Which demands affect optimal international portfolio choices?

This study analyzes the asset allocations of simple international portfolios that include domestic risky assets, foreign risky assets, and domestic risk-free bonds, through a theoretical analysis. A close-form solution for the optimal holding rates is derived, and can be further sub-divided into three categories of demand: speculative demand, diversified demand, and hedging demands. We carefully explore the essential problem of identifying the underlying reasons for asset allocations, which in turn allows us to answer the question of which of these demands are critical in influencing holding changes.     

Consistent pricing and hedging for a modified constant elasticity of variance model

Abstract

This paper considers a modification of the well known constant elasticity of variance model where it is used to model the growth optimal portfolio (GOP). It is shown that, for this application, there is no equivalent risk neutral pricing measure and therefore the classical risk neutral pricing methodology fails. However, a consistent pricing and hedging framework can be established by application of the benchmark approach.

Perfect hedging strategies can be constructed for European style contingent claims, where the underlying risky asset is the GOP. In this framework, fair prices for contingent claims are the minimal prices that permit perfect replication of the claims. Numerical examples show that these prices may differ significantly from the corresponding ‘risk neutral’ prices.     

Is stochastic volatility relevant for dynamic portfolio choice under ambiguity?

Literature on dynamic portfolio choice has been finding that volatility risk has low impact on portfolio choice. For example, using long-run US data, Chacko and Viceira [2005. “Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets.” The Review of Financial Studies 18 (4): 1369–1402] found that intertemporal hedging demand (required by investors for protection against adverse changes in volatility) is empirically small even for highly risk-averse investors. We want to assess if this continues to be true in the presence of ambiguity. Adopting robust control and perturbation theory techniques, we study the problem of a long-horizon investor with recursive preferences that faces ambiguity about the stochastic processes that generate the investment opportunity set. We find that ambiguity impacts portfolio choice, with the relevant channel being the return process. Ambiguity about the volatility process is only relevant if, through a specific correlation structure, it also induces ambiguity about the return process. Using the same long-run US data, we find that ambiguity about the return process may be empirically relevant, much more than ambiguity about the volatility process. Anyway, intertemporal hedging demand is still very low: investors are essentially focused on the short-term risk–return characteristics of the risky asset.     

Minimizing CVaR in global dynamic hedging with transaction costs

This study develops a global derivatives hedging methodology which takes into account the presence of transaction costs. It extends the Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239] framework in two ways. First, to reduce the occurrence of extreme losses, the expected utility is replaced by the conditional Value-at-Risk (CVaR) coherent risk measure as the objective function. Second, the normality assumption for the underlying asset returns is relaxed: general distributions are considered to improve the realism of the model and to be consistent with fat tails observed empirically. Dynamic programming is used to solve the hedging problem. The CVaR minimization objective is shown to be part of a time-consistent framework. Simulations with parameters estimated from the S&P 500 financial time series show the superiority of the proposed hedging method over multiple benchmarks from the literature in terms of tail risk reduction.     

Optimal investment and consumption under a continuous-time cointegration model with exponential utility

In this paper, we study the effects of cointegration on optimal investment and consumption strategies for an investor with exponential utility. A Hamilton-Jacobi-Bellman (HJB) equation is derived first and then solved analytically. Both the optimal investment and consumption strategies are expressed in closed form. A verification theorem is also established to demonstrate that the solution of the HJB equation is indeed the solution of the original optimization problem under an integrability condition. In addition, a simple and sufficient condition is proposed to ensure that the integrability condition is satisfied. Financially, the optimal investment and consumption strategies are decomposed into two parts: the myopic part and the hedging demand caused by cointegration. Discussions on the hedging demand are carried out first, based on analytical formulae. Then numerical results show that ignoring the information about cointegration results in a utility loss.     

Optimal Investment Strategy to Minimize the Probability of Lifetime Ruin

Abstract

I study the problem of how individuals should invest their wealth in a risky financial market to minimize the probability that they outlive their wealth, also known as the probability of lifetime ruin. Specifically, I determine the optimal investment strategy of an individual who targets a given rate of consumption and seeks to minimize the probability of lifetime ruin. Two forms of the consumption function are considered: (1) The individual consumes at a constant (real) dollar rate, and (2) the individual consumes a constant proportion of his or her wealth. The first is arguably more realistic, but the second has a close connection with optimal consumption in Merton’s model of optimal consumption and investment under power utility.

For constant force of mortality, I determine (a) the probability that individuals outlive their wealth if they follow the optimal investment strategy; (b) the corresponding optimal investment rule that tells individuals how much money to invest in the risky asset for a given wealth level; (c) comparative statics for the functions in (a) and (b); (d) the distribution of the time of lifetime ruin, given that ruin occurs; and (e) the distribution of bequest, given that ruin does not occur. I also include numerical examples to illustrate how the formulas developed in this paper might be applied.     

