estimated as follows: Portfolio manager A uses only daily data from the upcoming quarter, whereas manager B uses daily data from a rolling window of 10 years. Obviously, the risk forecasts for manager A are based on information that would not be available at the time of rebalancing. However, this risk model is a good benchmark because it is updated frequently and captures, by construction, any changes in volatilities and correlations that occur in the quarter following each rebalance. The risk model used by manager B, on the other hand, is updated very slowly. If market risk varies over time, this model may capture volatilities and correlations correctly on average, but is likely to underestimate/overestimate risk over shorter periods. Based on this setup, we should expect both managers to do equally well if their performance is mostly driven by their forecasting model for expected returns. If, though, the risk model is also relevant, then we may expect manager A to outperform manager B, due to the superiority of manager A's risk model. Over the 20 years in the sample, manager A's average excess return is equal to 5.52 percent per quarter, whereas manager B outperforms the cash benchmark by an average of 4.97 percent per quarter.2 In terms of realized risk, both managers experience a higher risk relative to their target. However, the quarterly volatility for manager A is equal to 1.78 percent, which is considerably lower than the 2.59 percent realized by manager B. Since investors like excess returns and dislike volatility, manager A outperforms manager B in both dimensions. In fact, the information ratio (the annualized excess return per unit of risk) of manager A is 60 percent higher than that of manager B. This result is quite striking, considering that it is driven only by differences in the covariance matrix estimators used by the two managers. Our two examples indicate that investment decisions and performance may be significantly affected by the choice of the covariance matrix estimator. Therefore, in the remainder of this chapter we discuss estimation techniques that can be used to produce covariance matrices with desirable statistical properties. Given the extensive literature on this topic, any attempt to provide a complete summary of the various methodologies proposed over the past few decades would be doomed to fail. We prefer to take a more practical approach. First, we identify some empirical regularities of financial data that should be captured by any covariance matrix estimator. Next, we discuss some relatively simple techniques that can be used to produce covariance matrix estimators with desirable statistical properties. Third, we discuss some data problems that are often faced by practitioners when building risk models, and we provide solutions for those problems. Finally, we discuss potential extensions and alternatives to our approach. SOME INTERESTING PROPERTIES OF FINANCIAL DATA The normal distribution is often used to characterize the uncertain outcome of an experiment. Finance is no exception to this tendency, and therefore in many applications the returns on sets of financial assets are assumed to follow a multivariate 2These numbers are considerably higher than those observed for actual portfolio managers. This is because our forecasting model uses data that are not observable at the time of rebalancing.