Optimal hedge fund portfolios under liquidation risk

We use an expected utility framework to integrate the liquidation risk of hedge funds into portfolio allocation problems. The introduction of realistic investment constraints complicates the determination of the optimal solution, which is solved using a genetic algorithm that mimics the mechanism of natural evolution. We analyse the impact of the liquidation risk, of the investment constraints and of the agent's degree of risk aversion on the optimal allocation and on the optimal certainty equivalent of hedge fund portfolios. We observe, in particular, that the portfolio weights and their performance are significantly affected by liquidation risk. Finally, tight portfolio constraints can only provide limited protection against liquidation risk. This approach is of special interest to fund of hedge fund managers who wish to include the hedge fund liquidation risk in their portfolio optimization scheme.     

Dynamic portfolio strategy by loss-averse fund managers facing performance-induced fund flows

In a continuous-time framework, we establish an optimal dynamic portfolio strategy for a loss-averse fund manager facing performance-induced fund flows. Using the martingale approach, we derive closed-form solutions to both the optimal terminal value and optimal dynamic strategy of the fund under management. The model shows that the loss-averse manager strives to earn high returns in good market conditions at the risk of losing all investments at the terminal date in bad market conditions. The prospect of higher fund inflows induced by superior performance motivates fund managers to take more aggressive investment strategies, increasing the fund's risk exposure, whereas the prospect of fund outflows due to underperformance has no impact on the fund manager's investment decision. While the prospect of higher fund inflows increases dynamic optimal wealth as well as optimal terminal wealth in good market conditions, in bad market conditions, it reduces dynamic optimal wealth and results in a higher chance of a complete loss at the terminal date. Finally, a manager with a higher degree of loss aversion tends to take a conservative investment strategy with a lower risk exposure especially in bad market conditions, leading to a lower dynamic and terminal wealth in good market conditions and also a lower chance of a complete loss in bad market conditions.     

Brokerage Commission Schedules

It is generally optimal for risk-sharing reasons to base a charge for information on the signal realization. When this is not possible, a charge based on the amount of trading, a brokerage commission, may be a good alternative. The optimal brokerage commission schedule is derived for a risk-neutral information seller faced with risk-averse purchasers who may differ in their risk aversion. Revenues from the brokerage commission are compared with those from a fixed charge for information and the optimal mutual fund management fee.     

A Time to Scatter Stones,and a Time to Gather Them: The Annual Cycle in Hedge Fund Risk Taking

Analyzing a sample of hedge fund daily returns from Bloomberg, we find a seasonal pattern in their risk taking. During earlier months of a year, poorly performing funds reduce risk. The reduction is stronger for funds with higher management fees, shorter redemption periods, and recently deteriorating performance, consistent with a managerial aversion to early fund liquidation. Toward the end of a year, poorly performing funds gamble for resurrection by increasing risk. It is largely achieved by increasing exposure to market factors, and can be linked to stronger indirect managerial incentives during the second half of a year.     

Locked Up by a Lockup: Valuing Liquidity as a Real Option

Hedge funds often impose lockups and notice periods to limit the ability of investors to withdraw capital. We model the investor's decision to withdraw capital as a real option and treat lockups and notice periods as exercise restrictions. Our methodology incorporates time-varying probabilities of hedge fund failure and optimal early exercise. We estimate a two-year lockup with a three-month notice period costs approximately 1% of the initial investment for an investor with constant relative risk aversion utility and risk aversion of three. The cost of illiquidity can easily exceed 10% if the hedge fund manager can arbitrarily suspend withdrawals.     

Commodity futures hedging,risk aversion and the hedging horizon

This paper examines the impact of management preferences on optimal futures hedging strategy and associated performance. Applying an expected utility hedging objective, the optimal futures hedge ratio is determined for a range of preferences on risk aversion, hedging horizon and expected returns. Empirical results reveal substantial hedge ratio variation across distinct management preferences and are supportive of the hedging policies of real firms. Hedging performance is further shown to be strongly dependent on underlying preferences. In particular, hedgers with high risk aversion and short horizon reduce hedge portfolio risk but achieve inferior utility in comparison to those with low aversion.     

A Termination Rule for Pension Guarantee Funds

A termination rule based on a critical funding ratio is proposed for a pension guarantee fund (PGF) that considers closing an underfunded pension plan. This ratio is determined by solving an expected utility maximization problem on behalf of plan beneficiaries subject to two constraints designed to preserve the PGF's viability. The first is an upper bound on the PGF's annual intervention probability; the second, a restriction on the expected shortfall of an underfunded pension plan that is not closed. Both too low and too high critical funding ratios hurt beneficiaries’ interests, depending on their degree of risk aversion.     

