A bootstrap-based comparison of portfolio insurance strategies

This study presents a systematic comparison of portfolio insurance strategies. We implement a bootstrap-based hypothesis test to assess statistical significance of the differences in a variety of downside-oriented risk and performance measures for pairs of portfolio insurance strategies. Our comparison of different strategies considers the following distinguishing characteristics: static versus dynamic protection; initial wealth versus cumulated wealth protection; model-based versus model-free protection; and strong floor compliance versus probabilistic floor compliance. Our results indicate that the classical portfolio insurance strategies synthetic put and constant proportion portfolio insurance (CPPI) provide superior downside protection compared to a simple stop-loss trading rule and also exhibit a higher risk-adjusted performance in many cases (dependent on the applied performance measure). Analyzing recently developed strategies, neither the TIPP strategy (as an ‘improved’ CPPI strategy) nor the dynamic VaR-strategy provides significant improvements over the more traditional portfolio insurance strategies.     

Portfolio Insurance with Liquidity Risk

This paper studies a portfolio insurance problem with liquidity risk. We consider an investor who wants to maximize the expected growth rate of wealth in a low liquid market. The investor can trade assets only at random times and his wealth must not fall below a predetermined floor. We find the optimal expected growth rate and an optimal strategy. The optimal strategy is closely related with a traditional constant proportion portfolio insurance strategy. Also we show that the same strategy maximizes the growth rate almost surely. Further we study the floor effect on the growth rate.     

Optimal asset allocation for participating contracts under the VaR and PI constraint

ABSTRACT

Participating contracts provide a maturity guarantee for the policyholder. However, the terminal payoff to the policyholder should be related to financial risks of participating insurance contracts. We investigate an optimal investment problem under a joint value-at-risk and portfolio insurance constraint faced by the insurer who offers participating contracts. The insurer aims to maximize the expected utility of the terminal payoff to the insurer. We adopt a concavification technique and a Lagrange dual method to solve the problem and derive the representations of the optimal wealth process and trading strategies. We also carry out some numerical analysis to show how the joint value-at-risk and the portfolio insurance constraint impacts the optimal terminal wealth.     

Dynamic mean–VaR portfolio selection in continuous time

The value-at-risk (VaR) is one of the most well-known downside risk measures due to its intuitive meaning and wide spectra of applications in practice. In this paper, we investigate the dynamic mean–VaR portfolio selection formulation in continuous time, while the majority of the current literature on mean–VaR portfolio selection mainly focuses on its static versions. Our contributions are twofold, in both building up a tractable formulation and deriving the corresponding optimal portfolio policy. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the original dynamic mean–VaR portfolio formulation. To overcome the difficulties arising from the VaR constraint and no bankruptcy constraint, we have combined the martingale approach with the quantile optimization technique in our solution framework to derive the optimal portfolio policy. In particular, we have characterized the condition for the existence of the Lagrange multiplier. When the opportunity set of the market setting is deterministic, the portfolio policy becomes analytical. Furthermore, the limit funding level not only enables us to solve the dynamic mean–VaR portfolio selection problem, but also offers a flexibility to tame the aggressiveness of the portfolio policy.     

A general equilibrium model of portfolio insurance

This article examines the effects of portfolio insurance onmarket and asset price dynamics in a general equilibrium continuous-timemodel. Portfolio insurers are modeled as expected utility maximizingagents. Martingale methods are employed in solving the individualagents' dynamic consumption-portfolio problems. Comparisonsare made between the optimal consumption processes, optimallyinvested wealth and portfolio strategies of the portfolio insurersand 'normal agents'. At a general equilibrium level, comparisonsacross economies reveal that the market volatility and riskpremium are decreased, and the asset and market price levelsincreased, by the presence of portfolio insurance.     

Optimal dynamic hedging in incomplete futures markets

This article derives optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of either a CARA or a logarithmic utility function. Existing futures contracts are not numerous enough to complete the market. In addition, in the case of CARA, the nonnegativity constraint on wealth is binding, and the optimal hedging demands are not identical to those that would be derived if the constraint were ignored. Fictitiously completing the market, we can characterize the optimal hedging demands for futures contracts. Closed-form solutions exist in the logarithmic case but not in the CARA case, since then a put (insurance) written on his wealth is implicitly bought by the investor. Although solutions are formally similar to those that obtain under complete markets, incompleteness leads in fact to second-best optima.     

