MEAN VARIANCE OPTIMISERS

One of the benchmarks of practical portfolio management is modern portfolio theory. MVO constructs are derived from this theory and use measures of risk, return and relative price movement to produce an “efficient portfolio”.

These models, in their current format, have significant drawbacks and are not suitable for the management of personalised equity portfolios where asset and liability management are integrated. These models revolve around three key inputs for their integrity.

Return

The use of average historical return builds a negative valuation bias into portfolio construction and does not reflect current valuation relationships, which may be at critical valuation points.

Use of forecast returns often leads to significant changes in recommended allocation where returns are subject to frequent revision. Where forecast returns are being used, forecast risk and covariance should be also derived from the one analytical process in order to be relevant. This is a “relative” valuation model all said and done.

MVO constructs are long term, static, strategic structures for allocating assets, a by product of converting a model into a set of quantitative formulas.

Unfortunately, we all live in the short term. MVO constructs cannot deal effectively with periods of negative returns, limiting their ability to manage significant short term valuation differentials. This contradicts an inviolate principle, buy low, sell high. MVO constructs therefore encourage long term average return and broad static allocation structures, limited in their ability to manage significant risk and significant return opportunities at critical periods, a necessity for liability management.

Risk

Risk is a measure of the monthly price movements of an investment relative to its average monthly price movement. MVO constructs that use historical (average) standard deviations will mask the current valuation risk and will not reflect the actual volatility of an investment.

While forecast volatility can be derived from option pricing models, these measures are again unrelated to valuation risk. In fact, if we are using variables subject to significant short term change, a static model which does not allow verification of wider risks and return opportunities should not be used.

Covariance

Covariance is a measure of relative price movement. It is actually the most important component of modern portfolio theory in that the ability to optimise allocation for risk and return revolves around this key variable. It is also the least sensitive to change, which is unfortunate since relative valuation is a key component of risk and return.

Historical covariance suffers from the same problem as historical standard deviation in that it does not reflect the magnitude of current relative price movements . At worst it is an average and because of this it lacks the necessary sensitivity to drive portfolio structure.

MVO constructs are also extremely sensitive to small changes in the models return inputs . In fact, MVO models are stating that you need to react to current change. The problem is that without a valuation and allocation interface, there is no way of knowing if the transactions are warranted. You need to retain the sensitivity but manage the change – see Management.

In the past this sensitivity has been managed by reducing the sensitivity of the models and by placing constraints on the allocation output.

In fact, if the market is efficient and expected standard deviations, covariance and return used to structure portfolios are correct, there should be no need to change the structure of the portfolio. The fact that changes are needed implies inefficiency in the actual application of the structure. The best way of managing inefficiencies within portfolio structure is via integrated valuation and allocation frameworks.

Another major problem with MVO constructs is the management of change. Since price, risk and price movement relatives change significantly over short time periods, portfolios will vary significantly from their recommended MVO allocation.

MVO constructs are really only capable, with their constraints and inefficiencies of creating a recommended portfolio allocation. They are incapable of managing allocation within liability space while short term market movements render them unstable.

Because MVO constructs do not track short term changes in relationships of valuation and allocation they cannot provide a valuation and allocation framework for the management of existing portfolios.
MVOs and transaction management

MVO constructs manage the deviation of allocation by introducing a transaction cost function into the allocation algorithms. Only if after transaction costs does the trade result in a more efficient portfolio, does the trade go ahead.

While this may sound sensible, it does have its drawbacks. For one, the calculation of the efficient portfolio at outset did not include the effects of future transaction costs on return, structure and strategy. Secondly, transaction costs imply trading, which means an implied valuation decision.

Without a valuation decision you could end up selling an under valued rising asset for purchase into an over valued falling asset, or “return contamination”.

MVOs and net liability profiles

Importantly, MVO constructs cannot react efficiently to the effects of inflows and outflows to and from portfolios. Unless portfolios are constructed and managed within liability space the ability to incorporate inflows and outflows into portfolio structure is a complex one.

It is difficult to manage risk and return without being able to personalise the structure and management of portfolios to clients’ liability profiles. Liabilities are a significant influence on allocation. MVO constructs are inefficient in liability space.

MVOs and absolute valuation risks

Another important issue is absolute valuation. The initial investment decision is important to long term financial security. MVO constructs are based on relative valuations and do not include absolutes in the initial investment decision.

MVO constructs separate the valuation analysis from the management of allocation. For asset management companies with specific expertise in the valuation of markets, styles and securities, these constructs divorce their expertise from the service provided.