24
votes
How did James Simons clinch that security prices didn't look random?
I'm sure Simons, as a first-rate pure and applied mathematician, had sufficient understanding of statistics to detect market inefficiencies and anomalies. As far as I know, the development and ...
- 3,700
12
votes
How did James Simons clinch that security prices didn't look random?
Jim Simons' initial intuitions about nonrandomness were probably driven by the very psychological/evolutionary predispositions to want to find the hidden meaning within noise that affect humanity in ...
- 3,015
11
votes
Accepted
What is the total correlation between assets in a portfolio?
This is indeed an interesting question.
According to this website, a paper by Goldman Sachs [Tierens and Anadu (2004)] proposes three alternative methods for estimating average stock correlations:
...
- 27.5k
9
votes
Accepted
Correlation between stock prices given correlation between returns
We can obtain a closed-form expression for price correlation given (log) return correlation when the two stocks follow geometric Brownian motion:
$$S_1(t) = S_1(0)e^{(\mu_1- \frac{1}{2} \sigma_1^2)t}...
- 3,700
8
votes
What is the total correlation between assets in a portfolio?
I just want to add to vonjd's answer some info on the comparison of the 3 methods. This is too big for a comment so I'm posting as a separate answer but please upvote his answer, not mine.
Do the ...
- 741
8
votes
Accepted
7
votes
Predict the behavior of a time series (P&L trading desk)
Without seeing your trading desk's P&L it's impossible to say whether it is predictable or not. But here are a few thoughts -
There's no reason to think that it isn't predictable. In general, ...
- 5,931
6
votes
How to calculate the JdK RS-Ratio
I think the normalisation step is incorrect. Since we would like have 100 as our baseline, it should be 100 + ((value-mean)/stddev + 1). Then we get fairly realistic results.
See the following Python ...
- 67
6
votes
Is R being replaced by Python at quant desks?
Also in the high frequency / medium frequency field here.
I received a "mixed" consensus regarding the use of R and its prevalence in the field (specifically HFT). Speaking with someone who works in ...
- 1,182
6
votes
Accepted
Interpreting Eigenvalues of Co-variance Matrix
What you basically do here is a Principal Component Analysis (PCA). A good starting point in the financial sphere is
Managing Diversification by Attilio Meucci (2010)
Page 3:
"The most natural ...
- 27.5k
6
votes
How did James Simons clinch that security prices didn't look random?
I will disagree with RPL's answer - Simons is not particularly known as an applied mathematician, but he did work for some time at the Institute for Defense Analysis [IDA] (he was fired for ...
- 369
6
votes
Accepted
How to test signifcance of a sharpe ratio
The answer above is not correct.
Let's go by parts:
Denote the mean of returns $\mu$. Denote the standard deviation of returns: $\sigma$.
Therefore the sharpe ratio is:
$$ SR = \frac{\mu-r_f}{\sigma} $...
- 8,561
6
votes
Accepted
Shrinkage of the Sample Covariance matrix, theory
Yes. It comes from a core theorem of statics, Stein's Lemma. It shook the foundations of the field of statistics when it came out. It blew up an entire way of viewing mathematical statistics. ...
- 4,319
6
votes
How can I measure returns such that the average is useful?
What does not work with the geometric mean?
The geometric mean is computed with the following formula: $${\displaystyle \left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots ...
- 9,349
5
votes
Should I use an arithmetic or a geometric calculation for the Sharpe Ratio?
The correct answer is "arithmetic mean, because Bill Sharpe says so". He invented the thing, and he's pretty clear on which one he was looking at.
If you use the geometric mean, which is lower the ...
- 51
5
votes
Accepted
A good book on option pricing from theoretical and practical aspect
My recommendations would be the following:
For starters in Quantitative Finance:
Hull - Options futures and other derivatives
Wilmott - Quantitative Finance
For an introduction to volatility:
...
- 853
5
votes
What machine learning method is more suitable for prediction of financial time series?
From what I have read, there are 3 popular algorithms for financial time series. Random Forests and SVMs, then followed by Neural Network Architectures.
There are a couple of good papers, to name a ...
- 934
5
votes
Principal Component Analysis of yield curve change
To put things in context, if $\{{\bf X}_i\}_{i=1}^n$ is a set of variables and $\{{\bf Y}_j\}_{j=1}^n$ denote the principal components of ${\bf X}$ then
$$
{\bf X}_j = \mu_j + \sum_{k=1}^n{\bf Y}_k ...
- 311
5
votes
Accepted
Can portfolio Value-at-Risk be calculated analytically for multivariate t-distributed returns?
Let the $n-$dimensional vector of returns $\mathbf{r}$ have a multivariate t distribution with $\nu$ degrees of freedom. The marginal distribution of any component $r_i$ has a univariate t ...
- 3,700
5
votes
log return of sp500. Stationary vs strictly stationary
We can talk about whether a strictly stationary or weakly stationary process might usefully describe that data. My answer to both would be yes.
I also have issues with other text that people have ...
- 6,994
5
votes
Filling a few missing data in time series?
I would personally delete those days so you dont change the data distribution. If you really need to fill those blanks, random sample imputation would be the way to go.
- 329
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
5
votes
Why is a smaller portfolio norm better?
Norm constraints are motivated by regularisation in regression analysis. L1 and L2 norm are similar to Ridge and Lasso Regression. The author who first introduced this method argued that it will ...
- 988
5
votes
Accepted
Advances in financial machine learning (Marcos López de Prado): explanation of snippet 3.1
I can't comment on why MLDP is calculating returns this way (perhaps there is a reason explained in the book, which I don't have). However, from a pure code point-of-view he seems to be calculating ...
- 1,906
5
votes
Accepted
Setup for proving equation 3.4 from Grinold
In order to derive the simplified portfolio volatility, there is also an assumption of equal variance $\sigma_i = \sigma$ for all $i$.
Assume we have an equally weighted portfolio of $n$ assets with ...
- 4,726
5
votes
Setup for proving equation 3.4 from Grinold
For sake of completeness, let me add the approach using linear algebra. Let the covariance matrix
$$
\begin{align}
\Sigma&=\sigma^2\begin{pmatrix}
1&\rho&\rho&\ldots&\rho \\
\rho&...
- 7,035
4
votes
Book recommendation for time series analysis
If you want to study time series particularly related to financial data, I would recommend Analysis of Financial Time Series by Ruey S. Tsay.
4
votes
Bayesian or Frequentist in Finance?
First of all, the area of statistics you need in finance is time series analysis. That being say, as usual is statistics: the more data you have, the more sophisticated models you can use. Typically ...
- 12.5k
4
votes
A good book on option pricing from theoretical and practical aspect
Here is some interesting things to consider, beyond the typical bibles like Hull and Wilmott etc.
For either route (buy/sell side), in terms of math, I think strong stochastic process would be great (...
- 123
4
votes
What machine learning method is more suitable for prediction of financial time series?
I wrote a masters thesis related to machine learning in finance, and during this process I surveyed about 200 of the research papers that were written about the topic since 2018. This is the ...
- 141
Only top scored, non community-wiki answers of a minimum length are eligible