Lionel Martellini, EDHEC

"From asset management to risk-and-asset management"

Asset management justifies itself by its capacity to add value. For many decades, the industry has focused on a single source of added-value: delivering alpha through security selection decisions subject to (often tight) tracking error constraints, and using commercial indices as benchmarks.

Given the difficulty in delivering added-value through security selection only, the old paradigm has been questioned. In particular, the focus on adding value through security selection has somewhat distracted the industry from another key source of added value: risk management. Today, the industry is witnessing a shift in perceived added-value - there is an emerging consensus about the need to move away from stand-alone asset management products towards risk and asset management solutions that can address investors' needs through customised dynamic asset allocation strategies.

One critical advance in risk and asset allocation techniques has been made possible by the work of Robert Merton (1971), who extended portfolio construction techniques beyond the static setting, and has shown how to solve dynamic portfolio optimisation problems using the dynamic programming approach. A key academic insight is that there is a deep correspondence between pricing and portfolio problems. On the one hand, asset pricing problems are equivalent to dynamic asset allocation problems. On the other hand, dynamic asset allocation problems are equivalent to asset pricing problems: martingale or convex duality approach to dynamic asset allocation problems.

From a practical standpoint, dynamic allocation strategies allow for the maximisation of investors' long-term objectives while respecting a number of short-term - self-imposed, accounting, or regulatory - constraints. One key practical implication of this approach, sometimes referred to as dynamic core-satellite (DCS) approach, is that optimal investment in a performance-seeking satellite portfolio (PSP) is not only a function of risk aversion, but also of risk budgets (margin for error defined in terms of a distance with respect to various kinds of floor levels of wealth), as well as probability of the risk budget to be 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. This stands in sharp contrast to fix-mix strategies, where the target allocation to the PSP is constant over time, regardless of the distance with respect to the investors' goals and constraints.

Theoretical arguments show that the quantity relating the risk budget to the allocation to performance-seeking assets, known as the multiplier, should be inversely proportional to the variance of excess returns of the satellite with respect to the core portfolio. As opposed to taking a constant multiplier value, as is typically done in base case examples of implementation, one can show that significant value can be added by making the multiplier a suitably-defined function of the forecasted level of tracking error between the core and satellite portfolios.

An effect of the volatility of risky asset returns is its persistence - or ‘clustering' - which implies a relatively high level of predictability in volatilities. Using a parsimonious GARCH model with a Student-t distribution (fatter tails) for the independent and identically distributed random shocks that accounts for the presence of autocorrelation, heteroskedasticity and asymmetry (leverage effect), and re-estimating the model parameters using a growing window sample to estimate the next period variance, we generate forward-looking estimates of tracking error levels, and used these forecasts to dynamically adjust the multiplier values.

On a fast-rising volatile bull market for the satellite (eg, a stock index), the time-varying multiplier value would lag with respect to a constant multiplier value calibrated with respect to the long-term unconditional mean. On the other hand, in a slowly-rising bull market and in all bear market environments, the strategy with time-varying multiplier value would perform better and it reacts fast enough to reversions due to the related increase in volatility. Using a strategy with time-varying multiplier value allows for substantial increase in mean returns, as well as a decrease in risk parameters relative to the benchmark case with constant parameter values.

While the original approach was developed in a simple framework, it can be extended, allowing for the introduction of more complex floors (max drawdown risk budget, liability-driven risk budget, competition-related risk budget, etc.), but also goals.

The goal-directed strategies recognise that the investor has no utility over a ceiling target level of wealth, which represents the investor's goal (actually a cap), which can be a constant, deterministic or stochastic function of time. Goal-directed strategies involve an optimal switching at some suitably-defined threshold level, which defines the switching point between fear- and hope-dominated behaviour.

It is not clear why any investor should want to impose a strict limit on upside potential. The thought 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 better chance of failing an almost-reached goal when their wealth level is very high.

Generally, the dynamic core-satellite framework can be extended to allow one to take into account forward-looking views if and when available, eg, views based on mean-reversion in equity returns, within the framework of a sound risk-control process.
This extension is a critical improvement where the two motivations behind dynamic asset allocation decisions, namely the risk management and the tactical motivations, are often perceived as inconsistent and mutually exclusive. Hence, dynamic risk-controlled strategies, which typically imply a reduction to equity allocation when a drop of equity prices has led to a substantial reduction of the risk budget, have often been blamed for their pro-cyclical nature that leads to sell equity holdings in those states of the world where equity markets have become particularly attractive for long-term investors believing in the presence of mean-reversion in equity risk premium.

In fact, an explicit analytical representation of the relationship between optimal strategies in the presence and in the absence of short-term constraints can be derived, which allows us to disentangle the impact of short-term constraints from the impact of return predictability on the optimal allocation decision. Depending on market conditions and parameter values, the risk-controlled motivation may outweigh the tactical motivation, or vice-versa, with risk management always prevailing ultimately. In other words, risk-control technology can be made entirely consistent with internal or external processes aiming at generating active asset allocation views. In fact, casting the active view generation process within the formal framework of a dynamic risk-control strategy can be shown to be the only way to successfully implement active asset allocation decisions while ensuring the respect of risk limits.

In the past, investment banks have been at ease with dynamic asset allocation techniques, but have typically applied them to inefficient underlying assets (typically market cap weighted indices), without any systematic effort to design optimal payoffs. Asset managers on the other hand have developed expertise for generating improved PSP through alpha and/or beta benefits, but have not significantly utilised the benefits of dynamic asset allocation strategies. Overall, by explicitly introducing investors' goals, constraints and risk budgets in the design of asset allocation solutions, the asset management industry has an opportunity to evolve towards providing more value-added towards investment solutions that better fit investors' need.



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