Portfolio Choice Problem Research Articles

Dynamic portfolio selection with market impact costs

This paper concerns optimal dynamic portfolio choice with quadratic utility when there are market impact costs. The optimal policy is difficult to characterize, so we look instead for sub-optimal policies. Our proposed suboptimal policy solves a tractable dynamic portfolio choice problem where the cost of trading is captured in the objective instead of the price dynamics. A multiple time scale asymptotic expansion shows that our proposed policy has sensible structural properties, while numerical experiments show promising performance and robustness properties.

The Standard Portfolio Choice Problem in Germany

We study behavior in an investment experiment conducted with a representative sample of German households. Respondents allocate a fixed budget between a safe asset and a risky asset whose returns are tied to the German stock market and earn monetary returns based on their decisions. Experimental investment choices correlate with beliefs about stock market returns and exhibit desirable external validity: They are a strong predictor for real-life stock market participation. The experimental set-up allows exogenous modification of the risky asset’s return but investments are inelastic except for financially savvy subsamples. A laboratory experiment accompanies the data collection and yields similar results.

Portfolio Choice with State-Dependent Adjustments: Analyzing Leveraged Positions Without Parametric Assumptions

In this paper, we discuss a new method for solving the portfolio choice problem which models state-dependent quantity adjustment using boundary crossing events. This new method has several advantages: first, we can solve for the optimal portfolio weights without parametric assumptions, by deriving them directly from the data. Next, we can describe the full distribution of the portfolio's value, not just its moments. Finally, we can easily deal with important practical issues, such as transaction costs, leveraged positions and no-ruin conditions, or the cost of margin financing. In particular, the method allows us to analyze leveraged positions in discrete time under zero ruin probability. Analyzing historical stock data suggests that historically, the log-optimal portfolio was a not too extensive leveraged purchase of a diversified stock portfolio, therefore leveraging does not necessarily imply risk-seeking behavior. We also show that depending on how much weight we allocate to this diversified stock portfolio, the downside risk measured as 5% VAR of the portfolio's value may be decreasing or increasing over time. Consequently, an objective functions which incorporates the VAR of the portfolio's value or operate with VAR constrains result in horizon-dependent portfolio weights. We also present some evidence suggesting that the log-optimal portfolio weights are time-dependent. Finally, irrespective of what weight we chose for the diversified stock portfolio, it is log-optimal to reduce exposure to the stock market if the predicted volatility is high, and increase it in low volatility periods.

Valuing Private Equity

We investigate whether the performance of private equity (PE) investments is sufficient to compensate investors (LPs) for risk, long-term illiquidity, management, and incentive fees charged by the general partner (GP). We analyze the LPs' portfolio-choice problem and find that management fees, carried interest, and illiquidity are costly, and GPs must generate substantial alpha to compensate LPs for bearing these costs. Debt is cheap and reduces these costs, potentially explaining the high leverage of buyout transactions. Conventional interpretations of PE performance measures appear optimistic. On average, LPs may just break even, net of management fees, carry, risk, and costs of illiquidity.

Student Portfolios and the College Admissions Problem

We develop a decentralized Bayesian model of college admissions with two ranked colleges, heterogeneous students, and two realistic match frictions: students find it costly to apply to college, and college evaluations of their applications are uncertain. Students thus face a portfolio choice problem in their application decision, while colleges choose admissions standards that act like market-clearing prices. Enrollment at each college is affected by the standards at the other college through student portfolio reallocation. In equilibrium, student-college sorting may fail: weaker students sometimes apply more aggressively, and the weaker college might impose higher standards. Applying our framework, we analyse affirmative action, showing how it induces minority applicants to construct their application portfolios as if they were majority students of higher caliber.

Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity

We consider the problem of optimal portfolio choice using the Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR) measures for a market consisting of n risky assets and a riskless asset and where short positions are allowed. When the distribution of returns of risky assets is unknown but the mean return vector and variance/covariance matrix of the risky assets are fixed, we derive the distributionally robust portfolio rules. Then, we address uncertainty (ambiguity) in the mean return vector in addition to distribution ambiguity, and derive the optimal portfolio rules when the uncertainty in the return vector is modeled via an ellipsoidal uncertainty set. In the presence of a riskless asset, the robust CVaR and VaR measures, coupled with a minimum mean return constraint, yield simple, mean-variance efficient optimal portfolio rules. In a market without the riskless asset, we obtain a closed-form portfolio rule that generalizes earlier results, without a minimum mean return restriction.

Portfolio Selection with Subsistence Consumption Constraints and CARA Utility

We consider the optimal consumption and portfolio choice problem with constant absolute risk aversion (CARA) utility and a subsistence consumption constraint. A subsistence consumption constraint means there exists a positive constant minimum level for the agent’s optimal consumption. We use the dynamic programming approach to solve the optimization problem and also give the verification theorem. We illustrate the effects of the subsistence consumption constraint on the optimal consumption and portfolio choice rules by the numerical results.

