This paper presents the results of multifractal testing of two sets of financial data: daily data of the Dow Jones Industrial Average (DJIA) index and minutely data of the Euro Stoxx 50 index. Where multifractal scaling is found, the spectrum of scaling exponents is calculated via Multifractal Detrended Fluctuation Analysis. In both cases, further investigations reveal that the temporal correlations in the data are a more significant source of the multifractal scaling than are the distributions of the returns. It is also shown that the extreme events which make up the heavy tails of the distribution of the Euro Stoxx 50 log returns distort the scaling in the data set. The most extreme events are inimical to the scaling regime. This result is in contrast to previous findings that extreme events contribute to multifractality.