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6

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 ...


5

Here is an example of such a product in Europe. (I don't personally own or recommend them., there are also other such issuers.) Commerzbank Faktor certificates: These should meet all your requirements, range of -10x to +10x constant leverage, open ended, no dividends, no knock-out's as well. ...


5

The real answer is that you should never try to predict the future behavior of anything. Instead, ask yourself what sorts of risk you are comfortable taking and work back from there. That being said, the quantitative finance textbook approach would look something like this: Come up with a model for equity movement - this is typically some sort of brownian ...


5

Two theoretical explanations regarding the long memory are given by: The mixture of distributions hypothesis of Tauchen and Pitts (1983). Essentially this hypothesis states that trading volume and return are driven by the same information flow process, therefore trading volume and return volatility should share the same long range dependence. ( see ...


4

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.


4

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: ...


4

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 ...


4

I think a very good paper that summarizes the empirical evidence on other measures of value is the Lettau and Wachter (2007). Take a look at their tables 1, 2 and 3 for the most standard uses of value measures which indeed match with AQRs measures. Below their table 1, just for completeness:


4

The best answer to your question: back test your ideas against historical data. If you think you can predict the market by learning past patterns prove it by testing it, not by discussion. I've done mistake few years ago and fell in love with one idea, which seemed to be like money printing machine, but instead testing it, I spent month discussing it on ...


3

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 ...


3

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 ...


3

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.


3

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 ...


3

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.


3

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 ...


3

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, ...


3

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 ...


3

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 ...


3

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 ...


3

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 ...


3

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 ...


3

Why not just use Geometric Mean Returns? Each time you buy/sell an ETF calculate the holding period return as a percentage and plug into the formula. The answer is a percentage that you can use to calculate the approximate money appreciation (or loss) against your "fixed notional"


3

Compustat supports unlimited data export keeps the history of disbanded entities provides restatements since 1950 + point-in-time data since 1986 coverage since 1950 list of variables (data guide) Compustat is a S&P subsidiary. It goes as a plugin for CapitalIQ (also S&P), WRDS, CRSP, and other platforms. Pricing starts from \$3k. A platform ...


3

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 ...


3

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, ...


3

structure a bespoke total return swap where you explicitly specify the reference index, it's calculation (i.e. stock price * factor etc..), payoffs, margins etc... an example of such swap could be contract for difference (CFD).


3

It could be done as a kind of Structured Product. I don't know of a specific name for this type of instrument. From what you describe, it doesn't actually involve any optionality, just leveraged exposure to an underlying. You also mention participating in downside risk, so it's not an option. But you do mention a 'constant factor', which you need to ...


3

This is not true. In the Black-Scholes setting, \begin{align*} S_T = S_t e^{(r-q-\frac{1}{2}\sigma^2)(T-t)+\sigma (W_T-W_t)}. \end{align*} Then $$E_t(S_T) = S_te^{(r-q)(T-t)}, $$ and \begin{align*} Var_t(S_T) &= E_t(S_T^2) - (E_t(S_T))^2\\ &=S_t^2e^{(2(r-q)+\sigma^2)(T-t)}-S_t^2e^{2(r-q)(T-t)}\\ &=S_t^2e^{2(r-q)(T-t)}\big[e^{\sigma^2(T-t)} ...


3

Check out the book of Teyssière & Kirman (2007) entitled "Long Memory in Economics". For instance, the model of Gaunersdorfer & Hommes features heterogeneous agents: fundamentalists believe that prices move to their fundamental rational expectations value, while chartists simply look at deviations of actual traded prices. The latter thus feature a ...


2

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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