- Email: [email protected]
Optimism bias, portfolio delegation, and economic welfare
Accepted Manuscript Optimism bias, portfolio delegation, and economic welfare Jian Wang, Xiaoting Wang, Xintian Zhuang, Jun Yang PII: DOI: Reference:
S0165-1765(16)30485-2 http://dx.doi.org/10.1016/j.econlet.2016.11.025 ECOLET 7422
To appear in:
Economics Letters
Received date: 29 September 2016 Revised date: 15 November 2016 Accepted date: 18 November 2016 Please cite this article as: Wang, J., Wang, X., Zhuang, X., Yang, J., Optimism bias, portfolio delegation, and economic welfare. Economics Letters (2016), http://dx.doi.org/10.1016/j.econlet.2016.11.025 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Highlights (for review)
Optimism Bias, Portfolio Delegation, and Economic Welfare
Highlights
We explore the effects of investor optimism bias in portfolio delegation. The optimistic investor increases portfolio delegation. The risk-averse fund manager reduces investment in the risky asset. The investor suffers welfare loss due to lower expected return. The fund manager enjoys increased compensation.
*Manuscript Click here to view linked References
Optimism Bias, Portfolio Delegation, and Economic Welfare Jian Wang a, b, c Xiaoting Wang d Xintian Zhuang a Jun Yang e, * a b
c
School of Business Administration, Northeastern University, Shenyang, 110167, China Institute of Behavioral and Service Operations Management, Northeastern University, Shenyang, 110167, China
College of Business, State University of New York-Stony Brook, Stony Brook, NY 11794, USA d e
Department of Economics, Acadia University, Wolfville, NS, B4P 2R6, Canada
School of Business Administration, Acadia University, Wolfville, NS, B4P 2R6, Canada
Abstract This study explores the effects of investor optimism bias in a portfolio delegation framework. We show that the optimistic investor increases his portfolio delegation, while the risk-averse manager reduces investment in the risky asset. The investor suffers welfare loss due to lower expected return, but the manager enjoys increased compensation. The investor’s optimism bias aggravates the moral hazard problem.
Keywords: optimism bias, portfolio delegation, investment strategy, economic welfare. JEL Classifications: D81, D82, G11
*
Corresponding author, [email protected], phone 1-902-5851791. 1
1. Introduction Since Bhattacharya and Pfleiderer (1985) extensive literature has investigated the moral hazard and information asymmetry issues in portfolio delegation between investors and portfolio managers under the assumption of full rationality. However, there is clear psychological evidence that people are often optimistic about the future prospects, expecting that good outcomes are more likely to happen than in actuality (Puri and Robinson, 2007; Shepperd et al., 2013). This paper intends to study the effects of investor optimism on delegation decision, equilibrium investment strategy, expected portfolio return, and economic welfare. In literature researchers have studied the impact of optimism bias on corporate decisions (Heaton, 2002; Campbell et al., 2011), executive behavior (Englmaier, 2010; Sen and Tumarkin, 2015), investment strategy of money managers (Puri and Robinson, 2007; Wang et al., 2013), and financial analyst reports (Easterwood and Nutt, 1999; Paleari and Vismara, 2007). Nevertheless, all these studies assume that the agent is optimistic, and very little is known about the impact of the principle’s optimism bias in portfolio delegation. We contribute to the literature in several ways. First, we find that the investor increases portfolio delegation when he is optimistic, which is consistent with findings by Odean (1998) and Chuluun and Graham (2016) in non-delegated investing. Second, we prove that the investor’s optimism bias reduces the portfolio return but increases compensation of the manager. These results support the empirical finding that rational agents would exploit the principals’ bias and information asymmetry to their advantage (Cooper et al., 2005; Baker and Wurgler, 2013). Third, we show that the investor’s optimism aggravates the effect of the manager’s risk aversion by further reducing investment level and causes additional Pareto efficiency loss, which complements Campbell et al. (2011) who suggest that managerial optimism benefits the principal by alleviating underinvestment problems caused by managerial risk aversion. 