You can't have negative eigenvalues. Do the eigenvalue matrix decomposition, if you can, and then substitute zeros for all the negative eigenvalues, then multiply back together to get a usable covariance matrix.

<t>VaR sometimes is annualized (or monthlised) in practice, but whether it is correct is a question. Annualization methods I have heard of concentrate on the first 2 moments only ('drift and variance grow with time'), hence are tacitly assuming i.i.d. normality or at least an elliptical distribution...

<r>Don't have it, but should be similar to this?<URL url="http://www.institutional-money.com/cms/fileadmin/Uploads/pdf/Vortraege_2009/wilmott.pdf"><LINK_TEXT text="www.institutional-money.com/cms/fileadm ... ilmott.pdf">www.institutional-money.com/cms/fileadmin/Uploads/pdf/Vortraege_2009/wilmott.pdf...

Quantitative Equity Portfolio Management: Modern Techniques and Applicationsby Edward Qian, Ronald Hua, and Eric SorensenThis is a start - see the discussion about alpha factors vs. risk factors. This is a large field, btw.

<t>How to calculate an average yearly return over the hole time?How to calculate an average 3year return?How to calculate an average yearly excess return over the hole time?How to calculate rolling 3 Year-Periods strategy outperforms?How to calculate the four numbers if the holding period is 7 month...

http://cdmrulebook.org/pageid/405http:/ ... _Mechanism

Spivak's Calculus is standard. If that's not enough, Apostol's Calculus in 2 volumes. If that's not enough, just go for real analysis. Both Spivak and Apostol wrote more advanced books, and there is always Rudin.

<t>Additive to what? Please elaborate a bit more. In Bodie Kane Marcus' Investments, they mention a special case where the Sharpe ratio (SR) of the portfolio follows a Pythagorean theorem which includes the information ratio (IR): (SR_portfolio)^2 = (SR_benchmark)^2 + (IR_portfolio)^2. But the infor...

<t>Another discussion of this is in Modern Investment Management by Litterman, p. 384 - 386. One idea for the weights is just to simply find the average weights over all time periods: for period 1, stock A is $100 out of a $1000 dollar portfolio; in period 2, $150 out of $1800. Average weight to use...

<t>The Jacobian determinant is a single number, but it doesn't show each factor separately.Another possibility is the derivative of a related quadratic form, w'Ew, which is (E + E')w, a vector. Each element of the vector is a single number which shows the marginal contribution to the quadratic form ...

<t>Is it the case that if we have AR(1) time series with x(t) = rho * x(t-1) + error, then the way to calculate variance across multiple time periods, if you have a different volatility in each time period (heteroskedasticity), is to use the quadratic form w'Ew, where w is an identity vector, E is r...

<r><URL url="http://www.thomasho.com/mainpages/analysoln.aspSome">www.thomasho.com/mainpages/analysoln.aspSome</URL> of the Excel workbooks (the Litterman model for interest rates) listed on Thomas Ho's site above use the following add in to compute eigenvalues/vectors, especially for PCA:<URL url="...

<r>Numerical Methods in Finance and Economics: A MATLAB-Based Introduction (Statistics in Practice) by Paolo Brandimarte (<URL url="http://staff.polito.it/paolo.brandimarte">http://staff.polito.it/paolo.brandimarte</URL>)Advanced Derivatives Pricing and Risk Management: Theory, Tools, and Hands-On P...

<t>"...I would class these 5 as other than mathematicians. That would leave 9 out of 14. That's not really "almost all" is it, in fact less than 2/3rds..."I said in the very next sentence that practictioners were there. There was no mistake and no spin - it was an honest answer - there are mathemati...

<t>Baruch's MFE is run out of the math dept, not the b-school. The teachers listed above are almost all mathematicians.They get practitioners to teach also - Lev Borodovsky used to be chairman of GARP, works at Tribeca Global. Other speakers come - Thomas Ho, Peter Carr, Andrew Kalotay, and others j...