# Tag Info

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You can forecast stock prices thru time-series models, cross-sectional, or panel models. There is considerable variation within these categories. In time-series models you would use an auto-regressive model such as an AR(1) where the independent variable is the dependent variable lagged by one period. Naturally, an AR(2) would consist of 2 lags and so on. ...

8

Two ways: Model the returns using an Ornstein-Uhlenbeck process You can control the variance of the residual noise in the process to your desired level of correlation. Conceptually you inject gaussian noise into the synthetic OU process to satisfy your requirement. For example, let's say you have time-series A which is what you are modelling. Time-series ...

7

A factor model has the form $$r_{j,t}=\sum_n \beta_{j,n} f_{n,t}+\epsilon_{j,t}$$ Where $r_{j,t}$ is the return of stock $j$ at time $t$, $\beta_{j,n}$ is the sensitivity (factor loading) of stock $j$ to factor $n$, $f_{n,t}$ is the return of factor $n$ at time $t$, and $\epsilon_{j,t}$ is the idiosyncratic non-factor return. One factor can be the constant. ...

6

If you want to learn more about price pressure, you should look after market impact of metaorders, which is a more adequate term. Because of the microstructure (i.e. the mix of orderbboks dynamics, trading rules, participants behaviours and habits, etc), the more you buy or sell, the more you influence the price an unfavorable way (for your trades). Just ...

6

Risk-free rate is that you get for letting someone else use your money in a riskless manner. Suppose we live in a world where there is no risk whatsoever. In particular, if you lend someone \$100 there is 100% certainty that he will pay you back in a year. Before the pay date, he can do whatever he wants with your$100, while you have no access to it. Even ...

5

I would reckon this to be a very hard exercise. Unless you know the inner workings of such algorithm and how the news was exactly interpreted you have no idea about what went "wrong" and on which side such opportunities reside. One thing I know for sure is that most all algos that capitalize on news capture primarily the numeric part of the news event. I ...

5

This the "Joint Hypothesis Problem". Basically, any test for abnormal returns is also implicitly a test of the model you use to define "abnormal". If you see a significant and positive $\alpha$, that could either mean that you actually are generating excess risk-adjusted returns, or it could mean that your risk model is incomplete. This is basically what ...

5

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 ... 5 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 ... 4 I mainly speak as market practitioner when I say that I believe in the end all models that are applied to data and real life pricing issues are discretized. Think about it, even the BS hedge argument is in the end just a "theoretical continuous time overlay" of actual discrete time steps and re-hedges. Thus some of the limiting assumptions re BS. You do not ... 4 Wilmott Forums - "How can I simulate correlated random numbers?" Generating correlated normal variates Random Correlated Series Generator (using R) All found with a Google search for "how to generate random correlated series". 4 Your equations are for cum-dividend prices, i.e. the price plus dividend today. The paper refers to ex-dividend prices. The correct two equations for investor group$a=1are \begin{align} p^1(0) =&\ \frac{3}{4} \left(\frac{1}{2}p^1(0) + \frac{1}{2}(1+p^1(1))\right) \\ p^1(1) =&\ \frac{3}{4} \left(\frac{2}{3}p^1(0) + \frac{1}{3}(1+p^1(1))\right) ... 4 Beware, oversimplification ahead! (This means that the following is technically not correct, in fact it is false! But: It gives an intuition what is going on!) If you toss a coin and calculate heads as-1$and tails as$1$you get a mean of$0$with a variance of$1$. When you add up multiple coin tosses, i.e. create a random process$dz(t)$, the mean ... 3 Portfolio returns are analyzed to account for risk factors only to determine what the risk factor contributed to the returns, was it the underlying assets or the skill of the portfolio manager. Fama French model explains the returns in terms of principal component such SMB and HML besides the market related returns from CAPM. These links have more detais ... 3 There are a few reasons to use factor models. Most importantly, stocks tend to move together. Stated alternately, the first principal component of the securities in a domestic market tends to explain a large share of the variance. If you're concerned with multiple securities (as in portfolio optimization), then you have to account for this or you will ... 3 What a great question -- it touches on many issues at the core of quantitative finance. This answer might be a lot more than you bargained for, but it's too interesting to pass up. References Mostly, this subject falls somewhere at the intersection of these three highly-interrelated topics: risk-neutral valuation, rational pricing and the fundamental ... 3 In my experience HFT has to balance the reward of any strategy with risk. In the case of a news-based trading strategy, the risk can be enormous, which means the algo will need a very high expected profit in order to trade the news. After important news events, volatility skyrockets and persists for some time (sometimes even days). If the market were able ... 3 You could create a rescaled stochastic indicator from your randomly generated, correlated series. 1) use whatever software/methodology you want to create your random series with 0.85 correlation to the original data. 2) find the maximum and minimum values of this new series and rescale the series to range between 0 and 1 using this formula; (series_value - ... 3 Let's consider a random process$X$. If$X$is an adapted process, then we know, without any uncertainty, what its value is at the present time. This idea is formalized with measure theory. For$X$to be a martingale, it needs to have the following property: at any given time, our best estimate of the value at some point in the future (i.e. forecast), is ... 3 The risk free rate is important and the reason for the inclusion and consideration of the risk free rate is that investors do not get compensated for not taking on risk. Now, we can argue whether the risk free rate truly provides risk free returns (we all should know that it does not, but ...) but it is important in the context of pricing risky assets that ... 3 Fitting Fama-French or Carhart is as simple as learning how to perform Bayesian regression. Pretty much every introductory book Bayesian estimation will cover this. There are analytic formulae under certain assumptions, but I would definitely try to learn the basics of MCMC and Gibbs sampling before trying this out in practice. Here are two papers. The book ... 3 Non overlapping periods would make for a far smaller sample 2 I have seen a technique which uses frequency domain and does pretty much what (I think) you are trying to do. The author does not give the complete details, so you might have to contact him for that, or take a look at the (free) software he has developed. Link here: ... 2 I think the market participants behavior on the micro-level is not different in principle from the behavior on the macro-level. The challenges of better news interpretation, and faster response time are very similar on all levels. There may be a little bit more trading opportunities in HFT, but building HFT strategy and infrastructure is very expensive, ... 2 If you can observe prices at a very high frequency, then "news" is defined as a lot more things than if you are observing prices at a lower frequency. So what you are calling corrections are also news for the high frequency guy because he can observe prices that fast, so do not consider these as corrections to the original news, consider this to be a ... 2 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, ... 2 I can understand your concerns, but I think you are expecting too much from these theories. We cannot explain aggregate behavior from first principle based on a sound theory of individual decisions under uncertainty and I personally doubt that there will ever be such a Grand Unification in economics. Consumption-based asset pricing models are more related ... 2 Another important reason for using risk-adjusted returns is to disentangle "skill" from "risk-taking". Think of a equation for a fund's performance like:$r_{i,t}-r_f=\alpha_i+\epsilon_{i,t}$where$\alpha_i$gives you the average excess return of fund$i\$. Alpha is often interpreted as measure of a managers' skill in timing the market and selecting ...

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A random process that is adapted to a filtration is measurable (ie X_t is F_t-measurable) but not necessarily a martingale. X_t is a martingale if E(X_t | F_s) = X_s for s < t.

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Pretty good explanation is in Schweser CFA Study Notes for CFA level III. Books 3 and 5, at least from 2009, if I remember right. See also Tsay R.S. Analysis of Financial Time Series (Wiley Series in Probability and Statistics). // 2010. - good example with implementation in R.

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