Asset allocation in markets with contagion: The interplay between volatilities,jump intensities,and correlations

We study the impact of financial contagion on the dynamic asset allocation problem of a CRRA investor facing an incomplete market with two risky assets. We apply a Markov chain regime-switching framework with state-dependent jump intensities, diffusion volatilities and diffusion correlations. The key model feature that a switch to the bad contagion regime is triggered by a loss in one of the risky assets allows for the implementation of a hedging demand against contagion risk. Moreover, a state-dependent diffusion correlation combined with heterogeneity in jump intensities and volatilities can, e.g., generate a flight to quality effect upon a systemic jump.     

Correlation Risk and Optimal Portfolio Choice

We develop a new framework for multivariate intertemporal portfolio choice that allows us to derive optimal portfolio implications for economies in which the degree of correlation across industries, countries, or asset classes is stochastic. Optimal portfolios include distinct hedging components against both stochastic volatility and correlation risk. We find that the hedging demand is typically larger than in univariate models, and it includes an economically significant covariance hedging component, which tends to increase with the persistence of variance–covariance shocks, the strength of leverage effects, the dimension of the investment opportunity set, and the presence of portfolio constraints.     

Absolute Ruin Probabilities in a Jump Diffusion Risk Model with Investment

Abstract

This article considers the compound Poisson insurance risk model perturbed by diffusion with investment. We assume that the insurance company can invest its surplus in both a risky asset and the risk-free asset according to a fixed proportion. If the surplus is negative, a constant debit interest rate is applied. The absolute ruin probability function satisfies a certain integro-differential equation. In various special cases, closed-form solutions are obtained, and numerical illustrations are provided.     

Investment Horizon Effects

Abstract:   Boudry and Gray (2003) have documented that the optimal buy‐and‐hold demand for Australian stocks is not necessarily increasing in the investment horizon when returns are predictable. Such finding is in contrast with Barberis (2000) who shows that positive monotonic horizon effects predominate for US stocks. Using a closed‐form approximation to the asset allocation problem, this paper relates the return dynamics to the investor's portfolio choice for different investment horizons. In the special case of a single risky asset, it is shown that return predictability under stationarity may induce both positive and negative horizon effects in the optimal allocation to the risky asset. The paper extends previous empirical results by solving for the optimal portfolio when two risky assets with predictable returns are available for investment.     

Modern portfolio management with conditioning information

This paper studies models in which active portfolio managers utilize conditioning information unavailable to their clients to optimize performance relative to a benchmark. We derive explicit solutions for the optimal strategies with multiple risky assets, with or without a risk-free asset, and consider various constraints on portfolio risks or weights. The optimal strategies feature a mean–variance efficient component (to minimize portfolio variance), and a hedging demand for the benchmark portfolio (to maximize correlation with the benchmark). A currency portfolio example shows that the optimal strategies improve the measured performance by 53% out of sample, compared with portfolios ignoring conditioning information.     

An Intertemporal International Asset Pricing Model: Theory and Empirical Evidence

We extend Campbell's (1993) model to develop an intertemporal international asset pricing model (IAPM). We show that the expected international asset return is determined by a weighted average of market risk, market hedging risk, exchange rate risk and exchange rate hedging risk. These weights sum up to one. Our model explicitly separates hedging against changes in the investment opportunity set from hedging against exchange rate changes as well as exchange rate risk from intertemporal hedging risk. A test of the conditional version of our intertemporal IAPM using a multivariate GARCH process supports the asset pricing model. We find that the exchange rate risk is important for pricing international equity returns and it is much more important than intertemporal hedging risk.     

An Out-of-Sample Analysis of Investment Guarantees for Equity-Linked Products

Abstract

In this paper we analyze the risk underlying investment guarantees using 78 different econometric models: GARCH, regime-switching, mixtures, and combinations of these approaches. This extensive set of models is compared with returns observed during the financial crisis in an out-of-sample analysis, bringing a new perspective to the study of equity-linked insurance. We find that despite the very good fit of recent models, too few of them are capable of consistently generating low returns over long periods, which were in fact observed empirically during the financial crisis. Moreover, tail risk measures vary significantly across models, and this emphasizes the importance of model risk. Most insurance companies are now focusing on dynamically hedging their investment guarantees, and so we also investigate the robustness of the Black-Scholes delta hedging strategy. We find that hedging errors can be very large among the top fitting models, implying that model risk must be taken into consideration when hedging investment guarantees.     

Minimizing the Probability of Lifetime Ruin under Random Consumption

Abstract

We determine the optimal investment strategy in a financial market for an individual whose random consumption is correlated with the price of a risky asset. Bayraktar and Young consider this problem and show that the minimum probability of lifetime ruin is the unique convex, smooth solution of its corresponding Hamilton-Jacobi-Bellman equation. In this paper we focus on determining the probability of lifetime ruin and the corresponding optimal investment strategy. We obtain approximations for the probability of lifetime ruin for small values of certain parameters and demonstrate numerically that they are reasonable ones. We also obtain numerical results in cases for which those parameters are not small.     