Transaction Costs, Shadow Prices, and Duality in Discrete Time

For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counterexample, we show that shadow prices may fail to exist even in seemingly perfectly benign situations, i.e., for a log-investor trading in an arbitrage-free market with bounded prices and arbitrarily small transaction costs. We also clarify the connection between shadow prices and duality theory. Whereas dual minimizers need not lead to shadow prices in above “global” sense, we show that they always correspond to a “local” version.

Dynamic Optimization of Futures Portfolio Strategies under Downside Risk Control

We introduce a novel out-of-sample approach to solve a real-time investor's multiperiod portfolio choice problem in a setting with (time-varying) conditional predictability, multiple assets and downside risk control. The method involves defining a discrete set of one-period portfolio allocation policies and choosing among them at portfolio revision dates within a discrete-time stochastic dynamic programming approach so as to maximize an investor's expected utility. Our framing of the portfolio problem overcomes the curse of dimensionality that is associated with time-varying investment opportunity sets and multiple assets. We apply our technique to dynamic investment decision problems in futures markets and demonstrate its feasibility and usefulness.

Dual Formulation of Controlled Markov Diffusions and Its Application

Information relaxation and duality in Markov decision processes have been studied recently to derive upper bounds on the maximal expected reward (or lower bounds on the minimal expected cost). The idea is to relax the non-anticipativity constraint on the controls and impose a penalty to punish such a violation. In this paper we generalize this dual approach to controlled Markov diffusions. We develop the weak duality and strong duality results, and explore the structure of the optimal penalty. We demonstrate the use of this dual formulation by computing upper bounds on the optimal expected utility in a dynamic portfolio choice problem.

Hedge Fund Seeding Via Fees-for-Seed Swaps Under Idiosyncratic Risk

We develop a dynamic valuation model of the hedge fund seeding business by solving the consumption and portfolio-choice problem for a risk-averse manager who launches a hedge fund through a seeding vehicle. This vehicle, i.e. fees-for-seed swap, specifies that a strategic partner (seeder) provides a critical amount of capital in exchange for participation in the funds revenue. Our results indicate that the new swap not only solves the serious problems of widespread financing constraints for new and early-stage funds (ESFs) managers, but can be highly beneficial to both the manager and the seeder if structured properly. We also find that the ESFs manager's risk aversion can over-turn the risk-shifting incentives when the fund is likely to default while a cash-out option gives the ESF manager a higher incentive to hit the targets when the assets under management (AUM) are nearing the prescribed cash-out boundary. We find that it is more likely for a more risk-averse ESF manager to engage in risk-shifting when the cash-out option is about to be exercised while less likely if the fund has higher probability to be liquidated.

Dynamic asset allocation with ambiguous return predictability

We study an investor's optimal consumption and portfolio choice problem when he is confronted with two possibly misspecified submodels of stock returns: one with IID returns and the other with predictability. We adopt a generalized recursive ambiguity model to accommodate the investor's aversion to model uncertainty. The investor deals with specification doubts by slanting his beliefs about submodels of returns pessimistically, causing his investment strategy to be more conservative than the Bayesian strategy. Unlike in the Bayesian framework, the hedging demand against model uncertainty may cause the investor's stock allocation to decrease sharply given a small doubt of return predictability, even though the expected return according to the VAR model is large. Over much of the parameter space, the robust strategy is very close to the Bayesian strategy with Epstein–Zin preferences and risk aversion chosen to match the same average portfolio holdings. This is true in particular when the IID model is unlikely and the dividend yield is low, as in recent years. However, differences in strategies can be substantial if the IID model is unlikely and the dividend yield is high.

Optimal Volatility Timing: A Life-Cycle Perspective

We study the role of time-varying stock return volatility in a consumption and portfolio choice problem for a life-cycle investor facing short-selling and borrowing constraints. Faced with a benchmark investment strategy that conditions on age and wealth only, we find that an investor is willing to pay a fee of up to 1%-1.5% of total life time consumption in order to optimally condition on volatility. Tilts in the optimal asset allocation in response to volatility shocks are considerably more pronounced than tilts in response to wealth shocks, and almost as important as life-cycle effects. Lastly, we find that the correlation between volatility and permanent labor income shocks may explain the low equity share of young households in the data.

When Do the Unemployed Jump in the Workforce?

This paper studies an optimal consumption and portfolio choice problem for unemployed people who have an option to work. Our problem is to find optimal consumption, risky investment, and workforce re-entry strategies for the unemployed. We find a closed form of the critical wealth level to re-enter the workforce. We show that the unemployed with a higher disutility of labor or a larger relative risk aversion are more reluctant to re-enter the workforce.

