Risk-Return Paradox

The risk-return paradox (English risk-return paradox is) in the economy , a postulate about the relationship between the two economic variables financial risk and return . A negative correlation is assumed, whereby the risk-return paradox is in contradiction to the classical capital market theory .

founder

The risk-return paradox was postulated in 1980 by Edward H. Bowman , who was a professor at the MIT Sloan School of Management in Cambridge, Massachusetts. During his professional career, he has mainly dealt with research areas such as operational decision-making, corporate strategies, corporate social responsibility and real options theory.

Theoretical foundations

Theoretical classification

The risk-return paradox is in contrast to the previously established classical capital market theory . His statements relate to risk management and risk controlling in companies .

Disambiguation

The concept of risk is defined by Bowman himself as a "(...) concept that captures the uncertainty, or more precisely, the probability distribution associated with the outcome of resource commitments" - i.e. H. a concept regarding the uncertainty or the probability distribution associated with the use of resources. In practice, risk is relevant ex ante, i.e. before the decision about the use of resources, but can only be measured ex post, i.e. after the decision, with various instruments. This is done, for example, with risk measures such as the variance or standard deviation of success measures, e.g. B. the return on equity .

The risk-return paradox relates not only to a specific risk, but to all potential corporate risks. Bowman sets the frequently used return on equity (RoE) as a measure of return . This results from the profit after taxes divided by the equity.

Risk-Return Paradox

Previous assumptions

Previous assumptions regarding the relationship between financial risk and return have been as follows: A typical manager is more risk averse. Thus, a riskier investment requires a higher expected return in order for it to be carried out and the associated risk to be accepted. Risk and return are therefore positively correlated: the more risk is taken, the higher the expected return (the "ex ante" return).

Bowman questions this assumption of a positive correlation. His empirical study is based on the hypothesis that higher risk is not associated with higher returns, but rather is associated with lower returns. In this contradiction lies the so-called risk-return paradox.

Empirical studies by Bowman

In order to empirically test this hypothesis, the average return of a company and its profit variability, i.e. its profit fluctuations, were examined. The observation period spanned five years (1972–1976). The companies were assigned ranks on the basis of these parameters and the median was then established. The resulting values ​​were classified in a 2x2 contingency table for each branch examined .

The only industry that contradicted Bowman's preliminary considerations was the metal and mining industry. A positive relationship between risk and return was shown here. In all of the other industries examined (e.g. packaging, banking), however, it was evident that - as Bowman assumed - there is a negative correlation between risk and return in the individual industries.

After this preliminary study, the results obtained so far were checked in a further, larger-scale empirical study. For this purpose, 1,572 different companies from 85 industries were examined over a period of nine years, from 1968 to 1976. The result was that the hypothesis of a negative risk-return relationship was supported by 56 industries and refuted by 21. No clear statement could be made for eight industries. Thus Bowman's hypothesis is largely supported by both studies so far.

Then the values ​​of around 300 companies from nine different industries were aggregated and also shown in the 2-field matrix. However, no correlation whatsoever between risk and return was evident, neither positive nor negative.

It should therefore be noted that, according to Bowman's results, there is usually a significant negative risk-return correlation within an industry. This refuted some of the previous findings. However, if several industries are viewed as an aggregate, there is no longer any correlation between risk and return.

It should also be noted, however, that the paradox would not occur in a perfect market.

Attempts to explain the results

Bowman explains these results by saying that competent management within an industry can generate higher returns with lower fluctuations. Other explanations lie in the risk attitude of the managers - they could be risk-averse instead of, as previously assumed, risk-averse - as well as in the strategy chosen by the company. For example, a company may benefit from a strategy implemented earlier and thus achieve higher profits with relatively low fluctuations at the same time. These can include, for example, an existing customer base, a high reputation for a product or the entire company, or high employee loyalty. In addition, more profitable companies are often more diversified than less profitable companies, which can also reduce risk.

Measures to Eliminate the Paradox

The anomaly discussed by Bowman can be eliminated, for example, by differently pricing the securities of the respective companies. According to Bowman, securities should be priced comparatively higher if they come from companies with low risk and high profits. In the process, the profit of the security buyer is reduced and the paradox described by Bowman is eliminated .

