optimization of conditional value-at-risk

by rockafellar and uryasev good description of cvar and why it's superior to var (value at risk) for portfolio optimization. they use a math technique sort of like a lagrange multiplier (not really, but works in a similar way) to transform the otherwise 2-step procedure for computing and optimizing conditional value at risk to a single stochastic optimization, convex (piecewise linear). it can then be solved with either linear programming or a nonsmooth optimizer.

interesting side note: they use a sobol sequence to get superior performance over straight-up mc. (the wikipedia article on sobol quasi-random sequences is quite dense and hard to understand, but here's a nice article that shows a monte-carlo integration example with a finance application, refs to niederreiter, sobol, and faure qrs. bottom line: niederreiter is (maybe) best.) also shows examples of portfolio optimization and optimal hedging with a butterfly spread.

certainly this is a better read than the highly mathematical paper that introduced cvar (convex measures of risk and trading constraints by f\"ollmer and schied). all i can really remember about that one is the point about cvar being convex (while var is not) and why that's important: diversification (mathematically, linearly interpolating between two portfolios) should not increase risk. still, i think it's interesting that an industry-standard book on portfolio optimization like 'active portfolio management' by grinold and khan would brush off all risk metrics other than variance so lightly. maybe return distributions really are close enough to gaussian (with exceptions for derivatives, etc.) that it doesn't matter in practice, as they claim. at least anything that can compute those quantities should also give the variance for comparison. call number:336.767 GRI ID:2406743083 Active portfolio management : a quantitative approach for providing superior returns and controlling risk / Richard C. Grinold, Ronald N. Kahn. good book to have in the personal library, although there will be an updated version out later this year or next.