Will and power: Investment diversification and systemic deviation from irrational risk

Liu, Yaping Article Will and power: Investment diversification and systemic deviation from irrational risk Cogent Economics & Finance Provided in Cooperation with: Taylor & Francis Group Suggested Citation: Liu, Yaping (2022) : Will and power: Investment diversification and systemic deviation from irrational risk, Cogent Economics & Finance, ISSN 2332-2039, Taylor & Francis, Abingdon, Vol. 10, Iss. 1, pp. 1-12, https://doi.org/10.1080/23322039.2022.2129367 This Version is available at: https://hdl.handle.net/10419/303823 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Cogent Economics & Finance ISSN: (Print) (Online) Journal homepage: www.tandfonline.com/journals/oaef20 Will and power: Investment diversification and systemic deviation from irrational risk Yaping Liu To cite this article: Yaping Liu (2022) Will and power: Investment diversification and systemic deviation from irrational risk, Cogent Economics & Finance, 10:1, 2129367, DOI: 10.1080/23322039.2022.2129367 To link to this article: https://doi.org/10.1080/23322039.2022.2129367 © 2022 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Published online: 29 Sep 2022. Submit your article to this journal Article views: 1125 View related articles View Crossmark data Citing articles: 2 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=oaef20 FINANCIAL ECONOMICS | RESEARCH ARTICLE Will and power: Investment diversification and systemic deviation from irrational risk Yaping Liu 1 * Abstract: Examining China’s stock market, mean variance is used to measure returns and risk and build an irrational risk-asset pricing model. The power of heterogeneous beliefs and risk-valuation deviation are found to affect capital asset pricing, presenting excessive fluctuations that neoclassical finance theory cannot easily explain. A diversified portfolio can disperse or aggregate irrational risk. Trading frequency and quantity reflect differences in investors’ rationality and reveal irrational risk effects. On that basis, regulatory tools and derivative products can be designed to build a rational risk anchor, prevent the systematic bias of irrational risk, and improve capital allocation. Subjects: Economic Psychology; Mass Communication; Investment & Securities Keywords: Irrational risk; risk aggregation; risk-valuation deviation; behavioral finance; equity premium 1. Introduction Neoclassical finance theory assumes that investors are rational, predictable, and consistent in their behavior under risk. Variance in the expected rate of return distribution is used to measure a portfolio’s risk. The portfolio with the highest expected rate of return at a given level of risk will be the best portfolio choice for investors (Markowitz, 1952). According to the capital asset pricing model (CAPM), investors’ optimal decisions should be made along the capital allocation line with the slope of the beta coefficient, and the risk-preference characteristics of investors influence their investment decisions under uncertainty (Sharpe, 1964). Yaping Liu ABOUT THE AUTHORS Yaping Liu is an associate professor in the Finance Department at Hunan International Economics University. He is mainly engaged in teaching and research on investment economics, behavioral finance and asset pricing, securities investment analysis, and other fields, particularly stock market anomalies. The present article pertains to key topics covered by the Hunan International Economic Risk Prevention and Management Research Base and Investment Research Institute, providing theoretical support for in-depth asset pricing preference, strong empirical justification, irrational risk monitoring, and irrational risk management. PUBLIC INTEREST STATEMENT Is the capital market a paradise for value investment? Why does diversification also make it difficult to manage and control risk? Why is it that arbitrage often cannot correct extreme market behavior and price manipulation? Intravalue is the anchor of capital market stability. Sometimes, the market is effective, and risks can be dispersed through portfolio allocation and value exploration. However, the market is also a game of “will and power.” Owing to the disturbance of information, when the systematic deviation of irrational risk forms, it will lead to violent price fluctuations. Individuals’ responses to information should be consistent with the overall response of the market. The overall behavior of the transaction price, target, quantity, and timing are intuitive tools for monitoring irrational risks. Liu, Cogent Economics & Finance (2022), 10: 2129367 https://doi.org/10.1080/23322039.2022.2129367 Page 1 of 12 Received: 12 June 2022 Accepted: 25 September 2022 *Corresponding author: Yaping Liu, Hunan International Economics University, No. 822 Fenglin Third Road, Yuelu District, Changsha City, Hunan Province 410205 China E-mail: [email protected] Reviewing editor: David McMillan, University of Stirling, Stirling, United Kingdom Additional information is available at the end of the article © 2022 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Real investors, however, are not homogenously rational, as assumed by neoclassical finance theory. Researchers have questioned homogenous rationality, suggesting that investors only possess bounded rationality, under certain constraints of cognitive ability, behavioral ability, and egoism (Simon, 2002). Indeed, there are three bounds of human nature: limited rationality, limited willpower, and limited self-interest (Mullainathan & Thaler, 2001). Researchers have verified market anomalies that neoclassical finance theory cannot easily explain. Specifically, a scale effect commonly exists in the markets of various countries: the larger the company, the lower its stock return rate (Banz, 1981). Analyzing the relationship between longterm stock price fluctuations and dividend changes reveals that excessive volatility and irrational bubbles exist in the market (Shiller, 2005). Further, a significant positive correlation exists between price and trading volume (Genesove & Mayer, 2001). Excessive trading with a high turnover rate exists (Odean, 1999; Sprenger et al., 2014). High returns will attract abnormal attention, which will become involved in trading (Barber et al., 2008; Da et ai., 2011; Hirshleifbr et al., 2009; Jinesh et al., 2021). In contrast to relative momentum payoffs, risk-managed momentum payoffs remain substantial even in extended time frames(Simarjeet et al., 2022). Such phenomena are not easily explained by neoclassical finance theory and in turn reveal differences in investors’ rationality. Based on investors’ bounded rationality, real-world decision-making behaviors under uncertainty are diverse (Kahneman & Tversky, 1979). Markets consist of multiple layers of rational investors and noise. When noise is included in asset pricing theory, asset prices will deviate from CAPM predictions (De Long et al., 1990). Under the influence of noise trader risk, the effective meanvariance boundary of a market portfolio will deviate from the CAPM level (Shefrin & Statman, 1994). Mood fluctuations are defined as changes in investors’ preference structure parameters (subjective discount factor and risk-aversion factor), and small changes in the subjective discount factor can lead to large fluctuations in stock prices (Mehra & Sah, 2002). There is evidence of irrational psychology or behaviors among investors—such as overconfidence bias, anchoring bias, loss aversion bias, and herd bias—in the capital markets of developed economies, such as France and the UK (Benkraiem et al., 2019) and the US (Gary, 2016). Evidence can also be found in emerging economies, such as Vietnam (Xuan & Dang, 2019), India (Jain et al., 2019; Muskan et al., 2021, 2022), Pakistan (Kashif et al., 2020), and Ghana (Banyen & Nkuah, 2015). Moreover, there is evidence of such phenomena in other markets, such as cryptocurrencies (Ghulame et al., 2022) and money markets (David & Alireza, 2020). Driven by incomplete information, psychological feedback, cognitive bias, and behavioral blindness, individual beliefs and behavioral biases are strengthened by the positive feedback mechanism of market price. This leads to irrationally optimistic fanaticism and irrationally pessimistic panic through market sentiment and social contagion, resulting in systematic group biases. Finally, part of the deviation in financial markets evolves into a systematic and comprehensive overall abnormal market performance. Under the premise of homogeneity and rationality, neoclassical financial theory focuses on studying information contained in the price, with the transaction price as the main research object. With the rise of behavioral finance, researchers have incorporated psychology to identify the factors that influence pricing. In transaction behavior, the technical analysis school uses securities investment technology to empirically investigate the quantity, time, and price of trading. In addition to transaction price, transaction behavior (e.g., decisions about the transaction target, transaction quantity, and transaction timing) also contains information about investors’ heterogeneous