Approaches to explaining the risk-return paradox

Prospect theory

The prospect theory by Daniel Kahneman and Amos Tversky   (1979) represents a theoretical frame of reference for the risk-return paradox . It modifies the normative expected utility theory. The decision of the individual is made in favor of the alternative with regard to their prospects (prospectuses). Prospect theory divides decision-making into two phases. In the first phase, the alternatives are presented and analyzed (editing phase). This is followed by the evaluation of the alternatives available for selection (evaluation phase). The editing phase can be described by six mental phenomena.  

1. Coding: The results of the decisions are not viewed in absolute numbers, but as gains (upward deviation) and losses (downward deviation) with regard to a reference point (zero point).

2. Combination: Simplification of decision-making by adding the alternatives with the same result.

3. Segregation: Excluding the safe component. (E.g .: a profit of 500 euros with a probability of 70% and a profit of 300 with a probability of 30% results in a certain profit of 300 euros.)

4. Cancellation: Alternatives with the same components are not taken into account.

5. Simplification: “Out of round” probabilities are mentally rounded up or down. For the sake of simplicity, extremely improbable results are excluded. 6. Elimination of strictly dominated alternatives. 

Course of the evaluation function

Each payout is assigned a value that reflects the subjective benefit of the payout for the decision maker. The payout results are viewed as a deviation (v) from a previously defined reference point (coordinate origin). The abscissa represents profit / loss (objective value), the ordinate the associated subjective values ​​of the decision-maker, which he ascribes to the profits / losses. The change in value in relation to the reference point is the bearer of the benefit, not the absolute number. The reference point for the benefit depends on the reference system (framing). For the decision maker, the value of the alternative depends firstly on the reference point and secondly on the amount of the deviation with regard to the reference point.

In the area of ​​positive prospectuses, i.e. events with a profit outlook, the curve of the value function is concave. The value function of the curve is steeper and more convex in the area of ​​negative prospectuses, events with a prospect of loss.

Justifications

The reason for this form lies in the psychological perception of the decision maker and the stimulus size. Kahneman and Tversky explain the curvature of the valuation function in the profit area with the fact that the absolute difference between the profits is of less importance for the decision maker, the larger the expected profit is. For example: A profit from 50 to 100 euros is valued higher by the decision maker than if a profit increases from 2000 euros to 2100 euros. This logic can be transferred to the loss area, which explains the convex shape. The steeper course of the evaluation function in the loss area compared to the profit area can be explained by the fact that the decision-maker is more influenced in his decision-making behavior by losses than by gains due to loss aversion. For this reason the evaluation function is not point symmetric . An explanation for the loss aversion is the endowment effect ( English endowment effect ), which is often not in the literature clear-cut from the status quo bias is deferred. The possession effect means that objects that are already in your own possession attach a higher value, ie the appreciation of an object depends on the ownership structure.

Combination of value and weighting functions

To evaluate the alternatives, a subjective value ( ) of a prospectus is used for risky alternatives. The subjective value V of a prospectus (choice between risky alternatives) results from an objective value and an objective probability , which are "distorted" by the subjective weighting of the prospect theory. ${\displaystyle V}$ ${\displaystyle x}$ ${\displaystyle p}$

${\displaystyle V(x,p)=v(x)\cdot \pi (p)}$.  

This is followed by the four-fold pattern of risk attitudes of prospect theory. The decision maker is risk averse in the areas of high probability wins and low probability losses. On the other hand, he is risk-prone in the area of ​​wins with small probabilities and losses with high probabilities.

With regard to the risk-return paradox, this means that the reference point for a decision is determined by the relative return position (often the return on capital or on sales in the sector).

Following the expected performance (prospectus) in relation to the reference point, the characteristic of the decision-maker (risk-averse, risk-averse) emerges depending on the situation. A company performance above the reference point in connection with positive prospectuses (a profit prospect) leads, according to the prospect theory, to a risk-averse behavior of the decision-maker. In contrast, a performance below the reference point and negative prospectuses (loss prospects) lead to risk-taking behavior on the part of the decision maker. This means that companies that underperform tend to accept higher risks. This risk-taking behavior, which results from the prospect of loss for the decision maker, can be justified by the fact that the decision maker tries to compensate for the poorer performance through the higher risk exposure in order to avoid losses. This can explain a negative performance (return) risk relationship.

Contingency approach

The contingency approach as an explanatory approach for the risk-return ratio is based on internal and external factors. The organization of a company is described by internal coordination mechanisms, the division of labor and internal and external context factors. Internal context factors represent e.g. B. the size of the company or the diversification of the service program, the geographical area of ​​activity as well as the production processes used. As a result of empirical studies, the diversification strategy could be determined as a successful strategy for reducing the risk.

