Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model

Under the assumptions of the Consumption-based Capital AssetPricing Model (CCAPM), Pareto optimal consumption allocationsare characterized by each agent's consumption process beingadapted to the filtration generated by the aggregate consumptionprocess of the economy. The wealth processes of the agents,however, are adapted to the finer filtration generated by aggregateconsumption and the conditional distribution of future aggregateconsumption. Therefore, in order to achieve pareto optimal consumptionallocations, a sufficiently varied set of assets must existsuch that any wealth process adapted to this finer filtrationcan be implemented by dynamically trading in that set of assets.We provide sufficient conditions for the existence of such aset of assets based on dynamically trading contingent claimson aggregate consumption. In addition, we give sufficient conditionsfor the existence of equilibria in a dynamically effectivelycomplete market in which agents are only able to trade in contingentclaims on aggregate consumption, the market portfolio of firms,and a (numeraire) zero-coupon bond. We demonstrate the roleof short- and long-term contingent claims on aggregate consumptionfor the implementation of Pareto optimal allocations inthe presenceof short- and long-term risks. In addition, in the presenceof personal risks, we demonstrate the role of insurance contracts.JEL Classification: G13.     

A Complete Analysis of Full Pareto Efficiency in Financial Markets for Arbitrary Preferences

This paper provides a complete analysis of the necessary and sufficient conditions for financial markets to achieve fully Pareto-efficient allocation of aggregate wealth through trade in economies with arbitrary preferences. We show that full Pareto efficiency obtains only if the market structure of contingent claims spans the information partition of a minimal aggregate wealth statistic and a Halmos-Savage sufficient statistic for the beliefs of the traders. All the known allocation efficiency results in the literature due to Arrow, Hakansson, John, Ross, and others are unified by this result.     

Insider Trading, Investment, and Liquidity: A Welfare Analysis

We compare equilibrium trading outcomes with and without participation by an informed insider, assuming inflexible ex ante aggregate investment choices by agents. Noise trading arises from aggregate uncertainty regarding other agents' intertemporal consumption preferences. The welfare levels of outsiders can thus be ascertained. The allocations without insider trading are not ex ante Pareto efficient, because our model differs from standard ones with negative exponential utility functions and normal returns. We characterize the circumstances under which the revelation of payoff-relevant information via prices—arising from insider trading—benefits outsiders with stochastic liquidity needs, by improving risk-sharing among them.     

A Parimutuel Market Microstructure for Contingent Claims

Parimutuel principles are widely used as an alternative to fixed odds gambling in which a bookmaker acts as a dealer by quoting fixed rates of return on specified wagers. A parimutuel game is conducted as a call auction in which odds are allowed to fluctuate during the betting period until the betting period is closed or the auction ‘called’. The prices or odds of wagers are set based upon the relative amounts wagered on each risky outcome. In financial microstructure terms, trading under parimutuel principles is characterised by (1) call auction, non‐continuous trading; (2) riskless funding of claim payouts using the amounts paid for all of the claims during the auction; (3) special equilibrium pricing conditions requiring the relative prices of contingent claims equal the relative aggregate amounts wagered on such claims; (4) endogenous determination of unique state prices; and (5) higher efficiency. Recently, a number of large investment banks have adopted a parimutuel mechanism for offering contingent claims on various economic indices, such as the US Nonfarm payroll report and Eurozone Harmonised inflation. Our paper shows how the market microstructure incorporating parimutuel principles for contingent claims which allows for notional transactions, limit orders, and bundling of claims across states is constructed. We prove the existence of a unique price equilibrium for such a market and suggest an algorithm for computing the equilibrium. We also suggest that for a broad class of contingent claims, that the parimutuel microstructure recently deployed offers many advantages over the dominant dealer and exchange continuous time mechanisms.     

A simulation analysis of the microstructure of an order driven financial market with multiple securities and portfolio choices

In this paper we propose an artificial market where multiple risky assets are exchanged. Agents are constrained by the availability of resources and trade to adjust their portfolio according to an exogenously given target portfolio. We model the trading mechanism as a continuous auction order-driven market. Agents are heterogeneous in terms of desired target portfolio allocations, but they are homogeneous in terms of trading strategies. We investigate the role played by the trading mechanism in affecting the dynamics of prices, trading volume and volatility. We show that the institutional setting of a double auction market is sufficient to generate a non-normal distribution of price changes and temporal patterns that resemble those observed in real markets. Moreover, we highlight the role played by the interaction between individual wealth constraints and the market frictions associated with a double auction system to determine the negative asymmetry of the stock returns distribution.     

Conditional portfolio allocation: Does aggregate market liquidity matter?

