 vote
1 answer
341 views

Factor Model Regression Market Factor Statistically Insignificant After Adding Extra Factors

I am running a simple 4 factor model which includes the factors: Benchmark (Market - FortyConsumerSixtyHealthcare), SMB, HML and MOM. When I simply apply the regression to the portfolio returns and ...
Simon Nicholls's user avatar
2 votes
1 answer
129 views

Low volatility in factor regression

Let's say we are working with the standard Fama-French 3 factor model and we want to add a low volatility factor. Is it alright to add a low volatility risk premium in a model such as the CAPM or FF3. ...
Circus_beta's user avatar
2 votes
1 answer
535 views

Are Fama French Factors market neutral?

I was wondering whether the famous fama-french factors such as e.g. SMB and HML are market neutral? I know that they are long-short factors in the sense that the net investment is essentially zero, ...
John's user avatar
  • 349
4 votes
2 answers
1k views

Comparing Investment Style with Fama French 3 Factor Model

How do you evaluate this? I have tried searching online but there are no matching results. Is it just a simple average of the 3 Betas? And how do we determine the investment style aggressiveness? In ...
SMLJKNN's user avatar
  • 103
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0 answers
110 views

Factor Loading with multiple exposures?

How do I decompose portfolio exposures when assets may have exposure to a few of my risk factors? For instance I have some sector and state specific risk factors. If I have a bond with exposure to ...
Ryan Wilkinson's user avatar
3 votes
1 answer
538 views

Why do Factor Models set up their factors differently from regression?

While this may be awkwardly-titled, I hope that my question becomes clearer upon reading. So this is what I gather about Factor Models: they are statistical models set up to explain the returns, ${...
Coolio2654's user avatar
2 votes
0 answers
102 views

explanation of factor tilts that uses mathematical notation

Can anyone provide a definition of "factor tilt" that uses mathematical notation? Perhaps factor tilts are based on factor regression models. Let's say that our returns vector $\mathbf{y}_t$ can be ...
Taylor's user avatar
  • 544
1 vote
1 answer
219 views

Correct choice of SMB factor for regression models

I am currently conducting a performance analysis, where I use the 3-, 4-, and 5-factor models, hence $R_{it}-R_{Ft}=\alpha+b_{i}RMRF+s_{i}SMB+h_{i}HML$ $R_{it}-R_{Ft}=\alpha+b_{i}RMRF+s_{i}SMB+h_{i}...
Mads 's user avatar
  • 13
3 votes
2 answers
2k views

Portfolio Weights to Maximize Information Ratio (Finding Alphas)

In Finding Alphas, Chapter 1, Introduction to Alpha Design, the authors state: An alpha can be represented as a matrix of securities and positions indexed by time. The value of the matrix ...
quant007's user avatar
1 vote
2 answers
2k views

How do I control for a firm's “factor loadings” based on the Fama French model in a regression model?

I asked this question before, but in the wrong community (sorry): I want to explain stock returns in a regression model. Besides regressing against my main explanatory variables, I want to control ...
Hans Leifson's user avatar
2 votes
0 answers
496 views

kalman filter for a multifactor model in R

I am trying to set up a time varying factor model for the purpose of return decomposition via kalman filter. Following this example and slightly modifying it so as to accommodate for more than one ...
sen_saven's user avatar
  • 441
0 votes
1 answer
5k views

How can I calculate Fama-French Beta, RMW and CMA factor for a particular stock?

I already have a method of calculating Size: the natural logarithm of the market value of equity at the end of the fiscal year. But how to account for the Market Risk Premium, RMW, CMA and MOM ...
user27532's user avatar
3 votes
1 answer
127 views

How to Cross-Validate whether fund returns are due to static factor exposures?

I'm currently dealing with the following problem. I'm using lasso regressions to model hedge fund returns and understand their exposures. The idea being, that if their returns are simply due to ...
Rafael Velásquez's user avatar
2 votes
1 answer
292 views

Help understanding factor modeling, solving for residuals

I am trying to understand and implement a factor model, and I think I might be having some issues. I am trying to solve for the residuals in the equation: $$ R_{i} = \sum_{A=1}^{K}\beta_{iA} f_{A} + ...
npp1993's user avatar
  • 159
2 votes
0 answers
328 views

Fama-French Factors for ETFs and MFs

Is there a public source or a paid service that provides FF3 (or FF4 = "Carhart") factor loadings for US traded ETFs and Mutual Funds? Something that is regularly updated and that provides comparable ...
nbbo2's user avatar
  • 11.4k
6 votes
0 answers
211 views

Interplay of statistical factors (PCA) and market factors (value, momentum, low vol, ...)