Semi-parametric modelling in finance: theoretical foundations

Abstract

The benchmark theory of mathematical finance is the Black-Scholes-Merton theory, based on Brownian motion as the driving noise process for asset prices. Here the distributions of returns of the assets in a portfolio are multivariate normal. The two most obvious limitations here concern symmetry and thin tails, neither being consistent with real data. The most common replacements for the multinormal are parametric—stable, generalized hyperbolic, variance gamma. In this paper we advocate the use of semi-parametric models for distributions, where the mean vector μ and covariance Σ are parametric components and the so-called density generator (function) g is the non-parametric component. We work mainly within the family of elliptically contoured distributions, focusing particularly on normal variance mixtures with self-decomposable mixing distributions. We show how the parametric cases can be treated in a unified, systematic way within the non-parametric framework and obtain the density generators for the most important cases.     

Home mortgage debt financing of nonhousing investments

Home mortgage debt is decomposed into a component that represents debt demand, derived from housing demand and a residual excess demand. This excess demand derives principally from the demand for nonhousing assets. An empirical model of the determinants of the demand for excess debt is specified and estimated using databases from the 1983 and 1986 Surveys of Consumer Finance. The estimations focus on evidence of linkages between debt demand and household preferences for illiquid risky assets, and on the substitutability of personal debt for mortgage debt. Positive linkages are found between household choices of investments in vacation homes, investment real estate, and closely held business and the demand for excess debt. However, personal debt and mortgage debt appear to have largely separate financing roles.     

Dynamic Portfolio Selection: the Relevance of Switching Regimes and Investment Horizon

This paper investigates the questions of dynamic portfolio selection and intertemporal hedging within a Markovian regime‐switching framework. The investment opportunity set is spanned by a well‐diversified home‐market portfolio and the risk‐free asset. Our results highlight the economic importance of regimes, as optimal portfolio weights are clearly dependent on the prevailing regime. We present evidence that the question of intertemporal hedging is a more complex issue than is hinted in the previous literature, since demand for intertemporal hedging is present in some regimes, but not in others. Finally, our main findings are qualitatively unchanged across the four largest stock markets in the world.     

Optimal Portfolio Selection with Transaction Costs

Abstract

This paper examines the lifetime portfolio-selection problem in the presence of transaction costs. Using a discrete time approach, we develop analytical expressions for the investor's indirect utility function and also for the boundaries of the no-transactions region. The economy consists of a single risky asset and a riskless asset. Transactions in the risky asset incur proportional transaction costs. The investor has a power utility function and is assumed to maximize expected utility of end-of-period wealth. We illustrate the solution procedure in the case in which the returns on the risky asset follow a multiplicative binomial process. Our paper both complements and extends the recent work by Gennotte and Jung (1994), which used numerical approximations to tackle this problem.     

Performance of utility-based strategies for hedging basis risk

The performance of optimal strategies for hedging a claim on a non-traded asset is analysed. The claim is valued and hedged in a utility maximization framework, using exponential utility. A traded asset, correlated with that underlying the claim, is used for hedging, with the correlation ρ typically close to 1. Using a distortion method (Zariphopoulou 2001 Finance Stochastics 5 61–82) we derive a nonlinear expectation representation for the claim’s ask price and a formula for the optimal hedging strategy. We generate a perturbation expansion for the price and hedging strategy in powers of ε²?=1?ρ². The terms in the price expansion are proportional to the central moments of the claim payoff under the minimal martingale measure. The resulting fast computation capability is used to carry out a simulation-based test of the optimal hedging program, computing the terminal hedging error over many asset price paths. These errors are compared with those from a naive strategy which uses the traded asset as a proxy for the non-traded one. The distribution of the hedging error acts as a suitable metric to analyse hedging performance. We find that the optimal policy improves hedging performance, in that the hedging error distribution is more sharply peaked around a non-negative profit. The frequency of profits over losses is increased, and this is measured by the median of the distribution, which is always increased by the optimal strategies. An empirical example illustrates the application of the method to the hedging of a stock basket using index futures.     

Consumption and Hedging in Oil‐Importing Developing Countries

We study the consumption and hedging strategy of an oil‐importing developing country that faces multiple crude oil shocks. In our model, developing countries have two particular characteristics: their economies are mainly driven by natural resources and their technologies are less efficient in energy usage. The natural resource exports can be correlated with the crude oil shocks. The country can hedge against the crude oil uncertainty by taking long/short positions in existing crude oil futures contracts. We find that both inefficiencies in energy usage and shocks to the crude oil price lower the productivity of capital. This generates a negative income effect and a positive substitution effect, because today’s consumption is relatively cheaper than tomorrow’s consumption. Optimal consumption of the country depends on the magnitudes of these effects and on its risk‐aversion degree. Shocks to other crude oil factors, such as the convenience yield, are also studied. We find that the persistence of the shocks magnifies the income and substitution effects on consumption, thus also affecting the hedging strategy of the country. The demand for futures contracts is decomposed in a myopic demand, a pure hedging term and productive hedging demands. These hedging demands arise to hedge against changes in the productivity of capital due to changes in crude oil spot prices. We calibrate the model for Chile and study to what extent the country’s copper exports can be used to hedge the crude oil risk.