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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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Decomposition of interest rate risk [closed]

Hi I needed some clarification on something. I have three variables: V1 which is an indicator of an interest rate risk premia V2 which is an indicator of a credit risk premia V3 which is an ...
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1answer
35 views

Cross Product Ratio Analysis

Can you please advise? I have been recently trying to sort this out for couple of days but cannot get the same numbers as previous authors: The equation is shown in Agarwal and Naik Multi-Period ...
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30 views

How to count [and report] the values of significance at 1% and 5%?

I am slightly confused with this: I have calculated the Chi square for the number of funds and the methods description tells me that if the values I have calculated are greater than 3.84 (6.64) that ...
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30 views

Is there a quantitative definition of a Quiet, Moderate or Accelerate market conditions?

i know the StdDev price technical indicator which is the standard deviation but this one has an absolute value. The market conditions are: Quiet: lower oscillation of price around a constant ...
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32 views

Log likelihood function, GARCH(1,1) with asymmetric term

I am modelling a GARCH(1,1) and a GARCH(1,1) with an asymmetric term. $$h(t)=\omega+\alpha\varepsilon(t-1)^2+\beta\sigma(t-1)^2$$ and $$h(t)=\omega+\alpha u(t-1)^2+\beta\sigma(t-1)^2 + \gamma (u(...
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Rolling sum of conditional variance

I have a model to compute the conditional expectation and variance for a return series, given various factor returns. Initially attempted to trade the deviations of actual return for the day from the ...
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1answer
100 views

How did Dickey and Fuller know something was wrong?

I am interested in testing if there is size distortion through simulations. I have recently been interested in replicating Dickey and Fuller (1979) and this source from another post helped a lot, here ...
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1answer
95 views

Most profitable? High % but low probability or Low % but high probability

I have identified a pattern in different assets where a quick spike/flash crash often occurs, dropping the price between -5% and -15% for a few seconds and then going back to previous average. I am ...
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2answers
85 views

Statistical estimation vs Stochastic calibration of models

I have never been able to deduce the precise differences between model building from the statistical perspective and the stochastic processes/calibration perspective. I can only infer that these are ...
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1answer
219 views

Fama MacBeth cross-sectional Regression

I am deeply confused right now and hope someone can help me out a bit. I want to replicate part of a paper from Fama/French (2008), Dissecting anomalies, specifically, Table IV "Average Slopes and t-...
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1answer
64 views

How to apply derived beta to daily change?

I've taken three months of price return data for two instruments and calculated a $\beta$ between the two using the formula $\beta = \frac{Cov(x,y}{Var(y)}$ with the goal of estimating what the ...
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2answers
133 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 ...
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51 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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88 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 ...
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1answer
77 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 ...
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1answer
474 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 ...
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33 views

Assessing goodness of a Technical Trading Rule using a ROC model

I am testing various technical trading rules (TTR) on the cryptocurrency market. I have already setup some significance tests, to compare the returns and volatilities. I would now like to test it ...
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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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1answer
113 views

For a trading strategy how many trades have to occur for statistical significance [closed]

I created a strategy using a regression on a price series. I tested it with many walk-forward analyses and it has passed. I am currently live trading it with real capital (the ultimate test). My ...
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75 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
92 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
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 ...
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127 views

Price Series vs Returns series for pairs trading

Consider two stocks A and B. Suppose we regress their price series and find a coefficient β. Specifically, Pi = βQi + Ei And we find that the Error is mean reverting. So the strategy ...
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194 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 ...
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2answers
161 views

Central limit theorem and normality assumption of asset return distribution

Can central theorem justify normality assumption of assets return distribution? And if it can why the empirical evidence show this assumption, which many finance models are based on, is a far cry from ...
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1answer
52 views

Brownian motion

Suppose I have the process $X = X(t)$ for $t \ge 0$ given by $X(t) = \sqrt{t}*Z \,\forall t \ge 0$ where $Z$ is normally distributed with $N(0,1)$. Is this a Brownian motion? Solution yields: $$X(...
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3answers
120 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 ...
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2answers
900 views

Implied Volatility of stock on Think or Swim

Think or swim has this thing where they have do a implied volatility of a stock. I have chatted with the TOS people but they aren't terribly helpful. Regardless they did send me two images of what ...
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1answer
86 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, "...
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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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68 views

Is there a mathematical way of showing the slowing down of economic markets?

I'm currently taking a introductory mathematical finance course in university and recently on the news (BBC, etc), it states that the economic markets are shown to be slowing down for the next few ...
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1answer
1k 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 ...
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1answer
115 views

Calculating a VWAP using close prices snapshot

I was wondering, is it possible to calculate a daily VWAP (Volume weighted Average Price) from the close snap shot (close price, high, low open and total volume traded over the day)? If so is there a ...
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1answer
59 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 ...
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34 views

Multi-Variate linear modeling: how to calculate mathematically vs brute force genetic optimization

I have a hand full of daily economic data. I am currently using a brute force approach. Genetic optimization is only used when k is very large. This method is beautiful to me, but isn't valuable ...
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2answers
191 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 ...
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61 views

Methods of de-trending stock market prices

I am interesting in de-trending stock market prices. What are the correct methods of doing this task?
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63 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 ...
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1answer
59 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
53 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
83 views

Kelly Variance - variance of the sum of logs

I am working through Thorpe's Ch 9 on the Kelly criterion. On page 9 Thorpe states: $$Var(ln(1+Y_if)] = p[ln(1+f)]^2 + q[ln(1-f)]^2 - m^2$$ Since $var(X) = E[X^2] - m^2$, $$p[ln(1+f)]^2 + q[ln(...
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47 views

CAPM Beta zero-correlation performance issue

I am working on a research project that requires me to run a CAPM regression on all intra-day stock quotes in NSDAQ, NYSE and all other U.S. exchanges since 1993. The precision of the quote data is ...
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99 views

Kelly's maximum for G(f)

In Thorpe's paper, Thorpe derives the Kelly criterion $$f^* = p - q$$ and plugs this into the equation $$G(f^*) = p \times \log(1+f^*) + q \times \log(1-f^*)$$ to get the following expression $...
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1answer
231 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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1answer
207 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 ...
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2answers
2k 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-...
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2answers
181 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 ...
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1answer
504 views

Which book would you recommend for beginners in Quantitative Finance? [closed]

I have a normal high school level of mathematics including some statistics and find the world of Quantitative Finance both alien and invigorating at the same time so, would like to learn more. What ...
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2answers
544 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 ...