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P&L Performance of MVO Asset Allocation

Mean-Variance Optimisation (MVO) is common and widely known method used to provide asset allocation decision.  Based on the work of Markowitz (1952), MVO relies on quadratic optimisation of instrument average returns and standard deviation of returns to produce an "optimal" portfolio composition.  For MVO type approaches "optimality" is in the sense that the resultant portfolio composition is either on the Efficient Frontier, or at some "chosen" or "user preference" risk/return point on the Securities Market Line.  MVO methods are (relatively) intuitive and (reasonably) simply to understand, providing a "consistent" approach to asset allocation and investment strategy considerations.  

But is MVO profitable, and if so is it acceptable on a risk-adjusted basis?

Please note, as ART Consulting/Research is a fee based service, in the following the results have been "sanitised" to disguise the specific markets, trading factors, strategy parameters and many other factors.  Of course all of the analyses is based on real market conditions and real world trading considerations.  For access to the "un-sanitised" results, and for analysis tailored to your needs please submit an email via  Request More Information.

Unfortunately, life is not so simple.  If MVO methods on their own were sufficiently "good", then there would be no need for investors and traders.  There is a considerable body of literature pointing to the shortcomings of MVO methods.  Indeed, we here at ART have also produced "observations" that illustrate the shortcomings of (naive) MVO methods.  For a "touch feely" discussion of MVO please see ARTicles: Optimisation and P&L - Part 1, and all of TG2RM1st - Chapter 12 is dedicated to the introduction of PaR analysis.  

Methods that are much more sophisticated than MVO exist (such as those in ART's Pr/rO), but these methods require the construction of very smart software, and are generally expensive to build.

So before you spend a great deal of money on a very sophisticated investment strategy software application, wouldn't it be nice to know how MVO performs?

An illustration of MVO performance

One approach is to back-test MVO against real (traded) market data and real trading constraints, and analyse the "holding period risk/return" for many periods.  Of course this is a big task, the software required to perform such analyses is necessarily complex, and importantly it must be aware of many real world implications such as transactions and funding costs, trading limits, market volatility impacts in between MVO rebalance points etc etc etc in addition to the usual quadratic optimisation issues.

Figure 1 illustrates the results for just this type of analysis.  Here 4 dimensions of risk/return from real world trading data spanning many years and applied to a particular trading strategy using MVO have been plotted.  There are 3,069 P&L results in the plot - each representing the Net P&L of an entire holding period.  The vertical axis is a measure of P&L, while the X & Y axis, and the "colouring" of the results are due to "trading factors" (so the colouring is a "fourth dimension").   

Figure 1

(Click to enlarge)

"Trading Factors" are sanitised terms to represent typical market and trading conditions/parameters used for rebalancing, such as volatility, moving average cross-over, GDP, etc.  Here, these have been "disguised" as part of sanitisation process and simply referred to as Trading Factors.

Any points that are above zero represents a trade that made money following this particular MVO strategy over the years tested.  Any points below zero represent trades that lost money using the same strategy.

At first glance it seems that the number of points above zero are greater than the number the number of P&Ls below zero, and so it appears that, at least on such a "crude basis" MVO did better than 50/50.  But this is misleading since a large percentage of the market instruments in the portfolio are equity based, and thus MVO was simply benefiting from the (usual) "up-trend" of the equity markets over the period tested (something that naive MVO does not know anything about and so it just got "lucky" - for proof just compare to the period March - Dec 2000).  Though, the full analysis of long run average return using MVO is withheld from this Overview.  Two of the other important observations are:

1) One important observation is that the "factors" used in Figure 1 have identified  "market/trading conditions" when MVO works and when it does not work.  For example, in the lower right hand plot one can see that the P&Ls tend to be above or below breakeven in discernable "groups".  But a 2-dimensional plot is not sufficient to extract meaningful results. Rather the combination of knowing all of  FactX, FactY, and FactC permits the separation into the coloured groups, which appears to have found "factors of forecastibility".

2) Another important point, however, is that moving to a higher dimensional analysis that simultaneously indicates the impact of several trading factors can be helpful not only in finding the "performance regions", but also the market conditions leading to the "buy/sell" decisions..  For example, the "conditions" when FactX is greater than .10 together with the "condition" that is measured by the colour "deep red[1]" in the marker colours indicates conditions where MVO fails, and in fact we should have "sold MVO" during those market/trading conditions.  In a similar manner one may proceed with quantifying market condition that lead to successful or "MVO-friendly" market conditions (such as some of those regions where the green markers reside).  One obvious implication is that an investor could then look at the market conditions on a particular day and decide if those market conditions are "MVO-friendly", and thus whether or not to use MVO.

Clearly, one would not proceed to make trading decisions based purely on this single analysis.  At the very least this backtesting must be repeated many times to test for the impact of many more "dimension" or "trading factors" such rebalance period, interim position risk impact, limits on compositions (long, shorts), and many other important issues that impact real world portfolio risk/return.

If you are interested in obtaining research results on this issue please Request More Information and please feel free to indicate a few specifics of interest to you.


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[1]  Please note that there appear to be "red" markers above zero as well, but in fact those are a different "regular red" as opposed to the "deep red" found almost exclusively below zero.



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Last modified: July 25, 2011