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Feb
3
comment On a source for a mean-variance portfolio optimization result
I think Markowitz' 1959 book does, but it's a straightforward optimization that is easy if you look up the relevant matrix derivatives. I think I went through the math in another question here, but can't find it now.
Jan
28
comment Why random walk Metropolis Hasting algorithm works bad on GARCH(1,1) parameters estimation
I would distinguish between Gibbs sampled MCMC and Metropolis-Hastings MCMC. Gibbs sampled MCMC (what I assumed you meant by random walk) does not do a rejection step the way that Metrpolis-Hastings does.
Jan
28
comment Why random walk Metropolis Hasting algorithm works bad on GARCH(1,1) parameters estimation
Rejecting the negative ones is Metropolis-Hastings. For MLE, you might look at the source code for Kevin Sheppard's MFE toolbox for Matlab. You can look at his implementation of multivariate Garch there as well. Alternately, fGarch or rugarch for R.
Jan
28
comment Why random walk Metropolis Hasting algorithm works bad on GARCH(1,1) parameters estimation
The Metropolis-Hastings step is that they have to ensure that alpha and beta are positive. I can't speak much more to this particular paper. I usually fit Garch with MLE because I have sufficient data. MC Stan has a good example on fitting Stochastic Volatility models in its manual that you might check out.
Jan
20
comment Black-Litterman, how to choose the uncertainty in the views $\Omega$ for smooth transitions form prior to posterior
You might also refer to Equations 21-23 in papers.ssrn.com/sol3/papers.cfm?abstract_id=1213325
Jan
20
comment What are the parameters of the function PORTVAR in Matlab?
Without looking at the source, I would guess that they use the Matlab function cov on the returns to get the covariance matrix. The only thing I'm not sure of is if they use the population or sample covariance matrix. You can think of this like what would have been the variance of a portfolio rebalanced in each time period.
Jan
17
comment Geometric Returns values less than -100%
@Kamster Thanks for the correction. I mean the log differences, but didn't do the Latex right.
Jan
16
comment Geometric Returns values less than -100%
The 2 makes it annualized.
Jan
13
comment Black-Litterman with simple portfolio
Two options. The first (and easiest if you generalize it) approach is to expand your mean and covariance to include the market. Then you can take the view directly. The second is to create a view on asset 1 that mimics this behavior. In particular, you'd take a view that asset 1 has a return of 40% (solving -60%=x-100%).
Jan
13
comment Black-Litterman with simple portfolio
Work through Idzorek's paper (the second thing that comes up when googling) corporate.morningstar.com/ib/documents/MethodologyDocuments/… it is pretty clear how to implement your example. If you can point to a specific thing that you're having trouble setting up, then I can help with that.
Jan
13
comment Log returns and GARCH models
@Ludo Check out this: symmys.com/node/85
Jan
13
comment Black-Litterman with simple portfolio
Have you tried googling for Black-Litterman. There are tons of examples out there.
Jan
3
comment Bayesian or Frequentist in Finance?
Frequentist is far more common. The best way to learn is reading books and then writing programs. In terms of what is better in practice, I think out-of-sample Bayesian and Michaud have better properties than Mean-variance.
Dec
11
comment How to find the best fitting GARCH model for a portfolio composed of 3 ETFs in R?
I'm pretty sure you can output the likelihood on rugarch, which means it's not much additional work to get the AIC. Then just write a function to compare the fits.
Nov
24
comment What are the canonical books for statistics applied to finance?
And his website has tons of support materials.
Nov
19
comment Different ways of portfolio optimization
@user8 I think James is pretty clear. For these problems, it is pretty easy to analytically show that they all produce the same efficient frontier. So for a $\lambda$ you could find a target return or target volatility problem that will produce the same optimal portfolio. Whether you want to use one or the other depends on what you're trying to do and what optimization software you have. Nevertheless, contra James I still could imagine a situation where I would optimize utility and still constrain variance or tracking error.
Nov
12
comment Mutivariate t markets
@Quartz I made a slight edit to throw in some basic background. I'm not sure how the elliptical point really helps you. I find that once I start working with heavy tail distributions, I typically just move to a Monte Carlo approach rather than work analytically. Any other issues I can help you with?
Nov
6
comment Factor Model - Minimum Variance Portfolio [Complete Proof]
It's not a coding issue so much as it's the result of using long short portfolios. If you do the optimization imposing the long-only constraint on weights, then the results will be more stable. I'm sort of loathe to do things in terms of factor weights because it might force me to go short a lot of positions I wouldn't want. You might alternately just allow yourself to be long and short liquid instruments (like long SPY short IWM to account for a size effect).
Nov
6
comment Factor Model - Minimum Variance Portfolio [Complete Proof]
Perhaps I wasn't particularly clear. The $\Sigma$ could be any invertible covariance matrix. I meant that you can plug in the formula for $\Sigma$ being whatever it is. Obviously, if you're only using the factor covariance matrix, then your weights would be $K \times 1$ (which seems silly to me), but you can easily transform that into the security covariance matrix and have it be $N \times 1$. So you could replace $\Sigma$ with whatever formula you need and then express the weights analytically in terms of each part.
Oct
27
comment Portfolio Optimization using S&P Universes
This question might be a bit too general to be able to answer. It might be improved by discuss within the context of a particular optimization or factor model.