< Quant View -- Investing by the Numbers -- Archives: September '07 Work in Progress

Click on Topic to Go
 


September 2007
Off Balance
A Three-Year Review of Blended Model 6

"Often the search proves more profitable than the goal."
-- E. L. Konigsburg

 

HREE-AND-A-HALF YEARS ago we thought it would be interesting to see how a quantitatively blended model of stocks and bonds would fare relative to a static benchmark. We created not one, but two combinations of indexes for comparison.

The first was a simple buy-and-hold strategy that was put in place at the model’s inception, January 1, 2004. No changes would be made to this mix. It’s pretty representative of the way many individual investors “manage” their portfolios.
Chart 1
CUMULATIVE PERFORMANCE
P6 and Benchmarks

From Inception, January 1, 2004
Graph -- P6 and Benchmarks, From Inception January 1, 2004
Data Source: S&P ComStock
For its first 2½ years, P6 maintained a slight lead over its benchmarks, but it slipped behind in mid-2006 and continued to trail on June 30, 2007.

The second was a “static” benchmark that would be periodically rebalanced back to the original blend. Rebalancing would occur on a quarterly basis whenever at least one of its components strayed more than 5% from its initial weighting.
OUR QUANT MODELS
Portfolio 3
  • Top 30 Stocks Based on Stepwise Regression Across All Stocks of the S&P 500
  • No Attempt is Made to Sector-Weight this Portfolio
  • Rebalanced Every 60 Days
  • Stocks Remain in the Portfolio Until Falling Below the Top 100
  • The Highest Rated Stocks Not Already in the Portfolio are Added When Existing Constituents are Removed
Portfolio 4
  • Top Stocks of Each Sector Based on Stepwise Regression of Each Individual Sector of the S&P 500
  • Number of Stocks Selected in Each Sector Determined by Current Sector-Weightings of the S&P 500
  • Rebalanced Every June and December
  • Stocks Remain in the Portfolio for 6 Months Unless Deleted for Special Circumstance e.g. Acquisition
  • Stocks Removed for Mergers and Acquisitions are Replaced by the Next Highest Rated Stocks in Their Specific Sector
  • Benchmark: S&P 500
Portfolio 5
  • Dynamic asset allocation model based on 9 different Growth/Value/Blend and Large/Mid/Small Cap styles as defined by Morningstar's "Stylebox"
  • Index SPDRs and iShares used to represent each component of the Stylebox
  • Stylebox sectors and weightings optimized using Ibbotson's Building Block methodology
  • Reallocated mid-first month of each calendar quarter
  • Benchmark: S&P 500
Portfolio 6
  • Dynamic asset allocation model based on 5 different stock and bond asset classes
  • Index SPDRs and iShares used to represent asset class
  • Classes are rebalanced using a mean-variance optimizing model
  • Reallocated mid-first month of each calendar quarter
  • Benchmarks: (1) Static asset allocation model: 25% Domestic Bonds, 48% Domestic Large Cap Stocks, 21% Domestic Small Cap Stocks, 6% Foreign Stocks, rebalanced quarterly
    (2) Buy-and-Hold model with same asset mix as (1), but no rebalancing.

Both benchmarks were based on what had historically been the “best” blend. To find this, we used data from 1984-2003 to create a mean-variance optimization of domestic large and small cap stocks, foreign stocks, and domestic government and corporate bonds.

The result, based on the midpoint standard deviation (risk) was a combination of 48% domestic large cap stocks, 21% domestic small cap stocks, 6% foreign stocks, and 22% government and corporate bonds. For benchmark purposes, these were represented by the S&P 500, Russell 2000, MSCI EAFE, and the Lehman Brothers Aggregate Bond Index.

Portfolio 6 is also a quantitative model. It’s rebalanced in the first month of each calendar quarter and uses exchange traded funds (ETFs) to represent each of the component series. This simplifies trading and would also minimize trading costs for anyone actually investing in the model.

All of our quantitative models are based on the assumption that once established, they won’t be materially changed for three years. This will give them an opportunity to be tested through varying market conditions and perhaps even a market cycle. With P6’s first three years now up, it’s time to review its performance and consider implementing changes if necessary.

 

A Lot of Bull
January 2004 – June 2007 was definitely not a market cycle. Although each year featured volatile periods, the entire period was best characterized as an equity bull market. Bonds didn’t fare as well with yields starting at low levels and then enduring a Federal Reserve tightening cycle. As a result, bonds actually held back performance.

Of course the same could be said for the benchmarks as well. Although P6 periodically cut back its bond exposure, the benchmarks didn’t have the option. Roughly one quarter of each was constantly invested in bonds.

That percentage holds for both benchmarks because for the majority of the period, they were the same index. They both started with the same allocation but were expected to quickly diverge when the static benchmark required rebalancing. What wasn’t anticipated was that this wouldn’t occur for almost 30 months, on April 21, 2006. Prior to that point both indexes were identical, and even though they now differ, returns have been quite similar (see Chart 1).