2. Optimism and Delegation The basic setup of the model is based on Gervais et al. (2005) who study portfolio delegation under rationality. Consider a portfolio management framework populated with a risk neutral investor who is wealthy but has no investment skill, and a money manager endowed with a constant absolute risk aversion (CARA) utility function with an absolute risk aversion coefficient ρ, who has no wealth but some investment skill a a （0,1）. There are two types of assets on the market: a risk-free asset with return rate normalized to one, and a risky asset with unconditional return 2
rate r , which is either r =rH 1 or r =rL 1 with equal probability, so that E (r ) rH / 2 rL / 2 1 .The investor can invest in the risk-free asset directly, or delegate his capital to the manager, and then the gross return of the portfolio is r ( x) (1 x) xr 1 x(r 1) , where x is the proportion invested in the risky asset by the manager. Suppose that the manager can receive a private signal about the return rate of the risky asset. Specifically, the signal indicates either good or bad news, s sH or s sL , corresponding to rH and rL respectively. The conditional distribution of the risky asset return rate generated by the manager is Pr(r =rH | s sH ) Pr(r =rL | s sL ) 1 a 2 Pr(r =rH | s sL ) Pr( r =rL | s sH ) 1 a 2
(1)
There is information asymmetry between the investor and the manager that the manager decides on the investment strategy according to the signal received, buying on good news ( x(sH ) 0 ) or selling on bad news ( x(sL ) 0 ), but the signal cannot be observed by the investor. We suppose that the investor is optimistically biased, which is known to the manager. Consistent with de Meza and Southey (1996) and Heaton (2002), we define optimism as the ex-ante belief that the distribution of the risky asset’s return is more favorable than the true distribution. Specifically, the optimistic investor believes that the probability of good state for the risky asset ( r =rH ) is [1 / 2, 1] ,1
Pr(r rH 1) Pr(r rL 1) 1
(2)
so d 1/ 2 [0, 1/ 2] measures the level of investor optimism bias. Then from Eq. (1), the optimistic investor thinks that Pr(r rH | a a) a(1 ) 1 2 d a(1 2 d ) Pr(r rL | a a) 1 a(1 ) 1 2 d a(1 2 d ) 1
(3)
and expects the return rate of the portfolio as R E(r )=1 2-1 x(rH 1) . At the outset, the manager announces a compensation contract W that she is willing to work for. Based on this contract, and on the observation of the manager’s skill a, the investor chooses the amount A of money he delegates to the manager. According to Stoughton (1993), suppose W (r ) Ar ( x) , where (0,1) represents the manager’s sharing proportion of the investment return. In light of Chen et al.’s (2004) empirical findings, we assume that the cost of operating the portfolio is kA 2 , 1
We can reach the same conclusions in the paper by assuming that the investor optimistically estimates (i.e., overestimates) the manager’s ability. 3
where k 0,1 . Similar to Berk and Green (2004), we assume that investors compete for the manager’s expertise in investing and make the manager acquire the entire surplus she creates, so in equilibrium A always makes the investor indifferent between portfolio delegation and direct investing. Thus at the outset, the amount of capital the investor delegates to the manager is
1 R 1 A max 0, k
(4)
When the manager chooses her contract β, in order to maximize her expected compensation W, she takes into account the investor’s expected reaction to her choice, Eq. (4). The equilibrium behaviors for the optimistic investor and the rational manager are characterized in the following lemma. Lemma 1. At the outset, the manager’s choice of the portfolio delegation contract is
2-1 x(rH 1) R 1 2R 2[1 2 -1 x( rH 1)]
(5)
The amount of capital the investor delegates to the manager is
A
R 1 2-1 x(rH 1) 2k 2k
(6)
By inspection of Lemma 1, since R 0 we realize that both and A are increasing in d. The investor increases his investment delegation when he is optimistic, which is consistent with investors’ irrational direct investing behavior in Odean (1998) and Chuluun and Graham (2016). Interestingly, the manager also increases her sharing proportion in the contract as d increases. The manager takes advantage of the investor's cheery expectation of the future by awarding herself a more generous contract. 3. Investment Strategy and Welfare Besides his delegation decision and agent contract, the investor's optimism bias also affects the manager’s investment strategy and the investment return. Proposition1. The optimal investment strategy for the risk-averse manager is 1 a 1 a x ( sH ) - x ( sL )= A(rH rL ) ln
