5

If you are looking for the official SEC filings then EDGAR is your best bet. QQQ is still listed under PowerShares, the old (and better IMHO) name for Invesco. POWERSHARES QQQ TRUST, SERIES 1 CIK#: 0001067839 This link should get you what you need; https://www.sec.gov/cgi-bin/browse-edgar?action=getcompany&CIK=0001067839&type=&dateb=&owner=...


5

Some approaches Use only common points - Exclude all holidays in any index. Reduced sample size Loss of information No 'made up' data (consistency) Fill forward - use previous day as you suggested. Issue here is that jumps in the market over holidays are recorded as zero change then a big change. Linear interpolation - linearly interpolate the price ...


5

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.


4

AP factors do not need to be excess returns. In case they are, corresponding prices of risk are conveniently equal to average factor values, since "factors price themselves": $$E[R_i] = \beta_{i} \cdot \lambda_f, \\ E[f] = 1 \cdot \lambda_f, \\ \Leftrightarrow \\ \lambda_f = E[f],$$ where there is just one factor $f$, $\beta_i$ is the loading of asset $i$ ...


4

The point of confusion may be in thinking that a predictable price process is synonymous with a mean-reverting process while using the definitions in these papers, it's actually the opposite! In the context of these papers, a random walk would be 100% predictable: the unpredictable component of a random walk (i.e. the period specific shock which has finite ...


4

The linked to answer does explain it all, but in brief because one set are stationary processes and the others are not. Correlation as a measures gives us the normalized degree of co-movement between process residuals, which assumes stationary processes. With non-constant mean term (ie, non-stationary processes), there's no way to parse out and relate ...


4

I prefer thinking in terms of well measured vs. poorly measured rather than significant vs. insignificant: arbitrary p-value cutoffs and ignoring sensible priors can both be problematic. On the question, "can poorly measured betas from time-series regressions give rise to well measured factor premiums from cross-sectional regression?" The abstract answer is ...


3

Data that includes the names of the parties is definitely not freely available, only exchanges would have it and they will share it only with their regulators. Regarding data without names, that is called tick-data as LocalVolatility states. To the best of my knowledge, you need to pay for this data.


3

Simulation for timeseries data is not a trivial matter and there are a number of methods to ensure you retain some of the relevant properties (mostly called dependent bootstrap methods): Block bootstrap - contiguous blocks of data chosen so that they are large enough to retain significant autocorrelations. Stationary bootstrap - randomised block size ...


3

I think the answer you're looking for is very similar to this question Expectation of maximum draw down in the Brownian motion case. just like your assumption that return is normally distributed with mu and sig, say price/portfolio value follows Brownian motion with same property, and if you're using log return, I found this article that provides an ...


3

On the community wiki answer for What are the quantitative finance books we should all have in our shelves?, Time Series Analysis by James Hamilton is mentioned. I recommend reading Applied Time Series for the Social Sciences, by Richard McClearly and Richard Hay. It is a great introduction to the field and goes into depth about various time series ...


3

To justify the use of tenors 2Y, 5Y, 10Y, 30Y for risk bucketing, you could analyse up to the first four principal components and examine which variables summarize better the information displayed on each axis using the factor score. For example, if the first four pc contains 90% of the available information (let's say 1st pc: 40%, 2nd pc: 30%, 3rd pc: 15% ...


3

So my question is how do I prove that the use of 2y, 5y, 10y and 30y is justified for risk bucketing and not other alternate buckets? Ok so just to pose a second viewpoint but why do you have to necessarily use PCA to do this? You are basically trying to show that given any underlying swap portfolio $P$ you can find a set of trades / risk exposures in ...


2

I'm not sure I'd call it 'subjective' or 'pre-conditioned'. Traditionally, ensuring the absence of arbitrage is a guiding principle for pricing, while the risk-neutral measure is most frequently used for theoretical results. Assuming you'll be using your forecasting for trading activities, using AoA to determine price is the right way to go. Consider ...


2

A very clear text for this is "Time Series Analysis" by Cryer. It even has a focus on using R to do these sorts of things.


2

My recommendation is to focus on improving estimates based on available data. For example, the returns of these assets classes tend to exhibit very strong serial correlations as a result of smoothing, which dampen observed volatilities. You can add a ton of value to the investment process by de-smoothing these returns and estimate risk thereafter. I'm ...


