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.
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.