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Nov
13
revised Mutivariate t markets
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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
12
revised Mutivariate t markets
added 300 characters in body
Nov
12
answered Mutivariate t markets
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.
Nov
6
answered Factor Model - Minimum Variance Portfolio [Complete Proof]
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.
Oct
27
comment How is stock data objectively different to this random walk?
You can have a random walk with a non-normal distribution. However, if the non-normal distribution is the result of some underlying process (like regimes per @vonjd or stochastic volatility), then it would not be a random walk anymore.
Oct
26
revised Statistical arbitrage using eigen portfolios
added 1 character in body
Oct
26
comment Statistical arbitrage using eigen portfolios
If you were implementing Section 5.3-4 in practice, then yes, you'd net things out across all the different arb trades you're making and betas on each portfolio to have to figure out how much of each stock to buy.
Oct
24
answered Statistical arbitrage using eigen portfolios
Oct
22
comment Where can I find a list of VaR and CVaR formulas for continuous distributions?
Other than the one posted by @YuliaV, I'm not aware of any papers like that off the top of my head. In practice, I just don't use the analytic formula often (really only for normal VaR). Not sure how common that is for others.
Oct
22
answered Weighting with restrictions, but no clear objective function?
Oct
22
answered Where can I find a list of VaR and CVaR formulas for continuous distributions?
Oct
22
comment Where can I find a list of VaR and CVaR formulas for continuous distributions?
I disagree with your assertion that CVaR is not a commonly used term. They are interchangeable, as far as I'm concerned.
Oct
20
answered Testing the validity of a factor model for stock returns
Oct
16
comment Expected Shortfall (CVaR) Backtesting
@emcor I had meant simply using the historical CVaR for the purposes of the backtest, rather than rely on any assumptions about the distribution of returns for the strategy. If you want a confidence interval on the ES, you can bootstrap from the historical returns. I've seen some literature on expectiles, but I haven't had the chance to read it yet.
Oct
7
answered “Adding” risk-free asset to covariance matrix after the fact
Oct
3
comment Portfolio Turnover Constraint
@Richard It's not just them being positive, it's the piecewise nature of the constraint. Optimizers that require continuous functions will tend to not like it when you use absolute values. Also, this approach can easily be extended to include transaction costs, though you probably need to add in non-linear constraints $b_{i}s_{i}=0$ to ensure that sells are zero if you have buys, and vice-versa. My recollection is that it's not usually needed for turnover, but there might be cases where it is.