Optimal life insurance with no-borrowing constraints: duality approach and example

We solve an optimal portfolio choice problem under a no-borrowing assumption. A duality approach is applied to study a family’s optimal consumption, optimal portfolio choice, and optimal life insurance purchase when the family receives labor income that may be terminated due to the wage earner’s premature death or retirement. We establish the existence of an optimal solution to the optimization problem theoretically by the duality approach and we provide an explicitly solved example with numerical illustration. Our results illustrate that the no-borrowing constraints do not always impact the family’s optimal decisions on consumption, portfolio choice, and life insurance. When the constraints are binding, there must exist a wealth depletion time (WDT) prior to the retirement date, and the constraints indeed reduce the optimal consumption and the life insurance purchase at the beginning of time. However, the optimal consumption under the constraints will become larger than that without the constraints at some time later than the WDT.     

Consumption and Investment Motives and the Portfolio Choices of Homeowners

This article investigates the portfolio choices of homeowners, taking into account the investment constraint introduced by Henderson and Ioannides (1983). This constraint requires housing investment by homeowners to be at least as large as housing consumption. It is shown that when the constraint is binding, the homeowner's optimal portfolio is ineffcient in a mean-variance sense. Thus, portfolio inefficiency is not an indication that consumers are irrational or careless in their financial decisions. Instead, inefficiency can be seen as the result of a rational balancing of the consumption benefits and portfolio distortion associated with housing investment.     

Underestimation of portfolio insurance and the crash of October 1987

We examine market crashes in the multiperiod framework of Glostenand Milgrom (1985). Our analysis shows that if the market'sprior beliefs underestimate the extent of dynamic hedging strategiessuch as portfolio insurance, then the price will be greaterthan that which would be implied by fundamentals if the extentof portfolio insurance were known with certainty. Over time,the market learns of the amount of portfolio insurance, andconsequently reevaluates the previous inferences drawn frompurchases that were erroneously regarded as based on favorableinformation. The result is that the price falls when the amountof portfolio insurance is revealed.     

Performance evaluation of portfolio insurance strategies using stochastic dominance criteria

This paper evaluates the performance of the stop-loss, synthetic put and constant proportion portfolio insurance techniques based on a block-bootstrap simulation. We consider not only traditional performance measures, but also some recently developed measures that capture the non-normality of the return distribution (value-at-risk, expected shortfall, and the Omega measure). We compare them to the more comprehensive stochastic dominance criteria. The impact of changing the rebalancing frequency and level of capital protection is examined. We find that, even though a buy-and-hold strategy generates higher average excess returns, it does not stochastically dominate the portfolio insurance strategies, nor vice versa. Our results indicate that a 100% floor value should be preferred to lower floor values and that daily-rebalanced synthetic put and CPPI strategies dominate their counterparts with less frequent rebalancing.     

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).     

Dynamic Portfolio Choice with Stochastic Wage and Life Insurance

We study optimal insurance, consumption, and portfolio choice in a framework where a family purchases life insurance to protect the loss of the wage earner's human capital. Explicit solutions are obtained by employing constant absolute risk aversion utility functions. We show that the optimal life insurance purchase is not a monotonic function of the correlation between the wage and the financial market. Meanwhile, the life insurance decision is explicitly affected by the family's risk preferences in general. The model also predicts that a family uses life insurance and investment portfolio choice to hedge stochastic wage risk.     

Portfolio selection with a drawdown constraint

When identifying optimal portfolios, practitioners often impose a drawdown constraint. This constraint is even explicit in some money management contracts such as the one recently involving Merrill Lynch’ management of Unilever’s pension fund. In this setting, we provide a characterization of optimal portfolios using mean–variance analysis. In the absence of a benchmark, we find that while the constraint typically decreases the optimal portfolio’s standard deviation, the constrained optimal portfolio can be notably mean–variance inefficient. In the presence of a benchmark such as in the Merrill Lynch–Unilever contract, we find that the constraint increases the optimal portfolio’s standard deviation and tracking error volatility. Thus, the constraint negatively affects a portfolio manager’s ability to track a benchmark.     

