26

The risk-neutral measure $\mathbb{Q}$ is a mathematical construct which stems from the law of one price, also known as the principle of no riskless arbitrage and which you may already have heard of in the following terms: "there is no free lunch in financial markets". This law is at the heart of securities' relative valuation, see this very nice paper by ...


25

It's an interesting question. I particularly agree with the $\mathbb{Q}-\mathbb{P}$ dichotomy mentioned by many. I would add to the other answers that, come to think of it, the Black-Scholes postulated Geometric Brownian Motion could be interpreted as an AR(1) process on the logarithm of the stock price as you discretise the SDE from which it is a solution,...


14

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. ...


14

I think you need to differentiate between Q-quants vs P-quants. The former might not use Econometrics, but P-quants use them a lot.


13

In a very, very general sense, what Renaissance Technologies does well [and others try to do, many do less well] is understand where the "true" signal is (i.e. where prices should be) and what is noise (i.e. over-/under-reactions by others in the market) in the total signal of market prices. Generally, trading profits are made by taking the opposing ...


11

Traditional econometric (time series) models are of little or no value in forecasting market prices for purposes of "making money", i.e, generating excess return over a benchmark in an asset management setting. They have some limited value in strategic and tactical asset allocation. The ineffectiveness of time-series modeling in asset management stems ...


10

A few thoughts. Yes, your return series are autocorrelated (i.e., stocks don't exactly follow a random walk), so you should use Newey-West standard errors. If you do this as a univariate regression $$R_{i,t} = \alpha_i + \beta_i R_{j,t-1} + \epsilon_{i,t}$$ then there's almost certainly an omitted variable inside $\epsilon$ that is moving both $R_i$ and $...


10

Upon close reading, this appears to be 3 (interesting) questions, not one. I'm not sure if the mods have the tools needed to split it up, so I'm just going to write down the three questions as I see them and then deal with them one by one. Note, it is simpler for me to talk about variance instead of volatility. This has no material impact on the answer. ...


9

You may want to consider splitting two important, yet very different concepts: Pricing a derivative security with contingent payoff and forecasting an asset. Pricing a derivative can be achieved through setting up a hedge portfolio and track its evolution and "value" at any point in time before the derivative security pays off. Risk-neutral pricing is a ...


8

I have been learning more about speech recognition motivated by its application to financial forecasting. I have identified a couple connect points. Turns out each of these tools can and are regularly used in financial modeling as well. Use of Markov Models Use of Fourier transforms (sine/cosine decompositions) Use of component analysis


8

Deutsche Bank's Quantitative Strategy (US) team put together the following piece on this topic (note: their research is available for clients, but I found that somebody uploaded the piece to a sketchy web site). In case the link dies, some of the academic papers they site are: Akbras, F., E. Kocatulum, and S. Sorescu, 2008, “Mispricing following public ...


8

There is a deeper issue. Frequentist distributions are not probability distributions because they are designed to be minimax distributions rather than actual distributions. This ignores all of the other problems and this also ignores risk-neutral versus any other measure of risk aversion. An even deeper issue is that these models presume that the ...


7

I just made a Genetic Algorithms calculator you can try at http://www.gregthatcher.com/Stocks/GeneticAlgorithmCalculator.aspx I'm not a "quant expert" like all of you (I'm just a programmer), but here is what I've found. 1.) If you set the constraints up correctly, the results are amazing. e.g. you can get portfolios that have very high return and low risk....


7

A cautionary tale on all these approaches it told by Tim Loughran and Bill MacDonald in the Journal of Finance, 2011 (When Is a Liability Not a Liability? Textual Analysis, Dictionaries, and 10-Ks, here). In their analysis they show that the commonly used Harvard Psychosociological Dictionary is inadequate for sentiment classification in a financial ...