(7)
where x ( sH ) 0 and x ( sL ) 0 represent the optimal trading proportions of the 4
risky asset bought and sold on good and bad news respectively. The portfolio's expected return rate under the strategy is:
E *[r ( x) | s ] 1
a 1 a ln 2 A 1 a
(8)
Proof: see Appendix. As discussed with respect to Lemma 1, since both β and A are increasing in d, we take note that x and E [r ( x) | s ] are both decreasing in d. When the investor is optimistic, the rise of the sharing proportion by the manager brings higher risk in her compensation, so she commensurately reduces trading of the risky asset in order to control her overall risk, which in turn lowers the expected return of the portfolio notwithstanding the manager’s investing skills. Therefore, the investor’s optimism bias is detrimental to his own welfare. The following proposition derives the managerial economic welfare by combining Lemma 1 and Proposition 1. Proposition 2. The expected compensation of the manager is
E[W (r )] A+
a 1 a ln 2 1 a
(9)
It is evident that E[W ( r )] is increasing in the investor’s optimism d. This result is somewhat shocking, since it shows that the manager makes more money for herself due to the increased sharing proportion and the investor's delegated amount, leaving the investor alone to bear the cost for his bias. This result braces the finding of Cooper et al. (2005) and Baker and Wurgler (2013) that the rational agent would aggravate the infraction of the principal's welfare by exploiting the principal's bias to maximize her own interest. To better understand the effects of investor’s optimism, consider an extreme case of our model in which the investor is rational (d = 0). Even when the investor is rational, the trading of the risky asset ( xd 0 ) and the expected return ( Ed0 [r ( x) | s ] ) are lower than in the ideal condition in which the investor receives the same signal as the manager, 2 which is the classic moral hazard problem due to information asymmetry. Since the investor’s optimism bias widens this gap (i.e., further reducing both variables), it aggravates the principal-agent conflict and causes further Pareto efficiency loss. 4. Conclusion
2
Proof is available from authors upon request. 5
While optimism has been studied in various economic and business contexts, the principal’s optimism in portfolio delegation has not drawn much attention. The results in this paper suggest that the unrealistic expectation of investors may have unintended consequences of reducing the expected return of the delegated portfolio while benefiting their rational agents. Investors should be aware of these potential effects caused by their optimism biases when making delegating decisions. The results in this paper echo findings on the detrimental effect of entrepreneurial optimism (de Meza and Southey, 1996; Hmieleski and Baron, 2009).
Acknowledgements We thank Danling Jiang and an anonymous reviewer for helpful comments. This study is supported by the National Natural Science Foundation of China (#71571038, #71671030) and the Fundamental Research Funds for Central Universities in China (#N150602001). Financial support from China Scholarship Fund (2016) is gratefully acknowledged. References Baker, M., Wurgler, J., 2013. Behavioral corporate finance: An updated survey, in: Constantinides, G.M., Harris, M., Stulz, R.M. (Eds.), Handbook of the Economics of Finance (vol. 2). North Holland, Oxford, pp. 357– 424. Berk, J.B., Green R.C., 2004, Mutual fund flows and performance in rational markets. J. Polit. Econ. 112(6), 1269–1295. Bhattacharya, S., Pfleiderer, P., 1985. Delegated portfolio management. J. Econ. Theory 36(2), 1–25. Campbell, C., Gallmeyer, M., Johnson, S.A., Rutherford, J., Stanley, B.W., 2011. CEO optimism and forced turnover. J. Financ. Econ. 101(3), 695–712. Chen, J., Harrison, H., Ming, H., Jeffrey, D.K., 2004. Does fund size erode mutual fund performance? The role of liquidity and organization. Amer. Econ. Rev. 94(5), 1276–1302. Chuluun, T., Graham, C., 2016. Local happiness and firm behavior: Do firms in happy places invest more? J. Econ. Behav. & Organ. 125(5), 41 – 56. Cooper, M.J., Gulen, H., Rau, P.R., 2005. Changing names with style: Mutual fund name changes and their effects on fund. J. Financ. 60(6), 2825 – 2858. de Meza, D., Southey, C., 1996. The Borrower's curse: Optimism, finance and 6
