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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26 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
49 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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0answers
26 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
80 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
69 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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1answer
90 views

ARMA+GARCH day-trading strategy

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-...
2
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0answers
61 views

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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1answer
56 views

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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0answers
37 views

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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1answer
74 views

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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1answer
93 views

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. ...
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1answer
82 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 ...
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1answer
145 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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42 views

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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39 views

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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0answers
36 views

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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0answers
38 views

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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0answers
49 views

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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0answers
51 views

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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1answer
95 views

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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1answer
46 views

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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0answers
45 views

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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0answers
30 views

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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0answers
20 views

Show that the variance of the portfolio market portfolio is function of the betas of its consituents [closed]

Let us assume that the market portfolio consists of n assets. Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
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2answers
59 views

How to obtain annualized IR from t-monthly IC?

When we checking the relation between some factors and Stock price, we could use Information Coefficient(IC) to meausre. And then I already have t-monthly IC for each factor, and I need to calculate ...
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0answers
27 views

Why Jarque - Bera values are so high? Is this normal? [closed]

Please advise whether the following is a normal occurrence: In the above table I have Autocorrelation at lag1, LB, Skew, Kurt and JB test. I have noticed that whenever the value of Kurt increases, ...
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1answer
51 views

Backtesting model results, but backtesting output sampled at different frequency than model output

So, I'm trying to backtest a model that computes P&L. This model pulls sensitivities on a weekly basis and applies market shocks to these sensitivities to project quarterly P&L. I want to ...
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3answers
141 views

bayes theorem probability Jar [closed]

I am trying to come up with different theoretical answers below. I believe the standard one is based on Bayes theorem, but I am struggling to prove it. A jar has 1000 coins, of which 999 are fair ...
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2answers
51 views

Annualisation of Downside Deviation

Is it possible to annualise the downside deviation? If so, on the basis of what theory? The downside deviation (DD) of a series of daily returns is computed according to the formula: $\text{DD} = \...
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0answers
50 views

Nonlinearity in returns?

Reading academic papers on hedge funds, I find that many authors saying that hedge fund returns are often non-linear and thus many simple quantitative techniques are not suitable. It seems like they ...
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1answer
418 views

How to calculate one-year forward one-year rate? [closed]

I'm just a little lost on how to calculate forward rates. I know this is an easy question, but, if we are given a one-year and two-year zero rate (let's say, for the sake of the argument, 2% and 3% ...
1
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1answer
53 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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0answers
32 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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0answers
38 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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1answer
105 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
56 views

Mean Variance optimization on hourly data with gaps

I'm building a mean variance optimizer for a portfolio of FX, commodity and bond futures. The input data is hourly returns for each underlying. Given each underlying has different market opening hours,...
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1answer
75 views

How to calculate number of round trips given volatility?

Suppose we know stock price volatility is normally distributed with mean = 0 and annual volatility say 20%. Let's assume markets never close and we can trade at 1 second intervals. Let's assume stock ...
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2answers
57 views

Testing which index is a better benchmark to track stock prices

Let's say a Hedge Fund is tracking a stock price. Now the fund has three columns of data, Stock price, Index 1, and Index 2. All of these have data from 2016/01/01 - 2017/01/01. If the fund is to ...
3
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2answers
117 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 ...
1
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1answer
78 views

Kalman filter state/measurement noise

In a linear Kalman filter, we assume that the state and measurement noise are white noise N(0,Q) and N(0,R) respectively. Is it common practice to test these hypothesis? And what are the most common ...
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0answers
22 views

Sample distribution of cross-sectional statistics of returns

Currently doing an application of VaR on sample of industry portfolios in the US. I have a matrix of $n$ industry portfolios with $m$ time-series observations. I calculate cross-sectionally (for each ...
2
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2answers
77 views

Sample from aggregate portfolio distribution versus individual asset distributions

Suppose I have three assets $x_1,x_2,x_3$ in a portfolio with weights $W=\begin{bmatrix} w_1 \\ w_2 \\ w_3 \end{bmatrix} $, expected returns $R=\begin{bmatrix} \mu_1 \\ \mu_2 \\ \mu_3 \end{bmatrix}$, ...
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0answers
25 views

Choosing observations/sample selection in behaviour credit scoring models

In retail banking the credit risk of a creditor after the credit had been granted is often modeled using behavioral credit scoring. In this setting the customer already has an account (or a few) and ...
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1answer
78 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 ...
2
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0answers
90 views

Does Academic Research Destroy Stock Return Predictability?

McLean/Pontiff (2016) give evidence that portfolio returns are 26% lower out-of-sample and 58% lower after publishing an academic paper on variables, which are likely to predict cross-sectional ...
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1answer
76 views

selecting key performance indicators for a stock

Say, I read a financial statement of a company, and it reports, maybe 20-30 metrics, both generic, like revenue, free cash flow and specific to the company, like iphone sales etc. Is there a ...
2
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1answer
139 views

Why does computing correlation between index levels vs. percentage changes yield completely different results?

I am examining the relationship between the S&P 500 and the Industrial Production Index. Computing the correlation between these these variables yield vastly different results if expressed in ...
2
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2answers
142 views

Estimating realised gains given growth rate and churn

If one can estimate that the value of an investment portfolio will grow at $g$% per annum, and can estimate that approximately $c$% of that portfolio will be churned each year (sold and reinvested), ...
3
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0answers
90 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
117 views

Why futures pricing not calculated like options?

I have read about futures and options ( from online resources ). I only have the basic understanding,not math heavy ( for eg. for Black Scholes I know only the intuitive idea from the khan academy ...