Mean-Variance Asset Liability Management with State-Dependent Risk Aversion

This article investigates the asset liability management problem with state-dependent risk aversion under the mean-variance criterion. The investor allocates the wealth among multiple assets including a risk-free asset and multiple risky assets governed by a system of geometric Brownian motion stochastic differential equations, and the investor faces the risk of paying uncontrollable random liabilities. The state-dependent risk aversion is taken into account in our model, linking the risk aversion to the current wealth held by the investor. An extended Hamilton-Jacobi-Bellman system is established for the optimization of asset liability management, and by solving the extended Hamilton-Jacobi-Bellman system, the analytical closed-form expressions for the time-inconsistent optimal investment strategies and the optimal value function are derived. Finally, numerical examples are presented to illustrate our results.     

Asset pricing and energy consumption risk

This paper proposes energy consumption in the US as a new measure for the consumption capital asset pricing model. We find that (i) industrial energy growth produces reasonable values for the relative risk aversion coefficient and the implied risk-free rate; (ii) compared to alternative consumption measures, industrial energy performs well in explaining the cross-sectional variation in stock returns with the lowest implied risk aversion and pricing errors; (iii) the industrial energy consumption risk model performs equally well as the Fama–French three-factor model in the cross-sectional asset pricing tests; and (iv) total energy consumption risk is priced in the presence of the Fama–French factor risks.     

Liquidity Risk and the Dynamics of Arbitrage Capital

We develop a continuous‐time model of liquidity provision in which hedgers can trade multiple risky assets with arbitrageurs. Arbitrageurs have constant relative risk‐aversion (CRRA) utility, while hedgers' asset demand is independent of wealth. An increase in hedgers' risk aversion can make arbitrageurs endogenously more risk‐averse. Because arbitrageurs generate endogenous risk, an increase in their wealth or a reduction in their CRRA coefficient can raise risk premia despite Sharpe ratios declining. Arbitrageur wealth is a priced risk factor because assets held by arbitrageurs offer high expected returns but suffer the most when wealth drops. Aggregate illiquidity, which declines in wealth, captures that factor.     

The bond–stock mix under time-varying interest rates and predictable stock returns

I investigate the allocation of wealth to cash, bonds, and stocks, along with the bond-to-stock ratio (BSR) when interest rates are time-varying and stock returns are predictable via the dividend-price ratio (DPR). The bond–stock mix and the BSR vary with the deviation of the current level of the DPR from its long-run mean and the correlations between all asset classes. The BSR may decrease over time, which contradicts both previously reported results on the matter as well as popular advice. Finally, I show that it is only at the investment horizon that the BSR is independent of risk aversion.     

Dynamic asset–liability management in a Markov market with stochastic cash flows

This paper provides a general model to investigate an asset–liability management (ALM) problem in a Markov regime-switching market in a multi-period mean–variance (M–V) framework. Emphasis is placed on the stochastic cash flows in both wealth and liability dynamic processes, and the optimal investment and liquidity management strategies in achieving the M–V bi-objective of terminal surplus are evaluated. In this model, not only the asset returns and liability returns, but also the cash flows depend on the stochastic market states, which are assumed to follow a discrete-time Markov chain. Adopting the dynamic programming approach, the matrix theory and the Lagrange dual principle, we obtain closed-form expressions for the efficient investment strategy. Our proposed model is examined through empirical studies of a defined contribution pension fund. In-sample results show that, given the same risk level, an ALM investor (a) starting in a bear market can expect a higher return compared to beginning in a bull market and (b) has a lower expected return when there are major cash flow problems. The effects of the investment horizon and state-switching probability on the efficient frontier are also discussed. Out-of-sample analyses show the dynamic optimal liquidity management process. An ALM investor using our model can achieve his or her surplus objective in advance and with a minimum variance close to zero.     

Asset pricing in production economies with extrapolative expectations

Introducing extrapolative bias into a standard production-based model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility, high investment volatility relative to output) and financial markets (high equity premium, volatile stock returns, low and smooth risk-free rate) with plausible levels of risk aversion and intertemporal elasticity of substitution. Furthermore, the model captures return predictability based upon dividend yield, Q, and investment. Intuitively, extrapolative bias increases the variation in the wealth–consumption ratio, which is heavily priced under recursive preferences; adjustment costs decrease the covariance between marginal utility and asset returns. Empirical support for key implications of the model is also provided.     

Time to wealth goals in capital accumulation

This paper considers the problem of investment of capital in risky assets in a dynamic capital market in continuous time. The model controls risk, and in particular the risk associated with errors in the estimation of asset returns. The framework for investment risk is a geometric Brownian motion model for asset prices, with random rates of return. The information filtration process and the capital allocation decisions are considered separately. The filtration is based on a Bayesian model for asset prices, and an (empirical) Bayes estimator for current price dynamics is developed from the price history. Given the conditional price dynamics, investors allocate wealth to achieve their financial goals efficiently over time. The price updating and wealth reallocations occur when control limits on the wealth process are attained. A Bayesian fractional Kelly strategy is optimal at each rebalancing, assuming that the risky assets are jointly lognormal distributed. The strategy minimizes the expected time to the upper wealth limit while maintaining a high probability of reaching that goal before falling to a lower wealth limit. The fractional Kelly strategy is a blend of the log-optimal portfolio and cash and is equivalently represented by a negative power utility function, under the multivariate lognormal distribution assumption. By rebalancing when control limits are reached, the wealth goals approach provides greater control over downside risk and upside growth. The wealth goals approach with random rebalancing times is compared to the expected utility approach with fixed rebalancing times in an asset allocation problem involving stocks, bonds, and cash.     

