Our next meeting will be at the Atrium Restaurant at 101 California Street, San Francisco on Monday January 12. The meeting will start at 5:30 pm. Please use the Acteva Link below to register for the meeting. SF QWAFAFEW members who have paid their 2008 dues can attend without registering.
http://www.acteva.com/booking.cfm?bevaid=172071
Topic: Tools for higher-order portfolio optimization
For a single asset or portfolio of assets, we are used to looking at the skewness and kurtosis of returns to understand aspects of risk not captured by standard deviation alone. For multiple assets, we often rely on the covariance matrix to describe the dependence relationship among assets. However, just as standard deviation is an incomplete description of the riskiness of individual assets, the covariance matrix is an incomplete description of the dependence structure for multiple assets.
Analogously to the (2-way) covariance matrix, the multivariate version of skewness and kurtosis are 3-way and 4-way objects called cumulant tensors. They can be used to model higher-order dependence and perform portfolio optimization that accounts for skewness and kurtosis as well as mean and variance. One can also build factor models using these objects. Factor models (e.g. "principal cumulant component analysis") also help make it practical to estimate the large number of variables involved and perform optimization. This approach is well suited to asset classes that exhibit non-normal returns and non-normal dependence structure but still have single-peaked return distributions.
Speaker: Jason Morton, Stanford University
Bio: Jason Morton worked in M&A at Credit Suisse before receiving an M.A. in Economics from the University of Michigan and a Ph.D. in Mathematics from U.C. Berkeley. He managed the $50M endowment of an educational nonprofit for five years and served as the director of research for a fund of hedge funds for two. He is currently a researcher at Stanford University, where he studies the geometry of statistical dependence with applications to machine learning and finance.
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