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We would argue in two ways: Firstly, uncertainty is not what warrants a premium as it is an insufficient description of risk. And secondly, the risk-premium is a misleading concept as it suggests that the premium is part of the distribution, but not the risk we receive it for. 

We believe risk is best defined as the probability of an adverse outcome as suitably defined for a cer- tain situation $^{8}$. Hence the risk should be part of the distribution describing our beliefs about all possible outcomes. If we are aware of possible negative out- comes we will demand compensating possible positive outcomes. 

Figure 3 shows a partial probability distribution which seems to have a significant “risk-premium” of about 15% above the risk-free rate of 10% (all log returns). Traditionally that would be seen as a com- pensation for the uncertainty (standard deviation) present. 

Figure 4 then shows the full distribution, which is actually a maximum-entropy distribution for a mean 

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