Behavioral Approach

Typical representatives of corporate behavior theory are Richard Cyert and James March with their study from 1963. They investigate the relationship between corporate performance and the willingness to take risks in decision-making in organizations. Their theory is based on the basic assumptions of Herbert A. Simon (1945): “Administrative Behavior. A Study of Decision-Making Processes in Administrative Organizations ", which states that business subjects can only perceive decision-making situations to a limited extent. The limited capacity to absorb and process information (bounded rationality), due to the complexity and uncertainty of the decision-makers, means that rational action is not possible in decision-making situations (intended rationality).  

This has an impact on the search for alternatives in a decision-making situation. The real behavior in the search for alternatives shows that the decision-maker perceives the situation of having a large number of options available as a nuisance. For this reason, the decision maker only includes a few alternatives in his considerations, which are very close to the previous decision. The decision maker tends to stick with the tried and tested. If a satisfactory solution is found that satisfies the level of demand, the search behavior for other alternatives is discontinued. The level of aspiration is lowered if it “seems too difficult” to find a solution. The search for new solutions is only pursued when the safeguarding of the level of entitlement is in danger or when urgent problems exist.

With regard to Bowmann's risk-return paradox, this means that decision-makers prefer to be satisfied than to optimize and thus the basis for decision-making is the company's performance in terms of reference points / reference matrix (level of aspiration) for essential success references. If the company's performance is greater than the reference point (s), the decision-maker acts in a risk-averse manner. If, on the other hand, the company's performance is lower than the reference point (s), they are willing to take risks. If the company's performance is at the level that the company can continue to do, the decision-makers are also risk-averse.

Current state of research

Supporting Studies

The relationship between risk and return has been examined in research by numerous studies, which show conflicting results. The table below shows a selection of the research results that support the paradox.

Head of Studies	Study design	Operationalization of risk & return	Correlation between risk and return
Treacy, M. (1980)	empirical quantitative investigation 1485 U.S. companies 54 industries Period: 1966–1975 Evaluation based on rank correlation	Return = ROE Risk = variance ROE Reference point = median (return)	negative correlation below median, positive correlation above median valid within and between industries Company size no explanation for correlation: negative relationship between size and risk, no relationship between size and return
Albach, H. (1987)	empirical quantitative investigation 295 industrial corporations 463 medium-sized companies Period: 1965–1984	Return = ROE Risk = variance ROE	negative relationship between risk and return valid for successful and less successful companies
Fiegenbaum, A. / Thomas, H. (1988)	empirical quantitative investigation 2322 US companies 47 industries Period: 1960–1979 Evaluation based on rank correlation, contingency tables	Return = ROE Risk = variance Reference point = median (ROE)	negative correlation below median, positive correlation above median valid within and between industries quadratic instead of linear relationship between risk and return
Miller, KD / Bromiley, P. (1990)	empirical quantitative investigation 526 companies (1978–1982), 746 companies (1983–1987) Period: 1978–1982, 1983–1987 Evaluation based on factor analysis, regression model	Return = ROE, ROA Risk = income risk, equity return risk, strategic risk	negative relationship between income risk and strategic risk with return
Wiemann, V. / Mellewigt, T. (1998)	empirical quantitative investigation 155 German listed companies Period: 1986-1991 Evaluation based on regression model, rank correlation	Yield = ROE, ROS Risk = standard deviation of returns Reference point = median (return)	negative correlation below median, positive correlation above median valid regardless of main branch External influences: no influence of environmental dynamics on risk Internal company influences: no influence of decentralization of decisions, degree of formalization and centralization of functions on risk, negative correlation between company size and diversification on risk
Chou, PH / Chou, RK / Ko, KC (2009)	empirical quantitative investigation 27,416 U.S. companies 45 industries Period: 1984-2003 Evaluation using a regression model	Return = ROA Risk = standard deviation of return Reference point = industry and market median (return)	negative correlation below median, positive correlation above median valid within industries and at market level Explanatory approach: evidence of loss aversion (prospect theory)
Holder, AD / Petkevich, A. / Moore, G. (2016)	empirical quantitative investigation 445,821 companies Period: 1969–2013 Evaluation using a regression model	Return = ROE, ROA (at the beginning and end of the period) Risk = standard deviation of the respective returns Reference point = median (return)	negative correlation below median, positive correlation above median Explanatory approach: short-term perspectives of the manager, decision preference based on short-term company performance instead of long-term company value

Refuting Studies

In contrast to the studies mentioned above, there are also some studies that refute Bowman's paradox or attribute it to statistical effects or methods. The table below shows an extract from these research results.

