A Few Words About Diversification
The important idea behind our asset allocation approach is that we
can quantify and optimize the balance of risk exposures in a
portfolio.
Diversification is simple to explain: it is the practice of
spreading your investment risk evenly, and on as many independent market
exposures as possible.
There is obviously the old adage of not putting all your eggs in one
basket. However, we don’t find that to be a very helpful way to think
about diversification, as it wrongly suggests that one can always
identify very easily whether the eggs are in fact in a one basket. A
better illustration would come from geology: if you think of earthquakes
around the world, they don’t all go off at the same time, and many are
independent from each other. If you were asked to build several houses
in seismic zones, you would try to avoid the possibility of seeing all
your properties destroyed by a single seismic event. That would require
understanding where the seismic fault lines are, how they are connected
and how they are evolving over time. Understanding diversification in a
portfolio of assets is a lot like that, with the added difficulty that
the “seismic fault lines” are shifting a lot more in financial markets
than in geology (luckily for civil engineers).
So, in order to measure appropriately the diversification of an
allocation, we start by identifying, using machine learning, independent
(orthogonal) empirical sources of risk / returns in a given universe of
securities (those factors are updated as new data comes in). We can then
calculate the diversification of any portfolio from the entropy of its
distribution of variance, which, mathematically, looks like this: \(D = e^{- \sum\limits_{i=1}^{n}{}p_{i}
ln(p_{i})}\).
Here are two simple chart to visualize what we mean:
In
a well diversified allocation, the variance is
distributed evenly across multiple exposures

In
a badly diversified allocation, two factors account for
nearly 80% of the portfolio variance
With this understanding of the asset universe, we optimize
diversification to reach a target allocation (nontrivial with the
various constraints that we apply).
That is an efficient approach to capture a variety of risk premia,
which leads to very robust target allocations that do not need frequent
rebalancings, typically have low volatility and a high Sharpe ratio
(although we are never targeting those metrics in our
optimizations).
We do not by default lever up the optimal allocations to target a
nominal level of volatility, although dynamic leverage can obviously be
applied to track a desired level if needed (with a good comprehension of
the risks that tracking market volatility entails).