5
votes
Accepted
how to I get the statistical significance of a backtested result
Compare Sharpe , Sortino Ratios, yearly Profit,Max Drawdowns per year of your strategy to
1) buy and hold all of the stocks in your universe
2) few strategies (with different random seeds) which ...
- 861
4
votes
Accepted
How to identify daily returns as an unusual daily return given a dataset
Given you have your returns
$$r_t = \frac{P_t - P_{t-1}}{P_{t-1}}$$
you can compute the absolute z-score as
$$Z_t = \frac{r_t-\mu(r)}{\sigma(r)}$$
where $\mu(r)$ and $\sigma(r)$ are the mean and ...
- 8,739
3
votes
Evaluate the significance of the relationship among VIX and the S&P 500
It is unlikely with so few observations that you will get statistical significance. Also you should benchmark your model against a "naive" model.
If your conjecture is that high VIX implies high ...
- 8,306
2
votes
R squared statistic in predictions of returns
The goal of regression is to account for the variance in $y$. If you are able to do that, then your predictions of the conditional mean of $y$ (conditioned on the values of your features) will be ...
- 353
2
votes
The use of $p$-value in finance after the recent statement of ASA (American Statistical Association)
Deidre McCloskey has been going on about this for as long as I can remember. See for example the aptly titled :
"The cult of statistical significance: How the standard error costs us jobs, justice and ...
- 4,337
2
votes
Does historical backtest data mean anything?
There's a field of study called Statistics, which to a large extent tries to answer questions like that both in a financial setting and in experimental sciences. Try to read something about it. To ...
- 1,551
2
votes
Accepted
Does historical backtest data mean anything?
If your model is only relating to historical price data of that single stock, then the model wouldn’t be useful. Historical price data is stochastic, and a lot of theory in financial mathematics is ...
- 174
2
votes
How to identify daily returns as an unusual daily return given a dataset
this won't be a very statistcally correct answer. But for a quick and dirty solution you could estimate the volatility using your return time series.
Then you check if there are any returns exceeding ...
- 1,578
2
votes
Does the default rate follow normal distribution or binomial distribution?
Normal rv can take negative values so won’t work for default rate (which is positive) without some form of transformation- classic approach is Vasicek, which by making assumptions about the default ...
- 6,204
2
votes
Accepted
N Needed for Statistically significant tracking error
Suppose you have a portfolio that has some unknown real mean tracking error, $t$, relative to the benchmark, with some real variance $\sigma_t^2$.
You have a sampling process generated from your ...
- 10.2k
1
vote
How to identify daily returns as an unusual daily return given a dataset
This is not really a question one can answer precisely. "Abnormal" is quite subjective. Thus, there are a lot of things you can do to identify such returns.
But first: the price level will ...
- 11
1
vote
Accepted
Test statistic of event study
If I understand it rightly, I have to take the mean of the abnormal returns for the 50 companes at $t_0$ as the numerator. for example:
$\bar A_{t} \ = \ \frac{1}{N_t}\sum_{i=1}^{n_t}A_{i,t'} $ ...
- 2,916
1
vote
How to test the difference between samples of sharpe ratios
Typically we have
$$\hat{\zeta}\approx\mathcal{N}\left(\zeta,\frac{1 + \frac{\zeta^2}{2}}{n}\right),$$
where $\hat{\zeta}$ is the observed Sharpe ratio, and $\zeta$ is the unobserved population ...
- 2,836
1
vote
CAPM alphas have unexpected p-value distribution
The distribution of p-values is uniform only when the null hypothesis is true and all assumptions are met. The difficulty with p-values is that they are composite functions.
Finding that an empirical ...
- 4,299
1
vote
question about significance level
I figured it out now.
When calculate the probability use Binominal itself, the result matches:
$$\alpha=1-(P(4)+P(3)+P(2)+P(1)+P(0))=1-(0.134+0.214+0.257+0.205+0.081)=0.108$$
- 213
1
vote
Pearson correlation significance : Issue with $t$-statistic increasing with $N$
The question of significance is not about the correlation but about the precision of the estimation. If the value estimated with more data is still near the same value estimated with less data, that ...
- 2,900
1
vote
Should Fama-French coefficients be calculated with daily or monthly returns?
In this context, I refer to the book on Empirical Asset Pricing by Bali, Engle and Murray (2016). They state on page 124 that
A minimum number of data points are usually required to ensure the
...
- 141
1
vote
Assessing goodness of a Technical Trading Rule using a ROC model
So ROC performance metrics are common place in machine learning applications, particularly for classification tasks.
Looking at the way you have setup the question here you wont be able to plot a ...
- 924
1
vote
Average Return Differential Calculation - Newey West t-Statistic
The values for $VaR$ and $CF-VaR$ are the time-series means for each cross-sectional values. As mentioned in the table description, you calculate both variables for each month from Jan. 1995 to Dec. ...
- 2,916
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