This paper investigates how aggregate liquidity influences optimal portfolio allocations across various US characteristic portfolios. We consider short-term allocation problems, with single and multiple risky assets, and use the nonparametric approach of Brandt (1999) to directly express optimal portfolio weights as functions of aggregate liquidity shocks. We find, first, that the effect of aggregate liquidity is positive and decreasing with the investment horizon. Second, at daily and weekly horizons, this effect is weaker on allocations in large stocks and gets stronger as we move toward small stocks, regardless of the other stock characteristics, suggesting that liquidity is the main concern of very short-term investors. Third, conditional allocations in risky assets decrease and exhibit shifts toward more liquid assets as aggregate liquidity worsens. Overall, conditioning on aggregate liquidity yields empirical results that are consistent with the so-called flight-to-safety and flight-to-liquidity episodes. Finally, we propose a simple tactical investment strategy and show how aggregate liquidity information can be exploited to enhance the out-of-sample performance of long-term strategies.     

Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty

In diffusion models, a few suitably chosen financial securities allow to complete the market. As a consequence, the efficient allocations of static Arrow–Debreu equilibria can be attained in Radner equilibria by dynamic trading. We show that this celebrated result generically fails if there is Knightian uncertainty about volatility. A Radner equilibrium with the same efficient allocation as in an Arrow–Debreu equilibrium exists if and only if the discounted net trades of the equilibrium allocation display no ambiguity in the mean. This property is violated generically in endowments, and thus Arrow–Debreu equilibrium allocations are generically unattainable by dynamically trading a few long-lived assets.     

The impact of keeping up with the Joneses behavior on asset prices and portfolio choice

This paper studies the asset pricing and portfolio choice implications of keeping up with the Joneses preferences. In terms of portfolio choice, we provide sufficient conditions on the utility function under which no portfolio bias can arise across agents in equilibrium. Regarding asset prices, we find that under Joneses behavior asset prices are a function of the economy's aggregate consumption, the agents preference parameters, the wealth endowment distribution and the weighting across agents in the Joneses definition. We present necessary and sufficient conditions such that equilibrium prices are only a function of aggregate wealth. Non-financial, non-diversifiable income is introduced in the model. In the presence of Joneses behavior, an under-diversified equilibrium emerges where investors will bias their portfolios towards the financial assets that better hedge their exposure to the non-financial income risk.     

Portfolio selection with mental accounts and delegation

Das et al. (2010) develop an elegant framework where an investor selects portfolios within mental accounts but ends up holding an aggregate portfolio on the mean-variance frontier. This investor directly allocates the wealth in each account among available assets. In practice, however, investors often delegate the task of allocating wealth among assets to portfolio managers who seek to beat certain benchmarks. Accordingly, we extend their framework to the case where the investor allocates the wealth in each account among portfolio managers. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we present conditions under which such portfolios are not on the mean-variance frontier, and conditions under which they are. Third, we show that the aforementioned analytical characterization is also applicable within the framework of Das et al. and thus improves upon their numerical approach.     

Optimal multi-period consumption and investment with short-sale constraints

This article examines agents’ consumption-investment problem in a multi-period pure exchange economy where agents are constrained with the short-sale of state-dependent risky contingent claims. In equilibrum, agents hold options written on aggregate consumption in their optimal portfolios. Furthermore, under the specific case of quadratic utility, the optimal risk-sharing rule derived for the pricing agent leads to a multifactor conditional consumption-based capital asset pricing model (CCAPM), where excess option returns appear as factors.     

Trading activity in the equity market and its contingent claims: An empirical investigation

Little is known about the joint dynamics of volume across the various contingent claims on the equity market. We study the time-series of trading activity in the cash S&P 500 index and its derivatives (options, the legacy and E-mini futures contracts, and the ETF), and consider their dynamic relation with the macroeconomy, over more than 3000 trading days during 1997–2009. Legacy futures volume has trended downward while other series have trended upward. Total futures volume has increased, suggesting that the trading in the legacy contract has been at least partially supplanted by trading in the E-mini contract. All series are highly cross-correlated and jointly dependent. Signed and absolute trading activity in contingent claims (most prominently, options) predicts shifts in aggregate state variables such as the short interest rate, and the term and credit spreads, as well as signed and absolute returns around major macroeconomic announcements. Overall, consistent with the informational role of options, their volume innovations have the strongest forecasting ability for fluctuations in the macroeconomic environment.     

Optimal portfolio choice in real terms: Measuring the benefits of TIPS

In this paper we solve an optimal portfolio choice problem to measure the benefits of Treasury Inflation Indexed Securities (TIPS) to investors concerned with maximizing real wealth. We show how the introduction of a real riskless asset completes the investor asset space, by contrasting optimal portfolio allocations with and without such assets. We use historical data to quantify gains from availability of TIPS in the presence of other asset classes such as equities, commodities, and real estate. We draw a distinction between buy-and-hold long-term investors for whom TIPS fully displace nominal risk-free assets and short-term investors for whom TIPS improve the investment opportunity set of real returns. Finally, we show how gains from TIPS are tempered by the availability of alternative assets that covary with inflation, such as gold and real estate.     

Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns

We develop a model in which the volatility of risky assets is subject to random and discontinuous shifts over time. We derive prices of claims contingent on such assets and analyze options-based trading strategies to hedge against the risk of jumps in the return volatility. Unsystematic and systematic events such as takeovers, major changes in business plans, or shifts in economic policy regimes may drastically alter firms' risk profiles. Our model captures the effect of such events on options markets.     

Alternate approach to unify CAPM and APT

We utilize the joint elliptical distribution to model a multi-factor return generating process and derive an equilibrium multi-beta capital asset pricing model (CAPM) in which the market portfolio and a set of nonelliptical factors are sufficient to price all financial assets. Most important, it is shown that the market portfolio, while generally nonelliptical, can proxy all elliptical factors and hence: including elliptical factors in addition to the market portfolio in the pricing equation contribute nothing to asset pricing. While the representative investor prices the exposure of aggregate wealth to various nonelliptical systematic risk factors, individual securities are priced in accordance to their contributions to different aspects of the risk of aggregate wealth. The present model collapses to the Sharpe-Lintner CAPM when either the market investor is neutral to nonelliptical risk factors or when all risk factors follow a joint spherical distribution. When residuals cancel out of the market portfolio, the present model collapses to Conner (1984) pricing model.     

PORTFOLIO CHOICES,CONSUMPTION, AND PRICES IN A MARKET WITH DURABLE ASSETS

Recent research in investments has focused almost exclusively on financial assets such as corporate stocks. Although durable assets constitute an important part of investors' holdings, little effort has been made to explore their role in individuals' investments decisions and on assets pricing. This paper establishes results concerning the role of durable assets in the determination of optimum portfolio choices. The paper explores the effect of consumption considerations related to the service flows generated by durable assets on optimum portfolio considerations and asset prices. The main result is tied to the existence, or lack thereof, of efficient rental markets. In the absence of rental markets (or with restrictions on renting), investors' portfolio choices are not independent of consumption considerations as they are assumed to be in the standard CAPM. Individuals may thus hold different portfolios, and prices reflect the owner's inability to trade consumption flows. Under perfect market assumptions with unrestricted rental markets, optimum portfolio choices are undistinguishable from those implied by the standard CAPM in the sense that they are mean-variance efficient and identical for all individuals. Consumption is adjusted by trading service flows in the rental market. Prices, and the price of risk, however, reflect the existence of durable assets service flows as well as the risks involved in trading these flows in the rental market. In the model, risky rental income is introduced by uncertain rental costs. Equilibrium rental rates, an important part of the return expected from holding durable assets, are determined in the context of the mean-variance framework as a function of return and undiversifiable risk.     

Testing market efficiency with the pricing kernel

Market efficiency and the pricing kernel are closely related. A non-monotonic decreasing pricing kernel implies the existence of a trading strategy in contingent claims that stochastically dominates a direct investment in the market. Moreover, a market is assumed to be efficient only if no dominating strategies exist. Empirically, many studies of the pricing kernel find non-monotonicity, apparently ruling out market efficiency. However, these results are often unreliable, because the pricing measures of the pricing kernel are estimated using differing filtration sets. We show this effect both theoretically and empirically, and we discuss recent approaches in the literature for achieving more reliable estimates of the pricing kernel, potentially leading to better tests of market efficiency.     

Comonotone Pareto optimal allocations for law invariant robust utilities on L 1

We prove the existence of comonotone Pareto optimal allocations satisfying utility constraints when decision makers have probabilistic sophisticated variational preferences and thus representing criteria in the class of law invariant robust utilities. The total endowment is only required to be integrable.     

Hedge funds and optimal asset allocation: Bayesian expectations and spanning tests

This paper analyzes the contribution of hedge funds to optimal asset allocations between 1993 and 2010. The preferences of specific institutional investors are captured by implementing a Bayesian asset allocation framework that incorporates heterogeneous expectations regarding hedge fund alpha. Mean-variance spanning tests are used to infer the ability of hedge funds to significantly enhance the mean-variance efficient frontier. Further, a novel democratic variance decomposition procedure sheds light on the dynamics in the co-movement of hedge fund returns with a set of common benchmark assets. The empirical findings indicate that portfolio benefits of hedge funds are time-varying and strongly depend on investor optimism regarding hedge funds’ ability to generate alpha. In general, allocations to hedge funds improve the global minimum variance portfolio even after controlling for short-selling restrictions and minimum diversification constraints. However, due to dynamics underlying the composition of the aggregate hedge fund universe, the factor structure of hedge fund returns has become more similar to the benchmark assets over time.     

Infrequent Extreme Risks

The main tools and concepts of financial and actuarial theory are designed to handle standard, or even small risks. The aim of this paper is to reconsider some selected financial problems, in a setup including infrequent extreme risks. We first consider investors maximizing the expected utility function of their future wealth, and we establish the necessary and sufficient conditions on the utility function to ensure the existence of a non degenerate demand for assets with extreme risks. This new class of utility functions, called LIRA, does not contain the classical HARA and CARA utility functions, which are not adequate in this framework. Then we discuss the corresponding asset supply-demand equilibrium model.