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6

I guess what they are trying to say here is that, assume you have two time series $X$ and $Y$ which are exactly the same i.e. $X=Y$, the correlation is : $$\rho_{X,Y}= \frac{Cov(X,Y)}{\sigma_X \sigma_Y}\overset{X=Y}{=}\frac{Cov(X,X)}{\sigma_X \sigma_X}=\frac{\sigma_X^2}{\sigma_X^2}=1$$ Now assume a time series $Z=2 \cdot X$, you have: $$\sigma_Z=2 ...


6

The primary quant skill needed to make the market is optimal control (a typical paper is Guéant, O., L, and J. Fernandez-Tapia (2013, September). Dealing with the inventory risk: a solution to the market making problem. Mathematics and Financial Economics 4 (7), 477-507), because you need to control your inventory and adjust your quotes accordingly: be ...


5

Why do you have 16180 observations? Is this daily data over 64 years or higher frequency data? I am guessing so by the magnitude of the intercept. At any rate, your test power would be huge with this large sample size, meaning small relationships will be statistically significant. What Cochrane said is contingent on data frequency. At a high frequency it ...


5

I think one has to distinguish between pricing and fitting/reproducing empirical stock returns. A model might fit the empirical stock returns extremly well but fail to reproduce derivative prices. In my answer I will assume that you are interested in reproducing the empirical stock returns. Mandelbrot and the Stable Paretian Hypothesis The most salient ...


5

Short answer It's complicated. A satisfactory solution is not known. Long answer A satisfactory solution is not known and research is ongoing. That doesn't mean there is nothing interesting to say about it. The phrasing in the question is not entirely correct: First off all, there's is no risk free arbitrage between bonds and stocks. Both are risky and ...


4

My take on the whole issue is as follows: We cannot be sure to find the one and only true model, the only thing we can do is to identify the most prevalent so called stylized facts and try to model them parsimoniously. The following paper was already mentioned in the comments: Empirical properties of asset returns: stylized facts and statistical issues by ...


4

In the chart below, I'm showing the rolling correlations between stock returns and bond returns. (The relationship would be flipped if you are studying stock returns vs interest rates). As you can see, for the bulk of the history since 1960s, bond returns and stock returns were indeed positively correlated; i.e., when stocks went up, bonds went up too (and ...


3

I can offer an intuitive answer. The limit when your equally weighted portfolio is continuously rebalanced will give you the geometric mean. This is because the excess return of the better performing strategies will be allocated towards the least performing strategies, compounding high returns with low returns.


3

2) Alternative to Fama-MacBeth is Fama-French approach. Explanation of difference see, for example, here: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1271935 Fama-French approach was used by Carhart (introduced momentum), Pastor-Stambaugh (introduced liquidity), Fama-French themselves (used it to build 5-factor model), and many other (elsevier or ...


3

There is a major bug when you are getting information from exchanges outside USA. If you get the adjusted prices for BOVESPA (Brazilian Stock Exchange) for example, it will only consider the events that happened using the US Calendar and not the Brazilian calendar of working days, this leads to a lack of information on other exchanges. Be aware of this if ...


3

Successful strategies in both areas can have the same math requirement. It just depends on the algorithm. PhD level mathematics is not a requirement in either area, despite the impression you may get from academic papers (note that a lot of these papers use math to build a sim market, which is completely dislocated from what a researcher needs to do). I feel ...


3

Unfortunately, the ability and tools to develop a low latency trading system are extremely commoditized and will be insufficient for you to make a living in this field. An overwhelming majority of electronic market makers are staffed 100% by PhDs because trading experience and research compose their primary differentiators, e.g.: SIG EMM - 100% PhD. DRW ...


3

Are you sure the return for two years is 0.7214? It should be 0.3422 per year if you are using 31/12/2011, and 0.3416 if you are using 01/01/2012 as the end date. Assuming the last number (because it makes for two full years, therefore easier to calculate), yes, there is a formula to derive it from the return of the individual years. It's the geometric ...


3

Short answer: It offers some degree -- and in many cases, a greater degree -- of comparability between two types of data (different assets, returns, etc.) Long answer: You may already know this, but keep in mind that "normalization" can mean different things (see this question). There are various methods and purposes for normalizing data (financial or ...