Is there any research done on the interplay between statistical factors (as a result of principle component analysis PCA) and the market factors (especially value, size, low vol, momentum, quality)? ...
Richi Wa's user avatar
  • 13.7k
3 votes
0 answers
171 views

Estimating factor returns with linearly dependent loadings

Given an $n\times 1$ vector of asset returns $r$, and a $n\times k$ matrix of factor loadings $X$, we can express the asset returns in terms of as-yet-unknown factors $f$ using $$ r = Xf + \epsilon $$...
Chris Taylor's user avatar
  • 5,931
0 votes
1 answer
271 views

Factor model to Portfolio optimization

By using the Fama and MacBeth methodology, I have identified the significant factors that explain the returns of my stocks. Now, I want to build a portfolio and backtest it. For that, I am trying ...
Vaibhav's user avatar
1 vote
1 answer
2k views

how can I calculate the factor loading (beta)?

I am writing my Thesis about hedge funds performance measurement and I want to use the seven factor model proposed by Fung & Hsieh (2004). Now, I am struggling to find out how to calculate the ...
srm's user avatar
  • 15
7 votes
3 answers
6k 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 ...
early_bird's user avatar
8 votes
1 answer
541 views

Why is Weighted Least Squares necessary in fundamental factor model?

Why is Weighted Least Squares necessary in fundamental factor model while it is not in a standard Macroeconomic factor model? I understand that $\mathbb{E}[\epsilon^2_{it}]=\sigma_i^2$ varies across ...
rbm's user avatar
  • 181
1 vote
0 answers
309 views

Variable Selection with Kalman Filter

I'm trying to estimate factor loadings on portfolios over time for portfolios that are traded pretty frequently. I have a sense that several portfolios are loading on the Fama-French HML factor ...
tragen907's user avatar
  • 151
3 votes
1 answer
271 views

After PCA on original factors, how to tell which original factors are dominant?

When doing the PCA analysis, you end up with eigenvalues which are ordered by how much variance they explained for each eigenvector. Say, the eigenvectors since they are orthogonal, do not represent ...
user12348's user avatar
  • 1,698
1 vote
2 answers
9k views

How can I calculate Fama-French betas for a particular stock?

For a particular stock, what's the simplest way to calculate betas for the Fama-French factors SMB and HML?
Thomas Johnson's user avatar
7 votes
2 answers
2k views

Non-negative matrix factorization for factor analysis of stocks

I stumbled over the term Non-negative matrix factorization in presentations such as Application of Machine Learning to Finance and this Big Data in Asset Management. The basic idea is to decompose a ...
Richi Wa's user avatar
  • 13.7k
1 vote
1 answer
1k views

Calculating Variance Explained from PCA Loadings

I have a return history for a universe of risky assets and I've run a principal component algorithm and obtained a loadings matrix (num_factors by num_assets) for the first 5 factors. I have a ...
rhaskett's user avatar
  • 1,641
4 votes
4 answers
2k views

Robust Returns-Based Style Analysis

Sharpe's Return-Based Style Analysis is an interesting theory but flawed in practice when working with long-short funds or funds that are changing strategies over shorter periods of time due to the ...
rhaskett's user avatar
  • 1,641
1 vote
1 answer
459 views

How to use financial ratios in a factor model?

I am trying to understand how factor loadings in a general factor model are computed. For simplicity sake, lets assume a simple model: $$ R = B \times F + \epsilon $$ $$ R = N \times 1 $$ $$ B = N \...
silencer's user avatar
  • 1,553
2 votes
1 answer
517 views

Combining covariances?

Consider an economy with assets with return processes $A$, $B$, $C$, $D$. Consider a weighted index with return process $I=aA + bB + cC + dD$ where $a,b,c,d$ are coefficients, and $a+b+c+d = 1$. ...
user avatar
38 votes
3 answers
12k 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 ...
Ram Ahluwalia's user avatar
13 votes
4 answers
1k views

What are the risk factors in analysing strategies?

What do you think of strategies displayed on timelyportfolio.blogspot.com? I really like the fact that there is some code to reproduce the strategies, but they seem very elementary because he does ...
nicolas's user avatar
  • 759
8 votes
4 answers
3k views

What does it mean to modify the factor loadings of a credit risk model?

I came across an example where a well-known weakness of a credit risk model was dealt with by augmenting some of the existing risk factors via increased factor loadings. This made the the model more ...
user40's user avatar
  • 2,707