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Since $dW_A$ and $dW_B$ are already correlated as per the way you construct it, your portfolio being the sum of the two is already correlated. If you want it very explicitity written out, then you could rewrite $dW_B = \rho dW_A + \sqrt{1-\rho^2}dW_Z$ where $dW_Z$ is independent of $dW_A$. More generally (higher dimensions) you can use Cholesky. Now with ...

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Surely, there is; search for aggregational gaussianity in Google Scholar or ScienceDirect. In fact, 5 minutes returns are leptokurtic and fat-tailed; then as you increase timeframe, returns become more and more normal. Yearly data is almost normal, if you have enough points.

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I was just like you when I started out: I had learned a lot about machine learning (mainly neural networks and genetic algorithms/programming) and used it heavily. I also had learned about classic statistics but not nearly as much as about ML. The problem with ML is - as I see it today - that you are often taking a sledgehammer to crack a nut, meaning: ...

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You are supposed to create a new portfolio using the tangency portfolio $P_t$ and the risk-free rate $r$. You know that the volatility of the tangency portfolio $\sigma_{P_t}=0.20$. You also know that the risk-free asset has: No risk: $\sigma_r=0$ Is not correlated with anything $\rho_{P_t,r} = 0$ So you're asked to create a portfolio with a higher ...

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The main reason to use traditional methods is interpretability. Specially when you are dealing with portfolios. Portfolios are nothing more than a linear combination of assets. Many Machine Learning methods are highly non-linear and therefore are hard to replicate with a real portfolio. For example if you want to minimize volatility of your emerging markets ...

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My main reference will be "Dan Xu, Christian Beck - Transition from lognormal to chi-square superstatistics for financial time series" Non-equilibrium statistical mechanics (more specifically, superstatistics) gives some ideas of explaining the relation between time frame and its distribution: "...to regard the time series as a superposition of local ...

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In the long term you will underperform buy & hold because you need an accuracy of at least 65%. See these papers for more: Bauer, R.; Dahlquist, J.: „Market Timing and Roulette Wheels Revisited“, CFA Institute, 2012. http://www.cfapubs.org/doi/pdf/10.2469/irpn.v2012.n1.10 Sharpe, W.: “Likely Gains from Market Timing”, Financial Analysts Journal, ...

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It's not bad but you have to backtest the method out-of-sample. Say you have discovered an indicator that works 100% in history, you still cannot be sure if it works next time. Another advise is you might want to investigate the distribution of loss when your system fails to work. If your system delivers 1% every time you trade, and loses 10% each time it ...

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The round-trip latency from point A to a matching engine at point B can be thought of being comprised of two components: $RTT_{total,A \rightarrow B} = RTT_{network\_transit,A \rightarrow B} + MPL_{matching\_engine,B}$ Where $RTT$ is the round-trip time and $MPL$ is the message processing latency (how long it takes to receive a message and produce an ...

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Most literature focus on comparing fund returns using a model alpha. A good overview is: Cahart (1997) and Berk and Binsbergen (2015). Basically you regress the fund returns on most common used factors (market return, HML, SMB, Liquidity and Momentum factors) and compare alphas after fees.

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You can use refined methodologies but if you just need a rough estimation of liquidity, you can simply use an average of daily volume over N days. In practice, for equities, people tend to use N = 20 or 30. Once you have the average daily volume (say 100,000 shares), you compare it to your holding (say 50,000 shares) to determine the the size of your ...

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I think there are a few conflating ideas here. With respect to the sum of logs idea, I think you're thinking about infinitely divisible distributions (https://en.wikipedia.org/wiki/Infinite_divisibility_(probability)). These ideas are indeed used to build more complicated models (i.e. Levy processes) for asset returns. With regards to the Efficient ...

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Generally Kurtosis measures the degree to which a distribution is more or less peaked than a normal distribution. Positive kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a relatively flat distribution. In time series we can encounter high kurtosis which is caused by "fat tails" (higher frequencies of outcomes) at the ...

