**Asset Allocation Part 2:
Technical and Fundamental Trading Rules**

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disguise the specific markets, trading factors, strategy parameters and many
other essentials. Of course all of the analyses is based on real market
conditions and real world trading considerations. For access to the
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Asset allocation between equity and
interest rate markets represents a very large component of the investing
communities resources. Though equities can provide higher returns,
they can also be riskier, and so the notion of a (relative) safe haven for
capital during "nasty" periods in the equity markets has driven considerable
interest [1].

So, are there any trading rules that
help improve (holding period) risk-adjusted returns when considering asset
allocation decisions?

For example, in another *ARBLab*
analysis (P&L Performance of MVO Asset Allocation,
and all of TG2RM1st
- Chapter 12 is dedicated to
the introduction of PaR analysis),
it was shown that "brute force" Mean-Variance Optimal (MVO)
methods (though intuitive and common) are not quite as effective in the
real world as theory might suggest. However, it was also shown that
careful analysis may be able to indicate market conditions which are more
"MVO-friendly", than a naive application, and so assist in the
decision whether or not to base asset allocation decisions on MVO.

Similarly, other traditional methods
may be used to assist asset allocation decisions, such as Technical
Analysis, and Fundamental Analysis.

In another *ARBLab*
analysis, **Asset Allocation Part 3: P&L-Optimal Calibrated
(POC) Trading Rules**, these methods are combined to see how TA
and FA methods can help "calibrate" MVO based asset allocation
as illustration of compound holding period risk-adjusted P&L analysis
of trading strategies.

#### An approach to trading rule verification

For the moment, though, consider
analysing the P&L of many (asset allocation) trades over a long period
using backward and forward testing of trading rules. For example, TA
trading rules may include pattern matching (bull flags, triangles, etc),
momentum/oscillators, Moving Averages (MA) and trends. One TA
rule may be: "allocate funds into equities (and out of bonds) when
the 100-day MA crosses above the 30-day MA. FA
methods include the assessment of economic parameters such as CPI, GDP,
Un-Employment, etc. and then rebalancing the portfolio accordingly.

There are, of course, a very large
number of possible trading rules, and within any one rule there may be a
large number or parameterisations (e.g. 30-day MA vs. 100-day MA
etc). As such this type of analysis is necessarily time consuming.

Even
worse, the results of such trading rules may have subtle "high
dimensional" interactions that are not immediately obvious when doing
any single trading analysis in isolation. For example, the figure to
the right (click to enlarge) illustrates a trading strategy based on
a combination of TA and FA rules. Each point in the chart is a
"net holding period P&L" for a complete trade cycle.
The "Factors" are "sanitised" market/trading rule
indicators (e.g. MA cross-overs, GDP, Bond yield, etc etc). The vertical
axis is a restated/normalised P&L. The colouring of the
P&L points represents yet another market/trading factor, and so the
pattern in the colours is also a beneficial indicator.

If only the 2-dimensional isolated
analysis were performed (as indicated by the smaller 2-D plots at the
right of image), then one may concluded that there is not very much
benefit to using the trading rules applied here. However, using the
4-dimensional combination of the 3-D plot + the colouring, a pattern
emerges. For example, if Factor X is in a specific range, then an
increasing Factor Y implies higher returns (i.e. if you were holding a
portfolio, as Y was increasing you would move increasing funds from bonds
to equities).

Importantly
it is also necessary to test the combined impact of other Factors
(trading rules and market conditions). The figure to the right
(click to enlarge) shows that making a small change to the trading
strategy above can, for the same market conditions, increase the relative
profitability (i.e. the Factor characteristics are the same, just now we
are making more money due to a more efficient rebalance process).

Moreover,
introducing additional Factors further helps to narrow the market/trading
conditions that lead to profitability as shown on the right. The
trick here is to compare the Figure above (in terms of Factor X & Y)
with this one (in terms of Factor X & Z). This "super
imposing" of views shows that certain combinations of Factors X, Y,
and Z are indicators of increased profitability.

As usual, caution is required.
The analysis here, though including thousands of trades, and incorporating
many real world factors cannot be taken as any perfect predictor of the
future. Moreover, there are all manner of wrinkles, for example, Fundamental
Analysis relies on economic factors which generally take a long time to
form patterns (e.g. economic cycles can be 4-11 years), and also economic
indicators can be notoriously unreliable (e.g. just compare the
"volatility" in economic release data vs. their
revisions). The implication being that deep assessment of all
reality impact components is required. Having said so, high
dimensional holding period P&L analysis appears helpful in the assessment
of asset allocation considerations and trading rules.

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]
It is noteworthy that during some market periods the returns and risk of
bond markets can rival that of equity markets, even though it is normal to
consider equities to be higher risk/return.