# Tag Info

49

Because of: The (extreme) dominance of noise over signal The prevalence of non-repeating patterns (many of which we know are not going to repeat) A pathetic sample size for cross-validation Regime changes due to exogenous events. These are typically in the cross-val window which makes it even worse. (GFC, financial integration, trade law changes, interest ...

48

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 practical work these differences are irrelevant. In the end, both models stipulate that returns and expected returns are linear functions of the factors: $$r_{i,... 20 Then for each month t, you run a cross-section regression: r_{i,t} = \lambda_0 + \hat{\beta}_i {\lambda}_t + \alpha_{i,t} Where: \hat{\beta}_i \equiv [\beta_{i, MktRf}, \beta_{i, SMB}, \beta_{i, HML}]', is a vector of the coefficients estimated on the first step. What you are looking for is to estimate the vector of \hat{\lambda}_t \equiv [\... 15 Based on your paper and variables, I assume you ask about the use in econometric models. There are some rules of thumb for taking logs (do not take them for granted). See for example Wooldrigde: Introductory Econometrics P. 46. When a variable is a positive  amount, the log is often taken (wages, firm sales, market value...) Same for variables such as ... 12 The two step Fama-Macbeth regression works as follows: First, run a cross sectional regression in each period. I believe that you want to estimate risk premia for each of the Fama and French factors. Therefore you run:$$r_{i,t} = \lambda_{t,MKT} \hat{\beta}_{i,MKT}+\lambda_{t,HML} \hat{\beta}_{i,HML}+\lambda_{t,SMB} \hat{\beta}_{i,SMB}+ \alpha_{i,t} \quad ...

11

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) would be zero. Discussion A carefully written version of a standard time-series regression of returns in excess of the risk free rate on market excess ...

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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 model of returns where: $$r^x_{it} = \alpha_i + \sum_j \beta_{i,j} f_{jt} + \epsilon_{it}$$ F-test / GRS Test If we assume the error terms $\epsilon_{it}$ ...

10

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 statistics but not nearly as much as about ML. The problem with ML is - as I see it today - that you are often taking a sledgehammer to crack a nut, meaning: ...

10

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 here: Practical Considerations for Factor-Based Asset Allocation by Kang, X. (Standard & Poor's), Ung, D. (Chartered Alternative Investment Analyst ...

10

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 correlation causes naively computed standard errors to be understated Let $r_{it}$ denote the return of firm $i$ in month $t$. An important statistical issue is that ...

8

It appears that you are re-running the regression with each new data point. Instead, you should use an update/online formula (see an excellent answer by the famous Dr. Huber at stats.se). You can find an implementation in the R package biglm. If it doesn't have all the features you need (no windowing out of old data) you can at least adapt it and use it ...

8

Glad you've asked :) Technically speaking, in factor model $\alpha$ stays for return or risk premia, which asset pays when all factor returns are zero. Then, to answer question in more details, we have to specify, are we dealing in our model with return ($R_i$ for asset $i$) or with risk premia over risk free ($R_i-R_f$). In the first case, ...

8

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 false restriction during estimation is problematic. More generally, taking factor models extremely seriously and imposing $\alpha=0$ in estimation to gain ...

7

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 the fundamental assumptions (together with exogeneity). Then estimators are unbiased, optimal (exhibit the minimum variance within the class of unbiased ...

6

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 statistical factor models. A good reference to factor models would be Chapter 15 of this book.

6

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-sectional regression to estimate the overall sensitivity of returns to beta. If I were to write down what the model looks like, I think you're talking about ...

6

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. I expect that you have used some library for estimating linear regression parameters. Now you need to think how will you "tune" Kalman filter - the constants F,...

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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 daily S&P 500 data as a regressor instead of just using the quarter end value of S&P 500. Usually we assume that the causality runs from S&P 500 to ...

6

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. Concerning your question: The R-squared tells you how much percent are explained by the factors. The intercept is your alpha, the coefficients of the factors tell ...

6

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 to one factor and 0 exposure to all others. These unit exposure portfolios are then used to estimate the risk premia for those factors ($\lambda_t$). In that ...

6

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 between the single index model (aka market model) (SIM) which reads as \begin{align*} r_{i,t} = \alpha_{i,t} + \beta_{i,t}(r_{m,t}-r_{f,t}) + \varepsilon_{i,t} \end{...

5

I was going to comment but it turned out to be quite elaborate. My experience with certain AI/ML methods is that they're not deterministic. Take RBM for instance, a very wide-spread paradigm. To train such a machine you have two approaches, backpropagation or Kullback-Leibler divergence. Both require you to initialise the machine to a random state. And ...

5

Note that you can understand the $\Delta$ as an "operator" acting on $r$. So just act on $r$ twice: $$\Delta^2 r_t = r_t - 2 r_{t-1} + r_{t-2}.$$ In fact if you write the $r$ as a vector, $r = (r_1, r_2, \ldots, r_N)$, then $\Delta$ is an $N\times N$ matrix with elements $\Delta_{i,j} = \delta_{i,j} - \delta_{i-1,j}$. The AR(2) model can be written as ...

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This isn't exactly what I would call advanced but running each regression on a separate core in a parallel foreach loop would help http://cran.r-project.org/web/packages/foreach/foreach.pdf

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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 this which gives a brief overview: http://www.moodysanalytics.com/~/media/Brochures/Enterprise-Risk-Solutions/RiskCalc/RiskCalcPlus-Fact-Sheet.ashx Edit- ...

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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 loans, consumer credit, credit cards, ... and all concerns the retail consumer world. Mainly, those listed are the principal sub-industries in the credit ...

5

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 smoothing of the coefficients.

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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 models and therefore known as the idiosyncratic volatility (IVOL) puzzle. This phenomenon is also persuasive in international stock markets, as shown in Ang et ...

5

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 on the efficient portfolio and the denominator the expected variance/covariance. Let me give you a the same equation using simpler notation (and derive it!). ...

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