# Tag Info

15

Recently I attended a presentation by the first author of the following paper who gave us quite a creative and illuminating (kind of meta-)use of random forests in Quant Finance: All that Glitters Is Not Gold: Comparing Backtest and Out-of-Sample Performance on a Large Cohort of Trading Algorithms (March 2016) by Thomas Wiecki, Andrew Campbell, Justin Lent, ...

11

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: Calculate a full correlation matrix, weighting its elements in line with the weight of the corresponding stocks in the portfolio/index, and excluding ...

11

1) Why would you trade the error on the residual instead of creating a long/short factor model and trade expected returns? I would posit that the biggest reason people do this is for orthogonality of return. There are about 2,000 incredibly mature firms trading value, momentum, vol, etc. You would be competing with the likes of AQR, LSV Asset Management, ...

10

What they gave you is Newton's formula. If you have a function $f(x)$ then you can find the value $x_0$ such that $f(x_0) = 0$ by this method. It uses the derivative $f'$ which in your case is the vega. Your function is: $$f(x) = BS(x) - M$$ where $BS$ is the theoretical price with volatility $x$ and $M$ is the marketprice. Then $f'(x)$ is the ...

8

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 differences in methodologies matter in practice? To gauge the practical importance of the biases in methods 2 and 3, we calculate the weighted stock correlation ...

8

In addition to getting the right transition model for the Kalman filter, the main obstacle to optimizing filter performance is to implement an optimal initialization. I use an iterative approach to initialize or "tune" the Kalman filter, known as adaptive tuning. I do this because I've found alternative methods of initializing the Kalman filter (...

6

As with many machine learning technologies, you can run a separate training and testing phase before deploying it live for prediction. All it does is build a collection of decision trees based on the parameters you give it - if the output field is a factor, you get classification (a finite enumerated set of values); if it's numeric, you get prediction. One ...

6

Physicists typically know PDEs but not stochastic calculus I have a masters in physics, so have a reasonable idea of the usual skillsets a physicist will know (at least at undergraduate level), and also then a masters in mathematical finance, so learnt the hard way the bits of maths physicists typically don't know but will need to know for quantitative ...

6

It depends. For example, if you're doing option pricing in the log normal world returns are completely described by the mean and standard deviation. If you add jumps, you would also need to parametrize the underlying Poisson process which is fully described by one parameter and the jump size. In other words, if you have a (log)normal distribution and the ...

5

Of course estimating expected returns is the very core of portfolio management. Finding a useful covariance matrix too. To find both fills a book. So I first thought about closing the question. But it is a chance to discuss today's approaches. A nice approach that is very up-to-date where mementum investing seems very fashionable is the following: Momentum ...

5

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 ...