2

I checked the VIX values that you report "missing" in 2007. They appear to be holidays (days when stocks don't trade and the VIX is not produced). For example 7/4/2007 is the Fourth of July holiday, 9/3/2007 is Memorial Day and so on. A possible solution is to fill in on these days the VIX value for the previous day, since this is the "last known value". ...


2

Multiply the weight of the assets times the 1 + returns of the corresponding asset. This will give you the value of each asset at the end of your horizon. In your example: (0.2)(1+0.05) = 0.21; (0.3)(1+-0.05) = 0.285; (0.5)(1+0.10) = 0.55; Now add all of these values to get Total Assets: (0.2)(1.05) + (0.3)(0.95) + (0.5)(1.10) = 1.045 Finally ...


2

Hi: Subtract $k$ from $z_t$ and add $k$ to $z_{t-k}$. Then you have $cov(z_{t-k,} z_{t})$ which by definition is $\gamma_{-k}$. But, by stationarity, this has to be equal to $cov(z_{t}, z_{t-k})= \gamma_{k}$ because the covariance is only a function of the lag difference.


2

If you want to study time series particularly related to financial data, I would recommend Analysis of Financial Time Series by Ruey S. Tsay.


2

On the technical side of things, make sure that your actual PCA analysis is correct. A reasonable check here is to plot the loadings of all tenors (not just the few you are interested in) for the first 3 factors and see if you recover level, slope and curveature components. Now if your results are correct, the reasoning goes something like: the first three ...


2

Sharpe ratio is calculated using arithmetic returns, not geometric return. It's most often calculated using monthly returns, taking an average less the risk-free rate and SD, and then usually annualizing using the square of 12. It's also not uncommon to omit the rf portion, and calculate a risk/return type stat and compare strategies that way.


2

You have estimated a cointegration relationship between $T_i, S_i$. $$ T_i=\hat{\beta_1}+\hat{\beta_2} S_i + \hat{u_i}$$ For each new observation $(T_{new},S_{new})$, replace to the existing equation and find the residual $\hat{u}_{{new}}=T_{new}-\hat{\beta_1}+\hat{\beta_2} S_{new}$. Standardize this value with $$\frac{\hat{u}_{{new}}-\bar{\hat{u}}}{\...


1

Preliminary calculations Consider a $n \times 1$ vector of asset returns $r_{it}$ for each time $t$, where each of it is calculated as $$r_{it} = \frac{P_{it} - P_{it-1}}{P_{it-1}}$$ i.e. simple returns, where stock prices $P_{it}$ should be adjusted for stock splits, dividends, etc. For calculating value weighted returns $r_{t}^{val}$ for each time $t$, ...


1

Agree with will that this approach will complicate things, mostly for the fact that GBM SDEs rely on log returns, and not discrete returns. To go from some finite underlying price level $S$ to $0$ means a log return of $-\infty$, whereas the equivalent discrete return is $-1$. To ensure a discrete return - based stochastic process, where $S$ can never take a ...


1

The dollar bars certainly allow for a partial recovery of normality through a price sampling process subordinated to a volume, tick, dollar clock. It is well known that returns are assumed to be normally distributed but in reality they have a high kurtosis and fat tails, they are leptokurtic. Dr de Prado posits in several papers but mainly in a well known ...


1

I think this should be handled as an essay type question, rather than a math problem. Ultimately you will conclude that "there is no reason why it cannot be ergodic" but you will have a few well written paragraphs before this to review some issues and show your understanding of the subtle concepts involved. The intuition of ergodicity is that a statistical ...


1

A completely different statistical approach is to pose your own machine learning problem: 1) Collect a set of full data where you have data values available for all instruments on any given day. 2) Propose a machine learning model that will devise its own optimised parameters for the task of regressing any missing data. 3) From your set of good data ...


1

For a VaR calc you might not want to interpolate missing values. By doing that you are inherently editing the returns distribution; potentially this will make a VaR look better or worse. Not good if your goal is an accurate risk distribution. Its worth considering what a missing value signifies. There are two cases. A missing value or unchanged value can ...


1

it's the difference between $\sum_{i=1}^n \frac{X_i}{X_{i-1}} -1$ and $\frac{X_n}{X_0}-1$ and has nothing to do with your data integrity


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