Questions tagged [statistics]

The study of the collection, organization, analysis, and interpretation of data. Questions may deal with descriptive statistics, probability distributions, random variables, sampling, regression, density estimation, filtering, inference, estimation theory, or computational statistics.

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18 views

How to annualize skewness and kurtosis of a forecasted distribution

I have a (non-normal) distribution of expected cumulative returns 10 quarters in the future, from which I have calculated mean, standard deviation, skewness and kurtosis. I would like to annualize ...
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56 views

Cointegration stationary test yields different results if the pairs are swapped

I've been backtesting on a spread mean reversion strategy on certain stock pairs. I observe the stationarity via scatterplot and plotting a histogram. Then I verify it using Augmented Dickey Fuller ...
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102 views

What are important statistical concepts used as a quant?

I'm interviewing for some quantitative researcher positions at some hedge funds, and I've been told that there will be one interview session focused on stats, and one focused on ML, among others. This ...
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1answer
36 views

Is there a way to formulate a Martingale series that will never explode?

Martingale's betting method can be seen here:https://www.investopedia.com/articles/forex/06/martingale.asp My question is if there is a way to put a non-exploding martingale, [There is one attempt to ...
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70 views

Proof of variance reduction of bagging

In Lecture 4 of the following course: Advances in Financial Machine Learning: 10 Lectures by Marcos Lopez de Prado link in the proof of variance reduction for a ...
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1answer
27 views

Mutual fund performance overtime

I am a little bit stuck with my dissertation thesis, so help will be greatly appreciated. I am trying to analyze the performance of different mutual funds, which I have classified according to ...
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1answer
33 views

Does the default rate follow normal distribution or binomial distribution?

I'm quite confused about the distribution of default rate. I understand the default can be seen as from binomial distribution
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1answer
106 views

How to test signifcance of a sharpe ratio

Let say you have measured a Sharpe Ratio of $S^*$. What is the simplest way (ie no fancy distributions) to do a hypothesis that this is different from $0$? So $H_0: \text{ The sharpe ratio is equal ...
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29 views

Backtesting conditional VaR

I'm writing a thesis about conditional VaR of Standard & Poor's 500 index. I have fitted my log-returns with GARCH(1,1)-proces and then made some conditional VaR-forecast (500 observations) with ...
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2answers
78 views

What's the difference between Statistics and Econometrics? [closed]

I can't really grasp the similarities and differences between Statistics and Econometrics. Is Econometrics includes every Statistical models inside it? or is there areas of Statistics outside of the ...
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52 views

Are intraday volatility estimators useful for close-to-close predictions

I am interested in predicting the PnL of a gamma scalping strategy which trades only once per day. For simplicity, let's say we can always trade at the daily close. So, what I need to predict are the ...
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34 views

Understanding output from Johansen Cointegration test

I have a VECM model that Im using to determine the revenues for a firm, based on factors like Interest rates, S&P 500 and company specific variables, as follows: Stage 1: $$z_t= a+ bX_t+e_t$$ ...
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11 views

A bounded random variable is sub-Gaussian, thus financial returns are not bounded?

Bounded random variables are sub-Gaussian, yet I, intuitively, assume financial returns are bounded random variables; however, they are not sub-Gaussian. Am I wrong to assume financial returns are ...
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1answer
67 views

Determining Value at Risk of a Poisson distribution

If my discrete random variable had a poisson distribution with both moments say equal to 10, how can I find the Value at Risk for a 95 percent confidence interval? I have seen that I need to ...
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72 views

Why doesn't the first principal component maximize the standard deviation of returns

I am trying to apply PCA to portfolio of securities. My understanding is that the first principal component can be used to evaluate weights for portfolio of maximum variance and each next principal ...
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1answer
31 views

What should basic statistical analysis of different price forecasts contain

we have set of historical data of different price forecasts and the real prices. When assessing "which forecasts are best", what parts of the analysis should one never miss out? We are at a very ...
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1answer
61 views

What's the meaning of linearity in classical statistics in Prado's book?

