Part 2 looks at how conditional rebalancing improves performance.
As I discussed in my first article, a study on
conditional rebalancing, done in 2002 by one of the young associates at
our firm using a 25% variance trigger, provided superior results
compared with calendar rebalancing or not rebalancing at all.
In early 2004, I decided to update the study by incorporating dates
through December 2003. I ran the study for a third time this year with
data that ends on March 31, 2005. In the 2002 analysis, which used data
through the end of 2001, five portfolios were selected from one
efficient frontier. This year, a more important question was first
asked, "Which efficient frontier?"
We addressed two issues identified in the first study at this point of the process:
1. Should sector funds be incorporated into this
study? Sector funds generally have a higher expected return than other
asset classes, yet their risk level (based on standard deviation) is
much higher than that of other U.S. equity asset classes.
2. Should the emerging markets asset class be
incorporated into this study? This asset class has garnered more
attention, but it has a shorter data history (December 1987) than most
other asset classes. This limited the beginning point for all
portfolios in the optimization process to this shorter data period.
Taking these issues into consideration, we
constructed five efficient frontiers using optimization software. That
approach was repeated in this study, yielding the following five
variations of efficient frontiers:
1. with emerging markets and sector funds (data beginning 12/87)
2. with emerging markets and without sector funds (data beginning 12/87)
3. without emerging markets and with sector funds (data beginning 12/87)
4. without emerging markets and with sector funds (data beginning 6/81)
5. without emerging markets or sector funds (data beginning 1/81)
The data horizon used in optimization has always
been one of those "angels on the head of a pin" issues debated among
financial planners. Here's the quandary: only a handful of asset
classes has data going back seven to eight decades. No one I know
limits client portfolios to Dow stocks, long-term government bonds and
cash. To be useful for a practitioner, the model must go well beyond
that limited menu of asset classes. Yet, when we expand our menu to
incorporate asset classes we really use, we limit the time horizon of
the data used in the calculations.
We selected the portfolio that includes both sector and emerging market
funds, although it's a toss-up whether to include emerging market funds
so long as the data period is 12/87 to 03/05.
Which Asset Classes?
Exhibit 1 lists the 22 asset classes that were used
as inputs in the construction of the optimized portfolios.
Several asset classes shared a beginning data point
in our database going back about 35 years. When government mortgages,
EAFE, European and Far East stocks, REITs and natural resource funds
were added, the beginning date jumps forward to January 1972. When one-
to three-year and one- to ten-year corporate bonds and international
bonds enter the mix, the beginning date moves to December 1979. The
addition of the S&P mid-cap index and health care funds moves the
beginning date to July 1981, and emerging market funds pushes it out to
November 1987. Where do you choose to draw the line? What asset classes
do you actually use in real portfolios?
Which Holding Period?
Exhibit 1 also shows the statistical data for both one-year and
five-year holding periods. The one-year data was more conservative,
because most asset classes generally had a lower expected return and a
much higher standard deviation. These should not be viewed as literal
holding periods; rather they are "black box opening" periods. Simply
put, if a client would view their portfolio as being placed into a
black box that they agree not to "open" for five years, we would use
those numbers. That would mean no TV, no newspapers or magazines that
have financial information, and it means that they cannot look at any
account statements or quarterly reports that have any information
shorter than a five-year time period. While this may sound good in
theory, we all know that human nature does not work that way. In
today's world, clients are constantly bombarded with data. For this
reason we focus on 12-month rolling returns as the review period for
evaluating short-term performance.
Which Portfolios?
Once the efficient frontier was chosen, five
portfolios were selected along the frontier. The portfolio with the
lowest risk was labeled "capital preservation" and the portfolio with
the greatest risk and return was labeled "aggressive growth." The other
three portfolios, labeled "income," "growth and income" and "growth,"
were selected to create a balanced spread of risk and return.
Selection of the specific asset classes was left to
the optimization software. Most asset classes were limited to 20% of
the portfolio, with the more volatile asset classes limited to 5%. The
portfolio with the least number of asset classes was ten, and the
greatest number was 13. Asset classes with the greatest negative
correlation to the dominant asset classes in a given portfolio
generally found their way into the mix. This is an area where, in
actual practice, we try to avoid the temptation of letting anecdotal
evidence or personal bias dominate our decision-making.