beliefs, as well as information about the conversion of heterogeneous beliefs, which is an intuitive tool for monitoring irrational risks. The goal of the present study, therefore, is to introduce the proportion of investment (e.g., turnover rate of changes in investment ratio) into the pricing model to illustrate the possible effects of irrational risks. This paper first describes heterogeneous rationality in China’s stock market, because it is an emerging capital market in a country with a rapidly growing economy. Then, the mean-variance Liu, Cogent Economics & Finance (2022), 10: 2129367 https://doi.org/10.1080/23322039.2022.2129367 Page 2 of 12 method of Markowitz’s asset portfolio theory is used to measure returns and risk, and an assetpricing model based on rational heterogeneity is constructed for comparison with neoclassical finance theory to show how asset pricing is affected by differences in rationality, which may lead to irrational risk bias. The power transformation reflecting investment proportion and the expression of risk-valuation deviation can be measured and described based on the number and frequency of transactions. This can provide ideas for improving the efficiency of capital allocation and controlling the deviation of irrational risks. 2. Irrational risk influence on diversified risk-asset portfolios 2.1. Scale effect and attention-driven transactions in the Chinese stock market The market measure of exchange activity and the premium can be observed by selecting the turnover rate (traded share capital/total share capital) and the turnover rate premium. The data used in this study come from the Wind Financial Terminal and include transaction data for all listed A-share companies in China, for a total of 1,272 companies (excluding those listed after the initial point and delisted during the study period), covering 191 consecutive months from 1 January 2005, to 30 November 2020. Based on the total amount of share capital at the beginning of the period (ranked from small to large), the companies were grouped into 24 portfolios, each of which consists of 53 listed companies who all have the same amount of investment. Specifically, from P1 to P24, the portfolios range from companies with a small amount of share capital to those with a large amount. The association between the range of the monthly average return rate (YIELD, %) and of the daily turnover rate (ADTR1, %), excluding the suspension date, is observed based on current total share capital. The underlying index is calculated as the monthly average of the Shanghai Composite Index and the Shenzhen Component Index in the same period. The riskfree rate is 2.5%. Comparing these portfolios, as total equity increases, YIELD decreases, and ADTR1 decreases. This means that smaller portfolios trade more actively, turn over more frequently, and earn higher returns (Figure 1). Figure 1. Price-volume trend chart of change in equity capital. Liu, Cogent Economics & Finance (2022), 10: 2129367 https://doi.org/10.1080/23322039.2022.2129367 Page 3 of 12 Andrea et al. (2018) introduced six factors, including the size factor “small-minus-big” (a strategy of going long on small stocks and short on large stocks). They suggest that Buffett’s returns are largely attributable to stock selection, and that Berkshire’s diminishing returns are related to an initial focus on small firms and a later bias toward larger stocks. Fama and French (1992) suggest that the scale effect is only a manifestation of risk premium; the smaller the company size, the greater the risk, and the higher return compensates for the high risk. However, the Treynor coefficient and the Sharpe coefficient of the 24-asset portfolio also decreases simultaneously, indicating that the small-equity portfolio has a higher relative risk return per unit. In terms of the average range of rise and fall, P1, P2, P3, and P4 increase by 13.3, 8.3, 6.8, and 12.6 times, respectively, while P21, P22, P23, and P24 increase by 4.6, 6.3, 4.1, and 5.9 times, respectively. The CSI 300 (China Securities Index), underlying asset of Stock Index Futures and Exchange Traded Funds, increases by five times. The correlation coefficient between YIELD and ADTR1 is 0.835558, indicating a good correlation. The Granger causality test for the sequence shows bidirectional causality from ADTR1 to YIELD. That is, YIELD has a significant positive effect on ADTR1, and ADTR1 has a significant positive effect on YIELD. This indicates that positive feedback exists between attention-driven and excessive trading. When the return is high, the risk exchange frequency is more frequent, and when the return is low, the willingness for risk exchange is less. The two-way influence of trading behavior on price decision-making and price change on trading behavior embodies the role of irrational risk. Is the endogeneity bias or omitted-variable bias a value factor or an information factor? 