Carlo A. Favero IGIER, Universita’ Bocconi Econometrics Carlo A. Favero IGIER, Universita’ Bocconi

What we shall do Consider the problem of optimally allocating a portfolio among n assets

Optimal weights Optimal weights are defined as follows hence for finding weights we need estimates of expected returns and their variance-covariance matrix for a given allocation risk depends only on the variance-covariance matrix

Course objective Evaluate the risk for a given allocation

The view from the 70’s CAPM is a good measure of risk and thus a good explanation why some stocks earn higher average returns than others Returns are close to unpredictable: any predictability is a statistical artifact or cannot be exploited after transaction costs Volatility is constant Fama (1970): Efficient Market Hypothesis (EMH)

The view from the 90’s Average returns cannot be explained by market betas Returns are predictable: observed variables and term premium can predict a certain amount of stock returns variation over business cycles and longer horizons Conditional mean and variance change through time, but do not move in lockstep. Mutual funds performance persistency

Financial assets returns returns are serially uncorrelated (correlation increases with the horizon) Squared returns display serial correlation, reflecting volatility persistence Nonlinearity is a reality of financial data: a natural approach to capture nonlinearity is to differentiate alternative regimes of the world that govern alternative description of dynamics (level of volatility in the market, level of growth in economy,…).

Forecasting Returns

Volatility Models Volatility Models (ARCH, GARCH,…) Correlation Models Simulation Based Methods

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