"It's The Losses, Stupid!"
The wisdom of this phrase became painfully clear in
our practice during the first few years of this century. You can only
encourage a client for so long with a verse from "you're beating the
market" when that means the market lost 24% and the client only lost
8%. Several consecutive years of that was tough on all of us.
When discussing a portfolio recommendation with a
client, it is tempting to focus on the expected return for a given
portfolio, but we have found it useful to start with the likely
downside return.
Exhibit 2 lists a "minimum return" for each
portfolio using a 95% confidence level. That level presumes two
standard deviations below the expected return. During the period
immediately after the first study, we saw the worst year of a
three-year, sustained decline in U.S. equity markets, which fell in the
range of a 99% confidence level or three standard deviations below the
expected return. In discussing this with clients, we equated this to
the "100-year flood" of investing.
Exhibit 3 shows, in blue, the efficient frontier.
The red line shows the expected minimum return for each discrete
portfolio along the efficient frontier. We find that this illustration
puts the information in a more understandable context for most clients.
Few understand the significance of a standard deviation of 10.10%, but
they do know what it means to lose 8.01% over a one-year period.
Using this approach, we have essentially married the
left-brain activity of portfolio construction using modern portfolio
theory with the right-brain activity of behavioral finance in our
communications process with clients. From the very beginning of the
financial planning process, we focus on the short-term (one-year)
downside of a portfolio as much as we focus on the long-term expected
rate of return. If the client cannot stomach short-term volatility, he
will never stick with the allocation and reap the long-term benefits
that lead to the realization of his hopes and dreams.
The Rebalancing Model
One drawback of portfolio optimization is that once
the portfolio is constructed, each asset class grows or declines over
the period examined without regard to target allocations. If Asset
Class A increases fourfold over a period of time, and Asset Class B
only increases by 50% over the same time, then the relative weighting
of the two asset classes will differ greatly from their original target
allocations. Here are the mechanics built into this model to try to
correct this imbalance. Since the data for the rebalancing model is
composed of monthly index pricing data, the value of each asset class
and the entire portfolio is recomputed monthly. This value is then
compared to the original target percentages. A "trigger point," such as
25%, is set as the allowed variance. If the actual allocation for any
asset class exceeds the target allocation for that asset class by the
absolute percentage of the "trigger point," then rebalancing occurs.
Trigger points ranging from 1% to 100% were used, successively. For
each trigger point, the mean, standard deviation, Sharpe ratio, the
number of rebalancings over the time period and the terminal value were
computed. The next few exhibits use the growth portfolio to demonstrate
the information contained in the model. Exhibit 4 shows the Sharpe
Ratio on the first Y-Axis, and the number of rebalancings (on the
second Y-Axis) for each trigger point for the growth portfolio. Notice
how quickly the number of rebalancings approaches zero.
In fact, while the Sharpe Ratio increases to .87 for
a trigger point of 48%, this results from only seven rebalancings over
the 17-year period. For most of us, this is too much of a "hit-or-miss"
proposal. Exhibit 5 condenses the data from Exhibit 4 to reflect
trigger points from 11% to 36%. The "sweet spot" shows up between
trigger points of 23% to 32%. These trigger points result in 13 to 24
rebalancings over the 17-year period, an average of one rebalancing
every ten to 16 months.
Since the Sharpe Ratio is computed using portfolio
return and standard deviation data, Exhibit 6 is included to
demonstrate how actual return and risk changes over this same range of
trigger points. It is interesting to note the standard deviation stays
fairly static across the range of trigger points; however the actual
returns, and resulting Sharpe Ratios, showed a noticeable increase over
the same range. This is the positive impact of conditional rebalancing.
Exhibit 7 presents the data for all methods of
rebalancing listed for the Growth portfolio. The items in blue show the
Terminal Value for the same trigger points in Exhibits 5 and 6, arrayed
by number of months between rebalancing. The items in red show the same
information for calendar rebalancing. Notice that the lowest terminal
value occurred with no rebalancing. This is the output you see from an
optimizer. While quarterly, annual and bi-annual calendar rebalancing
fell along the regression line, the more attractive results happened in
the "sweet spot" area noted earlier.