5

You can just take expectations on both sides of your SDE/corresponding integral equation and obtain an ODE on the expectation function $m_t = \Bbb E[x_t]$: $$\dot m = \theta(f - m)$$ which you can easily solve using ansatz $m_t = c_t \mathrm e^{-\theta t}$ which brings you to m_t = x_0\mathrm e^{-\theta t} + \theta\cdot\int_0^tf(s)\mathrm e^{\theta(... 5 Preliminary The main result of the Fama-MacBeth procedure is to calculate standard errors that correct for cross-sectional correlation in a panel. It is a commonly used method due to it's easily approach, and with regards to the time it was developed (1973), modern techniques like clustered robust standard errors were not yet invented. In this context, it ... 5 here is how to get covariance matrix from correlations: 4 I would argue that indeed none of the so-called stylized facts you mentioned can be explained by classical economic theory. That there was a gross delta between the predictions of classical economic theory and empirical data was foremost found out by Benoit Mandelbrot as far back as 1963 in his seminal paper: The Variation of Certain Speculative Prices In ... 4 PX_BID and PX_ASK are the static equivalents of BID and ASK, the latter two of which populate in "real time" (i.e. as they are dynamically updated). So the PX_BID and PX_ASK values are dependent upon when you pulled the data. Bloomberg's source depends on the asset in question and the exchange on which they are listed, but the data does come from the ... 4 It is very hard to answer this quiz as people might be good at different at tools. For example, if you are good at VBA, then you can achieve the same effect compared to R in most cases. The following parts are the reasons why I prefer to R based on my own situation. 'package'. This is the most obvious strength of R over Excel in terms of convenience. You ... 4 For the general solution in the case where f is not a constant, note that, from the SDE \begin{align*} dx_t = \theta(f(t)-x_t)dt + \sigma dW_t, \end{align*} we obtain that \begin{align*} d\big(e^{\theta t} x_t \big) = \theta e^{\theta t} f(t)dt + \sigma e^{\theta t} dW_t. \end{align*} Then \begin{align*} e^{\theta t} x_t = x_0 + \int_0^t \theta e^{\theta s}... 4 Theoretically speaking (as it's done in financial textbooks at b-school level), variance and covariance are calculated on historical performance of asset classes, forward looking returns are CAPM calculated returns. ARIMA. Practically speaking, ARIMA is useless for predicting long term returns (or portfolio management if you wish). Why? A short answer is ... 4 The CAPM is an economic theory that expected returns in excess of the risk free rate should be linear in the regression beta on the market. \operatorname{E}[R_i - R^f] = \beta_i \operatorname{E}[R^m - R^f]$$Graphically, it would look like this: As market beta increases, expected returns increase. Testing the CAPM with a cross-sectional regression ... 4 By definition, your loss cannot be positive, so you'd set the VaR to zero. But it really depends, on how you calculate your VaR. If you calculate your returns, sort them and look at the 5% quantile (which, as you say, may be positive), then you'd simply set your VaR to zero. But if you treat your returns as realizations of some (unknown) random variable, ... 4 The question above looks somewhat confused. Where's the error term? A recipe for a standard calculation It's customary to work with monthly returns. For each portfolio i, calculate monthly excess returns R^x_{i,t} = R_{i,t} - R^f_t where R^f_t denotes the 1-month risk free rate. Calculate or download the monthly excess return of the market R^m_t - ... 4 Richard's answer is the correct answer to a slightly different question. I think what you’re asking for is the weighted average option implied volatility for a stock. The implied volatility of a stock is analogous to the CBOE’s VIX Index for the S&P 500 Index (other securities have IV indices as well). The VIX uses a known methodology for imputing the ... 4 It depends upon how you define risk. Assume a constant, positive equity risk premium and an equity index following geometric Brownian motion (GBM):$$d \log S_t = \mu \, dt + \sigma \, dZ_t = (\hat{\mu} - \frac{1}{2} \sigma^2) \, dt + \sigma \, d Z_t.$$Let T denote the investment horizon. The standardized return is normally distributed as$$Z = \...

4

You are missing a few things. The function below assumes that returns is either a pandas series or a column of a pandas dataframe. Try this: def MDD(returns): cum_rets = (1 + returns).cumprod() - 1 nav = ((1 + cum_rets) * 100).fillna(100) hwm = nav.cummax() dd = nav / hwm - 1 return min(dd)

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B is the correct choice. I honestly would wish multiple choice would not even exist. It is the worst way of testing knowledge in my opinion. Without knowing the details of what was taught, I would say choosing C is definitely the wrong answer. The df in t-student can be used to estimate/model fat tails. According to Fat Tails in Financial Return ...

3

Some advantages of R over Excel: R is a scripting language, which allows to record a data manipulation script once and reuse it multiple times. R, as a [scripting] programming language is much more flexible than very limited Excel's GUI. In fact, R has become a de facto statistical programming environment, which delivers most recent statistical techniques. ...

3

I think there is a slight misconception into the purpose of an economic theory. The market is a complex entity to be modeled and yes, it is neither efficient nor arbitrage free but it is trading and there is a price process that corresponds to the market one. You could say that classical economic theory has failed, but I would argue the idea of a theory is ...

3

They represent the current BID and ASK at the time you query them. If you look up those fields in the terminal FLDS<GO> you will see they are marked as reference data, that means they are not continually updated. They are refreshed each time you query them. They come from the NBBO quote at the time you query them.

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