entrepreneurship. Econ. J. 106(435), 375–386. Easterwood, J.C., Nutt, S.R., 1999. Inefficiency in analysts' earnings forecasts: Systematic misreaction or systematic optimism? J. Financ. 54(5), 1777–1797. Englmaier, F., 2010. Managerial optimism and investment choice. Manage. Decis. Econ. 31(4), 303–310. Gervais, S., Lynch, A.W., Musto, D.K., 2005. Fund families as delegated monitors of money managers. Rev. Financ. Stud. 18(4), 1139–1169. Heaton, J. B., 2002. Managerial optimism and corporate finance. Financ. Manage. 31(2), 33–45. Hmieleski, K., Baron, R., 2009. Entrepreneurs' optimism and new venture performance: A social cognitive perspective. Acad. Manage. J. 52(3), 473–488. Odean, T., 1998. Volume, volatility, price, and profit when all traders are above average. J. Financ. 53(6),1887 – 1934. Paleari, S., Vismara, S., 2007. Over-optimism when pricing IPOs. Manage. Financ. 33(6), 352 – 367. Puri, M., Robinson, D.T., 2007. Optimism and economic choice. J. Financ. Econ. 86(1), 71–99. Sen, R., Tumarkin, R., 2015. Stocking up: Executive optimism, option exercise, and share retention. J. Account. Econ. 118(2), 399–430. Shepperd, J.A., Klein, W.M., Waters, E.A., Weinstein, N.D., 2013. Taking stock of unrealistic optimism. Perspect. Psychol. Sci. 8(4), 395–411. Stoughton, N., 1993. Moral hazard and the portfolio management problem. J. Financ. 48(3), 2009– 2028. Wang, J., Sheng, J., Yang, J., 2013. Optimism bias and incentive contracts in portfolio delegation. Econ. Model. 33(7), 493–499.
Appendix: Proof of Proposition 1 If the manager receives the signal s sH , she chooses x ( sH ) to maximize her expected utility 1 a 1 a (e A[1 x ( rH 1)] ) (e A[1 x ( rL 1)] ) 2 2 Its first-order condition yields x ( sH ) . Likewise, we can get x ( sL ) if s sL . Since E[U (W (r ( x))) | s ]
rH rL 2(rH 1) 2(1 rL ) , the portfolio's expected return rate is
7
1 1 a 1 1 a 1 x ( sH )( rH 1) * 1 x ( sH )( rL 1) E [r ( x ) | s ] * 2 2 2 2 1 1 a 1 1 a 1 x ( sL )( rH 1) * 1 x ( sL )( rL 1) * 2 2 2 2 a 1 a 1 ax ( sH )( rH 1) 1 ln 2 A 1 a
8
S0165-1765(16)30485-2 http://dx.doi.org/10.1016/j.econlet.2016.11.025 ECOLET 7422
To appear in:
Economics Letters
Received date: 29 September 2016 Revised date: 15 November 2016 Accepted date: 18 November 2016 Please cite this article as: Wang, J., Wang, X., Zhuang, X., Yang, J., Optimism bias, portfolio delegation, and economic welfare. Economics Letters (2016), http://dx.doi.org/10.1016/j.econlet.2016.11.025 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Highlights (for review)
Optimism Bias, Portfolio Delegation, and Economic Welfare
Highlights
We explore the effects of investor optimism bias in portfolio delegation. The optimistic investor increases portfolio delegation. The risk-averse fund manager reduces investment in the risky asset. The investor suffers welfare loss due to lower expected return. The fund manager enjoys increased compensation.
*Manuscript Click here to view linked References
Optimism Bias, Portfolio Delegation, and Economic Welfare Jian Wang a, b, c Xiaoting Wang d Xintian Zhuang a Jun Yang e, * a b
c
School of Business Administration, Northeastern University, Shenyang, 110167, China Institute of Behavioral and Service Operations Management, Northeastern University, Shenyang, 110167, China
College of Business, State University of New York-Stony Brook, Stony Brook, NY 11794, USA d e
Department of Economics, Acadia University, Wolfville, NS, B4P 2R6, Canada
School of Business Administration, Acadia University, Wolfville, NS, B4P 2R6, Canada
Abstract This study explores the effects of investor optimism bias in a portfolio delegation framework. We show that the optimistic investor increases his portfolio delegation, while the risk-averse manager reduces investment in the risky asset. The investor suffers welfare loss due to lower expected return, but the manager enjoys increased compensation. The investor’s optimism bias aggravates the moral hazard problem.
