Most of the papers that study the distributional and fractal properties of financial instruments focus on stock prices or exchange rates. This leads typically to mixed results concerning the distributions of log-returns and some multi-fractal properties of exchange rates, stock prices, and regional indices. It will be suggested to use a very well diversified world stock index in various denominations as the main object of empirical analysis. Such index has been formed using daily and intraday data. It aggregates, in principle, the non-diversifiable risk of the stock market. Compared to other global stock market indices it has extremely low volatility and, thus, a high signal to noise ratio when denominated in a currency. Furthermore, by diversification such an index can be shown to approximate the growth optimal portfolio or numeraire portfolio, which is the central object of the, so called benchmark approach. The paper will demonstrate that the above mentioned diversified index is an ideal object for studying the statistical properties of given securities. For instance, when denominating the savings account of a currency in units of this diversified global world index, one observes the movements of the currency against the entire market. This provides a practically undisturbed observation of the currency dynamics against the whole of the market. In this manner, one can conveniently disentangle, e.g., the superposition of the characteristic properties of the two currencies generating a given exchange rate. The exchange rate is then obtained as the ratio of the two currency denominations of the benchmark.

The proposed benchmark approach to the empirical analysis of financial data allows one to establish remarkable stylized facts. For instance, the log-returns of a well diversified global stock index, when denominated in a currency, are with high significance Student t distributed with about four degrees of freedom. The repeatedly documented multi-fractal appearance of financial time series turns out to be only very weak when analysed for a well diversified global index. The Hurst exponent of the observed mono-fractal behavior assumes typical values between 0.55 and 0.65. Accordingly, the quadratic variation vanishes asymptotically when reducing the observation time step size. These results can be contrasted with the mixed findings on empirical properties of FX rates or stock prices. A range of further empirical facts can be expected to be identifiable when using a well diversified index in the denomination of a given security as the object of study.