Optimal portfolios when volatility can jump

We consider an asset allocation problem in a continuous-time model with stochastic volatility and jumps in both the asset price and its volatility. First, we derive the optimal portfolio for an investor with constant relative risk aversion. The demand for jump risk includes a hedging component, which is not present in models without volatility jumps. We further show that the introduction of derivative contracts can have substantial economic value. We also analyze the distribution of terminal wealth for an investor who uses the wrong model, either by ignoring volatility jumps or by falsely including such jumps, or who is subject to estimation risk. Whenever a model different from the true one is used, the terminal wealth distribution exhibits fatter tails and (in some cases) significant default risk.     

Non-addictive Habit Formation and the Equity Premium Puzzle

I analyse a model in a simple representative-agent economy with one risky and one riskless asset, populated by habit forming consumer-investors. These consumer-investors exhibit non-addictive habit formation in the sense that the current consumption rate of the consumer-investors can fall below their past habit-forming consumption rate. I endogenise the real riskless rate of return in this representative-agent economy and find that the equity premium puzzle is resolved for plausible values of the coefficient of relative risk aversion, the discount rate, and the intensity of non-addictive habit formation. These values have been validated in previous empirical or survey-based studies. Non-addictive habit-formation studied here complements and extends current research on habit-forming preferences. Given a constant investment opportunity set, the real riskless rate in the economy increases with relative risk aversion of the consumer and decreases as the habit-formation intensity increases. Extensions with time-varying investment opportunity sets could explain the low risk-free rate and the relatively large variability of the market return over the variability of the risk-free rate through time.     

Optimal Reinsurance and Investment for a Jump Diffusion Risk Process under the CEV Model

Abstract

We consider an optimal reinsurance-investment problem of an insurer whose surplus process follows a jump-diffusion model. In our model the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a “simplified” financial market consisting of a risk-free asset and a risky asset. The dynamics of the risky asset are governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity. The objective of the insurer is to choose an optimal reinsurance-investment strategy so as to maximize the expected exponential utility of terminal wealth. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Explicit forms for the optimal reinsuranceinvestment strategy and the corresponding value function are obtained. Numerical examples are provided to illustrate how the optimal investment-reinsurance policy changes when the model parameters vary.     

Dynamic Asset Allocation under Inflation

We develop a simple framework for analyzing a finite-horizon investor's asset allocation problem under inflation when only nominal assets are available. The investor's optimal investment strategy and indirect utility are given in simple closed form. Hedge demands depend on the investor's horizon and risk aversion and on the maturities of the bonds included in the portfolio. When short positions are precluded, the optimal strategy consists of investments in cash, equity, and a single nominal bond with optimally chosen maturity. Both the optimal stock–bond mix and the optimal bond maturity depend on the investor's horizon and risk aversion.     

Corporate governance and the sensitivity of investments to cash flows

We find very strong and consistent evidence that investments in Strong‐Governance firms (managers not entrenched) are strongly sensitive to availability of internal cash flows while such sensitivity is not different from zero for Weak‐Governance firms (entrenched management). We interpret this as evidence in support of Kaplan and Zingales' (1997) contention that sensitivity of investments to cash flows is not an adequate measure of financing constraints. More importantly, our findings are consistent with Kaplan and Zingales’ conjecture that the observed sensitivity of investments to cash flows in firms that do not face financing constraints may be driven by excessive risk aversion of managers.     

Searching for a listed infrastructure asset class using mean–variance spanning

This study examines the portfolio-diversification benefits of listed infrastructure stocks. We employ three different definitions of listed infrastructure and tests of mean–variance spanning. The evidence shows that viewing infrastructure as an asset class is misguided. We employ different schemes of infrastructure asset selection (both traditional asset classes and factor exposures) and discover that they do not provide portfolio-diversification benefits to existing asset allocation choices. We also find that defining and selecting infrastructure investments by business model as opposed to industrial sectors can reveal a very different investment profile, albeit one that improves the mean–variance efficient frontier since the global financial crisis. This study provides new insights into defining and benchmarking infrastructure equity investments in general, as well as into the extent to which public markets can be used to proxy the risk-adjusted performance of privately held infrastructure investments.     

TACTICAL ASSET ALLOCATION: CAN IT WORK?

Market events of the past ten years have sparked an interest in tactical asset allocation. In the current study we develop and test a model that incorporates currently available information into the tactical asset allocation process. The model provides an estimate of the probabilities that the upcoming market period will be bullish or bearish. Logit analysis is employed to determine which of the various timely and readily available data significantly affect these probabilities. These estimated probabilities are used to suggest the optimal allocations of funds over time between the risk-free asset and the market portfolio. Then, several timing strategies are compared with a buy-and-hold portfolio. An asset allocation strategy based on the probabilities assigned by the logit model appears to achieve greater terminal wealth with less variability of returns. Similar results are obtained for both an initial sample (1962–76 in our model) and a holdout sample (1977–88).     

