Risk taking

Risk appetite is a redirect to this article. Risk appetite can also be used as a generic term for different degrees of risk attitude .

Utility function of a risk-affine (risk-taking) market participant
CE - security equivalent ; E (U (W)) - expected value of utility (expected utility) of the uncertain payout; E (W) - expected value of the uncertain payout; U (CE) - utility of the safety equivalent; U (E (W)) - utility of the expected value of the uncertain payoff; U (W ₀ ) - use of the minimum payout; U (W ₁ ) - use of the maximum payout; W ₀ - minimum payout; W ₁ - maximum payout; RP - risk premium

Risk affinity ( risk appetite or risk sympathy ) referred to in the decision theory , the property of a market participant or decision maker , z. B. an investor , when choosing between several alternatives with the same expected value, always prefer the alternatives with the greater risk in terms of the result - and thus also the highest possible profit. The opposite of willingness to take risks is risk aversion , in between is risk neutrality .

Formal definition

Risk affinity visually corresponds to the fact that the function graph of the individual utility function of the market participant is curved to the left or convex (see figure), i.e. it is a function with increasing marginal utility : the prospect of potential asset gains outweighs the risk of potential asset losses when making a decision. ${\displaystyle u(w)}$ ${\displaystyle u'(w)}$

Or as André Kostolany once put it: “A bullshit is more likely to take losses when the stock market falls than missed profits when it rises and he is not there.”… “After all, a share can rise by 1,000 or 10,000 percent, but only fall by a maximum of 100 percent. "

Accordingly, a market participant is called risk- loving or risk-affine if the following relationships always apply to a payout in an uncertain amount : ${\displaystyle w}$

${\displaystyle E(u(w))>u(E(w))\ \quad {\text{bzw.}}\quad CE>E(w).}$.

The expected benefit from the payout is greater than the benefit from the expected payout . ${\displaystyle E(u)}$ ${\displaystyle w}$ ${\displaystyle u}$ ${\displaystyle E(w)}$

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

${\displaystyle ARA(w)=-{\frac {u''(w)}{u'(w)}}}$

be quantified, which is always negative in the case of the risk affinity of the market participant. As already mentioned, the same applies to the difference between the expected uncertain payout and its security equivalent , the so-called risk premium : this is also always negative in the case of a risk-conscious market participant. The following also applies accordingly: ${\displaystyle E(w)}$ ${\displaystyle CE}$ ${\displaystyle RP}$

${\displaystyle E(u(w))=u(CE)=u(E(w)-RP)=u(E(w)+|RP|)\!\,}$.

Further forms of risk attitude are:

• Risk aversion or risk aversion :

${\displaystyle E(u(w))<u(E(w))\ }$ and

• Risk neutrality :

${\displaystyle E(u(w))=u(E(w))\ }$.

Examples

• An investor has the choice between a secure return of 100 euros and a lottery , which pays out a profit of 0 euros with a probability of 50% and a profit of 200 euros with a probability of 50%. And although the expected payout of the lottery is on average no more than 100 euros, the risk-taking market participant is nonetheless ready to participate in it, even if he has to invest more for the chance of a higher profit than for the secure return.
• A consumer has the choice between a "tried and tested" product and a new product, which is 50% better and 50% worse than the previous product. If the price of both products is the same, the risk-taking consumer prefers the new product - he is only willing to buy the old one if he has given up on the chance of getting a better product than the previous one by means of a price reduction (in this Case of a negative risk premium) is compensated.

Practical meaning

Decision theory usually assumes that investors are risk averse under normal circumstances and expect a corresponding risk premium for the risks they take. On the other hand, it can be observed that many people play the lottery regularly , although the average expected payout (profit minus price of a lottery ticket) is negative, i.e. usually a loss (on the part of the lottery player) is to be expected. This can be explained u. a. in that the utility function of a real market participant usually has both concave and convex sections, i.e. the same market participant, for example, acts risk-averse as long as the assets are high, but loves risk with low “stakes”. In addition, lottery players usually ascribe such a high subjective benefit to the high, albeit very improbable, profit that the average expected benefit ${\displaystyle u(w_{1})}$

${\displaystyle E(u(w))=u(w_{0})\cdot p(w_{0})+u(w_{1})\cdot p(w_{1})}$

so that it always remains greater than the benefit of the average payout to be expected (with lotteries regularly negative) . ${\displaystyle u}$ ${\displaystyle E(w)}$

economic aspects

Market participants who are willing to take risks therefore prefer the highest possible profit, even if this makes it uncertain. This means in particular that the certainty equivalent (CE, English certainty equivalent ) of the operator, so the one safe amount that has equal value to the market participants as the statistically expected uncertain payoff, it is always greater than this withdrawal itself, between the difference so-called risk premium (RP, English risk premium ) is defined so in this case always negative.

The risk premium is directly related to the risk attitude of a decision maker. The following risk settings can therefore be assigned to the risk premium : ${\displaystyle RP}$

${\displaystyle RP=0}$ risk neutral,

${\displaystyle RP>0}$ risk averse,

${\displaystyle RP<0}$ risk taker.

A risk-free investment has a standard deviation of zero, a zero correlation with all other risky forms of investment, and offers a risk-free return. Risk-neutral investors expect a return in the amount of the risk-free interest rate, because they do not demand a risk premium and assign a disuse to the risk . Risk-averse investors, on the other hand, prefer investments that pay a risk premium. In turn, risky investors even receive a risk premium from the counterparty . There is a risk premium for the systematic risk because the investor cannot avoid this risk through risk diversification . In the case of unsystematic risk, market participants can optimize their portfolio through skillful risk diversification , so no risk premium is paid here.

Individual evidence

1. ^ Matthias EF Wurster: Multidimensional restructuring management ; DUV 2003, p. 209.
2. ↑ Oliver Everling / Monika Müller: Risk Profiling of Investors , Banken-Verlag Cologne 2009.
3. ^ André Kostolany: The great Kostolany ; Ullstein, Berlin 2005, p. 226.
4. ^ André Kostolany: The art of thinking about money ; Econ, Munich 2001, p. 181.
5. ↑ Milton Friedman / LJ Savage: Utility Analysis of Choices Involving Risk . In: Journal of Political Economy . 56, No. 4, 1948, pp. 279-304.
6. ↑ Wolfgang Breuer, Marc Gürtler: The Friedman / Savage Paradoxon , University of Aachen, 2006. ( Memento of the original from March 17, 2014 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. 
7. ↑ Florian Bartholomae / Marcus Wiens, Game Theory: An application-oriented textbook , 2016, p. 11
8. ↑ Matthias Kräkel, Organization and Management , 2007, p. 70
9. ↑ Thomas Schuster / Margarita Uskova, Financing: Bonds, Shares, Options , 2015, p. 154
10. ↑ Florian Bartholomae / Marcus Wiens, Game Theory: An application-oriented textbook , 2016, p. 11