Head of Studies	Study design	Operationalization of risk & return	Correlation between risk and return
Fiegenbaum, A. / Thomas, H (1986)	empirical quantitative investigation 1188 companies 198 branches Period: 1960–1964, 1965–1969, 1970–1974, 1975–1979 Evaluation: contingency tables, "Negative Association Ratio"	Return = ROE Risk = variance in return Differentiation between market risk and accounting risk	dynamic behavior of the relationship: between 1965–1969 positive correlation, between 1970–1974 and 1975–1979 negative correlation between risk and return Explanatory approach: Direction of the relationship depending on the uncertainties / forecast inaccuracies of the time periods and the choice of risk (market risk or accounting risk)
Perlitz, M. / Löbler, H. (1989)	empirical quantitative investigation 428 small and medium-sized companies 14 industries Period: 1978–1982	Return = ROE Risk = variance in return	positive correlation between risk and return within 11 of the 14 industries examined Explanatory approach: for small and medium-sized companies, profit smoothing is of negligible importance
Ruefli, TW (1990)	Conceptual & quantitative research 31 US companies (airlines) Period: 1968–1985 Evaluation: Rank correlation according to Spearman	Return = ROA Risk = variance in return	Rejection of a “mean variance” approach in order to make generalizable and verifiable statements about the risk-return relationship No distinction is made as to whether the relationship results from the movement on a “mean variance” curve or the result of shifts in unspecific relationships between the variables risk and return in one or more sub-periods
Henkel, J. (2000)	empirical quantitative investigation 1,250 German companies Period: 1988–1997 Evaluation based on regression model, correlation coefficient, rank correlation according to Spearman	Return = ROE Risk = variance in return	negative relationship between risk and return Results, however, can be attributed to statistical effects: return distribution is skewed on average (skewed to the left)

Further development of the risk-return paradox: the U-curve

A study by Fiegenbaum and Thomas from 1988 turned the discussion about the characteristics of the linear relationship between risk and return into a new debate.

Basic idea

In their study, they assume a quadratic relationship between the two variables and assume a U-curve. They postulate a negative correlation between risk and return for companies whose performance is below the reference level of the return on equity and a positive correlation of the sizes for companies that are above this level. These considerations result from the core idea of ​​the prospect theory, which assumes that decision-makers below the reference point have a risk-related attitude and above this point a risk-averse attitude. As a result, risk-conscious managers accept a lower return in terms of a higher risk, whereas risk-averse managers only accept a higher risk if the return is correspondingly high. Fiegenbaum and Thomas also assume that the quadratic relationship occurs both inside and outside a certain industry.

Data collection and operationalization of the sizes

To test these hypotheses, Fiegenbaum and Thomas analyzed 2,322 American companies in 47 industries within a period from 1960 to 1979. Disjoint five-year intervals (1960–1964, 1965–1969, 1970–1974, 1975–1979) and ten-year intervals (1960–1979) were used to test these hypotheses. 1969, 1970–1979) and the entire period differed.

The average return on equity is used as an indicator of the return and the variance in the return on equity is used as a measure of the risk. In the studies, the reference level is operationalized within the industry by the industry median return on equity, outside the industry by the entire sample median.

evaluation

The data collected is evaluated using the Spearman correlation coefficient and 2x2 contingency tables, in which the companies are classified according to two criteria:

1. Is the return on equity smaller or larger than the median?
2. Is the return on equity variance smaller or larger than the median?

A high number of companies in the two quadrants “high RoE and small variance” or “small RoE and high variance” indicate a negative relationship between risk and return. In contrast, a large number of companies in the quadrants “high RoE and high variance” or “small RoE and small variance” suggest a positive correlation between the sizes.

