By
Paul
Allen
:
In recent years, new portfolio construction techniques focused
on risk and diversification rather than expected average returns
have become quite popular. This success has been due to an
increasing acknowledgment that a traditional balanced portfolio,
where 60 percent is allocated in equities and the remaining 40
percent is invested in bonds, is not diversified at all. It may
look balanced from a capital allocation point of view, but it is
not from a risk perspective, as equities are the main risk
contributor within such a portfolio. After we have already written
about the
risk parity approach
in our last article, we would like to review a portfolio
construction technique, called "Maximum Diversification," which has
shown incredible results so far and which is being updated on a
regular basis on our
website
.
The basic idea behind the maximum diversification approach is to
construct a portfolio that maximizes the benefits from
diversification. First of all, diversification can be measured by
the so-called diversification ratio. This ratio is the portfolio's
weighted average asset volatility to its actual volatility. The
result of this calculation measures the essence of diversification.
Since different asset classes are not perfectly correlated to each
other, this ratio in general > 1. In other words, a
well-diversified portfolio is greater than the sum of its
investments, as the overall risk of such a portfolio is less than
the weighted-average risk of its component holdings. Therefore,
every investor can measure the degree of diversification within its
portfolio quite easily, with the following metric:
(wi = portfolio weight in asset i, σi = the risk of asset i, σp
is the total risk of the portfolio)
Moreover, for a given set of underlying assets, there is only
one portfolio combination that has the highest diversification
ratio and thus represents the most diversified portfolio. In other
words, it is possible to put the maximum weight into each asset
class whereas the overall portfolio volatility is not being
increased at all.
In our article, we would like to review a maximum
diversification portfolio with the following investment
universe:
- Vanguard Total Stock Market ETF (
VTI
)
- Vanguard MSCI Europe ETF (
VGK
)
- Vanguard MSCI Emerging Markets ETF (
VWO
)
- SPDR Gold Shares ETF (
GLD
)
- Vanguard REIT Index ETF (
VNQ
)
- iShares Barclays TIPS Bond ETF (TIP)
- Shares Barclays 20+ Year Treasury Bond ETF (TLT)
- Shares Barclays Aggregate Bond ETF (AGG)
- Shares iBoxx $ Invest Grade Corp. Bond ETF (LQD)
In our example, there is no allowance for transaction costs or
brokerage fees. In order to minimize transaction costs, we
rebalance the portfolio on a monthly basis, whereas 1-day slippage
is included. By applying the maximum diversification approach, it
is absolute necessary to determine the weightings of each asset
class on a regular basis, since the correlation among asset classes
is not stable over time. We have used a rolling
variance/co-variance matrix to determine the optimal
diversification weights.
If we have a look at the diversification benefits this portfolio
has utilized in the past (Chart 1), we can see that the
diversification ratio reached a maximum score of 6, meaning that
the overall portfolio risk was reduced by 500 percent. In this
specific time period, the correlation among the underlying asset
classes was extremely low. On average, the overall risk (Chart 1)
within the portfolio was reduced by a factor of 2.7, while the
minimum diversification factor had been 1.5 in September 2006.
Apart from 2008, where the financial crisis hit the markets, the
portfolio volatility itself swung between 2 and 9 percent, whereas
the average volatility is around 5.5 percent. Since it is possible
to put the most weight to each underlying asset class without
increasing the total portfolio volatility, the expected returns of
each security and thus the expected return of the portfolio remains
unchanged.
(click to enlarge)
(Chart 1)
Another interesting fact is that the weighting of each asset
class (Chart 2) is mainly driven by its diversification
characteristic. In other words, if the correlation coefficient of
an underlying security increases, the less weighting it will
receive, since its diversification benefits are decreasing
(according to the diversification factor). Therefore it can be
possible, that certain high correlated securities will have no
weight at all, or the other way round. As a result of this, it can
be theoretically possible, that equities have a higher weighting
than bonds, in times when the correlation coefficient of stocks to
the overall portfolio tends to be lower than bonds. That is one of
the main advantages versus the risk parity approach, where every
asset class has the same contribution risk, whatever the
correlation of those looks like! Another main advantage of this
"All Weather Portfolio" over a risk parity strategy is the fact
that it does not need leverage to achieve an attractive return
profile.
(click to enlarge)
(Chart 2)
Since we have only focused on risk and portfolio weightings so
far, we would like to examine how this portfolio has performed so
far versus the S&P 500 (IVV). Table 1 is showing the results
from December. 16, 2005 until Nov. 11, 2012 (including one day
slippage). The first column tests the maximum diversification
approach while the second on represents the S&P 500.
The maximum diversification approach has an annualized return of
10.6% while the S&P 500 (IVV) has only generated an annualized
rate of return of 3.2%. More importantly, on a risk-adjusted basis
(Sharpe Ratio), this "All Weather Portfolio" is strongly
outperforming the broad benchmark. However, it was only slightly
underperforming the S&P 500 (IVV), when equity markets have
been in a strong bull market (2006).
(click to enlarge)
If we have a closer look on the diversification benefits
(reducing risk during turbulent market conditions), we can see that
this amazing portfolio construction approach has also shown
significant lower draw-downs in the past. The maximum draw down for
the so called "All Weather Portfolio" was only 15.6 percent,
compared with 56.2 percent for the S&P 500 (IVV) [Chart 3 &
Chart 4]. That makes roughly 3.5 times more. In total, the maximum
diversification portfolio was reaching a new high after 76 weeks
while the S&P 500 (IVV) is still struggling to reach its latest
high in 2007.
(click to enlarge)
(Chart 3)
(click to enlarge)
(Chart 4)
The bottom line:
the maximum diversification approach is a perfect tool if investors
who are searching for a highly diversified portfolio, which tends
to perform reasonably well in every market environment. Since it
can fully utilize the benefits of diversification, so then the
portfolio is able to reduce draw-downs considerably, especially in
times of market turbulence. Therefore this asset allocation
approach is perfectly suitable for investors who are searching for
compound returns instead of a strategy that tries to capture every
gain when equity markets are strong. Nevertheless, the outcome of
the strategy depends mainly on chosen asset classes, as this
investment strategy allocates the most to those
ETFs
that have the lowest correlation coefficient. Therefore please bear
in mind that any approach is only as good as the expected future
value of its underlying asset classes as well as their future
diversification characteristics.
Disclosure:
I have no positions in any stocks mentioned, and no plans to
initiate any positions within the next 72 hours. I wrote this
article myself, and it expresses my own opinions. I am not
receiving compensation for it. I have no business relationship with
any company whose stock is mentioned in this article.
See also
The Fed Prints More Money, The Gold Price Falls.
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on seekingalpha.com