Keywords: optimism bias, portfolio delegation, investment strategy, economic welfare. JEL Classifications: D81, D82, G11
*
Corresponding author, [email protected], phone 1-902-5851791. 1
1. Introduction Since Bhattacharya and Pfleiderer (1985) extensive literature has investigated the moral hazard and information asymmetry issues in portfolio delegation between investors and portfolio managers under the assumption of full rationality. However, there is clear psychological evidence that people are often optimistic about the future prospects, expecting that good outcomes are more likely to happen than in actuality (Puri and Robinson, 2007; Shepperd et al., 2013). This paper intends to study the effects of investor optimism on delegation decision, equilibrium investment strategy, expected portfolio return, and economic welfare. In literature researchers have studied the impact of optimism bias on corporate decisions (Heaton, 2002; Campbell et al., 2011), executive behavior (Englmaier, 2010; Sen and Tumarkin, 2015), investment strategy of money managers (Puri and Robinson, 2007; Wang et al., 2013), and financial analyst reports (Easterwood and Nutt, 1999; Paleari and Vismara, 2007). Nevertheless, all these studies assume that the agent is optimistic, and very little is known about the impact of the principle’s optimism bias in portfolio delegation. We contribute to the literature in several ways. First, we find that the investor increases portfolio delegation when he is optimistic, which is consistent with findings by Odean (1998) and Chuluun and Graham (2016) in non-delegated investing. Second, we prove that the investor’s optimism bias reduces the portfolio return but increases compensation of the manager. These results support the empirical finding that rational agents would exploit the principals’ bias and information asymmetry to their advantage (Cooper et al., 2005; Baker and Wurgler, 2013). Third, we show that the investor’s optimism aggravates the effect of the manager’s risk aversion by further reducing investment level and causes additional Pareto efficiency loss, which complements Campbell et al. (2011) who suggest that managerial optimism benefits the principal by alleviating underinvestment problems caused by managerial risk aversion. 2. Optimism and Delegation The basic setup of the model is based on Gervais et al. (2005) who study portfolio delegation under rationality. Consider a portfolio management framework populated with a risk neutral investor who is wealthy but has no investment skill, and a money manager endowed with a constant absolute risk aversion (CARA) utility function with an absolute risk aversion coefficient ρ, who has no wealth but some investment skill a a （0,1）. There are two types of assets on the market: a risk-free asset with return rate normalized to one, and a risky asset with unconditional return 2
rate r , which is either r =rH 1 or r =rL 1 with equal probability, so that E (r ) rH / 2 rL / 2 1 .The investor can invest in the risk-free asset directly, or delegate his capital to the manager, and then the gross return of the portfolio is r ( x) (1 x) xr 1 x(r 1) , where x is the proportion invested in the risky asset by the manager. Suppose that the manager can receive a private signal about the return rate of the risky asset. Specifically, the signal indicates either good or bad news, s sH or s sL , corresponding to rH and rL respectively. The conditional distribution of the risky asset return rate generated by the manager is Pr(r =rH | s sH ) Pr(r =rL | s sL ) 1 a 2 Pr(r =rH | s sL ) Pr( r =rL | s sH ) 1 a 2
(1)
There is information asymmetry between the investor and the manager that the manager decides on the investment strategy according to the signal received, buying on good news ( x(sH ) 0 ) or selling on bad news ( x(sL ) 0 ), but the signal cannot be observed by the investor. We suppose that the investor is optimistically biased, which is known to the manager. Consistent with de Meza and Southey (1996) and Heaton (2002), we define optimism as the ex-ante belief that the distribution of the risky asset’s return is more favorable than the true distribution. Specifically, the optimistic investor believes that the probability of good state for the risky asset ( r =rH ) is [1 / 2, 1] ,1
Pr(r rH 1) Pr(r rL 1) 1
(2)
so d 1/ 2 [0, 1/ 2] measures the level of investor optimism bias. Then from Eq. (1), the optimistic investor thinks that Pr(r rH | a a) a(1 ) 1 2 d a(1 2 d ) Pr(r rL | a a) 1 a(1 ) 1 2 d a(1 2 d ) 1
(3)
and expects the return rate of the portfolio as R E(r )=1 2-1 x(rH 1) . At the outset, the manager announces a compensation contract W that she is willing to work for. Based on this contract, and on the observation of the manager’s skill a, the investor chooses the amount A of money he delegates to the manager. According to Stoughton (1993), suppose W (r ) Ar ( x) , where (0,1) represents the manager’s sharing proportion of the investment return. In light of Chen et al.’s (2004) empirical findings, we assume that the cost of operating the portfolio is kA 2 , 1
