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Questions tagged [statistical-finance]

Statistical finance, which is also called 'econophysics' is the application of statistical tools to the study of financial markets data.

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10answers
8k views

Usage of Random forests in Quantitative analysis of stocks

I have a question about Random forests and how they could be utilized in trading? I heard Random forests are used for classification, is that accurate? If so, could someone give an example of what ...
15
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2answers
368 views

How reliable is Benford's Law in forecasting crises?

I was recently reading an article about how financial accounting has increasingly deviated from the ratios expected by Benford's Law. (Benford's Law and Decreasing Reliability). The author discusses ...
12
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1answer
888 views

statistical arbitrage vs factor trading

I've recently read Avellaneda & Lee which seems to be widely recommended as an introduction to Statistical Arbitrage methods in trading. For those who aren't familiar with the paper, the method in ...
9
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2answers
1k views

What is the total correlation between assets in a portfolio?

Suppose I have portfolio with 10 assets, each one of them with a weight of 10% from the total portfolio (equally weighted). It's well known how to measure from historical prices->returns a variance-...
8
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2answers
3k views

What are the econometric assumptions in the Fama-Macbeth procedure (1973)?

Fama-Macbeth (1973) introduce a two stage cross-sectional regression method (http://en.wikipedia.org/wiki/Fama%E2%80%93MacBeth_regression). 1) If I was to regress stock prices (or returns) on a ...
8
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5answers
391 views

Can classical economics explain *any* of the so-called stylized facts of finance?

I am doing some reading on the (historical) emergence of the Black-Scholes implied volatility smile for index options (yes - post 87), and I stumbled across an economic paper attempting to explain the ...
6
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0answers
203 views

Applications of distance correlation

This question mentions distance correlation. Where has this concept been applied to financial data and provided new insight? Do you know any examples or references?
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1answer
420 views

Does Chan use the wrong state transition model in his Kalman filter code?

In his book, Algorithmic Trading: Winning Strategies and Their Rationale, Ernie Chan shows how to use a Kalman filter to improve the returns of a cointegrated portfolio. Recall that the state equation ...
4
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3answers
592 views

Measuring historical earnings surprises, their frequency and severity

This is my first post to Quantitative Finance, so I hope my question is formatted the right way. I am starting to research the effects of earnings surprises on certain equity indices. Is there a ...
4
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0answers
186 views

Is it more accurate to analyze returns on a calendar day basis than a trading day basis?

I'm rather new to the actual practice of this kind of analysis, but it just seems wrong to me to throw Mondays' returns in with the rest without accounting for the passage of time on the weekend when ...
3
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2answers
678 views

Basic question on Portfolio Theory

I was revising my stuff about portfolio theory and I noticed that every single time, expected return and corresponding variance or covariance are given! (not calculating ourselves). So I'm just ...
3
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2answers
177 views

Value at Risk - What if an account has never suffered from a negative return

I want to implement an algorithm that calculates an account's 95% value at risk on a monthly return base. The case I want to describe in this question is rather academic and will probably never happen ...
3
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2answers
415 views

What are the assumptions in the first-stage of Fama-MacBeth (1973)?

According to the CAPM, the expected return of asset $i$ is: $E(Z_i) = \beta_{im} E(Z_m)$ where $Z_m$ is the excess return on the market portfolio, and $Z_i$ is the excess return of asset $i$ over ...
3
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1answer
212 views

Compare events effect on stock prices from different time periods

I’m going to test for the effect corporate credit rating announcements have on stock prices through different economic climates (good times vs. bad times). I want to research whether or not the stock ...
3
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0answers
84 views

Which areas of statistical physics do not get enough attention in quantitative finance?

It seems that over the past few decades many ideas from statistical physics have been successfully incorporated into economics and finance to form the sub-discipline of econophysics. However, it is ...
3
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0answers
91 views

Negative constant in GARCHX model

I am fitting the following ARX(1,1)-GARCHX(1,1,1): \begin{align*} y_t&=c+a_1y_{t-1}+\gamma_1x_t+\varepsilon_t\\ h_t&=\delta+\omega_1h_{t-1}+\theta_1\varepsilon_{t-1}^2+\pi_1x_{1,t} \end{align*...
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0answers
75 views

Test for difference in security returns before and after financial regulation

I'm going to study the effect of corporate credit rating changes (Moody's) on stock prices before and after a specific financial regulation. So far i have used an event study where i have divided the ...
2
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2answers
822 views

What are the advantages of financial modelling in R? [closed]

Recently I've found out that quantitative department in my company uses mostly R software for modeling in general. What is the advantage of modeling financial data in R instead of Excel, or some ...
2
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4answers
11k views

Are PX_BID and PX_ASK on Bloomberg closing bid/ask? or are they daily averaged?

