• Implementing our investment principles means that it would be useful to measure the complexity of different assets and asset allocations via a complexity ranking.
  • As complexity increases the average expected return tends to increase but the average fund manager fee also increases.
  • Increasing complexity can be a way of increasing returns without increasing risk.
  • Low complexity portfolios may not be the best solution for clients needing high returns.


Two of our investment principles are:

“Investment strategy should be as simple as possible but as complex as necessary to meet client objectives”

“Investment strategy only works if it is implemented; a strategy can only be optimal if a client will execute it”

Putting these principles into action means it would be useful to have a way of quantifying the complexity of a portfolio. This report looks at one such method and how increasing complexity affects asset allocations.

Ranking Assets by Complexity

One method to measure complexity is to assign asset classes to one of four categories; Low, Medium, High and Very High Complexity, with an associated numerical score of 1 (low complexity) to 4 (very high complexity). The complexity score is based on the perception of the asset class, rather than the actual complexity of the underlying strategies. For example, relative value DGFs are often viewed as less complex than risk parity, even though the underlying strategies in a DGF are far more complicated. A complexity ranking will thus tend to favour alpha led products compared to multiple “alternative” beta products. The table below shows a provisional mapping of assets to complexity scores.




The graph above shows the average expected return and fund management fee for assets of different complexity. While the average expected return does increase as complexity increases, this is at the expense of higher fund management fees.

Example Portfolios

Consider a pension fund with a risk budget of 6% for the 95% Funding Ratio at Risk. The scheme is 85% funded with an interest rate and inflation hedge equal to the funding ratio. The example asset allocations shown below will consider liquid assets only as not to confuse complexity and illiquidity premia. How does the complexity of an asset allocation affect the expected return that can be achieved in the context of a set risk budget?

Low Complexity Asset Allocation




The low complexity portfolio has exposure to low complexity assets such as index-linked gilts, corporate bonds and developed market equities, giving it the lowest complexity rating of 1. There are exposures to three risk premia to produce an expected return of LIBOR + 125bp to stay within the 6% FRaR budget. Manager fees are relatively low at 14 basis points.

Medium Complexity Asset Allocation




The addition of vol-controlled equities, relative value DGF and absolute return bonds (credit) increases the complexity score to 1.6. The expected return increases to 174bp, an increase of 49bp for the same level of risk, but manager fees increase to 27 basis points. Expected returns come from relative value alpha and credit alpha in addition to equities, credit spreads and z-spreads.

High Complexity Asset Allocation



Increasing the complexity score to 2.7 increases expected returns further to LIBOR + 231bp, an increase of 57 basis points from the medium complexity portfolio. There are now nine separate sources of return, triple that of the low complexity portfolio. Fund manager fees increase to 55bp.

Drawbacks of Low Complexity Portfolios

The main drawback of low complexity portfolios is they will tend to rely on a small number of return drivers, which means that diversification will be less and thus the expected return for a level of risk will be lower. This is because many non-equity and credit risk premia can only be accessed via relatively complex strategies (certainly ones that have the perception of complexity).

The example above shows that, for a given level of risk, expected returns can be substantially enhanced by increasing the complexity of the portfolio. Based on the outlined complexity ranking and our risk model, intricacy does seem to be a “rewarded risk premium”.

Of course if equities are the best performing asset class they may still outperform higher complexity portfolios but for clients that need high returns, the “complex as necessary” part of the investment principle may mean that a more complex portfolio is required.



Author: Philip Rose

Philip is responsible for co-managing the firm’s quantitative analysts and driving innovative client solutions. He was previously an Executive Director in Morgan Stanley's FIG Structuring Group where he was responsible for structuring fixed income and equity derivative strategic solutions for pension funds and insurance companies. Formerly a Director and Chief Structurer at Merrill Lynch, Philip started his career at NatWest Capital Markets in 1994.