October 2013

EDHEC RESEARCH: Different horizons

IslandEdhec argues that long-term investment objectives and short-term constraints need not be mutually exclusive. Meeting the challenges of modern investment practice involves the design of novel forms of investment solutions, as opposed to investment products, customised to meet investors’ long-term objectives, while respecting a number of constraints expressed in terms of both dollar budgets and risk budgets, which are often set over short horizons. In recent research conducted as part of the Asset-Liability Management and Institutional Investment Management research chair, supported by BNP Paribas Investment Partners, we have reiterated that designing investment solutions that meet investors’ needs requires the conflict inherent in the coexistence of long-term objectives and short-term constraints to be addressed. While it is perceived that tension exists between a focus on hedging long-term risk and a focus on insurance with respect to short-term constraints, we cast new light on this by arguing that long-term objectives and short-term constraints need not be mutually exclusive. Our analysis shows that both may naturally coexist within the context of a long-term investing strategy consistent with short-term performance constraints. In the absence of short-term risk constraints, the presence of a mean-reverting equity risk premium justifies that the allocation to equities should be anti-cyclical and increasing with time-horizon. Investors endowed with consumption/liability objectives need to invest in two distinct portfolios, in addition to cash: one performance-seeking portfolio and one liability-hedging portfolio; this is the liability-driven investing paradigm. The allocation to the “risky” performance-seeking portfolio versus “safe” liability-hedging portfolio is found to be increasing in the performance-seeking portfolio Sharpe ratio. As such, the optimal strategy displays a state-dependent component, suggesting the allocation to equity should be increased (respectively, decreased) when equity has become cheap (respectively, expensive), as measured through a proxy for the equity risk premium. In the context of a model with a stochastic mean-reverting equity risk premium, one can show that the optimal allocation also involves a hedging demand against unexpected changes in the performance-seeking portfolio Sharpe ratio, known as a risk premium hedging portfolio, which implies a deterministic decrease in the allocation to equity as the investor gets closer to the time-horizon. SHORT-TERM CONTRAINTS
The presence of short-term constraints justifies that the allocation to equities should also be an increasing function of the current value of the short-term risk budget, in addition to being an increasing function of time-horizon and the current value of the equity risk premium. These short-term constraints are managed through dedicated insurance strategies. The practical implication of their introduction is that optimal investment in a performance-seeking satellite portfolio (PSP) is not only a function of risk aversion, but becomes a function of risk budgets, as well as the probability of the risk budget being spent before horizon. In a nutshell, a pre-commitment to risk management allows one to adjust risk exposure in an optimal state-dependent manner, and therefore to generate the highest exposure to upside potential of PSP while respecting risk constraints. Tension exists between a focus on hedging long-term risk and a focus on insurance with respect to short-term constraints: dynamic risk-controlled strategies typically, which imply a reduction in equity allocation when a drop in equity prices has led to a substantial diminution of the risk budget, have often been blamed for their pro-cyclical nature, and long-term investors are often reluctant to sell equity holdings in those states of the world where equity markets have become particularly attractive in the presence of mean-reversion in equity risk premium. METHODOLOGY
Our research suggests that long-term objectives and short-term constraints need not be mutually exclusive. The risk-control methodology can be made entirely consistent with internal or external processes aiming at generating active asset allocation views. Casting the active view generation process within the formal framework of a dynamic risk-control strategy appears to be the only way to successfully implement active asset allocation decisions while ensuring the respect of risk limits. In practice, a number of key improvements can be used in implementation. While the original approach was developed in a simple framework, it can be extended in a number of important directions, allowing for the introduction of more complex floors. A variety of floors can be introduced so as to accommodate the needs of different kinds of investors. For example, capital guarantee floors, which allow for the protection of a fraction of the initial capital. In addition to accounting for the presence of floors, the dynamic risk-controlled strategies can also accommodate the presence of various forms of caps or ceilings. These strategies recognise that the investor has no utility over a cap target level of wealth, which represents the investor’s goal. From a conceptual standpoint, it is not clear a priori why any investor should want to impose a strict limit on upside potential. The intuition is that by forgiving performance beyond a certain threshold, where they have relatively lower utility from higher wealth, investors benefit from a decrease in the cost of the downside protection (short position in a convex payoff in addition to the long position – collar flavour). Putting it differently, without the performance cap, investors have a greater chance of failing an almost reached-goal when their wealth level is very high. Opportunity costs implied by the short-term constraints are significantly lower when they are optimally addressed through insurance strategies, as opposed to inefficiently addressed through an unconditional decrease in the equity allocation. Our analysis shows asset allocation and portfolio construction decisions are intimately related to risk management. The quintessence of investment management is essentially about finding optimal ways to spend risk budgets that investors are reluctantly willing to set, with a focus on allowing for the highest possible access to performance potential while respecting such risk budgets. Risk diversification, risk hedging and risk insurance are three useful approaches to optimal spending of investors’ risk budgets. In this context, improved forms of investment solutions rely on a sophisticated exploitation of the benefits of the three competing approaches to risk management, namely risk diversification (key ingredient in the design of better benchmarks for performance-seeking portfolios), risk hedging (key ingredient in the design of better benchmarks for hedging portfolios) and risk insurance (key ingredient in the design of better dynamic asset allocation benchmarks for long-term investors facing short-term constraints). In the end, risk management, which focuses on maximising the probability of achieving investors’ long-term objectives while respecting the short-term constraints they face, appears to be the key source of added value in investment management. The results we obtain confirm that dynamic asset allocation benchmarks can be designed so as to allow for more efficient spending of investors’ risk budgets. Intuitively, this is because the pre-commitment to reduce the allocation to equity in times and market conditions that require such a reduction so as to avoid over-spending risk budgets, allows investors to invest on average more in equities compared to a simple static strategy that is calibrated so as to respect the same risk budget constraints. The welfare gains involved in this higher allocation to equities are found to be substantial for reasonable parameter values, especially for long-term horizons and in the presence of a mean-reverting equity risk premium. Authored by Romain Deguest and Vincent Milhau of the Edhec-Risk Institute, along with Lionel Martellini, professor of finance, Edhec Business School and scientific director, Edhec-Risk Institute ©2013 funds europe

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