Results

For companies below the reference level, both inside and outside a certain industry, a negative correlation between risk and return could be determined for almost every industry and every time span. In addition, positive relationships between risk and return for companies above the reference level could be recorded. This applies both within individual sectors and across sectors. The study by Fiegenbaum and Thomas thus provides an explanation for the risk-return paradox using the concept of risk attitude or prospect theory. According to their results, a U-shaped relationship should be assumed instead of a linear relationship.

literature

• Literature on the risk-return paradox in the catalog of the German National Library

Individual evidence

1. ^ Bowman of Sloan School dies at 73rd MIT News, October 28, 1998, accessed July 17, 2018 . 
2. ^ Edward H. Bowman: Risk Seeking by Troubled Firms . In: Sloan Management Review . tape 23 , no. 4 , June 1982, pp. 4 .
3. ↑ ^{a b c} Miller, AC (2013): Expectation Formation of Economic Actors: An Explication on the Basis of the Basic Model of a Dynamic Theory of Economic Actors, Writings of the Center for Controlling & Management . Ed .: Weber, J. Band 10 . Deutscher Universitas-Verlag, ISBN 978-3-8244-7866-8 , p. 120-166 .
4. ↑ ^{a b} Beck, H. (2014): The Prospect Theory and its consequences, Behavioral Economics, pp. 101–195.
5. ↑ Mark Schweizer: § 6 Prospect Theory - a descriptive model of human risk behavior. Retrieved July 18, 2018 . 
6. ↑ Harbaugh, W. T, Krause, K. & Vesterlund, L. (2010): The fourfold pattern of risk attitudes in choice and pricing tasks, The Economic Journal, vol. 120, pp. 595–611.
7. ^ ^{A b} Günther, Thomas / Detzner, Martin (2012): Are managers and controllers risk averse? Results of an empirical study, in: Controlling, 24th year 2012, pp. 247–254.
8. ↑ ^{a b c} Fiegenbaum, A & Thomas, H. (1988). Risk-Attitudes and the Risk Return Paradox: Prospect Theory Explanations. Working Paper (College of Commerce and Business Administration) University of Illinois at Urbana-Champaign, WP 1214.
9. ↑ ^{a b c} Wiemann, V. & Mellewigt, T. (1998). The risk-return paradox. State of research and results of an empirical study. Schmalenbach's magazine for business research , 50 years, issue 6, pp. 551-572.
10. ↑ Ossasnik, W. / Dorenkamp, ​​A. & Wilmsmann, D .: Diversification and risk management: Effects on the relative risk-return position . Ed .: The company. 2004, p. 1165 -1168 .
11. ↑ Jitendra V. Singh (1986): “Performance, Slack and Risk Taking in Organizational Decision Making”, Academy of Management Journal, Volume 29, No. 3, p. 562.
12. ↑ Simon, HA (1945): Administrative Behavior. A Study of Decision-making Processes in Administrative Organizations. New York: Macmillan
13. ↑ German Academy for Management: Behavioral Decision Theory (Cyert / March, Simon et al.). 2018, accessed September 30, 2018 . 
14. ↑ Torben J. Andersen, Jerker Denrell and Richard A. Bettis (2007): Strategic Responsiveness and Bowmann's Risk-Return Paradox . Ed .: Strategic Management Journal. S. 426-427 .
15. ↑ Treacy, M. (1980). Profitability Patterns and Firm Size. Working Paper (Alfred P. Sloan School of Management) Massachusetts Institute of Technology, WP 1109-80.
16. ↑ Albach, H. (1987). Investment policy of successful companies. Zeitschrift für Betriebswirtschaft , vol. 57, issue 7, pp. 636–661.
17. ↑ Miller, KD & Bromiley, P. (1990). Strategic Risk and Corporate Performance: An Analysis of Alternative Risk Measures. Academy of Management Journal , Volume 33, Issue 4, pp. 756-779.
18. ↑ Chou, PH, Chou, RK & Ko, KC (2009). Prospect Theory and the Risk-Return Paradox: Some Recent Evidence. Review of Quantitative Finance and Accounting , Volume 33, Issue 3, pp. 193-208.
19. ^ Holder, AD, Petkevich, A. & Moore, G. (2016). Does Managerial Myopia explain Bowman's Paradox ?, American Journal of Business , Volume 31, Issue 3, pp. 102-122.
20. ^ Fiegenbaum, A. & Thomas, H. (1986). Dynamic and Risk Measurement Perspectives on Bowman's Risk-Return Paradox for Strategic Management: An Empirical Study, Strategic Management Journal , 7th year, Issue 5, pp. 395-407.
21. ↑ Perlitz, M. & Löbler, H. (1989). The innovation behavior in medium-sized industry . Stuttgart: Poeschel.
22. ↑ Ruefli, TW (1990). Mean-Variance Approaches to Risk-Return Relationships in Stragtegy: Paradox Lost. Management Science , Volume 36, Volume 3, pp. 368-380.  
23. ↑ Henkel, J. (2000). The Risk-Return Fallacy. Schmalenbach Business Review , Volume 52, Issue 4, pp. 363-373.