A Theory Of Large-investor Premium

We develop a theoretical model to study large shareholders’ influence to firm’s equi-ty performance.The large shareholders’ influence is measured by a regression coefficient on large shareholders’ portfolio holding in firm’s equity premium.When the market achieves an equilibrium,the impact coefficient is endogenously determined which is positive-proportional to shareholders’s investment.Furthermore,our model also pro-vides a theoretical interpretation why corporations with concentrated ownership aver-agely outperforms those with dispersed ownership.Calibration shows that,even the current equity premium is negative,a large shareholder’s investment is still plausible.It is well understood that the presence of large,concentrated claimholders may have impacts on managerial incentives,which,in turn,may enhance firm value.The literature on the influence of concentrated large investors has been almost exclusively focusing on empirical evidences for equity markets([39],[10],[40],[32])and references therein.[2]provided evidence on subprime mortgage securities for the effect of large investors on asset quality.In this paper,we construct a game-theoretical model in continuous-time to study how firm’s equity premium is influenced by concentrated shareholdings.We start with a model specification in which firm’s equity premium is affected by large investors’shareholdings via a linear regression coefficient.The coefficient measures marginal pre-mium of large shareholders.To large investors,who can perceive the impact of their sharing-holding on asset returns,they significantly increase the magnitude of their in-vestment if they have positive impact on the firm.In a transparent market,small investors as price-takers behave rationally in a sense that they track large shareholders’trading closely and form expectation on the impact of large shareholders’holding on asset returns.Nevertheless,small investors do not long/short so much as the large in-vestors do.Accordingly,small investors can be treated as free raiders who benefit from concentrated shareholding without bearing so much consequent risk.As illustrated in Chapter 3 below,small investors may even achieve greater Sharpe ratios than the large investor.When market achieves equilibrium,the resulting impact coefficient can be analyti-cally determined.We show that the impact coefficient is positive-proportional to large investors’share endowment(or relative wealth level to the total market value of the firm),while it is negative-proportional to small investors’aggregated endowment.In a situation there is a self-serving large investor,a notion to be made precise in the context,its impact coefficient is larger than that of a large investor does not self-serve.The analyses are extended to economies when there are more than one large in-vestors.We show that an economy with a single large investor,whose impact coefficient equaling to the summation impacts of the multiple large shareholders,would bring high-er equity premium than that of an economy with several large investors who have diverse impacts on asset returns.Thus the equity premium demonstrates a U-shape style when the impact coefficient is divided.The model is also extended to the case when equity premium admits a multi-factor decomposition in addition to the large shareholding premium.It is interesting to discover that,even when the current equity premium is negative,a large shareholder’s portfolio holding may still be positive.We also consider the model with volatility uncertainty and under the CRRA utility function.If the volatility is uncertain in our model,we can find a robust equilibri-um strategy for both large investors and small investors.We can also prove that the equilibrium strategy is equivalent to the optimal strategy under the CRRA criterion.Empirical evidences are found from China market that companies with large-shareholders significantly yield better performance than those with dispersed ownership.There are only several related mathematical models on market impact of large in-vestors.[15]shows that large investors in options hedging could affect stock price,precisely they find that stock volatility increase caused by overpricing the option.See also[30]who study large investor trading impacts on volatility.The closest paper is[14]which examines the individual’s optimal consumption and investment problem for a large investor,whose portfolio choices affect the assets’ expected returns.Their main result is related to the existence and characterization of optimal policies under fairly general assumptions on the security price coefficients and on the income process.In our paper,we adopt an affine relation between equity premium and the proportional investment,which allows us to obtain explicit strategies and to describe easily the strategic behavior of large/small investors.Another closely related paper is[44]which builds a single peri-od mean-variance model in an oligopolistic setting in which the stock price is positively affected by the volume of the demand for the asset.Their model validates the claim that large investors enhance their portfolio performance in relation to the standard market.Our paper confirms their findings not only in complete market,but also in incomplete market with a time-varying Gaussian mean-reverting return.Besides,we also reveal the strategic behaviors of multiple large investors.To illustrate the problem in an intuitive way,we employ the dynamic mean-variance(MV)model recently developed by[16].The dynamic MV problem is not a trivial extension of its static couterpart,due to the natural time-inconsistence of the strategies introduced by the variance item.The strategy which is optimal today seems not to be optimal tomorrow,and the dynamic programming principle does not hold and thus the traditional PDE method fails.A pioneering work[35]treats this time-inconsistent problem as an intrapersonal non-cooperative games where the optimal strategies are described using Nash equilibrium.Within this framework,suppose there is one player at each time and every player maximizes her reward function.Then the Nash equilibrium,if exists,is the "optimal" strategy.See[20]and[21]for Merton’s portfolio management with non-constant hyperbolic discounting.[4]is the first to study this problem under MV criteria over terminal wealth.They employ the total variation principle to derive a system of extended HJB equations,and t.his system can be solved explicitly under a risk-neutral measure.[7]generalized the MV problem to a general time-inconsistent control problem.As an application,[8]considers wealth-dependent risk aversion.[16]is the first to apply the dynamic MV criterion to log-returns and obtain a CRRA’s type strategy which is consistent with traditional wisdom such as richer should invest more amount and younger should invest more proportion of his wealth to risky assets.In this paper,we adopt the log-return MV model and take into account the large shareholder premium.We first consider a complete market and then extend it to the case with stochastic return.The rest of the thesis is organized as follows.In Chapter 1,I give a brief review to the mean-variance model of optimal strategy under discrete time and continuous time setting.Recently,time-inconsistent stochastic control method is developed to find an equilibrium strategy for continuous time mean-variance model.A time-inconsistent stochastic control theory is also presented.In Chapter 2,Some empirical evidences from my research papers are presented to show the behaviors of large investors are totally different from that of small investors.The existence of large investors have influence to firm’s performance.In Chapter 3,I present my theory of large investor in this chapter.This theory gives rise to many financial implications as the empirical evidences shown in Chapter 2.In Chapter 4,Some methods are considered to measure the large investors’ influ-ences to the firm.I adopt a market equilibrium method,a statistical method,and strong laws of large numbers methods.In Chapter 5,I put the conclusion and all the proofs in this chapter.