Nevertheless, bonds had a big influence on P6 – it never had less than 20% in the Lehman Aggregate and at times as much as 51%. Interestingly, it never put a dime in intermediate government bonds until 31% went there in May 2007.

From January 2004 through March 2005, P6 never used more than two asset classes together one, of course, being bonds. After that, it grew more diversified, never holding less than three and sometimes four. (All five were finally used simultaneously after the August 6, 2007 rebalancing, but that was outside the period monitored here ending June 30, 2007.) Small cap domestic stocks and foreign stocks received large allocations, with large cap domestic shares occasionally participating as well.
Chart 2
ANNUAL RETURNS, P6 vs. BENCHMARKS
January 1, 2004 - June 30, 2007
Graph -- Annual Returns, P6 vs. Benchmarks, January 1, 2004 - June 30, 2007
Data Source: S&P ComStock
In 2004, P6 got off to a good start versus its benchmarks, but the going has been a tougher ever since.

Chart 1 compares P6 to its two benchmarks. After getting off to an impressive start, P6 fell behind the benchmarks in early 2006. It’s been behind ever since.

Chart 2 shows the annual performance of the model, its benchmarks, and two stock indexes, the S&P 500 and Russell 2000. With the exception of its first year, 2004, P6 has failed to keep up.

Over the entire period, P6’s average annual return was about 1% less than that of its benchmarks and even more than that relative to the equity benchmarks. This is to be expected given that it always maintained such a large fixed income exposure.

Risk, on the other hand, was very consistent between the model and its benchmarks. The annualized standard deviation was the same for P6 and the Buy and Hold benchmark, and a mere 0.2% less for the Static benchmark. 

 

What Happened?
The goal was to construct an actively reoptimized model that would beat its benchmarks. While that happened in 2004, it hasn’t since, nor did it work over the entire 42-month period. What went wrong?

Actually that may be putting it a bit strongly. Perhaps nothing “went wrong” other than stocks dominated longer than is typically the case. Many market watchers and analysts called for an end to the bull market – one which never occurred. The model’s reliance on bonds was arguably a prudent thing. In addition, with the Static benchmark allocating 20-30% to bonds, the model was never that far off.

No, if there’s a problem with this model, it’s not the bonds. If anything, it’s how it moved around its equity positions.

The period January 1, 2004 through June 30, 2007 was dominated by small cap domestic stocks. Despite foreign equity’s strong performance, shares of small domestic firms did even better. You can clearly see this from Chart 3.
Chart 3
P6 Allocation Percentages
January 1, 2004 - June 30, 2007
Graph -- P6 Allocation Percentages, January 1, 2004 - June 30, 2007
P6 has made some major bets, but they've swung back and forth from quarter to quarter, often working against the model relative to its benchmarks.

Aside from aggregate bonds, small caps were the most heavily used class in P6. This is evident from Chart 5 which shows the periodic compositions of the model. There you’ll notice that small caps have been a constant component of the model ever since January of 2005.

But also notice the sawtooth pattern of the small cap holdings. One quarter they’ll be up over 50%, the next they’ll be down around 10%. Also notice how the foreign stock position is almost a mirror image, rising when small the small cap holdings are cut and falling when they hit their peaks. In January 2006, the foreign stock holdings go to zero while small caps fall to 8%. At the same time, large caps go from zero to 50%. Quantview 10-Year Anniversary, Sept. 1997 - Sept. 2007

Obviously there was a lot of equity trading going on in these quarters yet they were precisely the ones when P6 fell behind its benchmarks. Curiously, it did its best in 2004 when it was simply a combination of large cap stocks and aggregate bonds: Fewer holdings, yet more stability and better performance.

All this suggests that the model was whipsawed by short-term moves in the market. When small caps had a great month, it moved more into them. When foreign stocks led the way in the short term, it sold small caps and bought foreign. When stocks sold off in may 2006, P6 had 21% in small caps and 51% in large caps. Small caps led the recovery, but that wasn’t reflected in P6 until July 20 when all the large caps were sold and small caps were brought up to 45%. It was also after the majority of the small cap rally. Archive Index

A similar thing happened in earlier this year when riskier, more overpriced assets took a dive in late February. At that point 71% of the portfolio was divided between small cap and foreign stocks – the two riskiest alternatives. After that, small caps were trimmed back to 10% -- just in time to miss the ensuing rally.

Arguably then, it’s not the model’s algorithm that’s the problem, it’s the timing of the reallocations. Quarterly optimizations may be too frequent. We’ve noticed similar problems with P3 which is reoptimized on a bi-monthly basis.

Even so, we still feel it’s too early in the process to make a change in the rebalancing frequency. It is certainly something to keep an eye on over the next 2½ years until we again review this model for potential revisions. Somewhere in there it may encounter a bear market, something it hasn’t weathered so far. In the meantime, it will continue to be optimized each quarter.


 

E-mail your comments.

Search this site! Just enter you key word or words:

PicoSearch

Get current quotes or follow your own custom portfolio, courtesy of E-Line Financials:
 

Search:TickerName
 

 
Homepage Return to Top