Abraham Lioui

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.

Interest Rate Risk and the Cross-Section of Stock Returns

We derive a macroeconomic asset pricing model in which the key factor is the opportunity cost of money. The model explains well the cross section of stock returns in addition to the excess market return. The interest rate factor is priced and seems to drive most of the explanatory power of the model. In this model, both value stocks and past long-term losers enjoy higher average (excess) returns because they have higher interest rate risk than growth/past winner stocks. The model significantly outperforms the nested models (capital asset pricing model (CAPM) and consumption CAPM (CCAPM)) and compares favorably with alternative macroeconomic models.

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.

Practitioner Portfolio Construction and Performance Measurement: Evidence from Europe

Responses to a survey of investment management practitioners in Europe show that most practitioners are aware of key academic concepts in portfolio construction. But they still resort to ad hoc heuristics when they construct portfolios. Consideration of risk–return matters is less common in performance evaluation than in portfolio construction. An economically significant firm-size effect plays a role in the use of sophisticated (versus unsophisticated) portfolio construction but not in performance measurement. We surveyed 229 investment management practitioners in Europe for information on their methods of constructing portfolios and measuring performance. Our purpose was to assess the impact of academic finance research on investment industry practices. The responses show that most practitioners are well aware of key academic concepts in portfolio construction and frequently consider risk–return trade-offs. They often resort to ad hoc heuristics, however, when they construct their portfolios. For example, investment managers are aware of the importance of extreme risks, but the instruments they use to measure them are inadequate. To deal with estimation risk, practitioners use arbitrary weight restrictions rather than portfolio construction methods that explicitly address estimation risk. Responses relating to measurement of ex post performance show that risk–return considerations are less common in this area than in portfolio construction. Extreme risks are hardly taken into account in performance measurement, and adjustments for risk are crude. In general, practitioners use both sophisticated and unsophisticated techniques. When we analyzed the response patterns to determine what drives the differences in sophistication, we found an economically significant firm-size effect for portfolio construction. That is, response patterns from large institutions are markedly different from those from small institutions; small firms tend to use less sophisticated tools than large firms use. For performance measurement, we found a firm-size effect, but it is less pronounced than it is for portfolio construction. In view of the current failure of the industry to adopt sophisticated measures, one is compelled to wonder why investors do not demand better risk assessment in portfolio construction and performance evaluation. Some would argue that greater financial literacy of investors is key in improving matters; others would call for external regulators to mandate the use of appropriate risk measures. Although the evidence reported in this article does not allow us to take a stance on that issue, we believe that ensuring a sufficient transfer of knowledge about portfolio and risk management concepts from research results to practice is a necessary condition for sound investment processes in the industry.

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.

Spillover Effects of Counter-Cyclical Market Regulation: Evidence from the 2008 Ban on Short Sales

The ban on shorting had negative effects on the hedge funds industry. It also had a negative impact on the returns and the market quality of the stocks placed off limits by the ban. We look at the impact of the ban on broad market indices in the US and in Europe (the United Kingdom, France and Germany). Since these indices and their performance are of great concern to the asset management and hedge fund industries, it is important for practitioners and policy makers to understand the impact of changing the rules of the game (banning short sales) on the return distribution of these indices and to assess the potential spillover effects of a counter-cyclical regulation affecting only one segment of the financial market. We show that the ban had a broad impact on the markets. It was responsible for a substantial increase in market volatility. The impact of the ban on the higher moments of index returns is not systematic (skewness and kurtosis of the return distribution of only few indices were affected) or robust (using some robust measures of higher moments makes the impact of the ban disappear). Thus, the ban didn’t ease the downturn pressure in the financial markets. The market seems not to believe that short sellers or the hedge fund industry were responsible for the turmoil of 2008.

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.

Currency risk hedging: Futures vs. forward

Abstract The objective of this paper is to address the issue of choosing between currency forward and currency futures contracts when hedging against currency risk within a stochastic interest rates environment. We compare between the hedging effectiveness of the two derivative assets both within a narrow sense (i.e., volatility minimization) and within a wide sense (i.e., risk-return trade-off). When judging hedging effectiveness in the narrow sense, forward and futures contracts give identical results even if they do not have identical prices. When judging hedging effectiveness in the wide sense, the choice between the two contracts is determined by the correlation between the domestic and the foreign term structures dynamics.