# 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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97 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 ...
74 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 ...
50 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: ...
22 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, ...
35 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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### 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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### 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 ...
29 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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### 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 ...
50 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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### 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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### How to calculate R for strategies with dynamic exit points

Calculating R is easy when trading a straight forward strategy which has its entry and exit points clear: ...
26 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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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 $(... 1answer 64 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 ... 0answers 63 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 ... 1answer 51 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 = ... 0answers 40 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 ... 0answers 48 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 ... 0answers 29 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. ... 1answer 52 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 ... 0answers 27 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 ... 2answers 85 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 ... 1answer 84 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:...
207 views

I have a question regarding this particular post on quantstart: https://www.quantstart.com/articles/ARIMA-GARCH-Trading-Strategy-on-the-SP500-Stock-Market-Index-Using-R In it, he designs a day-...
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### How to determine expected returns of an options portfolio?

Lets say I have a delta neutral portfolio, iron condors on spy for example. I'm short a call credit spread and a put credit credit spread of equal widths. I would like to determine the expected ...
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### Barra model: why standardize the fundamental risk factors?

The two main types of risk factors included in the famous Barra model are called the "fundamental factors", and "industry factors," and the thing that I do not understand is why are only the former ...
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### How to normalize stock exchange indexes

I am doing an academic research in behavioral finance and I need to calculate my abnormal return based on the normalized returns of the stock exchange index being the S&P 500. In other words, I ...
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### Modeling mortgage loan defaults

I have a machine learning model trained with a list of mortgage features that include macro variables where the field to predict (the label) is "Mortgage Defaulted" = 1 or 0 (Yes or No). Now, I need ...
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### How can stationary time series data be used as input in an ML model?

I am halfway through "Advances in Financial Machine Learning" by Marcos Lopez de Prado. I understand that a time series like stock prices can be transformed to make it sufficiently stationary. ...
90 views

### Exponential Smoothing - Alpha greater than 1

Simple stats question. I'm having trouble finding anything in the literature as to why the smoothing coefficient can never be greater than 1. This question was started by me doing time series ARIMA ...
154 views

### Correlation between stock prices given correlation between returns

assume I have two stocks with known volatilities and a known correlation coefficient of returns - does anyone know how to determine the correlation between the prices and NOT THE RETURNS
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### How to work with vine copula in R?

I have returns of 4 stocks: stock1, stock2, stock3, stock4. And I use R and library(VineCopula) to do: ...
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### Problem in copula fitting

I have returns of 2 stocks: stock1 and stock2. And I want to fit pair copula. I use this libraries library(VineCopula) library(copula) then I select an ...
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### Approximation of portfolio VaR (after mapping) when Delta and Gamma both equal zero

As titled, I am having trouble estimating the VaR of a portfolio mapped as a function of a single risk factor $S$, in the form : $$V(S) = S^3 - 30S^2 + 300S + 150$$ with current value $S = 10$. $S$...
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### Fit a copula model in R

I want to accomplish the task of creating an optimal portfolio of stocks, the yield between which is modeled using kopulas. And I have data: return of 4 stocks: ...
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### Convolution of Dependent Random Variables with Copulas

Lets say I have 2 different observations which are fitted to a parametric distribution. And lets say that they are dependent and can be modeled by one of the copulas. I want to calculate “a value” ...
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### statsmodels's granger causality tests return value

im a developer(with no background in statistics) and i need to use granger causality test, i cant seem to understand the results of the func. one result: Granger Causality ('number of lags (no zero)'...
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### when a co-integrated times series pair has broken the leash

I have two times series, say $T_i$ and $S_i$ over a reasonably large time window, and I have calculated their cointegration (using python's OLS and Adfuller) . Say that the test has passed with high ...
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### serial correlation and CUSUM results

I have the following CUSUM test resulted from autoregressive distributed lag models (ARDL). Does the CUSUM results show that the model is stable? I am a bit confused because the red line in CUSUM ...
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### Statistical distribution of MACD

I was (unsuccessfully) trying to find results on what the distribution of the MACD values for a stationary time series with IID returns would be. Are there any such results or any that go in a similar ...
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### Using CFNAI index for identifying sample periods

I'm doing my Thesis on Asset pricing models and I would like to find out the effects of business cycles on the performance of asset pricing models for industry portfolios. My initial idea was to ...
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