3

VG belongs in the family of variance-mean mixture models. Given a horizon $T$ the distribution of log-returns $f$ is a mixture of Gaussians $f_G$ with randomised mean and variance. The randomisation density is $g$ and its mean and variance increase with $T$. For the VG process this randomised factor is Gamma-distributed. More concretely, denote with ...


3

This mean that the reason why apple stock price went from 3 to 100 in 10years is the overnight variation in price. This is quite unexpected, if there was no overnight variation the stock price would have died a long time ago... Why is that ? Have we been lying to us ? This is because many business and financial news are reported at market close, either ...


3

As you've mentioned, it depends on the trading venue and the exact market data product that you're subscribed to. Unless otherwise stated, the data is usually updated at every occurrence of an event (explains the irregualr intervals), and often, the data is not disseminated immediately and multiple events may be batched in a single message informing you of ...


2

To complement @SRKX comment ,i'll try to explain the "simple mathematical proof" beetween both formula : I assume you know the geometric or arithmetic brownian motion : Geometric: \begin{equation*} dS = \mu S dt + \sigma Sdz \end{equation*} Arithmetic : \begin{equation*} dS = \mu dt + \sigma dz \end{equation*} Then another important stochastic tool you ...


2

No, it would be $$(RI_{t}-RI_{t-1})/RI_{t-1}$$


2

The key assumption is that there is no time-series correlation between the error terms. Fama-MacBeth can deal with cross-sectional correlations. See Samuel Thompson's "Simple formulas for standard errors that cluster by both firm and time" in the Journal of Financial Economics (2011) for a treatment of different regression methods for testing equity ...


2

There are no "fundamental algos" analogous to "technical algos". Instead, quantitative useof fundamental data assumes applying multifactor models to predicting returns and other intrument parameters. That models vary from "academical" (like Fama-French 3-factor or Chen, Roll, Ross) to proprietary models of guys from industry: MSCI Barra, Bloomberg, CSFB, ...


2

Since MiFID 1 in Europe (you may have heard MiFID 2 has been recently adopted), all trades have to be reported somewhere. Reporting channels are numerous: regulated markets have in books and off the book reporting feeds MTF have their own, sometimes one for their Lit book and the other for their Dark one remaining OTC trades have been reported for long on ...


2

In the chapter that deals with NMF of the book "Programming collective intelligence" , the author did NMF on several stock trading volumes and found some comovement. I googled a little. This did NMF on 40 chinese stock close prices. This developed A variant of nonnegative matrix factorization for Stock Trend Extraction. Another google found this also did ...


2

I just ran the Mathematica code below to make a list of stocks and sectors you can access here: https://www.dropbox.com/s/zkzpcnksvfygamp/nyse.xls Mathematica uses curated data from Yahoo. Items that lack sector information have been omitted. The list may be incomplete but it might provide something for you to work with. members = FinancialData["NYSE", ...


2

I do not believe that the exchange is capable of tracking down the person or legal entity who has been part of any recorded transaction and in particular linking the activity of market intermediaries to the ultimate interests of beneficial owners. However, under certain conditions, the person or legal entity has to report to the SEC his identity and his ...


2

On exchanges, there is such orderbook with sufficient amount of limitorders, so when you place an order (market or limit), the "best" limitorders for you will be hitted and change the price last traded price. The price you see is actually just the midpoint between the currently best available bid and ask prices in the orderbook. Therefore, this price might ...


2

Actually, the historical returns, going back to the 1920s, took place in two different ways over two distinct time periods; 1980-present, and 1925-80. This is a more important premise than the fact that stocks have an average total return of 10 percent over the past 80-odd years, and bonds have an average total return of only 5 percent a year over that time. ...


2

One possible route would be to get the historical price data from Yahoo and use disparities between the Close returns and the Adjusted Close returns, given a certain threshold value, and where the disparity passes that threshold is where the splits have occurred. Find the Close returns where that condition was met, maybe round the number to the nearest ...


2

If you are investing an amount $M$, split over deals indexed by $i$ and with a weight $w_i$, then your dollar position in each share will be $w_i M$. The exposure to the index will be $\sum \beta_i w_i M$ You should realize that this will not hedge idiosyncratic risks. In general, the more deals you have, the better this type of hedge should work (assuming ...



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