## Asset Allocation: Advanced Techniques

The basic methodology we have just outlined can be used to calculate asset weights that maximize expected portfolio return for any given constraint on portfolio standard deviation (or other measure of risk, such as value-at-risk). Conversely, this approach can be used to minimize one or more portfolio risk measures for any given level of target portfolio return. These are all variants of the asset allocation methodology known as mean–variance optimization (MVO), which is an application of linear programming (for example, as found in the SOLVER function in an Excel spreadsheet). Although MVO is by far the most commonly used asset allocation methodology, it is, as we have shown, subject to many limitations.

Fortunately, there are techniques that can be used to overcome some, if not all, of the problems highlighted in our example. We will start with alternatives to the MVO methodology, and then look at alternative means of managing errors in the estimation of future asset class returns, standard deviations, covariances, and other model inputs.

### Alternative Approaches to Portfolio Construction

The simplest alternative to MVO is to allocate an equal amount of money to each investment option. Known as the 1/*n* approach, this has been shown to be surprisingly effective, particularly when asset classes are broadly defined to minimize correlations (for example, a single domestic equities asset class rather than three highly related ones, including small-, mid-, and large-cap equities). Fundamentally, equal weighting is based on the assumption that no asset allocation model inputs (i.e. returns, standard deviations, and correlations) can be accurately forecast in a complex adaptive system.

Another relatively simple asset allocation methodology starts from the premise that, at least in the past, different investment options perform relatively better under different economic scenarios or regimes. For example, domestic and foreign government bonds and gold have, in the past, performed relatively well during periods of high uncertainty (for example, the 1998 Russian debt crisis and the more recent subprime credit crisis). Similarly, history has shown that inflation-indexed bonds, commodities, and commercial property have performed relatively well when inflation is high, whereas equities deliver their best performance under more normal conditions. Different approaches can be used to translate these observations into actual asset allocations. For example, you could divide your funds between the three scenarios in line with your subjective forecast of the probability of each of them occurring over a specified time horizon, and then equally divide the money allocated to each scenario between the asset classes that perform best under it.

When it comes to more quantitative asset allocation methodologies, research has shown that—at least in the past—some variables have proven easier to predict and are more stable over time than others. Specifically, relative asset class riskiness (as measured by standard deviation) has been much more stable over time than relative asset class returns. A belief that relative riskiness will remain stable in the future leads to a second alternative to MVO: risk budgeting. This involves allocating different amounts of money to each investment option, with the goal of equalizing their contribution to total portfolio risk, which can be defined using either standard deviation or one or more downside risk measures (for example, drawdown, shortfall, semi-standard deviation). However, as was demonstrated by the ineffective performance of many banks’ value-at-risk models during 2008, the effectiveness of risk budgeting depends on the accuracy of the underlying assumptions it uses. For example, rapidly changing correlations and volatility, along with illiquid markets, can and did result in actual risk positions that were very different from those originally budgeted.

The most sophisticated approaches to complicated multiyear asset allocation problems use more advanced methodologies. For example, rather than a one-period MVO model, multiperiod regime-switching models can be used to replicate the way real economies and financial markets can shift between periods of inflation, deflation, and normal growth (or, alternatively, high and low volatility). These models typically incorporate different asset return, standard deviation, and correlation assumptions under each regime. However, they are also subject to estimation errors not only in the assumptions used in each regime, but also in the assumptions made about regime continuation and transition probabilities, for which historical data and theoretical models are quite limited.

### Rebalancing Strategies

Multiperiod asset allocation models can also incorporate a range of different rebalancing strategies that manage risk by adjusting asset weights over time (for example, based on annual rebalancing, or maximum allowable deviations from target weights). When it comes to identifying the best asset allocation solution for a given problem, these models typically incorporate sophisticated evolutionary search techniques. These start with a candidate solution (for example, an integrated asset allocation and rebalancing strategy), and then run repeated model simulations to assess the probability that they will achieve the investor’s specified objectives. An evolutionary technique (for example, genetic algorithms or simulated annealing) is then used to identify another potential solution, and the process is repeated until a stopping point is reached (which is usually based on the failure to find a better solution after a certain number of candidates have been tested or a maximum time limit is reached). Strictly speaking, the best solutions found using evolutionary search techniques are not *optimal* (in the sense that the word is used in the MVO approach)—meaning a unique solution that is, subject to the limits of the methodology, believed to be better than all other possible solutions. In the case of computationally hard problems, such as multiperiod, multiobjective asset allocation, it is not possible to evaluate all possible solutions exhaustively. Instead, much as for real life decision-makers, stochastic search models aim to find solutions that are robust—ones that have a high probability of achieving an investor’s objectives under a wide range of possible future conditions.

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