Читать книгу Asset Allocation - William Kinlaw, Mark P. Kritzman - Страница 24

 Asset allocation requires investors to forecast expected returns, standard deviations, and correlations whose values vary over time.

 Long-run averages are poor forecasts because they fail to capture this time variation.

 But extrapolating from a short sample of recent history is ineffective because it introduces noise and assumes a level of persistence that does not reliably occur.

 As an alternative, investors often regress these asset class variables on economic variables to derive forecasts, but this approach may not help because additional variables contribute noise along with information.

 The investor's challenge is to maximize the information content and minimize the noise, thereby generating the most reliable predictions.

 The prediction from a linear regression equation can be equivalently expressed as a weighted average of the past values of the dependent variable in which the weights are the relevance of the past observations of the independent variables.

 Within this context, relevance has a precise mathematical meaning. It is the sum of statistical similarity and informativeness.

 Statistical similarity equals the negative of the Mahalanobis distance of the past values for the independent variables from their current values, and informativeness equals the Mahalanobis distance of the past values of the independent variables from their average values. In other words, prior periods that are more like the current period but different from the historical average are more relevant than those that are not.

 Investors may be able to improve the reliability of their forecasts by filtering historical observations for their relevance and using this mathematical equivalence to produce new forecasts.