I am reading Prado's new book, Machine Learning for Asset Managers. In the page1 of his book, there is this sentence. To a greater extent than other mathematical disciplines, statistics is a ...
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1answer
23 views

Performance attribution of indices to their sector weights

Is it possible to attribute performance of indices (monthly returns and risk measures - Sharpe ratio, etc.) to their sector weights (if I know them)? Example: I know the monthly performance of ...
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1answer
50 views

Hurst Exponent and fractional differencing

I have a quick question. Currently I study daily OHLCVs of some stocks and find that many of them have the Hurst exponent not being equal to 0.5. I know that if it is less than 0.5 then it is a mean ...
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1answer
58 views

Predicting time series based on another

This is more of a generic question, but I'm sure it has a best answer/methodology which is what I'm trying to reach. I'm trying to figure out a solid line of thought when looking at a time series X ...
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36 views

Optimal Cash Deployment in a Bear Market

Assume: You can't time the market bottom You have a finite amount of cash to buy equities There are P dip/bear periods you're gonna purchase the equity 2 Problems: You deploy too much cash early, ...
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1answer
82 views

Can someone prove (or disprove) this assertion about the normal distribution? [closed]

Let $X$ be distributed as a $Normal (\mu, \sigma^2)$. Then for a fixed $\mu$ it is always the case that: \begin{equation} \frac{90th quantile-10th quantile}{\sigma}=constant \quad \forall \sigma>0 ...
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1answer
52 views

Why combining market share behaviours brings a different conclusion

Please check the following dummy example to explain the paradox. Both areas in the company keep the same market share during the years, but at the end company lost share in the market! Math is 100% ...
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19 views

Sample conditional multivariate random variable?

There's multivariate random variable, future prices of assets, 5 years from now: $$X = [Gold, Silver, SP500]$$ There's historical prices for $X$ available for last 50 years. It's possible to fit ...
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27 views

Unbalanced Panel Data in Excel and Stata

We have unbalanced panel data (columns for date and firm identifier as well as other variables) that is heavily unbalanced involving several thousand firms. We would like to turn it into what ...
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1answer
285 views

Forecasting Volatility using GARCH in Python - Arch Package

Disclaimer: Posted this on stackoverflow, but maybe here should be the right place to ask something about GARCH I'm testing ARCH package to forecast the Variance (Standard Deviation) of two series ...
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1answer
139 views

Two Probability Questions from Quantitative Finance Interview Book

I posted the two questions in math stack exchange one month ago but cannot get an answer, so I post it here and appreciate your advice:) I'm reading an interview book called A Practical Guide to ...
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1answer
85 views

how to I get the statistical significance of a backtested result

If I have a simple long/short value strategy (say long stocks with high e/p and short stocks low e/p or any other parameter) rebalanced monthly, and a look back window of say 15 years. How do I ...
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58 views

Why is SPY daily adjusted close negatively autocorrelated?

I took daily adjusted close prices (all history) from Yahoo Finance and ran the following code: ...
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25 views

Interpretation of $\alpha$ (confidence level) in mean CVaR optimization

How are an investors risk preferences related to $\alpha \in (0,1)$ in a mean CVaR optimization? Would a risk averse investor choose a higher value of $\alpha$, and if so why? My understanding is, ...
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84 views

Fama-Macbeth Regression: Weird Risk Premia

I just conducted a Fama-Macbeth regression where in the first step I calculated a time-series regression for each individual stock to get three betas (for mkt-rf, smb, hml) for each stock. Then I ran ...
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3answers
103 views

How to get know when CUSIP is changed

CUSIP code is not a constant, it could be changed. Does anybody know how to detect a CUSIP change? Is there any report with this info? Where can i find it? Thank you.
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56 views

Old codes for Companies (CUSIP/ISIN/SEDOL)

I found that for example ISIN have following rules: Merger and acquisition: Old ISINs for stock become inactive and are replaced by securities with a new ISIN. Bonds only need new ISINs if old ones ...
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33 views

Asset prices Boom,Bust and Recovery cycles

Is there any systematic way to detect the Boom, bust and Recovery cycles in Asset Prices ? Are there any good references about the Topic ? Thanks in advance.
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1answer
59 views

What does a regression of squared returns of stock on squared index returns and lags show?