Bloomberg provides PX_BID and PX_ASK on a daily basis, but it's not clear exactly where these numbers come from. Are they closing bid and ask prices, or are they averaged over the entire day? For ...
2
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3answers
117 views

Does longer time horizon necessarily imply reduced risk?

Is there a mathematical/statistical basis for the commonly-held belief that the longer certain assets (particularly equities) are held, the less risk the investor is exposed to? Alternatively, is ...
2
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2answers
182 views

Applying my Machine Learning class (possibly to small markets) [closed]

I've finished a university course in statistical machine learning that covered topics such as regression, classification, neural networks, SVM, PCA etc. The class was quite tough and rigorous (we had ...
2
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1answer
196 views

CAPM Calculations

Im trying to calculate Alpha using CAPM & I have data on everything necessary. $$R_t-R_f={\alpha}+{\beta}\times(R_m-R_f)$$ i.e. $${\alpha}=R_t-R_t-{\beta}\times(R_m-R_f)$$ In more detail, I ...
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2answers
605 views

Variable Drift Ornstein–Uhlenbeck Process

The Ornstein–Uhlenbeck process is defined as the stochastic process that solves the following SDE: $dx_t = \theta (\mu-x_t)\,dt + \sigma\, dW_t$ where $\theta>0$, $\mu$ and $\sigma>0$ are ...
2
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2answers
124 views

Utility functions, are they used in the real world by hedge funds, banks, etc?

I am starting to study mathematical finance. When I studied microeconomics and macroeconomics I studied utility functions, but I never saw how they are in the real world. I do not see how they can be ...
2
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1answer
153 views

Where can I find ideas for strategies? [closed]

Every book I read refers me to many other books, there is practically no way I can read all this text in my life time. Once and for all, where is the best place to fish for ideas?
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3answers
2k views

Detrending price data for analysis of signal returns

I'm looking to conduct hypothesis tests on some of my trading signals to see if the signal returns are statistically significant enough to falsify my null hypothesis that the signal has no predictive ...
2
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1answer
68 views

Showing the Gaussian shift theorem for bivariate case

I was reading about the Gaussian shift theorem in "An Introduction to Exotic Option Pricing" by Peter Buchen and came across a question that I can't seem to figure. In the book, he uses F(Z) (a ...
2
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1answer
138 views

How to construct a cointegrating vector using more than 2 price series in R?

I use now this code from hier Why does the following data fail my cointegration test? with slightly modification of possibility to load something directly from Dropbox file storage . ...
2
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1answer
755 views

Running a simple alpha estimation test for statistical significance of a signal

I'm looking for some direction on testing whether a simple entry signal has statistical significance. Let's say this is my simple entry signal: Buy when some indicator has a positive slope and is ...
2
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0answers
155 views

Frequency Arbitrage

We know that the volatility is lower when the sampling period is longer, for example $\sigma_{7days} < \sigma_{1day}$, Then I came across this strategy that I cannot quite understand how to exploit ...
2
votes
1answer
22 views

why do we use greater than or equal to for submartingale?

I've just learned about martingale, but i could not find any reason that we use greater than or equal to sign when we define submartingale. In stead of using greater than or equal to symbol, can't we ...
2
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1answer
133 views

Regarding “Two Singular Diffusion Problems” by William Feller

I'm currently reading the research paper, Two Singular Diffusion Problems, by William Feller (1950). However, I don't understand how Feller derived the solution $(3.5)$ given equation $(3.4)$ in his ...
2
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0answers
85 views

I want to optimize an equity portfolio for the four central moments can anyone help me with the problem formulation

Basically i am confused as to which formula to use for portfolio skew and kurtosis and how to use the same in the optimization problem. I would also like to know the options available regarding the ...
1
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3answers
1k views