We can reach the same conclusions in the paper by assuming that the investor optimistically estimates (i.e., overestimates) the manager’s ability. 3
where k 0,1 . Similar to Berk and Green (2004), we assume that investors compete for the manager’s expertise in investing and make the manager acquire the entire surplus she creates, so in equilibrium A always makes the investor indifferent between portfolio delegation and direct investing. Thus at the outset, the amount of capital the investor delegates to the manager is
1 R 1 A max 0, k
(4)
When the manager chooses her contract β, in order to maximize her expected compensation W, she takes into account the investor’s expected reaction to her choice, Eq. (4). The equilibrium behaviors for the optimistic investor and the rational manager are characterized in the following lemma. Lemma 1. At the outset, the manager’s choice of the portfolio delegation contract is
2-1 x(rH 1) R 1 2R 2[1 2 -1 x( rH 1)]
(5)
The amount of capital the investor delegates to the manager is
A
R 1 2-1 x(rH 1) 2k 2k
(6)
By inspection of Lemma 1, since R 0 we realize that both and A are increasing in d. The investor increases his investment delegation when he is optimistic, which is consistent with investors’ irrational direct investing behavior in Odean (1998) and Chuluun and Graham (2016). Interestingly, the manager also increases her sharing proportion in the contract as d increases. The manager takes advantage of the investor's cheery expectation of the future by awarding herself a more generous contract. 3. Investment Strategy and Welfare Besides his delegation decision and agent contract, the investor's optimism bias also affects the manager’s investment strategy and the investment return. Proposition1. The optimal investment strategy for the risk-averse manager is 1 a 1 a x ( sH ) - x ( sL )= A(rH rL ) ln
(7)
where x ( sH ) 0 and x ( sL ) 0 represent the optimal trading proportions of the 4
risky asset bought and sold on good and bad news respectively. The portfolio's expected return rate under the strategy is:
E *[r ( x) | s ] 1
a 1 a ln 2 A 1 a
(8)
Proof: see Appendix. As discussed with respect to Lemma 1, since both β and A are increasing in d, we take note that x and E [r ( x) | s ] are both decreasing in d. When the investor is optimistic, the rise of the sharing proportion by the manager brings higher risk in her compensation, so she commensurately reduces trading of the risky asset in order to control her overall risk, which in turn lowers the expected return of the portfolio notwithstanding the manager’s investing skills. Therefore, the investor’s optimism bias is detrimental to his own welfare. The following proposition derives the managerial economic welfare by combining Lemma 1 and Proposition 1. Proposition 2. The expected compensation of the manager is
E[W (r )] A+
a 1 a ln 2 1 a
(9)
It is evident that E[W ( r )] is increasing in the investor’s optimism d. This result is somewhat shocking, since it shows that the manager makes more money for herself due to the increased sharing proportion and the investor's delegated amount, leaving the investor alone to bear the cost for his bias. This result braces the finding of Cooper et al. (2005) and Baker and Wurgler (2013) that the rational agent would aggravate the infraction of the principal's welfare by exploiting the principal's bias to maximize her own interest. To better understand the effects of investor’s optimism, consider an extreme case of our model in which the investor is rational (d = 0). Even when the investor is rational, the trading of the risky asset ( xd 0 ) and the expected return ( Ed0 [r ( x) | s ] ) are lower than in the ideal condition in which the investor receives the same signal as the manager, 2 which is the classic moral hazard problem due to information asymmetry. Since the investor’s optimism bias widens this gap (i.e., further reducing both variables), it aggravates the principal-agent conflict and causes further Pareto efficiency loss. 4. Conclusion
2
Proof is available from authors upon request. 5
While optimism has been studied in various economic and business contexts, the principal’s optimism in portfolio delegation has not drawn much attention. The results in this paper suggest that the unrealistic expectation of investors may have unintended consequences of reducing the expected return of the delegated portfolio while benefiting their rational agents. Investors should be aware of these potential effects caused by their optimism biases when making delegating decisions. The results in this paper echo findings on the detrimental effect of entrepreneurial optimism (de Meza and Southey, 1996; Hmieleski and Baron, 2009).
