Risk neutral

The concept of risk neutrality, in the decision theory, the property of a market participant, such as investor, when choosing between different alternatives same expected value neither safe nor unsafe to prefer alternatives but to orient themselves alone in their mathematical expectation.

This means in particular that the certainty equivalent ( CE, English certainty equivalent) of the operator, ie the one safe amount which is equal value to market participants as the statistically expected uncertain payoff, always as high as this withdrawal itself, as the difference between insecure and secure payment defined absorbed. Risk premium (RP, English riskpremium ) so regularly disappears in this case.

Formal definition

Risk neutrality corresponds visually to the fact that the graph of the individual utility function of the operator is linear (see figure), it is therefore a function with constant marginal utility is: the risk of potential financial losses and the prospect of possible capital gains equal to weigh heavily in the decision.

Accordingly, an operator is called risk neutral if always the following relations hold for a payout in unsafe height:

In words, the expected utility E ( u) from the payment w is as high as the utility u from the expected payoff E (w).

The degree of risk aversion or risk appetite of a market participant can use the Arrow / Pratt measure of absolute risk aversion

Be quantified, which is always in the case of risk neutrality of the operator is zero. The same is true, as already told to input, for the difference between the expected payoff and uncertain of their safety equivalent, the so-called. Risk premium: they too, in the case of a risk-neutral market participant always zero. Accordingly, following also applies:

Other forms of risk adjustment are:

• Risk aversion or risk aversion:
• Risk appetite and risk taking:

Examples

• A market participant has the choice between the secure payment of the amount of 100 euros and a lottery that pays a profit of 200 € with a probability of 50 % and a profit of 0 € with a probability of 50 % also. While the risk-neutral market participants in this lottery and the sure amount of money is indifferent to, the risk-averse market participants pulls the safe amount of money before, and the risk-seeking market participants the lottery.
• A consumer has the choice between a " traditional" and a new product that better with a probability of 50 % and a probability of 50 % worse than the previous product. While the risk-neutral consumer the old and the new product is indifferent to, the risk-averse consumers, the tried and the venturesome consumer prefers the new product.