**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.

"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.

*ART
Consulting/Research*

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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.