Exhibit 8 shows the "sweet spot" for the five
portfolios. In general, the trigger point range moved slightly upward
along with the level of risk. Selling too quickly or buying back into
an asset class too quickly would not have been rewarded during the
volatile market swings during the period used.
Finally, "lower volatility" does not mean "no
volatility." Exhibit 9 shows the resulting values and 12-month rolling
returns for the growth portfolio. From January 1995 until January 2000,
we had a nice upward ride. From January 2000 until October 2002 we had
a very bumpy ride. And these are the results obtained with rebalancing;
the same charts with no rebalancing look even worse.
Taxes And Transaction Costs
What, you may ask, did we do with taxes and
transaction costs? We ignored them. In today's world, transaction costs
have virtually vanished. The pricing pressure from discount brokers
during the late '90s put us in a world of $8.95 to $29.95 to trade
1,000 shares of stock. Mutual fund companies are under great pressure
to disclose, and therefore better manage, their costs. Furthermore, if
you are rebalancing only once every year or two, transaction costs no
longer have the impact they once did.
Taxes are another matter. Taxes do not attach to
each transaction. Models that treat taxes in that manner do a
disservice to their users. Taxes are only meaningful in the annual
aggregate of transactions for nonqualified portfolios. If your client
has assets held for his children in educational accounts, they may have
little or no taxation. If your client's portfolio has a substantial
portion of assets in retirement plans, most of the tax liability can be
mitigated by selling the gains inside those plans and managing the gain
and loss sales in the nonqualified plans. Further, the tax rate on
capital gains and dividends is the lowest we've seen in generations. An
accurate computation of income taxes, without more information, is
beyond the scope of this study.
Summary And Observations
With an overall 16-year data period in the first
study, two additional years of data may not intuitively seem to warrant
much change in these portfolio statistics. Yet, remember what we
experienced during 2002. First the Enron story broke, and then WorldCom
and Martha Stewart followed. By the end of March, public sentiment was
beginning a downward trend. Over the next six months the S&P 500
experienced a brutal 33% free-fall. Coming after the two previous years
of losses, this incident proved to be more than many investors could
handle. These experiences demanded better analytical tools in the
briefcase of financial planners managing investment portfolios.
Although "conclusions" may be too strong a word, three observations can be drawn from this study:
Over a long period of time any rebalancing appears better than no rebalancing.
Conditional rebalancing is generally superior to calendar rebalancing.
25% for conservative portfolios to 30% for
aggressive portfolios appear to be appropriate mid-point triggers to
initiate rebalancing.
People have asked me why conditional rebalancing
seems to work so well. It is actually common sense: It allows the
markets, not a calendar, to tell us when to rebalance. Exhibit 10 shows
the power of this tool by demonstrating how conditional rebalancing
actually would have operated during the "tech bubble." The process
would have not just let it run up and then run back down. Using a 25%
trigger, it would have been shaved six times over a five-year period
and losses would have caused you to buy back in four times over the
same period. You would have done the opposite of what your emotions
were telling you. You would have first harvested gains by selling part
of your "winner" and later bought more of what is now a "dog"-in a
disciplined fashion. That is called selling high and buying low.
This study has had a profoundly positive impact on
our practice. Once Dusty Huxford, owner of dbCAMS, our portfolio
management software, added the feature to dbCAMS that permitted us to
actually apply these principles, I didn't know whether to laugh or cry.
We had well over 20 pages of client asset classes out of tolerance the
first time we ran an exception report for our entire clientele. Yet, we
have been able to focus our time and energy on getting those exceptions
down so that today this is a much smaller, manageable number.
This study presumed a $100,000 infusion of cash in
1987 and then tracked the rebalancing of the portfolios over a 17-year
period. However, our clients' portfolios do not behave in the same
manner. They add cash, they take away cash, bonds mature, bonds move
from one class to another (long to intermediate to short), asset
classes run up and asset classes run down. Any of these actions can put
a portfolio out of balance. Having a decision rule that will help the
practitioner know which portfolios to rebalance amid all of this
activity is a piece of good fortune. I hope this study not only moves
the profession in this direction, but also inspires academicians to
carry the study forward. This would give those of us in the trenches
answers that would help us to better serve our clients.
