MMF 1922F -- Statistical Methods for Investment & Finance

(This course is offered in the Masters in Mathematical Finance Program.)

Overview of Probability & Statistics. Randomness, probability, random variables, expectation & moments, variances & covariances, dependence & conditioning, Markowitz mean-variance portfolio theory, mean-square optimal prediction, the multivariate normal distribution, estimation (maximum likelihood approach), hypothesis testing (likelihood ratio tests), some basic tests including randomization and bootstrap ideas, brief intro to Monte Carlo.

Regression Methods. Ordinary and generalized least squares, multicollinearity, lagged dependent variables, autocorrelated errors (serial correlation), regression diagnostics, robustness issues, nonlinear methods.

Multivariate Methods. Covariance functions. Principal components. Factor analysis. Discussion of applications, including Litterman-Scheinkman's approach to immunizing bond portfolios, and BARRA's approach to modeling portfolio risk.

Time Series. Univariate and multivariate time series. Stationarity, ARIMA models, Spectral Analysis (briefly!). Basic ideas of stochastic volatility modeling (ARCH and GARCH). Scenario generation.

(A) More on ARCH/GARCH modeling and (B) Value at Risk and statistical issues of the J.P. Morgan RiskMetrics document.

Some references:

Brockwell, Peter J.; Davis, Richard A. Introduction to time series and forecasting. Springer-Verlag, New York, 1996.
Campbell, J.Y., Lo, A.W. and MacKinlay, A.C. 1997. The Econometrics of Financial Markets. Princeton University Press.
R. Dennis Cook and Sanford Weisberg. (1982). Residuals and Influence in Regression. Chapman and Hall, New York.
Cootner, P.A. (ed) (1964) The Random Character of Stock Market Prices. MIT Press, Cambridge, Massachusets.
Draper and Smith. Applied Regression Analysis.
Engle, R.F. (1995) ARCH: Selected Readings. Oxford University Press.
Grinold, R.C and Khan, R.N. 1995. Active Portfoliio Management. Probus, Chicago.
R.V. Hogg and A.T. Craig, Introdution to Mathematical Statistics.
Jackson, J.E. 1991. A User's Guide to Principal Components. Wiley, New York.
Jorion, P. (2000). Value at Risk: The New Benchmark for Measuring Financial Risk. 2nd ed. McGraw-Hill.
Knez, P.J. and Ready, M.J. (1997). On the robustness of size and book-to-market in cross-sectional regression. J Finance, 52, 1355-1382.
Litterman, R. and Scheinkman, J. (1991). Common factors affecting bond prices. J. of Fixed Income, No. ??, 54-61
Markowitz, Harry M. 1991. Portfolio Selection: Efficient Diversification of Investments. Cambridge, Mass., Blackwell.
Mills, T.C. (1993) The Econometric Modelling of Financial Time Series. Cambridge University Press.
A.M. Mood, F.A. Graybill and D.C. Boes. Introduction to the Theory of Statistics.
Press, J.S. Applied Multivariate Analysis. Holt Rinehart.
RiskMetrics - Technical Document. (1996) Global Research and Market Risk Research, J.P. Morgan Guarantee Trust Company. New York.
Taylor, S. 1986. Modelling Financial Time Series. Wiley, New York.