How to convert weekly data to monthly in r (or in Julia)

I have weekly series on financial risk index data as follows: DATE NFCIRISK 1/8/1971 0.58 1/15/1971 0.61 ......through 10/6/2017 -0.88 10/13/2017 -0.89 10/20/2017 -0.89 ...
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1answer
55 views

Ljung_Box Statistic of R and R^2 values in Return analysis

I have found a result that I find truly puzzling. Here is an extract from a GARCH-Analysis I have performed: Test______________Statistic_______p-Value Ljung-Box Test_____R Q(10)_____0....
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1answer
86 views

How can I compare two mutual funds' performance with a sparse set of data?

I want to compare the performance of two mutual funds. The only data I have is annual returns for the past 7 years. So I have 7 observations for Fund 1 and 7 observations for Fund 2. In addition, I ...
1
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1answer
49 views

Testing the accuracy of a created Index

So long story short, I created a Oil/Energy Index from a basket of 5 stocks in the asset class. I am looking to use mean-reversion, in order to help rebalance the allocation of funds between ...
1
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1answer
54 views

which method is the roubust method to estimate the Hurst parameter?

I know there exist lots of method to estimate the Hurst parameter, such as R/S, V/S, GHE, DFA, DMA, Wavelet Spectral Density, Whittle and so on. Can you tell me which one is the best one. Is anyone ...
1
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1answer
52 views

Thorp's var caclulation

I have been working through Thorp's paper, and with some guidance have got as far as page 20, but I am now stuck with Thorp's result in Ex 6.2 (on that page) where I cannot get the result for $Cor(X_1,...
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1answer
187 views

Likelihood Ratio Method - Delta

I was checking Glasserman(2004) - Monte Carlo for Financial Engineering and got to the likelihood ratio method. I am also looking in my textbook (M. Cerrato: The Mathematics of derivatives securities ...
1
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1answer
128 views

Simple simulation model of bond plus cash returns

Is there a robust way to model 'bond plus cash' simulated returns, say in Excel, for an asset allocation problem between stocks vs bond plus cash? For equity, ...
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1answer
199 views

Financial Mathematics essay topic

I have a mathematics background and I am currently doing a Masters in Financial Mathematics. I am required to write an essay in a financial mathematics area but I have little knowledge about it since ...
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2answers
384 views

Feature Selection Effect on Deep Multi-Layer-Perceptron for Financial Applications

I am trying to build a machine learning system for financial price prediction. I am using a 3 layer MLP (a deep network) with 3 outputs (buy,hold,sell). I am using different features such as price ...
1
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1answer
410 views

Why are indifference equations in mean-variance portfolio theory convex shaped

As the title suggests why is the indifference equations in mean variance portfolio theory convex shaped? Indifference Equation: https://en.wikipedia.org/wiki/Indifference_curve A graph:
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0answers
22 views

Pricing methods in the real world when there is more than one free arbitrage price

Perhaps this question sounds trivial and obvious, but I am starting to study this new field. When we are in a complete market without arbitrage opportunities there is only one risk-neutral martingale ...
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0answers
68 views

Dubious math in Thorp's magnum opus

I started reading Thorp's "Beat the Market" book and stumbled on a formula I can't figure out: https://imgur.com/a/xqfViKt What's the point in adding time to price and the whole probabilites ...
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0answers
73 views

Which stats are the best predictors of model sucess in real time? [closed]

What are the best predictors of real time model success in quantitative trading, i.e. # of transactions, length of backtest, StdDev, Skewness, Excess Kurtosis etc and what are the numerical values of ...
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1answer
91 views

Asset class dynamics differences

If we compare daily return dynamics of the main asset class time series (e.g. Stock indexes, bonds, precious commodities, etc) do we observe quantifiable differences? Are there some reference paper on ...
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1answer
84 views

Longterm memory in interest rate data - R/S analysis

Am currently investigating long term memory in interest rate data. The two sources I am using are Peters (1996), "Fractal Market Analysis" and an article published in the Journal of Fixed Income, "...
1
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0answers
61 views

Moving average variance [closed]

I have generated a random series of returns drawn from a normal distribution and generated a random price series by compounding these returns (X) so $P_i = P_1(1+X)^i$. I want to show the analytic ...