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Perhaps an answer coming from a different angle and giving you some perspective: The typical approach taken by statistics is top-down: Just looking at the data and finding patterns and stylized facts (like excess volatility, volatility clustering, fat tails, no autocorrelation in returns but significant autocorrelation in absolute returns etc.) The problem ...

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The dummy function is always used to construct non-linear models. In your model, it is interpreted that the announcements have an non-linear effect on the return. So it is incorrect to say it is a linear regression problem, it should be called as a non-linear regression problem. In total, it means the announcements have asymmetric effects in explaining the ...

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Well, it wasn't easy because you didn't mentioned how your data is formatted. I create my own data.frame() basing on data you provided. You can skip this part if your data.frame is ready. Here's code I used to create a dataframe: > #given dates > dates=c("2000-1-3","2000-1-4","2000-1-5","2000-1-6","2000-1-7","2000-1-10","2000-1-11") > #formating ...

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You borrow that money from your broker. If you are retail client with for example IG they will offer this service to you. They will charge you some interest for the lending. There will be a margin account into which you need to deposit your cash. If the leveraged position you have loses money on the M2M and amount in margin account goes below a threshold, ...

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Some of the issues with this sort of request is: a) Today's S&P 500 components are not the same from 1 Jul 2013. By using today's components you are introducing pre-inclusion/survivorship bias. Are you going to be able to find data on the delisted stocks? eg. Since 1 Jul 2013, Sprint Corporation, BMC Software, NYSE Euronext, Molex, Life Technologies, ...

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I faced the same issue some years ago and I solved by implementing the R script reported here; now, with new Yahoo disclaimer rules, it seems to be broken, but, anyway you should be able to replicate the data mining process using that script together with this. If you're pretty confident with R, you should be able to do that. Alternatively, you can visit ...

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The TA_lib Technical Analysis library here has open source code for numerous indicators.

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Quote: Starting in 2003, the NYSE started disseminating automatically, with a software called autoquote, any change in the best quotes in its listed stocks. Before that specialists had to update manually new inside quotes in the LOB. This implementation considerably accelerated the speed at which algorithmic traders receive information Endquote Source: ...

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Both R and Python can do this very nicely. For Python you would need the pandas package and its dependencies. pandas has a lot of basic statistics, but for more advanced statistics like it looks like you want to do, you can use the statsmodels package, which can work directly with pandas data types. It can also download the csv files directly off the ...

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In Japan we get ISIN data with http://www.isin.org/isin-database they have free search tool.

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It's not unusual to find a financial time series with positive trend samples biased between 55-60%, depending on the period sampled. Stocks tend to have an upward drift over the long run. When you account for the drift, I would say, that number is really not much better than chance. A better way to verify your question would be to make certain to build ...

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Directional forecast is insufficient. You could have a signal that has 100% accuracy and you would not necessarily be able to profit from it because of transaction cost, implementation etc.

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If you have a friend studying at almost any university you can get access to WRDS. Inside WRDS just go to Compustat which has all the info you need for dates since 1950.

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To answer your question consider the following example using actual prices for SPY ETF on 7/31/15: "hopey.netfonds.no" By looking at the last 19 trades that occurred at the very last second, you will see a notable price movement on prices. If you go to Google/Yahoo Finance the Closing Price for the ETF is 210.50 (largest trade at the close?) but the very ...

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The easiest way to think of this is as follows: Settlement Price - Price at which the exchange margins all accounts for those options. Closing Price - Mid/Bid/Ask of Active Market at the exchanges last trade time. E.g. for TY Contracts this is at 5pm EST vs. a Settle Time of 3pm EST. Last Trade Price - Not all options trade every day. This is the price ...

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I cannot seem to find that article for free, so here is a more generalized answer. 1.what are the hidden states and what are the observation states. The hidden states are said to be that of an unobserved parameter process following the Markov property. The observation states are generated by the hidden parameter process. The parameter process changes ...

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Yes, the greenshoe option, technically called overallotment option is described in the prospectus. Yes, in the event the greenshoe option is exercised by the underwriters, the company issues additional shares and receives additional proceeds. Essentially it is as though a small secondary offering took place.

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