Bond portfolio optimization using dynamic factor models

A general class of dynamic factor models is used to obtain optimal bond portfolios, and to develop a duration-constrained mean-variance optimization, which can be used to improve bond indexing. An empirical application involving two large data sets of U.S. Treasuries shows that the proposed portfolio policy outperforms a set of yield curve strategies used in bond desks. Additionally, we propose a dynamic rule to switch among alternative bond investment strategies, and find that the benefits of such dynamic rule are even more pronounced when the set of available policies is augmented with the proposed mean-variance portfolios.     

Optimal investment of an insurer with regime-switching and risk constraint

We investigate an optimal investment problem of an insurance company in the presence of risk constraint and regime-switching using a game theoretic approach. A dynamic risk constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our technique is to transform the problem into a deterministic differential game first, in order to obtain the optimal strategy of the game problem explicitly.     

Behavioral portfolio insurance strategies

Financial Markets and Portfolio Management - Portfolio insurance strategies that ensure a certain minimum portfolio value or floor such as the Constant Proportion Portfolio Insurance (CPPI) and the...     

An algorithmic approach to deriving the minimum-variance zero-beta portfolio

This paper examines the problem of deriving Black's (1972) minimum-variance zero-beta portfolio. Long's (1971) methods, used by Morgan (1975), are briefly mentioned. Then the complementary pivot algorithm of Lemke (1965), which has been shown to be capable of deriving the optimal solution to certain quadratic programming problems that are subject to a non-negativity constraint, is described. Finally, Lemke's algorithm is shown to be capable of deriving the minimum-variance zero-beta portfolio efficiently from samples of risky assets where both long and short positions are allowed by reformulating the problem so as to avoid the difficulties encountered by having a non-negatively constraint.     

PORTFOLIO OPTIMIZATION UNDER TRACKING ERROR AND WEIGHTS CONSTRAINTS

The performance of active portfolio managers who must comply with a weights constraint is often assessed against a benchmark. The weights constraint is common as the funds are committed by their own prospectus to a minimum (or maximum) portfolio concentration. We characterize the optimal asset allocation and analyze the implications of the weights constraint on the manager's performance and on the relevance of the information ratio. We obtain that because of the weights constraint, at the optimum, the information ratio often decreases when the manager is free to deviate more from the benchmark.     

Optimal investment-reinsurance with dynamic risk constraint and regime switching

We study an optimal investment–reinsurance problem for an insurer who faces dynamic risk constraint in a Markovian regime-switching environment. The goal of the insurer is to maximize the expected utility of terminal wealth. Here the dynamic risk constraint is described by the maximal conditional Value at Risk over different economic states. The rationale is to provide a prudent investment–reinsurance strategy by taking into account the worst case scenario over different economic states. Using the dynamic programming approach, we obtain an analytical solution of the problem when the insurance business is modeled by either the classical Cramer–Lundberg model or its diffusion approximation. We document some important qualitative behaviors of the optimal investment–reinsurance strategies and investigate the impacts of switching regimes and risk constraint on the optimal strategies.     

Dynamic portfolio optimization with ambiguity aversion

This paper investigates portfolio selection in the presence of transaction costs and ambiguity about return predictability. By distinguishing between ambiguity aversion to returns and to return predictors, we derive the optimal dynamic trading rule in closed form within the framework of Gârleanu and Pedersen (2013), using the robust optimization method. We characterize its properties and the unique mechanism through which ambiguity aversion impacts the optimal robust strategy. In addition to the two trading principles documented in Gârleanu and Pedersen (2013), our model further implies that the robust strategy aims to reduce the expected loss arising from estimation errors. Ambiguity-averse investors trade toward an aim portfolio that gives less weight to highly volatile return-predicting factors, and loads less on the securities that have large and costly positions in the existing portfolio. Using data on various commodity futures, we show that the robust strategy outperforms the corresponding non-robust strategy in out-of-sample tests.