2.2. An irrational risk-asset pricing model The returns of assets tend to be partially correlated with each other. In addition to the risk factors of the underlying assets, some of the returns come from the actors’ understanding of, and behavior coordination based on, information in the market, or even from behavioral coordination with each other. The definition of uncertainty in investors’ cognitive and behavioral biases in capital asset price decision-making is distinguished from the definition of rational risk (RR) under the rationality condition of neoclassical finance theory, which can be defined as irrational risk (IR). The expected return rate of a single asset (or portfolio of assets) is a linear function that contains two groups of factors affecting the return rate of the asset: rational risk and irrational risk. Trading activity includes the exchange of irrational pessimism (IP) and irrational optimism (IO) relative to the forecast of homogenous rationality. Assume the capital market is composed of a risk-free asset f (FSt is quantity at time t) and a risk asset (RSt is quantity at time t; P is price); transaction costs are zero. Investors’ optimistic expectations are consistent with and in the same direction as the absolute rational risks, and irrationally optimistic investors will allocate high-risk assets. Assume there is a positive correlation between the irrationally optimistic asset IO and the rational asset RR; that is, ρRR:IO ¼1. Later, this will be relaxed in favor of more restrictive assumptions. Assume that in a Z portfolio, there are both rational investors and irrationally optimistic investors. If the investment ratio of rational investors is λ, and that of irrationally optimistic investors is 1-λ, and yield is r, then, rZ¼λrRR þ1λð ÞrIO (1) σZ¼λσRR þ1λð ÞσIO (2) Rearranging Equations (1) and (2) yields rZ¼σZσIO σRR σIO rRR þσRR σZ σRR σIO rIO (3) Liu, Cogent Economics & Finance (2022), 10: 2129367 https://doi.org/10.1080/23322039.2022.2129367 Page 4 of 12 Namely, the yields of Z portfolios from the two elements σZσIO σRRσIO rRR is the product of the RRsensitive coefficient and RR yield; σRRσZ σRRσIO rIO is the product of the IO-sensitive coefficient and IO yield. Further arrangement yields rZ¼rfþσZσIO σRR σIO ðrRR rfÞþ σRR σZ σRR σIO ðrIO rfÞ(4) Investors use three stages (t = 1, 2, 3) to complete investment transactions. The time stages refer to the cycle of heterogeneous belief conversion: the initial period, irrational optimism, and rationality. Investors have a limited amount to invest. Market information is It, investors’ cash flow is V ,,NV ;σ2 V , � �, the number of irrationally optimistic investors is N, and collected market information is �1i¼I1 f g;�2i¼I2 f g;�3i¼I2;I3 f gT. Irrationally optimistic investors cannot accurately anticipate risk-asset prices and believe they are independent, following a normal distribution. Investors risk repugnance, and their utility function is UðWtiÞ ¼  eaWti , where a is the absolute risk-aversion coefficient, and W is wealth. The equilibrium price-risk valuation of rational investors is σ2 e, the risk valuation of the irrationally optimistic equilibrium price is kσ2 e, and k is the deviation degree of risk valuation; the value is overestimated when k>0. The investor’s decision at time t = 1, 2, 3 based on utility maximization and exchange point equivalence is given by max E0½ eaWiþ1;i�ti j � s:t:PtRSti þFSti ¼PtRSt1þFSt1;i (5) At t = 3, based on standard normal distribution, Equation (5) becomes max RS3i E0½ eaW4;ij�3i� ¼  eaFS3ieaRS3iE0½ðV j�3iÞþ1 2α2RS2 3iVar0ðV j�3iÞ� (6) The optimization of Equation (6) yields @E0½ eaW4;i�3i j � @RS3i¼0. Thus, the optimal decision of investors is RS3i¼E0½~ V�3i j � P3 αVar0½~ V�3i j � ¼0 (7) According to the right triangle altitude theorem, irrationally optimistic investment expectation and its variance are E0½V ,�3i j � ¼ � VþCOVð~ V;�3i j ÞTCOV0ð�3i;�3iÞ1f�3iE0ð�3iÞg (8) Var0½~ V�3i j � ¼ σ2 V ,þCOVð~ V;�3i j Þ1COV0ð�3i;�3iÞ1ð~ V;�3iÞ(9) Then, the expectation function value and covariance value of investors’ investment are E0½�3i� ¼ E0½E0ð~ I2Þ;E0ð~ I3Þ�T¼ ð� V;� VÞT(10) Liu, Cogent Economics & Finance (2022), 10: 2129367 https://doi.org/10.1080/23322039.2022.2129367 Page 5 of 12 COV0ð�3i;�3iÞ ¼ COV0ð~ I2;~ I2ÞCOV0ð~ I2;~ I3Þ COV0ð~ I3;~ I2ÞCOV0ð~ I3;~ I3Þ � �¼σ2 � Vþkσ2 e;σ2 � V σ2 � V;σ2 � Vþkσ2 e ! (11) COV0ð~ V;�3iÞ ¼ COV0ð~ V;~ I2Þ;COV0ð~ V;~ I3Þ h iT¼ ðσ2 � V;σ2 � VÞ2(12) which further yield E0½~ V�3i j � ¼ � Vþðσ2 � V;σ2 � VÞσ2 � Vþkσ2 e;σ2 � V σ2 � V;σ2 � Vþkσ2 e !1~ I2� V ~ I3� V ! ¼σ2 � Vð~ I2þ~ I3Þþkσ2 e� V kσ2 eþ2σ2 � V (13) Var0ð~ V�3i j Þ ¼ σ2 ~ V ðσ2 ~ V;σ2 ~ VÞσ2 ~ Vþkσ2 e;σ2 ~ V σ2 ~ V;σ2 ~ Vþkσ2 e !1σ2 ~ V σ2 ~ V !