duces its own risks. This then has to be a subjective process involving all information available 5 and not just historic data. Subjective and Implied Probability Distribu- tions We argue that every market-participant has their own subjective probability distribution based on the information available to him . Because peo- ple have different information available (and differ- ent levels of rationality when forming beliefs about the future) the distributions and hence valuations are subjective. These differing valuations then lead to trading and the observed market prices determine implied prob- abilities — one can consider them the beliefs of the market as an “organism” $^{6}$. Futures imply expected returns for these implied distributions, but more de- tailed implied distribution features can be extracted from option prices (volatility smiles) [2]. Hence we argue that there are only the beliefs of each market participant (which do not have to be hu- man, as computer trading illustrates) and an implied probability distribution (or for sparse data rather im- plied probabilities), which represents the “beliefs of the market”. Futures Futures are arguably the most simple con- tracts and they tell us directly the implied expected return. In the traditional approach it is argued that this is true, but it is the expected return of the “risk- neutral” distribution (which obviously should be the risk-free rate) and the “real” distribution could have a different expected return, and in fact generally should have to allow for a risk premium. We disagree and argue that there is nothing like a “real” distribution that exists objectively. Part of the confusions seems to originate from the mislabelling of uncertainty as risk. It is clear that there are situations where we are not certain about the precise outcome, yet we are certain that we will not have an adverse outcome. Such a situation is rep- resented by the green line in figure 1 — here we are almost certain not to lose money (with a long posi- tion), but there is a significant uncertainty (standard deviation) about the precise outcome. Should uncertainty then attract a risk-premium as is for example assumed in Modern Portfolio Theory? Hence it is misleading to say that arbitrage does imply futures prices. Arbitrage trades move spot and futures markets to be compatible with hedging costs. (See figure 2 for an analogy from physics.) In effect this enforces an implied expected return compatible with the hedging cost. For assets with no storage and transaction costs and available funding at the risk-free rate, this is the risk-free rate. But if the implied expected return is the risk-free rate, where is the risk premium? Interaction of Spot and Future Markets We first observe here that a future arbitrage trade does not only move the futures price, but also the spot price as assets will have to be bought or shorted. The net effect is a move towards equilibrium of both mar- kets. The less liquid market will adjust more than the liquid one $^{7}$. There is just an implied distribution, of which fu- tures determine the expected return. This implied expected return is not necessarily the risk-free rate, but a return compatible with hedging expenses (and feasibility) (this is a well-known fact for commodi- ties with storage costs like oil, but also for perishable agricultural products). By pricing options on such assets off the futures value one implicitly uses the fu- tures price as an expected return — now different to the risk-free rate. 3.1 Risk and Risk Premium 7 Note that the spot market is not always the more liquid one. One example are illiquid grain markets. 5 Interesting feedbacks arise as people use historic data as information. If it is known how people use historic data this influences the interpretation of the historic data itself. We just want to mention here momentum effects. 6 In fact, the economy as a system seems to satisfy most criteria for a living organism. Even Darwinian evolution can be observed in the way business structures, political systems, and commercial products change over time. 4