49 votes
Accepted

How to build a factor model?

1. Determine Factors Economically, the use of factor models can be either motivated using the ICAPM or the APT. Although there are some theoretical differences between the model, for empirical and ...
user avatar
  • 2,320
20 votes
Accepted

Fama-Macbeth second step confusion

Then for each month $t$, you run a cross-section regression: $r_{i,t} = \lambda_0 + \hat{\beta}_i {\lambda}_t + \alpha_{i,t}$ Where: $\hat{\beta}_i \equiv [\beta_{i, MktRf}, \beta_{i, SMB}, \beta_{i,...
user avatar
  • 6,810
17 votes
Accepted

Why and when we should use the log variable?

Based on your paper and variables, I assume you ask about the use in econometric models. There are some rules of thumb for taking logs (do not take them for granted). See for example Wooldrigde: ...
user avatar
  • 4,748
12 votes

Fama-Macbeth second step confusion

The two step Fama-Macbeth regression works as follows: First, run a cross sectional regression in each period. I believe that you want to estimate risk premia for each of the Fama and French factors. ...
user avatar
12 votes

Choosing the right statistical test for Mutual Fund Performance Evaluation

Define excess return $r^x_{it} = r_{it} - r^f_{t}$ as the return $i$ minus the risk free rate, and $f_{jt}$ similarly denotes the excess return of factor $j$ at time $t$. Let's say we have some factor ...
user avatar
  • 6,354
11 votes

Machine Learning vs Regression and/or Why still use the latter?

I was just like you when I started out: I had learned a lot about machine learning (mainly neural networks and genetic algorithms/programming) and used it heavily. I also had learned about classic ...
user avatar
  • 27k
11 votes
Accepted

Calculating alpha and its meaning

Alphas from a time-series regression are error terms in the cross-sectional, linear relationship between expected returns and factor betas. If a factor model were correct those error terms (the alphas)...
user avatar
  • 6,354
10 votes

How to build a factor model?

The following paper (and the references given within) focuses on the practical aspects of implementation of factor-based investing and gives an overarching framework for the more technical answers ...
user avatar
  • 27k
10 votes

Fama Mac-Beth (1973) vs Fixed effect

A more apples to apples comparison would be between (i) Fama-Macbeth procedure and (2) clustering standard-errors by date. Adding fixed-effects is somewhat different. Problem: cross-sectional ...
user avatar
  • 6,354
8 votes
Accepted

CAPM model as a regression

If you really believed the CAPM's prediction that $\alpha=0$, then imposing $\alpha=0$ in your estimation would indeed lead to your 2nd formula. The problems? The CAPM doesn't work so imposing a ...
user avatar
  • 6,354
8 votes

Definitions of Beta

I slightly disagree with Alex’s comment. The CAPM does not read as \begin{align*} r_{i,t} = r_{f,t}+ \beta_{i,t} (r_{m,t}-r_f) + \varepsilon_{i,t}. \end{align*} There is an important difference ...
user avatar
  • 13.9k
7 votes

Ran multivariate linear regression, checked normal probability plot, residuals are not normal. What can I do?

Regression analysis, as a minimization of the sum of squared errors, does not require normality of the error term. The requirements are that errors are homoscedastic and uncorrelated. And these are ...
user avatar
  • 4,227
7 votes
Accepted

Interpreting the coefficients of Fama-MacBeth regression

No, you cannot interpret the average return for the factor as the risk premium. The second stage regression is equivalent to building a set of portfolios that have no net investment, a unit exposure ...
user avatar
  • 1,356
6 votes

How to build a factor model?

Time Series Factor modelling is a very good and practical manual to building time series factor models. FactorAnalytics is a very good R package that allows you to fit timeseries, fundamental and ...
user avatar
  • 603
6 votes
Accepted

Using cross-sectional factor model (BARRA type) returns in a time series factor model (Fama-French type)?

