Patrice Poncet

On Optimal Portfolio Choice under Stochastic Interest Rates

In an economy where interest rates and stock price changes follow fairly general stochastic processes, we analyse the portfolio problem of an expected utility investor. When the investment opportunity set is driven by an arbitrary number of state variables, the optimal portfolio strategy is known to contain a speculative element and Merton-Breeden hedging terms against the fluctuations of each and every state variable. While the first component is well identified and easy to work out, the implementation of the last ones is problematic as the investor must identify all the relevant state variables and estimate their distribution characteristics. Using a new decomposition of the optimal wealth, we show that the optimal strategy can be simplified to include, in addition to the speculative component, only two Merton-Breeden type hedging elements, however large is the number of state variables. The first one is associated with interest rate risk and the second one with the risk brought about by the co-movements of the spot interest rate and the market prices of risk. The implementation of the optimal strategy is thus much easier, as it involves estimating the characteristics of the yield curve and the market prices of risk only rather than those of numerous (a priori unknown) state variables. Moreover, the investors horizon is shown explicitly to play a crucial role in the optimal strategy design, in sharp contrast with the traditional decomposition.

Optimal hedging in a dynamic futures market with a nonnegativity constraint on wealth

Abstract This paper examines the issue of optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of lognormal, rather than normal, returns and of a constant absolute risk aversion utility function. In this context, the nonnegativity constraint on wealth is binding and the optimal hedging demands are not identical with those encountered in the bulk of the literature, which has largely overlooked this problem. Negative results concerning the derivation of equilibrium in the futures markets and the computation of the open interests then follow.

International asset allocation: A new perspective

We consider an international economy where purchasing power parity (PPP) is violated and financial asset returns and exchange rates follow, in real terms, general diffusion processes driven by K state variables. A country-specific representative individual trades on available assets to maximize the expected utility of her final consumption. Her optimal strategy is shown to contain, in addition to the usual speculative component, only two hedging components, however large is K. The first one is associated with domestic interest rate risk and the second one with the risk brought about by the co-movements of the interest rates and the market prices of risk. The implementation of the optimal strategy is thus much easier, as it involves estimating the characteristics of the yield curve and the market prices of risk only rather than those of numerous (a priori unknown) state variables. Thus, as to the necessity for rational investors to account for predictability in their optimal portfolio strategy, our results make it much easier than the traditional decomposition a la Merton. Since one hedging term depends on interest rate differentials across countries and encompasses hedging against PPP deviations, our decomposition turns to be also an elegant way to achieve optimal (indirect) currency risk hedging as opposed to usual ad hoc route to achieve such a hedging component followed by previous studies. Therefore, our decomposition gives new insights as to the pricing of foreign exchange risk at equilibrium.

Optimal Benchmarking for Active Portfolio Managers

Within an agency theoretic framework adapted to the portfolio delegation issue, we show how to construct optimal benchmarks. In accordance with US regulations, the benchmark-adjusted compensation scheme is taken to be symmetric. The investor’s control consists in forcing the manager to adopt the appropriate benchmark so that his first-best optimum is attained. Solving simultaneously the manager’s and the investor’s dynamic optimization programs in a fairly general framework, we characterize the optimal benchmark. We then provide completely explicit solutions when the investor’s and the manager’s utility functions exhibit different CRRA parameters. We find that, even under optimal benchmarking, it is never optimal for the manager, and therefore for the investor, to follow exactly the benchmark, except in a very restrictive case. We finally assess by simulation the practical importance, in particular in terms of the investor’s welfare, of selecting a sub-optimal benchmark.

General equilibrium real and nominal interest rates

We derive the general equilibrium short-term real and nominal interest rates in a monetary economy affected by technological and monetary shocks and where the price level dynamics is endogenous. Assuming fairly general processes for technology and money supply, we show that an inherent feature of our equilibrium is that any real variable dynamics, in particular that of the short-term real interest rate, is driven by both monetary and real factors. This money non-neutrality is generic, as it does not stem from any friction such as price stickiness, or from a particular utility function. Non-neutrality obtains because the ex ante cost of real money holdings is random due to inflation uncertainty. We then analyze in depth a specialized version of this economy in which the state variables follow square root processes, and the representative investor has a log separable utility function. The short-term nominal rate dynamics we obtain encompasses most of the dynamics present in the literature, from Vasicek and CIR to recent quadratic and, more generally, non-linear interest rate models. Moreover, our results pave the way to several new nominal term structures.

Investment and hedging under a stochastic yield curve: A two-state-variable, multi-factor model

Abstract This paper examines portfolio decisions involving both fixed and non-fixed income securities. Two state variables, the short-term and the long-term interest rates, fully determine the bonds prices and partly influence the other assets prices. We propose first a methodology for determining optimal portfolios in such a context and then use that methodology to solve the portfolio problem of investors whose long-term bond holdings are constrained, which generates undesirable interest rate risk that are hedged with futures contracts. The individual futures positions, which involve several hedging components and the futures market equilibrium open interest are derived and analysed.

Dynamic Asset Pricing With Non-Redundant Forwards

In an incomplete market in which non-redundant forward contracts contribute to span the uncertainty, some standard results of portfolio theory must be amended. When the investment opportunity set is driven by K state variables, a (K+3)-mutual fund separation theorem is obtained in lieu of Mertons (K+2)-fund separation result. The additional fund is a portfolio that hedges the interest rate risk brought about by the optimal portfolio strategy itself. Second, the mean-variance efficiency of the market portfolio of cash assets is neither a necessary nor a sufficient condition for the linear relationship between expected return and beta to hold. Third, the pricing equation for a forward contract is shown to contain an extra term relative to that for a cash asset, term we name strategy risk premium.

Mean‐variance efficiency of the market portfolio and futures trading

We derived an intertemporal capital asset pricing model in which the mean‐variance efficiency of the market portfolio is neither a necessary nor a sufficient condition. We obtained this result by modeling a frictionless, continuously open financial market in which nonredundant futures contracts are available for trade, in addition to cash assets. Introducing such contracts modifies the way investors optimally allocate their wealth. Their portfolios then comprise the riskless asset, a perturbed mean‐variance‐efficient portfolio of cash assets, and a perturbed mean‐variance‐efficient portfolio of futures contracts. Furthermore, a (3 + K) mutual fund separation is obtained, with K being the number of economic state variables, in lieu of the usual (2 + K) fund separation. Mean‐variance efficiency of the market portfolio is a necessary condition only when cash assets are the sole traded assets.

Optimum consumption and portfolio rules with money as an asset

This article generalizes Mertons optimum consumption and portfolio rules in continuous time by introducing money as a capital asset and allowing for uncertain inflation. Assuming that prices are log-normally distributed, a three-funds theorem is derived and the introduction of money is shown not to change the form of the standard inflation-adjusted CAPM but to change the market price of risk. The individuals consumption-portfolio problem is completely solved under uncertain inflation if his utility function is iso-elastic in its arguments. Comparative statics are used to assess the influence of changes in exogenous parameters on the individuals optimal rules.

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.