Portfolio choice with skewness preference and wealth-dependent risk aversion

This paper studies a dynamic portfolio choice problem for an investor with both wealth-dependent risk aversion and wealth-dependent skewness preferences. In a general economic setting, the solution is characterized in terms of a system of extended Hamilton-Jacobi-Bellman (EHJB) equations and the solution is given in closed form in some special cases. We demonstrate the effects of higher order risk preferences and state-dependent risk aversion on the optimal asset allocation decisions. We find that wealth-dependent risk aversion facilitates risk taking and the skewness preference leads to a more positively skewed portfolio in certain circumstances.     

Optimal Control of DC Pension Plan Management under Two Incentive Schemes

Since the late 1990s, a performance fee arrangement has been approved as a managerial incentive in direction contribution (DC) pension plan management to motivate managers. However, the fact that managers may take undue risk for the larger performance fees and thus reduce members’ utility has been a subject of debate. As such, this study investigates the optimal risk-taking policies of DC pension fund managers under both the single management fee scheme and a mixed scheme with a lower management fee, as well as an additional performance fee. The analytical solutions are derived by using the duality method and concavification techniques in a singular optimization problem. The results show the complex risk-taking structures of fund managers and recognize the win-win situation of implementing performance-based incentives in DC pension plan management. Under the setting of geometric Brownian motion asset price dynamics and constant relative risk aversion utility, the optimal risk investment proportion shows a peak-valley pattern under the mixed scheme. Further, the manager gambles for gain when fund wealth is low and time to maturity is short. As opposed to the existing literature, this study found that the risk-taking policy is more conservative when fund wealth is relatively large. Furthermore, the utilities of the manager and members could both be improved by appropriately choosing the performance fee rate.     

Uncertainty avoidance and mutual funds

We study how culture influences mutual funds around the world. Uncertainty Avoidance (UA), which is related to ambiguity aversion, is negatively associated with flow-performance sensitivity, deviation from the fund benchmark, fund alpha, and the fraction of active management across the 25 countries in our sample. This is true even when controlling for an exhaustive set of fund- and country-level characteristics. We also find that a fund's deviation from its benchmark is not only affected by the UA of its domicile country but also by the UA of its fund family's country of origin. Our results highlight the importance of considering cultural characteristics, and UA in particular, when studying mutual funds across countries.     

Pension Fund Design under Long-term Fairness Constraints

We consider optimal portfolio insurance for a mutually owned with-profits pension fund. First, intergenerational fairness is imposed by requiring that the pension fund is driven towards a steady state. Subject to this condition the optimal asset allocation is identified among the class of constant proportion portfolio insurance strategies by maximising expected power utility of the benefit. For a simple contract approximate analytical results are available and accurate, whereas for a more involved contract Monte Carlo methods must be applied to pick out the best design. The main insights are (i) aggressive investment strategies are disastrous for the clients; (ii) in most cases it is optimal to gear the bonus reserve; and (iii) the results are far less sensitive to the agent's risk aversion than in the classical case of Merton (1969), and as opposed to Merton horizon matters even with constant investment opportunities (because of the serial dependence between bonuses).     

Risk aversion under preference uncertainty

We show that if an agent is uncertain about the precise form of his utility function, his actual relative risk aversion may depend on wealth even if he knows his utility function lies in the class of constant relative risk aversion (CRRA) utility functions. We illustrate the consequences of this result for optimal asset allocation: poor agents that are uncertain about their risk aversion parameter invest less in risky assets than wealthy investors with identical risk aversion uncertainty.     

United States current account deficits: A stochastic optimal control analysis

The “Pessimists” and the “Optimists” disagree whether the US external deficits and the associated buildup of US net foreign liabilities are problems that require urgent attention. A warning signal should be that the debt ratio deviates significantly from the optimal ratio. The optimal debt ratio or debt burden should take into account the vulnerability of consumption to shocks from the productivity of capital, the interest rate and exchange rate. The optimal debt ratio is derived from inter-temporal optimization using Dynamic Programming, because the shocks are unpredictable, and it is essential to have a feedback control mechanism. The optimal ratio depends upon the risk adjusted net return and risk aversion both at home and abroad. On the basis of alternative estimates, we conclude that the Pessimists’ fears are justified on the basis of trends. The trend of the actual debt ratio is higher than that of the optimal ratio. The Optimists are correct that the current debt ratio is not a menace, because the current level of the debt ratio is not above the corresponding level of the optimum ratio.     