¼kσ2 ~ Vσ2 e kσ2 eþ2σ2 ~ V (14) The first-order condition is RS3i¼ σ2 ~ Vð~ I2þ~ I3Þþkσ2 e~ V kσ2 eþσ2 ~ VP3 ασ2 ~ Vkσ2 e kσ2 eþ2σ2 ~ V (15) According to the equilibrium principle of capital markets, RS3i¼� R� S3 and ∑N i¼1RS3i¼N�� R� S3, and the asset pricing at t = 3 is P3¼kσ2 e~ Vak σ2 ~ Vσ2 e� R� S3 kσ2 eþ2σ2 ~ Vþσ2 ~ V kσ2 eþ2σ2 ~ V ~ I2þσ2 ~ V kσ2 eþ2σ2 ~ V ~ I3(16) Similarly, the asset pricing at t = 2 is P2¼2σ2 Vþkσ2 e ð Þ� Vakσ2 Vσ2 e� R� S32σ4 Vα� R� S2 kσ2 eþ2σ2 V σ2 V� Vασ2 V� R� S2 ð Þ kσ2 eþσ2 Vþσ2 V kσ2 eþσ2 VI2 (17) According to Equations (4) and (17), asset pricing consists of three elements: the risk-free rate of return, the product of the rational risk premium and factor sensitivity, and the product of the irrational risk premium and factor sensitivity. The irrational risk premium originates from the disturbance of market information I, which leads to differences in investors’ expectations. Factor sensitivity depends on the correlation between irrational risk and rational risk. When 0<ρ�1, irrational risk is positively correlated with rational risk; that is, irrational optimism. When 0�ρ�  1, irrational risk is negatively correlated with rational risk; that is, irrational pessimism. 2.3. Aggregation effect of irrational risk Assume that in a Z portfolio of n securities, each security has the same amount of investment, the investment proportion of each security is 1=n, and the respective risks of n securities are σ1;σ2;...;σn, in which the least risk is greater than a constant σa, and the greatest risk is less than a constant σb. When the correlation coefficient is ρ¼1, it means that n securities’ returns show irrational optimism, and they have a positive correlation with each other: Liu, Cogent Economics & Finance (2022), 10: 2129367 https://doi.org/10.1080/23322039.2022.2129367 Page 6 of 12 σ2 Z¼∑ n i¼1 ∑ n j¼1 λiλjCOVij ¼∑ n i¼1 1 n � �2 σ2 iþ2∑1�i<j�nCOVij 1 n � �2 (18) σ2 a�∑ i¼1 n 1 n � �2 σ2 iþ2∑1�i<j�nCOVij 1 n � �2 �σ2 b(19) Therefore, even if n tends to infinity—that is, as the number of securities in the portfolio increases infinitely—the risk of the portfolio will always be between the lowest and highest risk level, and risks cannot be effectively dispersed. In other words, when an information disturbance leads to irrational expectation overlap among investors, their trading strategies, based on the hypothesis of efficient market behavior, are mutually irrelevant, and mutual offset cannot be achieved. Based on Equations (16) and (17), the variance of P describes the fluctuation in capital market prices as VarðP3Þ ¼ σ4 ~ V ðkσ2 eþ2σ2 ~ VÞ2Varð~ I2þ~ I3Þ ¼ 2σ4 ~ Vð2σ2 ~ Vþσ2 eÞ ðkσ2 eþ2σ2 ~ VÞ2(20) VarðP2Þ ¼ σ4 V kσ2 eþ2σ2 V  �2VarðI 2Þ ¼ σ4 V2σ2 Vþσ2 e  � ðkσ2 eþ2σ2 VÞ2(21) Taking the partial derivatives with respect to k yields @VarðP3Þ @k¼  2σ4 ~ Vð2σ2 ~ Vþσ2 eÞ ðkσ2 eþ2σ2 ~ VÞ3σ2 e<0 (22) @VarðP2Þ @k¼  σ4 ~ Vðσ2 ~ Vþσ2 eÞ ðkσ2 eþ2σ2 ~ VÞ3σ2 e<0 (23) The volatility of capital market prices is a diminishing function of investors’ irrational optimism— that is, the more investors overestimate the capital market, the greater the asset-price volatility, and the greater the likelihood of ·price-fluctuation risk. Meanwhile, when investors are irrationally pessimistic, the more they underestimate the capital market, the lower the asset-price volatility. 2.4. Systemic bias of irrational risks Because of the disturbance and influence of information, capital market investors may occupy a position between rational and irrational, between irrational pessimism and irrational optimism. This is caused by the rational risk of the investment target itself, as well as the irrational pessimism and irrational optimism caused by differences in investors’ rationality. Assume that for asset Z, its price is determined by three heterogeneous beliefs: RR, IO, and IP. RR is positively correlated with IO while IP is negatively correlated with RR and IO; later, it will be relaxed in favor of more restrictive assumptions. That is, ρRR:IO ¼1, ρRR:IP ¼  1, and ρIO:IP ¼  1; λ is the investment ratio. Thus, we have σ2 Z¼∑n i¼1σ2 iλ2 iþ2∑i�jCOVðσi;σjÞλiλj ¼ ðλRRσRR þλIOσIO λIPσIP Þ2(24) Liu, Cogent Economics & Finance (2022), 10: 2129367 https://doi.org/10.1080/23322039.2022.2129367 Page 7 of 12