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( 1990 ) ). this particular specification describes, in broad terms, the historical distribution of daily stock prices returns in the us over the past 80 or so years, though it clearly under - estimates the fatness of the tails ( chart 11 ). the true model is known, but not to outside investors. to manage their assets, investors use a model to forecast return volatility. the success of these models is measured by their out - of - sample prediction errors. these errors can be further decomposed into two components : bias ( deviations of estimated values from their “ true ” value ) and variance ( the degree of variation across the set of estimators ). the second component captures model uncertainty. the models used by investors are assumed only to vary by their degree of parametric complexity. in particular, the models are assumed to range from the parsimony of a garch ( 1, 1 ) to the complexity of a garch ( 5, 5 ). clearly, both simpler and more complex specifications are possible, as are different dimensions of complexity. by generating random samples from the underlying stochastic process, the out - of - sample performance of these different models can be compared. 18 charts 12 to 17 show the estimated mean squared prediction errors ( mspe ) from the different models, together with their breakdown into bias and variance. this mspe is shown using different - sized data samples for estimation of the model, ranging from 20 days ( one month ) to 250, 000 days ( one millennium ). when sample sizes are small, simpler models are unambiguously superior ( charts 12 to 13 ). with highly imperfect information, adding model complexity simply increases prediction errors. indeed, in this hypothetical setup, for samples smaller than around two years, the simple model does better even than the true model. simple does not just defeat complex ; it trumps the truth. as the sample size expands, model uncertainty decreases and prediction errors fall. the performance of the complex models begins to improve relative to the simple ones. in general, prediction errors converge to a u - shaped pattern centred on the true model, with models which are either too simple or too complex inferior. this is a standard statistical finding. but it is only at sample sizes in excess of 100, 000 days ( 400 years ) that estimates of the “ true ” model outperform a much simpler one. moreover, the simple model is only materially worse than complex models when the sample size rises to