Acknowledgements We thank Danling Jiang and an anonymous reviewer for helpful comments. This study is supported by the National Natural Science Foundation of China (#71571038, #71671030) and the Fundamental Research Funds for Central Universities in China (#N150602001). Financial support from China Scholarship Fund (2016) is gratefully acknowledged. References Baker, M., Wurgler, J., 2013. Behavioral corporate finance: An updated survey, in: Constantinides, G.M., Harris, M., Stulz, R.M. (Eds.), Handbook of the Economics of Finance (vol. 2). North Holland, Oxford, pp. 357– 424. Berk, J.B., Green R.C., 2004, Mutual fund flows and performance in rational markets. J. Polit. Econ. 112(6), 1269–1295. Bhattacharya, S., Pfleiderer, P., 1985. Delegated portfolio management. J. Econ. Theory 36(2), 1–25. Campbell, C., Gallmeyer, M., Johnson, S.A., Rutherford, J., Stanley, B.W., 2011. CEO optimism and forced turnover. J. Financ. Econ. 101(3), 695–712. Chen, J., Harrison, H., Ming, H., Jeffrey, D.K., 2004. Does fund size erode mutual fund performance? The role of liquidity and organization. Amer. Econ. Rev. 94(5), 1276–1302. Chuluun, T., Graham, C., 2016. Local happiness and firm behavior: Do firms in happy places invest more? J. Econ. Behav. & Organ. 125(5), 41 – 56. Cooper, M.J., Gulen, H., Rau, P.R., 2005. Changing names with style: Mutual fund name changes and their effects on fund. J. Financ. 60(6), 2825 – 2858. de Meza, D., Southey, C., 1996. The Borrower's curse: Optimism, finance and 6
entrepreneurship. Econ. J. 106(435), 375–386. Easterwood, J.C., Nutt, S.R., 1999. Inefficiency in analysts' earnings forecasts: Systematic misreaction or systematic optimism? J. Financ. 54(5), 1777–1797. Englmaier, F., 2010. Managerial optimism and investment choice. Manage. Decis. Econ. 31(4), 303–310. Gervais, S., Lynch, A.W., Musto, D.K., 2005. Fund families as delegated monitors of money managers. Rev. Financ. Stud. 18(4), 1139–1169. Heaton, J. B., 2002. Managerial optimism and corporate finance. Financ. Manage. 31(2), 33–45. Hmieleski, K., Baron, R., 2009. Entrepreneurs' optimism and new venture performance: A social cognitive perspective. Acad. Manage. J. 52(3), 473–488. Odean, T., 1998. Volume, volatility, price, and profit when all traders are above average. J. Financ. 53(6),1887 – 1934. Paleari, S., Vismara, S., 2007. Over-optimism when pricing IPOs. Manage. Financ. 33(6), 352 – 367. Puri, M., Robinson, D.T., 2007. Optimism and economic choice. J. Financ. Econ. 86(1), 71–99. Sen, R., Tumarkin, R., 2015. Stocking up: Executive optimism, option exercise, and share retention. J. Account. Econ. 118(2), 399–430. Shepperd, J.A., Klein, W.M., Waters, E.A., Weinstein, N.D., 2013. Taking stock of unrealistic optimism. Perspect. Psychol. Sci. 8(4), 395–411. Stoughton, N., 1993. Moral hazard and the portfolio management problem. J. Financ. 48(3), 2009– 2028. Wang, J., Sheng, J., Yang, J., 2013. Optimism bias and incentive contracts in portfolio delegation. Econ. Model. 33(7), 493–499.
Appendix: Proof of Proposition 1 If the manager receives the signal s sH , she chooses x ( sH ) to maximize her expected utility 1 a 1 a (e A[1 x ( rH 1)] ) (e A[1 x ( rL 1)] ) 2 2 Its first-order condition yields x ( sH ) . Likewise, we can get x ( sL ) if s sL . Since E[U (W (r ( x))) | s ]
rH rL 2(rH 1) 2(1 rL ) , the portfolio's expected return rate is
7
1 1 a 1 1 a 1 x ( sH )( rH 1) * 1 x ( sH )( rL 1) E [r ( x ) | s ] * 2 2 2 2 1 1 a 1 1 a 1 x ( sL )( rH 1) * 1 x ( sL )( rL 1) * 2 2 2 2 a 1 a 1 ax ( sH )( rH 1) 1 ln 2 A 1 a
8