A different approach to portfolio construction.

By Joel Bruckenstein

Most financial advisors have a decent grasp of
portfolio construction and asset allocation. They know that Harry
Markowitz started the ball rolling with his 1952 academic paper
entitled Portfolio Selection, and that 38 years later he was awarded a
Nobel Prize, along with Merton Miller and William Sharpe for, their
work on what is now known as Modern Portfolio Theory.

Essentially, Markowitz argued that risk/return
characteristics should be evaluated at the portfolio level, not the
individual security level. Using volatility as a proxy for risk, and
expected returns as a return component, Markowitz illustrated how an
efficient frontier can be graphed if one knows the correlations between
the asset classes.

The efficient frontier is a set of optimal
portfolios. Theoretically, all are equally efficient. So how do we, as
advisors, decide which one to use with clients? Well, suppose a couple
engages you to determine how much money they need to accumulate for
retirement. Given their assets and their ability to save, you determine
that they must achieve a 9% nominal rate of return on their assets and
their savings to reach their goal.

Under this scenario, the clients might choose to
select a portfolio with the required anticipated return along the
efficient frontier. This will offer them the portfolio(s) that can
deliver the return they need with the least amount of risk.

Another common use of the efficient frontier is for
advisors to first evaluate a client's tolerance for risk, and then
select a portfolio on the efficient frontier that coincides with the
client's risk tolerance. In this case, the advisor is looking for the
greatest achievable level of return available at a given risk level.

The two examples above are flip sides of the same
coin. In the first instance, we are supplying a required rate of
return, and the model is telling us the "optimal" or lowest level of
risk we need to take in order to achieve that return In the second
instance, we are supplying the level of risk we are willing to take,
and the model supplies us with the highest possible return we can
achieve for that level of risk.

Gravity Investments, LLC, a firm that specializes in
something they call "Diversification Intelligence," has built a
software application called G-sphere that attempts to extend the
utility of the efficient frontier for advisors and their clients.
Rather than presenting the whole efficient frontier and leaving it to
advisors to select the "right" portfolio along the frontier, G-sphere
is designed to pinpoint the "best" efficient portfolio residing on the
frontier.

The G-Sphere approach is built upon the same
foundations as the traditional approach to portfolio optimization, but
it adds some unique ingredients to the mix. First, it starts by
optimizing for diversification, and then it adjusts the asset
weightings to account for the differences in attractiveness of the
various asset classes. A utility factor, in this case the Sharpe ratio,
is used to measure an asset's relative attractiveness. This differs
from the traditional approach in that it seeks to explicitly quantify
diversification.

Under the G-Sphere methodology, rather than arriving
at a continuum of efficient portfolios (the efficient frontier), the
software will solve for a single efficient portfolio on the frontier,
one that maximizes the benefits of diversification while providing
acceptable returns (as illustrated in Figure 1).

Another unique aspect of the software is the three
dimensional modeling approach it takes. All assets are plotted from a
starting point. The starting point is the risk-free rate of return,
represented here as Cash (see Figure 2). Advisors set their own
risk-free rate of return assumptions (the expected return on cash).

The various assets are depicted in Figure 2 as lines
extending out from the cash starting point. The length of the line
graphically represents the Sharpe ratio. The longer the line, the
higher the Sharpe ratio; so in Figure 2 MID has a higher Sharpe ratio
than GI.

The angle between the assets indicates their correlations. An acute
angle represents a high correlation. The greater the angle, the lower
the correlation. A 90-degree angle represents no correlation. A
180-degree angle represents a negative one, or perfectly uncorrelated
asset.

In this illustration, for example, MID shows a very
high correlation with MB, but it appears uncorrelated with SPX.

All of this sounds complicated, and the math behind it is, but essentially, what G-sphere provides that differentiates it from other software is a three-dimensional graphical depiction of the portfolio that equates portfolio diversification with symmetry. The size and shape of the portfolio indicate the anticipated risk-adjusted return of the portfolio. While the traditional efficient frontier graph only depicts risk and return, the G-sphere 3D model also displays correlations among the assets clearly. Under this methodology a large, symmetrical shape represents a "good" portfolio.

Now that we've summarized the underpinnings of the model (full details
are available at www.gravityinvestments.com) let's turn our attention
to the software itself. The list price of G-sphere is about $4,500 per
year. This includes the software as well as the data that supports it.
When you subscribe to G-Sphere, is comes with a full set of data on
U.S. and Canadian equities, U.S. and Canadian mutual funds (open end,
closed end and ETF's) and futures data. The numbers are updated
regularly, and advisors have access to that data through an Internet
connection to the Gravity servers.

Once the software is installed, you can create individual client
portfolios or model portfolios. The first step is to name a portfolio
and create a type (model or client, for example), select a home
currency and add comments as necessary. Next, you type in the portfolio
assets or import them from a spreadsheet. You can enter ticker symbol
and a number of shares, or you can enter a value, and the software will
calculate the number of shares based upon the current price. If all of
the holdings are equally weighted, you can just type them in and then
tell the software to weight them equally. If you wish to place any
constraints on the optimization process, you can enter the constraints
here.

The next step is to enter the time series you want to use to examine
the data. You can choose a single series, or multiple series, and you
can weight them to your liking; you can even use different intervals
for different time periods. For example, if you wanted to use a time
series for 2004, 2005 and 2006, you could use monthly data for 2004,
weekly data for 2005 and daily data for 2006. In a case where an asset
has a limited data set, the software can extrapolate the data over a
longer time period if you want it to.

Next, you can condition the data. If you want you use a historical benchmark for comparison, you might first run an unconditioned portfolio. Then, you could run the same one using tools to shrink the range of returns or range of risk. You also can run the model using more than one measure of risk. Standard deviation is the traditional measure of risk, but advisors can also choose semivariance and maximum drawdown as a measure of risk. Semivariance represents standard deviation with respect only to adverse price changes, as opposed to standard deviation, which makes no distinction between good (price appreciation) and bad (price depreciation) volatility.

Maximum drawdown is designed to look at the worst-case scenario. It answers the question: "What if an investor bought the portfolio at a market peak and held it for a period of time through a bad decline, selling at the bottom; how much of the portfolio would be left?" The software even allows you to alter the cross-correlations for a time series, overriding the historical data for that period.

Next, you would run the optimizer and analyze the results. If the results are satisfactory, your work is almost done; if not, you might want to make some changes to the assumptions, or run multiple scenarios, using different measures of risk, different time series, etc. Analytical tools allow the advisor to view all of the portfolio statistics commonly taken into account (portfolio rate of return, Sharpe ratio, etc.) as well as some less familiar ones like Inter-Portfolio Correlation (IPC). This number, a measure of diversification usually presented as a range between 1 and -1, is converted into a percentage for easier viewing here. According to Michael Kerins, regional sales director at Gravity: "The typical advisor-constructed portfolio we see generally starts off with an IPC of 15% to 25%. Through the use of G-Sphere, advisors can boost that number to anywhere between 35% to 60%."

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