We have a squared stock return at t regressed on 3 variables: squared index return, squared stock return at t-1, and squared index return at t-1. My two questions would be: 1. What does this test ...
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2answers
62 views

Cash flows regression on macroeconomic data

I'm looking into a research project and am struggling to find any existing work on this or whether I'm asking the right question. My question is to test the relationship between macroeconomic ...
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0answers
28 views

Average of R squared correct/allowed/useful?

I just conducted a Fama-Macbeth analysis to estimate the risk premia of Fama/French. In short, I estimated the betas on a company-individual basis first and then conducted a cross-section regression ...
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1answer
54 views

How to calculate R for strategies with dynamic exit points

Calculating risk-reward ratio R is easy when trading a straight forward strategy which has its entry and exit points clear: ...
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35 views

Markov Switching ARMA-GARCH

I am looking for R function for modelling Markov Switching ARMA-GARCH. I found package MSGARCH but that package can not accommodate mean model. Do you have an idea for my case?
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66 views

Classical Cramer Lundberg model - Ruin Theory Simple Question

I am trying to solve the following problem: 'An insurance company has an initial surplus of 150 and premium loading factor of 15%. Assume that claims arrive according to a compound Poisson process $(...
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1answer
149 views

Fama/Macbeth Regression - negative estimate for market premium

I just conducted a Fama-Macbeth regression to estimate the risk premia of Mkt-Rf, HML and SMB. As a result, I got a negative risk premium for Mkt-Rf which makes no sense in my opinion. As I couldn't ...
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0answers
64 views

Why is R^2 negative on random data? [closed]

The introductory book says R^2 is between 0 and 1, but I have two randomly generated sequences and the R^2 is negative. So I read further and now understand the negative value is because R^2 ...
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1answer
65 views

0.0006 r-squared after trying to test whether the intercepts differ significantly. Did I do it wrong?

I am trying to test if the intercepts of two linear regression (CAPM) differ significantly or not. I have 2 fund's monthly return in the same period and regress them on the same market variable (MKT = ...
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0answers
41 views

Correlation coefficient without cash flows?

I'm an intern at a company and one of our tasks is to calculate the the probability of default of both participants of a Swap(a Client and a Bank), for which we first need the correlation coefficient ...
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0answers
56 views

William K. Bertram's sharpe formula checking

I have some issues to verify by simulation the formulas in the paper of William K. Bertram "Analytic solutions for optimal statistical arbitrage trading". first, the reversion parameter alpha=180 in ...
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31 views

Estimator for Conditional value at risk (average value at risk)

I am following a book: Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi I'm learning about average value at risk. ...
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1answer
74 views

Adjust calculation of Sharpe ratio when portfolio is subjected to cash outflows

I have a portfolio with cash and marketable securities, a benchmark, and a desire to calculate its Sharpe ratio. However, this portfolio has cash outflows. Sometimes securities are sold to produce the ...
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28 views

Which technique determines if var x1 leads var y? Assuming var x1 may need to be transformed

Suppose I want to predict future changes in variable y (stock price over time). I notice that variable x1, inverted and delayed three months, tends to lead y. Which technique can I use to find other ...
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2answers
92 views

Do we need to assume underlying returns are normal in BSM model, given Central Limit Theorem?

I am trying to get a better understanding of Central Limit Theorem and how it can be used in life and in finance. From what I have read, the BSM model assumes the underlying asset's simple returns ...
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1answer
92 views

Jensen’s Inequality for returns on short positions

this is puzzling me. Say you have an asset A, that on day t+1 returns 1%, and then on day t+2 returns 1% again. If you invest $1 in A on day t (take a long position), then on day t+2 you have earned:...

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