Risk aversion

The concept of risk aversion or risk aversion always referred to in the decision theory, the property of a market participant, such as investor, in the choice between several alternatives same expectation value, the alternatives with the lower risk in terms of the result - and therefore the least possible loss - to prefer.

So Risk-averse market participants prefer a safe profit as possible, even if this fails by less.

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 is less than such payment itself, as the difference between insecure and secure payment defined absorbed. Risk premium (RP, English riskpremium ) So in this case, is always positive.

Formal definition

Risk aversion corresponds visually to the fact that the graph of the individual utility function of the operator rather curved or concave (see picture), so it is a function with decreasing marginal utility: the risk of possible loss of assets outweighs the possible risk of capital gains in decision-making.

Accordingly, a market participant is risk-averse or risk-averse called if always following relationships apply for a payment of uncertain height:

In words, the expected utility E ( u) from the payment w is less than 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 positive in the case of risk aversion of the market participant. 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-averse market participant always positive. Accordingly, following also applies:

Other forms of risk adjustment are:

• Risk neutrality:
• Risk appetite and risk taking:

Examples

• An investor has the choice between a secure income 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%. And although the expected payoff of the lottery amounts to an average of 100 euros also, the risk-averse market participants is only willing to participate in it, even if he must only invest less because of the risk of a lower return than the safe yield.
• A consumer has the choice between a " traditional" and a new product, which is with a probability of 50 % better and with a probability of 50 % worse than the previous product. Is the price of both products equal, the risk-averse consumer derives the time-tested product at the moment - to buy the new, he is at best be ready when, in this case, a positive for the risk to get a worse product than the previous, with a discount ( risk premium ) will be compensated.

Practical significance

In decision theory, it is assumed that investors are risk averse under normal circumstances and expect an appropriate risk premium for risks taken usually.

So also the Capital Asset Pricing Model (CAPM ) calls for explicit risk premiums. However, these can also be negative, so that the securities in question can survive in the market even with a return below the risk-free rate and a negative correlation between the considered securities and the market portfolio. However, it is very difficult to find such securities with negative betas, so that one starts as a rule of positive risk premium in the Arbitrage Pricing Model ( APM).