What you're describing sounds like the reverse of a Fama-Macbeth regression. The original Fama-Macbeth approach estimated rolling time series regressions to get CAPM betas and then doing a cross-...
user avatar
  • 5,311
6 votes

Does Kalman filter always improve over linear regression?

There is no a "yes/no answer" to that question. Generally Kalman Filter tends to be better than linear regression, but everything depends on the data which you have, how you calibrate your model. ...
user avatar
6 votes
Accepted

Modelling and forecasting mixed frequency financial data

MIDAS is useful when you have a low frequency series and you want to include high frequency data in the regression. So for instance, if you want to forecast quarterly GDP data and want to include ...
user avatar
  • 5,311
6 votes

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

The clearest hands-on explanation I have seen so far is the following: Bernstein, W.: Rolling Your Own: Three-Factor Analysis Everything is explained very clearly and step-by-step with Excel. ...
user avatar
  • 27k
5 votes

Using Financial Ratios to get credit rating or PD

This is what Moody's does to calculate default probabilities, but I don't believe they give a whole lot of detail on their exact methodology because they sell their models as software. I quickly found ...
user avatar
5 votes
Accepted

Actually benefiting from logistic regression to estimate probability of default

Firstly, the use of the logit models to estimate the PDs is particularly appreciated in some credit industries, as, for instance, the credit retail one. The logit model predicts pretty well the PD on ...
user avatar
  • 2,446
5 votes

Does Kalman filter always improve over linear regression?

There is no magic in the Kalman Filter. The linear regression model usually assumes the coefficients follow a random walk and as such it essentially boils down to an estimation followed by exponential ...
user avatar
  • 199
5 votes
Accepted

What drives the idiosyncratic volatility puzzle?

Preliminary The empirical finding of a strong negative cross-sectional relation between idiosyncratic volatility and future stock returns is highly inconsistent with the predictions of all theoretical ...
user avatar
  • 2,996
5 votes
Accepted

Linear Regression vs Mean Variance Optimization

In a linear regression approach you do the following: $$ (X \beta - y)^2 \rightarrow Min $$ thus you try to predict something. Your objective is quadratic. You usually add constraints on $\sum \...
user avatar
  • 13.3k
5 votes
Accepted

Hansen and Jagannathan distance

It would be easier to answer if you tell us where that equation came from (there are many ways of deriving the HJ distance) - in any case the numerator of your equation should be the expected return ...
user avatar
  • 6,810
5 votes
Accepted

How to do Fama French (1993) cross sectional regressions? A few questions

You say: At this point I don't really get any further, as I am unsure about which "cross section" is being talked about here. Since I have created 25 portfolios, I can only have all in all ...
user avatar
  • 6,810
4 votes

Filtering out AR(1) effects before using stochastic volatility model

Even though it's a straightforward extension, it took me a while (a year? yikes!); but now you can easily incorporate Bayesian ar(1) (or more generally, Bayesian regression) in joint estimation by ...
user avatar
4 votes

CAPM Calculations

The question above looks somewhat confused. Where's the error term? A recipe for a standard calculation It's customary to work with monthly returns. For each portfolio $i$, calculate monthly ...
user avatar
  • 6,354
4 votes

Is my data fittet to be significant?

The question you ask is in fact about what people in machine learning call overfitting: the more you choose your "metaparameters" to provide high returns on your sample of days the less you can trust ...
user avatar
  • 10.6k
4 votes

Calculating fund alpha using Fama-French 3 factor model?

In the long run, you'd probably be better off learning a real programming language like Python, R, or MATLAB. While you can do this in Excel using mmult, ...
user avatar
  • 6,354
4 votes

Why and when we should use the log variable?

I cite from the fantastic book by Bali, Engle, and Murray (2016): Empirical Asset Pricing: The Cross Section of Stock Returns. In what follows, they talk about the pricing of size in the stock market (...
user avatar
  • 13.9k

Only top scored, non community-wiki answers of a minimum length are eligible