In this paper we test the efficiency hypothesis in financial market. A market is called efficient if the price variations "fully reflect" relevant information, i.e. a speculator cannot make a profit out of it. A currency exchange market is a natural candidate to check efficiency because of its high liquidity. We perform a statistical study of weak efficiency in Deutschemark/US dollar exchange rates using high frequency data. In the weak form of efficiency the information can only come from historical prices.The presence of correlations in the returns sequence implies the possibility of a statistical prevision of market behavior. We show the existence of correlations by means two statistical tools. A first analysis has been performed using structure functions. This approach gives an indication on the returns distributions at different lags τ . We have also computed the generalized correlation functions of the return absolute values; roughly speaking this is a test of the independence of the fluctuations of fixed size. In both cases we have obtained a clear evidence of long term return anomalies. This implies a failure of the usual "random walk" model of the returns; nevertheless the presence of long term correlations does not directly imply the fault of the weak efficiency hypothesis : it is not obvious how to use time correlation to make a profit in a realistic investment.Then we show how this information is relevant for a speculator. First we introduce a measure of the available information relevant from a financial point of view, with a technique which reminds the Kolmogorov ǫ-entropy. Second in the case of no transaction costs, we propose a simple investment strategy which leads to an exponential growth rate of the capital related to the available information.We have performed two kind of information analysis in the return series. We show that the available information is practically zero if the speculator wants to change his portfolio systematically after a fixed lag τ : for him the market is efficient. Instead, a finite available information is observed by a patient investor who cares only of fluctuation of given size ∆. This is the first case, as far as we know, in which the available information obtained by a suitable data analysis is directly linked to the possible earnings of a speculator who follows a particular trading rule.
We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in repeated multiplicative games originally introduced by Kelly. As particular cases we obtain the Cox-Ross-Rubinstein and Black-Scholes in the complete markets case and the Schweizer and Bouchaud-Sornette as a quadratic approximation of our prescription. Technical and numerical aspects for the practical option pricing, as large deviation theory approximation and Monte Carlo computation are discussed in detail.
Analysing the database made available by the European Central Bank and by the European Banking Authority, we evaluate the Comprehensive Assessment (Asset Quality Review and Stress Test) of banks carried out in 2014. In a nutshell, the main results are: i) risk-adjusted capital ratios are negatively related to the Asset Quality Review shortfall, but not to the Stress Test shortfall, whereas the leverage ratio plays a significant role in both cases; ii) the Comprehensive Assessment predominantly concentrated on traditional credit activity rather than on banks' financial assets; iii) the Comprehensive Assessment seems to be characterized by double standards. The Asset Quality Review was severe with banks operating in non-core countries, while medium-sized banks were either riskier or were treated severely in both exercises. The analysis leads to a puzzle: comparatively, the assessment per se led to significant adjustments for solid banks and large shortfalls for weak banks. The puzzle can be resolved by referring to the legacy of the country's former supervisory activity and to the low level of capitalization of weak banks mostly in peripheral countries.
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