Research On Optimal Policies And Valuation Of Hedge Funds And Alternative Investments

Given that the "new normal" stage of China’s economy and the lack of high-quality assets in the financial market, alternative investment vehicles, especially hedge funds, are becoming more and more popular, expanding the range of options to investors. Research on optimal policies and valuation of hedge funds and alternative investments are of great significance for fund management companies, investors,as well as market regulators.The theoretical models in this paper are based on the stochastic control theory and un-der the time-continuous framework. Our research involves hedge fund manager’s optimal management decisions and the valuation of high-water mark contracts,as well as investors,optimal hedging strategy, consumption decision and implied value of the option to invest.Firstly, we mainly develop a model measuring the optimal effort and valuing the com-pensation contracts of a risk-neutral hedge fund manager. The manager chooses the optimal effort to reduce liquidation risks and maximize the present value of her total fees, and at the same time make a trade-off between extra return benefits and the cost of the effort. The manager exerts greatest effort when the fund is close to liquidation. And when the fund value is approaching the HWM, the optimal effort still decreases, but the rate of decline becomes far slower. The optimal effort induced by both the high-water mark contracts and endogenous fund liquidation contributes to increasing the survival likelihood for the fund and maintaining the fund as a going concern. A growth of degree of the effort cost,volatil-ity of the fund value, exogenous liquidation intensity or endogenous liquidation boundary decreases the optimal effort. Comparing with performance fees, management fees play a major role in the compensation contracts.Secondly, this paper develops a dynamic framework to analyze hedge fund leverage choice and the valuation of high-water contracts, in which the extra return and volatility of the fund’s alpha-generating strategy shift between good and bad states at random times.The leverage, the manager’s risk attitude and her expected present value of payoffs in each state reflect the possibility for state shifts, all of which are distinct from the results derived from the general one-regime model. The manager always intends to increase leverage when the probability of a coming crisis is higher, in both good times and bad times, to recover the potential revenue loss from the crisis, or gamble for more payoffs. Moreover, in a crisis, the leverage is significantly reduced, comparing with the one in good times. And the manager also tends to increase risk-taking when facing tail risks and large investors9 redemptions.Finally, we conduct a real option valuation model in an incomplete market with partial information, based on filter theory and consumption utility indifference pricing method. By solving a three-dimensional free-boundary partial differential equation (PDE), we obtain the implied value of the option to invest and investment threshold, and identify the optimal consumption decision and portfolio selection. The conclusion has some reference valuefor the estimation of alternative investment assets and asset management in practice. The volatility of the investment has two opposite effects on the option value, and assets with great uncertainty are not suitable for highly risk-averse investors. An increase of the mean appreciation rate estimation risk decreases the option value, which implies that incompleteinformation disclosure has significantly negative effects on the option value. Moreover,if the investment return has negative correlation with the market portfolio, the hedging effectiveness would be better.