Abstract
Covariance models of stock returns appear throughout the investment process, e.g., forecasting portfolio risk, hedging, constructing Markowitz return-risk optimal portfolios, and algorithmic trading. Models are usually point estimates, often classically inferred. Techniques are later applied to try to improve the forecast and generate distributions. However, making a decision requires one’s best prediction given the information at hand, along with estimates of accuracy. This paper presents a method for specifying a covariance model’s forecast errors and formulas for the consequent error in portfolio variance forecasts. The knowledge can be used statically to report uncertainty of fixed portfolios or considered during portfolio optimization.
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