Hedge fund strategies,performance &diversification: A portfolio theory & stochastic discount factor approach

For 5500 North American hedge funds following 11 different strategies, we analyse the stand-alone performance of these strategies using a stochastic discount factor approach. Employing the same data, we then consider the diversification benefits of each hedge fund strategy when combined with a portfolio of US equities and bonds. We compute the out-of-sample Black-Litterman portfolios, with Bayes-Stein, higher moments, simulations, desmoothed data and allowance for regimes as robustness checks. All but two hedge fund strategies out-perform the market as stand-alone investments; and all but one provide significant diversification benefits. The higher is an investor’s risk aversion, the more beneficial is diversification into hedge funds.     

Risk preferences and the marketing of financial services: Segmentation by birth order

Traditional investment questionnaires may yield an incomplete measure of clients’ risk tolerance. Birth order has the potential to provide additional insight into the true nature of customers’ risk aversion, thereby assisting financial advisors to formulate the optimal investment portfolio for each client. We summarize research findings on birth order-related personality traits that have potential impact on the financial services industry. Marketing implications for investment firms are discussed in a framework that considers customers’ birth order differences in risk tolerance, patience, financial goals and conformity.     

Saving and investing for early retirement: A theoretical analysis

We study optimal consumption and portfolio choice in a framework where investors adjust their labor supply through an irreversible choice of their retirement time. We show that investing for early retirement tends to increase savings and reduce an agent's effective relative risk aversion, thus increasing her stock market exposure. Contrary to common intuition, an investor might find it optimal to increase the proportion of financial wealth held in stocks as she ages and accumulates assets, even when her income and the investment opportunity set are constant. The model predicts a decrease in risk aversion following strong market gains like those observed in the nineties.     

Multidimensional Screening in a Monopolistic Insurance Market

We consider a population of individuals who differ in two dimensions, their risk type (expected loss) and their risk aversion, and solve for the profit-maximising menu of contracts that a monopolistic insurer puts out on the market. Our findings are threefold. First, it is never optimal to fully separate all the types. Second, if heterogeneity in risk aversion is sufficiently high, then some high-risk individuals (the risk-tolerant ones) will obtain lower coverage than some low-risk individuals (the risk-averse ones). Third, because women tend to be more risk averse than men (in that the risk aversion distribution for women first-order stochastically dominates that for men), gender discrimination may lead to a Pareto improvement.     

基于规模与风格的证券投资基金最优组合构建研究

本文选择中国2004年10月1日前成立的8种投资风格共133只证券投资基金,根据其在2005年1月1日-2008年3月31日共161周的数据,依照非回置等权抽样方法构建基金组合。在研究了基金组合规模与组合风险和绩效关系的基础上,着重探讨了基金组合所含风格类型以及基金组合风格丰富化指标与组合风险和绩效的关系。在上述研究的基础上,论文提出了综合规模和风格双因素的基金最优组合构建原则,并得出了最适度风格类型模型和最适度风格丰富化指标模型。     

The effect of temporal risk aversion on liquidity preference

In most instances, investors are not indifferent to risk. Their attitudes toward it influence their decisions. Temporal risk aversion, the dynamic analogue of the usual concept of risk aversion, has a marked effect on investors' decisions but is usually ignored in the literature. This paper investigates the liquidity preference of temporally risk-averse investors. The analysis shows that, all other things being equal, temporal risk aversion reduces the liquidity premium investors must receive to hold an asset that is not perfectly reversible. Thus, the optimal investment policy is closer to what one would expect had a frictionless exchange market existed for the irreversible asset. As far as an individual's investment behavior is concerned, temporal risk aversion counters the effects of an asset's irreversibility and tends to compensate for the absence of frictionless exchange.     

Macroeconomic risk and hedge fund returns

This paper estimates hedge fund and mutual fund exposure to newly proposed measures of macroeconomic risk that are interpreted as measures of economic uncertainty. We find that the resulting uncertainty betas explain a significant proportion of the cross-sectional dispersion in hedge fund returns. However, the same is not true for mutual funds, for which there is no significant relationship. After controlling for a large set of fund characteristics and risk factors, the positive relation between uncertainty betas and future hedge fund returns remains economically and statistically significant. Hence, we argue that macroeconomic risk is a powerful determinant of cross-sectional differences in hedge fund returns.