The success of the range of CPR growth funds [1], which has become a reference among diversified funds market comes from this multi-model scenarios [2] and it is a reference for the management team.

Let’s review this model multi-scenario with Sylvie Bourmaud, Financial Engineer at CPR Asset Management

In the beginning was Markowitz

By 1996, the need for a quantitative approach was felt in diverse management team. The model has evolved regularly to respond better to the market environment, the expectations of management teams and customer feedback. This model is part of the internal diversified management process of CPR AM.

The approach was initially based on modern portfolio theory. It was developed by H. Markowitz in 1952. It was one of the first to make the connection between risk and the expected gain of a portfolio. This theory is based on the concept of diversification that a combination of assets perfectly chosen to reduce the risk of a portfolio expected return. I.e. the optimal portfolio "or efficient" is one that maximizes the expected return for a given minimum risk. Like any theory, it is based on several assumptions, to mention only the most important: efficient market and rational investor with risk aversion, assets mean-variance modeling and stable correlations and volatilities through time between assets.

The limitations of the Markowitz model

In practice, the limitations of the model are quickly reached. We will not return to the assumptions of rationality and efficiency, which in practice are very unrealistic.
By choosing to model assets by a normal distribution, extreme events, such as crises, for example, are strongly underrepresented.

Another limitation of the model is the instability of correlations through time between financial assets. To illustrate this point, the graph below shows the evolution of correlations between bond assets and equity assets since 1988. We can see very clearly that considering geographical areas, the correlations between assets do not vary in the same direction: over the recent period there is a strong correlation for the euro area but a decorrelation for the U.S. Accordingly, based on the correlation matrix calculated the optimal portfolio composition may be substantially very different

The weakness of the Markowitz model is also a limitation that we can discuss. The quality when estimating parameters is very important because a small variation in inputs causes significant changes in the optimal portfolio. Optimizations are very sensitive to expectations of expected returns. At this level the Markowitz model is not robust, since it is very dependent on the quality of forecasts.

The CPR AM approach: Probabilistic multi-model scenarios tested in 1998

To try to overcome the difficulties encountered in the use of mean-variance model, an internal model has been in production since 1998. In this financial crisis, develop a consensus scenario proved to be difficult. Difficulties were even greater for accurately determining the expected yield for a portfolio of assets. From These discussions the multi-scenarios model came out. Taking into account simultaneously several probabilistic scenarios with crisis scenarios, the hazard is better considered with more realistic optimal portfolios. The multi-scenario model is a generalization of the Markowitz in the case where only one scenario is taken into account.

The model simultaneously takes into account several market scenarios, a central scenario and two or three adverse scenarios. For each scenario a probability of occurrence is affected. Volatilities and correlation matrices used are determined according to each scenario. These choices allow adequate dynamic risks and understand the specific and extreme risks.

Optimizations are performed under constraints.

The multi-scenario approach can consider all types of distributions (MML, thick tail…) for each asset independently of each other. We free ourselves as one of the limits of the Markowitz model mentioned above. To illustrate this point, the graph below is an example of the contribution of this model compared to a log-normal distribution used in the case of a model with a single scenario such as Markowitz. The implementation approach allows modeling the assets taking into thick tail and therefore extreme risks.

Since its inception the multi-model scenarios is stronger and more stable than the single-scenario models. It allows you to limit the impact of forecasts "errors" or "uncertainties".

The model portfolios are optimized under investment constraint (geography, asset class...) for a given level of risk. Asset allocations are reviewed monthly to reflect market developments and enable active management. Optimizations are performed on each asset where each asset class is represented by an index. The optimal allocation is set considering indices and regardless of the securities.

Since the implementation of the model in the process of diversified management, the ability to anticipate jointly several market scenarios has always been used. In addition to the central scenario, two adverse scenarios are generally taken into account. Scenarios are reviewed every month, but can be updated based on the latest financial news (e.g. September 2001). The probabilities assigned to each scenario can vary greatly from one month to another.

A permanent enrichment approach

To gain flexibility and representativeness, changes are made in management processes. Our attention was focused on the following: investment universe and risks. The investment universe is expanded regularly to take advantage of investment opportunities and better risk diversification. For example in September 2012, the euro area bond universe was "broken" in order to take into account the investment opportunities in peripheral countries such as Italy and Spain. In terms of risk management, performance constraints were included in the model: the portfolio maximum loss management in the case of anticipated adverse scenarios is taken into account during optimization. To improve the responsiveness of the model, the risk level of the portfolio is adjusted to market conditions. In case of high market volatility risk criterion may be adjusted.

All these developments were possible because from its inception we have tried to build a model sufficiently "general" to be robust while allowing adaptability to new requirements.

As part of the CPR Growth funds management, the asset allocation model is a major support, because, beyond the role of guardian to implement asset allocation, it plays the role a real conductor. In relation to an asset allocation based solely on a discretionary management or in other words the convictions of a single manager, the asset allocation model leads to much more diverse benefits.

For example, 18 months ago while the market consensus was very negative about the detention of American or German bonds given the low level of interest rates, the pattern of asset allocation has led us to maintain weight and thus very significant sensitivity bond asset classes considered by consensus as being too expensive. The consensus was ultimately wrong.

Sylvie Bourmaud, Financial Engineer at CPR Asset Management

The very good performance of the German and U.S. debt last year helped CPR Reactive Growth and CPR Reactive Growth - with the help of the asset allocation model - display performance significantly positive in 2011 despite the market downturn in the euro zone.