Defection of Traditional Standard Deviation Scaling of Capital Asset Returns

In this paper, we investigate the adequacy of scaling, a method frequently used in estimation of standard deviation of stock returns. Scaling is based on the assumption that standard deviation is proportional to the square root of the length of the time interval of the sample (for example daily, monthly or annual data). We analyze the cases when this assumption is justified, and emphasize possible weaknesses of this procedure. As an example, we test the assumptions of scaling on three market indices: Slovak SAX, Czech PX-50 and the S&P 500 index. We conclude that in case of Czech and Slovak index we find significant deviations from stated assumptions. Hence, contrary to the common practice, time-series scaling cannot be used on all time series and requires prior careful examination of the analyzed data.