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

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

3. 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

4. Course objective
Evaluate the risk for a given allocation

5. 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)

6. 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

7. 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,…).

8. Forecasting Returns

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

10. Website