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

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March 2007
Stock Parts
Portfolio 6's Equity Management

"The stability of the whole is guaranteed by the instability of its parts."
-- Karin Meißenburg

 

IMING MATTERS, AT LEAST IN THE short term. If you need proof, look no further than quantitative Portfolios 3 and 4. These unfortunate growth models were launched on July 1, 2000, just as the equity bear market was getting under way. After 6½ years, P4 was still off 16.9% while P3 was down 46.8%. Things would have been a lot different had the launch been delayed by only two years (+56.9% and +65.2%, respectively).

Quantitative Portfolio 6 also suffers from poor timing. Launched at the start of 2004, it's a balanced portfolio with bonds as well as stocks. Unlike P3 and P4, it's based on exchange traded funds (ETFs) instead of individual stocks. This provides greater diversification potential than simply the combination of stocks and bonds.
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.

Although the bonds distinguish P6 from the other models, they're also the source of the bad timing. Bonds enjoyed a prolonged bull market as equities languished at the start of the decade. But as stocks recovered, bonds fell off -- just about the time P6 came into being. Archive Index

Through December 31, 2006, P6 was up 21.0%. That sounds pretty good until you realize that a similarly constituted buy-and-hold portfolio was up 24.7% over the same period. That suggests P6's dynamic approach didn't add any value or even worse, may have hurt.

But that may be too harsh. Could the problem simply lie in P6's allocation between stocks and bonds? Would it have been better off without the bonds?

 

Simply Stocks
P6 has five potential holdings represented by their iShares ETF proxies: the Lehman Brothers Intermediate Government Index, the Lehman Brothers Aggregate Bond Index, the S&P 500 Index, the Russell 2000 Index, and the MSCI EAFE Index.

In its 6½ years, P6 has never held intermediate government bonds. On the other hand, it's always had an aggregate bond component. What if it didn't?

To test that, we looked back at each quarterly allocation but without the bonds. In essence, this was an examination of the effectiveness of P6's equity allocations.

For comparison purposes, it was also necessary to adjust P6's blended benchmark to eliminate the bond element.

Actually, P6 has two blended benchmarks. The first is the buy-and-hold blend which started as 20% aggregate bonds, 49% S&P 500, 24% Russell 2000, and 8% MSCI EAFE. As a buy-and-hold benchmark, it's never rebalanced.

The second benchmark started out like the buy-and-hold, but was designed to be rebalanced in any quarter whenever any component was more than 5% off of its original allocation. This didn't occur until April 2006. On December 31, 2006, the static benchmark was 24% aggregate bonds, 49% S&P 500, 20% Russell 2000, and 6% MSCI EAFE.

Interestingly, when we stripped the bond element out of the original blend, the static benchmark never came into existence. At no point did any of the equity components ever stray more than 5% from their original weight. For the record, the largest drift was 2.6%. As a result, there was only one benchmark for this test.

 

Clear Winner?
The measurement period was the same as for P6: January 1, 2004 through December 31, 2006. Over that period, P6 had a total return of 21.8% and trailed the buy-and-hold benchmark by 3.7%.
Chart 1
CUMULATIVE EQUITY RETURNS
P6 vs. BUY and HOLD BENCHMARK

January 2004 - December 2006
Graph -- Cumulative Equity Returns, P6 and Buy & Hold Benchmark, 1/2004 - 12/2006
Source: S&P ComStock
The equities of P6 and their buy-and-hold benchmark moved together from 2004-2005. After that, however, P6's moved out well ahead.

Given how poorly bonds performed over the measurement period, both P6's and the buy-and-hold model's equities fared much better. The benchmark was up 33.7% while P6 climbed a cumulative 45.8%.

The two series actually moved in tandem for most of the first two years of the period. In late 2005, however, P6 moved ahead and never looked back. By the end of 2006 it was ahead by 12.1%. Over that same period, P6 -- with its fixed income -- trailed the benchmark by 5.7%.

Can you conclude anything from all this? Statistics may not bear it out, but it's hard not to intuitively conclude that P6's travails are mostly (if not totally) attributable to the bond component. After all, if P6's equities handily outpaced those of the benchmark, how could they be responsible for the model's overall weakness?

What you can't conclude is that P6's equity selection process is superior to the buy-and-hold approach of the benchmark. In both cases, the equity allocation doesn't stand alone, it's all part of the overall allocation between both stocks and bonds.

In regard to the benchmark, the equity component represents what worked best in the past along with the bonds. Put differently, had the benchmark had no bond component, the equity mix could, and probably would be different. The same holds for P6's various allocations.

In actual practice, you can't simply strip out a component of an optimization process and expect to come up with the same optimal blend of the remaining components. The process is based on three elements of each component: risk, return, and correlation. It's the absence of that latter element that will change the mix.

Specifically in the case of P6, the model has always included bonds not only because of their expected risk and return, but because of the way they correlate with the equity components. As you'd expect, bonds tend to have lower correlations with stocks series than do other stock series.

One of the benefits of the mean-variance optimization process is that by combining risky but non-highly correlated asset classes, you can control risk while potentially boosting overall portfolio return. So for P6, the inclusion of a bond weighting may have allowed a greater proportion of the equities to be allocated to riskier stocks (small or foreign). But if bonds -- and their low correlations with riskier equity classes -- weren't an option in the optimization process, the resulting all-equity mix could (and probably would) have had a higher allocation to the "safer" equity classes (large cap domestic stocks).

As a result, the foregoing analysis while interesting, isn't statistically sound. By simply studying the returns of the stock allocations that were created with bonds in the optimization, we're really not looking at what would have happened had bonds not been an option. To truly do that, we'd have to go back to each period and rerun the optimization process excluding bonds. That would be an interesting study, but it really wouldn't answer the questions posed here.

A review of the portfolio analytics can show which component is doing well and which isn't. Here the equities have clearly outperformed for both the model and benchmark. Yet both are blends of the two components and in that regard, the benchmark has clearly outperformed. In the end, that's what really matters.

P6 is unique in comparison to the other five models because it incorporates fixed income as well as equities. Ironically, that's also why it trails its benchmark.


 

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