The premium of dynamic trading in a discrete-time setting

Chiu and Zhou [Quant. Finance, 2011, 11, 115–123] show that the inclusion of a risk-free asset strictly boosts the Sharpe ratio in a continuous-time setting, which is in sharp contrast to the static single-period case. In this paper, we extend their work to a discrete-time setting. Specifically, we prove that the multi-period mean-variance efficient frontier generated by both risky and risk-free assets is strictly separated from that generated by only risky assets. As a result, we demonstrate that the inclusion of a risk-free asset strictly enhances the best Sharpe ratio of the efficient frontier in a multi-period discrete-time setting. Furthermore, we offer an explicit expression for the enhancement of the best Sharpe ratio, which was referred to as the premium of dynamic trading by Chiu and Zhou [op. cit.], although they do not present a computational formula for it. Our results further show that, in the case with a risk-free asset, if an investor can extract some money from his initial wealth at time 0, the efficient frontier with a risk-free asset can be tangent to that without a risk-free asset. Finally, based on real data from the American market, a numerical example is provided to illustrate the results obtained in this paper; a numerical comparison between the discrete-time case and the continuous-time case is also provided. Our numerical results reveal that the continuous-time model can be considered to be a limit of the discrete-time model.     

Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model

Discounting cash flows requires an equilibrium model to determine the cost of capital. The CAPM of Sharpe and the intertemporal asset pricing model of Merton (1973) offer a theoretical justification for discounting at a constant risk adjusted rate. Two problems arise with this application. First, for mean reverting cash flows the risk adjustment is unknown, and second, if the present value is compounded forward then the distribution of future wealth is likely right skewed. I develop equilibrium discount rates for cash flows whose level or growth rate is mean reverting. Serial correlation also largely eliminates the skewness problem.     

Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model

We consider an optimal time-consistent reinsurance-investment strategy selection problem for an insurer whose surplus is governed by a compound Poisson risk model. In our model, the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a simplified financial market consisting of a risk-free asset and a risky stock. The dynamics of the risky stock is governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity as well as the feedback effect of an asset’s price on its volatility. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Closed-form solutions for the optimal reinsurance-investment strategies and the corresponding value functions are obtained in both the compound Poisson risk model and its diffusion approximation. Numerical examples are also provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary.     

Decision making with Expected Shortfall and spectral risk measures: The problem of comparative risk aversion

We analyze spectral risk measures with respect to comparative risk aversion following Arrow (1965) and Pratt (1964) for deterministic wealth, and Ross (1981) for stochastic wealth. We argue that the Arrow–Pratt-concept per se well matches with economic intuition in standard financial decision problems, such as willingness to pay for insurance and simple portfolio problems. Different from the literature, we find that the widely-applied spectral Arrow–Pratt-measure is not a consistent measure of Arrow–Pratt-risk aversion. Instead, the difference between the antiderivatives of the corresponding risk spectra is valid. Within the framework of Ross, we show that the popular subclasses of Expected Shortfall, and exponential and power spectral risk measures cannot be completely ordered with respect to Ross-risk aversion. Thus, for all these subclasses, the concept of Ross-risk aversion is not generally compatible with Arrow–Pratt-risk aversion, but induces counter-intuitive comparative statics of its own. Compatibility can be achieved if asset returns are jointly normally distributed. The general lesson is that these restrictions have to be considered before spectral risk measures can be applied for the purpose of optimal decision making and regulatory issues.     

Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps

This paper considers a robust optimal excess-of-loss reinsurance-investment problem in a model with jumps for an ambiguity-averse insurer (AAI), who worries about ambiguity and aims to develop a robust optimal reinsurance-investment strategy. The AAI’s surplus process is assumed to follow a diffusion model, which is an approximation of the classical risk model. The AAI is allowed to purchase excess-of-loss reinsurance and invest her surplus in a risk-free asset and a risky asset whose price is described by a jump-diffusion model. Under the criterion for maximizing the expected exponential utility of terminal wealth, optimal strategy and optimal value function are derived by applying the stochastic dynamic programming approach. Our model and results extend some of the existing results in the literature, and the economic implications of our findings are illustrated. Numerical examples show that considering ambiguity and reinsurance brings utility enhancements.     

Risk,uncertainty, and asset prices

We identify the relative importance of changes in the conditional variance of fundamentals (which we call “uncertainty”) and changes in risk aversion in the determination of the term structure, equity prices, and risk premiums. Theoretically, we introduce persistent time-varying uncertainty about the fundamentals in an external habit model. The model matches the dynamics of dividend and consumption growth, including their volatility dynamics and many salient asset market phenomena. While the variation in price–dividend ratios and the equity risk premium is primarily driven by risk aversion, uncertainty plays a large role in the term structure and is the driver of countercyclical volatility of asset returns.