Stable and Efficient Portfolios

DeMiguel et al. (2009a) show that estimation errors lead to mean-variance portfolios that underperform naive diversification (1/N). In response to this finding, new studies have developed more efficient sample-based portfolio strategies that offer higher risk-adjusted returns than 1/N . In this paper, I show that the latter portfolio may still be superior in the presence of transaction costs. This is because sample-based strategies tend to be unstable over time. Instability leads to high transaction costs that significantly reduce portfolio returns. I resolve this issue by introducing a stability penalty to the standard mean-variance objective that controls the deviation from the investor’s portfolio before rebalancing. In contrast to other techniques in the literature that account for transaction costs, the stability penalty offers intuitive analytical solutions to the portfolio choice problem. As such, it allows to treat estimation errors and transactions costs in a joint manner and it can be directly applied to any portfolio strategy. I evaluate the stability approach by applying it to nine sample-based strategies from the literature and study their performance in five data sets of monthly returns. The results confirm that it leads to stable and efficient portfolios that offer higher Sharpe ratio than 1/N and equal or lower turnover.

Default Risk of Life Annuity and the Annuity Puzzle

This paper considers a model of optimal consumption and portfolio choice of the retired person who has partially annuitized her wealth and faces default risk of her annuity provider. We develop a new method for solving the optimal consumption and portfolio choice problem in an incomplete financial market. We find that the effects of default risk on the retiree's optimal investment strategies and annuity demand depend crucially on the level of default risk, risk aversion, wealth, and investment opportunity. Higher default risk may lead retired people to increase their stock holdings. Lower default risk can substantially increase the demand for annuities. The annuity demand increases as risk aversion increases if default risk is small, whereas the annuity demand decreases as risk aversion increases if default risk is large.

Transaction Costs and Shadow Prices in Discrete Time

For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices may fail to exist even in seemingly perfectly benign situations, i.e., for a log-investor trading in an arbitrage-free market with bounded prices and arbitrarily small transaction costs. We also clarify the connection between shadow prices and duality theory. Whereas dual minimizers need not lead to shadow prices in the above global sense, we show that they always correspond to a local version.

Event risk, contingent claims and the temporal resolution of uncertainty

We study the pricing and hedging of contingent claims that are subject to Event Risk which we define as rare and unpredictable events whose occurrence may be correlated to, but cannot be hedged perfectly with standard marketed instruments. The super-replication costs of such event sensitive contingent claims (ESCC), in general, provide little guidance for the pricing of these claims. Instead, we study utility based prices under two scenarios of resolution of uncertainty for event risk: when the event is continuously monitored, or when it is revealed only at the payment date. In both cases, we transform the incomplete market optimal portfolio choice problem of an agent endowed with an ESCC into a complete market problem with a state and possibly path-dependent utility function. For negative exponential utility, we obtain an explicit representation of the utility based prices under both information resolution scenarios and this in turn leads us to a simple characterization of the early resolution premium. For constant relative risk aversion utility functions we propose a simple numerical scheme and study the impact of size of the position, wealth and expected return on these prices.

On Portfolio Choice with Savoring and Disappointment

We revisit the model proposed by Gollier and Muermann [Gollier C, Muermann A (2010) Optimal choice and beliefs with ex ante savoring and ex post disappointment. Management Sci. 56(8):1272–1284; hereafter, GM]. In the GM model, for a given lottery, agents form anticipated expected payoffs and the set of possible anticipations is assumed to be exogenously fixed. We propose sets of possible anticipations that are endogenously determined. This permits us to compare and evaluate in a consistent manner lotteries with different supports and to revisit the portfolio choice problem. We obtain new conclusions and interesting insights. Our extended model can rationalize a variety of empirically observed puzzles such as a positive demand for assets with negative expected returns, preference for skewed returns, and underdiversification of portfolios. This paper was accepted by Rakesh Sarin, decision analysis.

Mean semi-deviation from a target and robust portfolio choice under distribution and mean return ambiguity

We consider the problem of optimal portfolio choice using the lower partial moments risk measure for a market consisting of n risky assets and a riskless asset. For when the mean return vector and variance/covariance matrix of the risky assets are specified without specifying a return distribution, we derive distributionally robust portfolio rules. We then address potential uncertainty (ambiguity) in the mean return vector as well, in addition to distribution ambiguity, and derive a closed-form portfolio rule for when the uncertainty in the return vector is modelled via an ellipsoidal uncertainty set. Our result also indicates a choice criterion for the radius of ambiguity of the ellipsoid. Using the adjustable robustness paradigm we extend the single-period results to multiple periods, and derive closed-form dynamic portfolio policies which mimic closely the single-period policy.