7

I don't think that it is a real applicable trading system but it is more general work concerning the connection between chaos and financial markets. A good starting point is this (relatively recent) article: http://deepeco.ucsd.edu/~george/publications/08_ecology_bankers.pdf You can find his publications here: http://sio.ucsd.edu/Profile/gsugihara#pubs


7

As far as I know the short answer is negative: there isn't a well developed theory of how to forecast cross-sectional realized volatility. From the perspective of statistics/econometrics, most of the recent research is still trying to find its way around estimation of cross-sectional realized volatility, and so far even in these area the progress is slow. ...


7

I think the answer to your question is very dependent on the respective indicators. It can be argued for example that moving averages not only smooth out time series but because they are a shifted version of the original series signals on crossovers make use of the momentum factor. In general you might want to check out the book Evidence Based Technical ...


7

The only "indicators" that I believe add value in academic research are time series smoothing functions. ( I don't call them indicators because they are all lagging thus do not indicate anything into the future). There is clear empirical evidence and a number of academic papers have been published that show that none of the common indicators (common defined ...


7

Having thought about this I think the following reason is also important and wasn't mentioned so far: When you look at the inner working of this whole class of econometric models it all boils down to the following: It is possible (under some reasonable assumptions) to express any $MA(q)$ model as an $AR(\infty)$ model (and vice-versa for expressing $AR(p)$ ...


6

Benoit Mandelbrot, pioneer of fractals theory, has a set of papers on the Multifractal Model of Asset Returns. I believe when most people in finance are saying they use "chaos theory", they are really referring to fractals, and particularly multifractals. I am skeptical as to whether it can be useful to predict stock prices or even to predict volatility, ...


6

Have you considered fitting ARIMA with exogenous regressors model? Linear regression with autocorrelated errors might be appropriate. R can do this with the arima() function via specifying the xreg argument.


6

They are not mutually exclusive. For example, the class you refer to as "econometric" are simply linear regression models that include as factors prior returns or residuals of the return series sometimes with weightings on the observations. You could easily design a neural network with no hidden layers and the same inputs. So each of the econometric models ...


6

Pre-payment rates are difficult to forecast because of path dependency. The historical interest rate path - not just current market conditions and borrower characteristics - matters because borrowers may have exercised their right to call the mortgage bond and re-finance if rates had previously been at lower levels than the current rate. None on the ...


6

My answer is very much in the spirit of Kiwiakos' answer. E.g. in this paper (where I am one of the coauthors) we use VMA (vector moving average) models (in the multivariate case) and AR models in the univariate case to calculate proper scaling of volatility or its contributions if there are (cross-) auto-correlations. This happens in the P world due to ...


6

In their book "Counterparty Credit Risk, Collateral and Funding" D. Brigo, M. Morini and A. Pallavicini start with a dialogue between a Physics PhD graduate and an experienced practitioner of Quantitative Finance. The topic of P vs Q is presented in that dialogue in a manner meant to be understandable to a new comer. I would certainly recommend you to have ...


6

Interest rate futures enable you to build an interest rate projection curve which you can think of as representing the risk neutral expectation of rates in the future, therefore providing you with a "forecast" of rates in the future. Likewise, stock index futures enable you to build a dividend yield and repo cost projection curve which you can think of as ...


5

The Brown et al. paper and its connection with trading is discussed here: http://jochenleidner.posterous.com:80/from-speech-recognition-to-trading (mirror)


5

Speech recognition signal processing is complex and possibly similar to the complexity of financial markets. They are similar as per characterictics the non stationarity, noise types and other aspects such us the existence of a cepstrum etc conceptual frequency and the grammar to construct and articulate concepts is not evenly and randomly distributed; so ...


5

Check out A Blocking and Regularization Approach to High Dimensional Realized Covariance Estimation. Abstract: We introduce a blocking and regularization approach to estimate high-dimensional covariances using high-frequency data. Assets are first grouped according to liquidity. Using the multivariate realized kernel estimator of Barndorff-Nielsen et al....


5

This is indeed one of the most difficult tasks to do (if not next to impossible). I would say the standard reference is the following: Expected Returns: An Investor's Guide to Harvesting Market Rewards by Antti Ilmanen An abridged (but still about 170 pages long), yet more current - and free (!) version in different formats (pdf, mobi for the Kindle and ...


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