Hi

I came across the following 2 paragraphs in the subject “Asset Allocation”, chapter " Capital Market Expectations, Part 1: Framework and Macro Considerations" in Los “Challenges to Forecasting”.

**Para 1:** In general, the analyst should use the longest data history for which there is reasonable assurance of stationarity. This guideline follows from the fact that sample statistics from a longer history are more precise than those with fewer observations. Although it is tempting to assume that using higher-frequency data (e.g., monthly rather than annual observations) will also provide more-precise estimates, this assumption is not necessarily true. Although higher-frequency data improve the precision of sample variances, covariances, and correlations, they do *not* improve the precision of the sample mean

**Doubt:** Why would only the sample variance, covariance and correlation be affected while the mean would be unaffected when higher frequency data is used.

**Para 2:** When many variables are considered, a large number of observations may be a statistical necessity. For example, to calculate a sample covariance matrix, the number of observations must exceed the number of variables (assets). Otherwise, some asset combinations (i.e., portfolios) will spuriously appear to have zero volatility. This problem arises frequently in investment analysis, and a remedy is available. Covariance matrices are routinely estimated even for huge numbers of assets by assuming that returns are driven by a smaller set of common factors plus uncorrelated asset-specific components.

**Doubts:**

a) In the case of Covariance Matrix, why should the number of observations must exceed the number of variables (assets) and why would it otherwise cause some assets to spuriously have 0 variance.

b) In simple lay man terms, what is the last line in this 2nd para trying to imply

Thanks