# Tag Info

6

I basically agree with @John, let me expand: We want to model $y$ using a simple linear model, the most basic setup is $$y = c + \mathbf{X}\beta$$ with $y$ the $N$ observations, $c$ a constant, $\mathbf{X}$ the $N \times M$ matrix of regressors and $\beta$ a $M$-dimensional vector of coefficients. This model has $M$ parameters, the elements of $\beta$. ...

6

Let $R$ be a random vector of risky returns and let $r_f$ denote the risk free rate. Let vector of expected returns $\boldsymbol{\mu} = \operatorname{E}[R]$ and covariance matrix $\Sigma = \operatorname{Cov}(R)$. The maximum Sharpe ratio portfolio among risky assets is called the tangency portfolio. Quick method to tangency portfolio Let's find the ...

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To complement @skoestimeier's answer on the shortselling-allowed case, I provide a vectorised version. Using the original notation in my post (you may change $r$ to something like $r-r_f$, but this doesn't affect the algebraic structure). Our goal is to find the maximiser for the problem $$\max_{w}f(w):=\frac{w^T r}{(w^T\Sigma w)^{1/2}}.$$ Let $$\phi: w\... 4 What you are talking about is called regression using fractional polynomials and it has its merits. The canonical reference is this one: Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling by Royston and Altman (1994) From the abstract: The relationship between a response variable and one or more ... 4 There are two cases, where short sales are allowed: With riskless lending and borrowing and without. As mentioned in the comments, you just have to solve a linear system. With riskless lending and borrowing The existence of a riskless lending and borrowing rate r_f implies that there is a single portfolio of risky assets, that is preferred to all other ... 3 In full generality this is a very difficult question. The closest you will get to a general framework is Vapnik-Chervonenkis theory. You can read about this in Chapter 7.9 of "The elements of statistical learning" by Hastie, Tibshirani and Friedman which can be downloaded from their website . But be warned that this is a theoretical approach. Often more ... 3 The following is a good way to judge the quality of fits for a model. http://en.wikipedia.org/wiki/Akaike_information_criterion 3 We know that -1\le\rho_{imp}\le 1 so perhaps the simplest approach is to try the possible values \rho_{imp}=\{-1,-0.9,-0.8,\cdots,0.8,0.9,+1\}, to calculate resulting \sigma values, d± values, and M_{quote} values, then see which of these is closest to the observed market price. If desired you can then search a finer grid between two adjacent assumed ... 3 Interesting idea. I'm guessing this isn't used for two reasons: First, the only algorithm I could find is O(n^3), which is horrible if you're using a moderately-sized high-frequency dataset. Least squares is O(nk^2) (n is the number of rows, and k is the number of predictors; typically k<<n). More relevantly, L1 regression is almost as ... 2 Let \rho\triangleq\rho_{imp}. Note that:$$\frac{\partial \sigma}{\partial \rho}(\rho)=-\frac{\sigma_0\sigma_1}{\sigma(\rho)}<0$$Therefore \sigma is monotonic in implied correlation. In addition, the Margrabe pricing function M(\cdot) is also monotonic in volatility \sigma thus you can find an unique solution to the equation:$$\tag{1}M_{\text{...

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This book might be what you are looking for: Theory of Financial Risk and Derivative Pricing. From Statistical Physics to Risk Management by J.-P. Bouchaud and M. Potters As one reviewer from amazon wrote: Econophysics (the application of techniques developed in the physical sciences to economic, business and financial problems) has emerged as a ...

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Just brainstorming here, could you possibly approach risk of an option from a probabilistic perspective? Because the price of the option ($S - X$, where $S$ is lognormally distributed) is lognormally distributed with the same standard deviation as $S$ (aside from being truncated at 0 and having the probability go to infinity as $S$ decreases or $X$ ...

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An approach to consider is: Computing the total return streams of all the instruments in the portfolio Calculate the risk parameters using 1 Weight appropriately (Equal risk contribution, min variance etc)

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As you suggest, in the case of non-stationary time series, the Hurst exponent is not suitable to measure the time seires persistence for the reasons you cited in the question. Particularly, when $H(q)$ is a non-linear function of q, as in the non-stationary time-series case, the time-series has to be analysed as it is a multi-fractal system (to deal this ...

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