Quant View -- Investing by the Numbers -- Archives: March '06 Work in Progress

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March 2006
Past as Prologue
Backtesting P6's Benchmarks

"Statistics: The only science that enables different experts using the same figures to draw different conclusions."
-- Evan Esar (1899 - 1995)

 

UANTITATIVE PORTFOLIO 6 WAS launched a little over two years ago, effective January 1, 2004. As a balanced portfolio with both stocks and bonds, a pure equity or bond index wouldn't be the appropriate benchmark. Instead, it needed a "blended" benchmark -- in fact it got two.

The first simply mimics the way a lot of investors handle their own portfolios: It's just buy-and-hold. When we considered returns from 1979 - 2003 we found that 25% corporate bonds, 48% domestic large cap equities, 21% domestic small cap equities, and 6% foreign stocks would have been the "best" mix. This was adopted as the buy-and-hold benchmark.
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 I-Shares 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 I-Shares 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.

As time passes, however, this initial "best" mix will give way to other changing combinations. As soon as the underlying assets begin to trade, the initial mix is altered. Presumably, it should be necessary to periodically rebalance back to the original mix to capture optimal performance. That's P6's second, or "static", benchmark.

Oddly enough, in the two-plus years that P6 has been out of sample, the two benchmarks have never strayed more than 5% -- the trigger we set for rebalancing -- from the original allocation. As a result, the two remain identical, something we clearly did not anticipate.
Chart 1
BUY-AND-HOLD AND STATIC BENCHMARKS
January 1979 - December 2003
Graph -- Buy-and-Hold and Static Benchmarks, Cumulative Returns, January 1, 1979 - December 31, 2003
Source: Ibbotson Associates
Although they look quite similar, the "static" or rebalanced mix was a little over 8% ahead of the buy-and-hold approach. The biggest differences occurred when stocks ran up in the late-1990s and again in the bear market of 2001 and 2002.

Is this normal or is this just the result of a relatively trendless market? One way to address this question is to observe the same mixes in the time before P6 came into being. Did both benchmarks behave the same then?

 

Similar But Different
To test this, we considered the 25 years prior to the launch of P6. This covered the period January 1, 1979 - December 31, 2003. Both benchmarks started with the 25/48/21/6 mix of domestic government bonds, 48% domestic large cap equities, 21% domestic small cap equities, and 6% foreign stocks. The same trading rule held, an asset class must move by 5% or more before it would be reallocated.

The results are illustrated by Chart 1's cumulative return graph. Despite appearing to track almost identically, the reallocated benchmark actually managed to beat out the buy-and-hold approach. After the full 25 years, a dollar invested in the rebalanced benchmark would have grown to $17.89 while it would only be worth $16.55 in a buy-and-hold scenario.  That's a difference of 8.1%.

This review doesn't reveal when the first rebalancing would have occurred or how frequently thereafter, yet the difference in cumulative return suggests rebalancing did occur.

Just looking at Chart 1, it would appear the buy-and-hold mix followed stocks up in the late-1990s while the other was rebalanced. This makes sense given that domestic large cap stocks were far and away the major market winners.

The exact opposite occurred in 2001 and 2002 as stocks plunged and rebalancing allowed the static benchmark to regain the lead over the buy-and-hold mix.
Chart 2
BUY-AND-HOLD AND STATIC BENCHMARKS
Five-Year Period Returns
Graph -- Buy-and-Hold and Static Benchmarks, Five-Year Period Returns, January 1, 1979 - December 31, 2003
Data Source: Ibbotson Associates
Except for the 1990's stock market bubble, rebalancing in the static approach enabled it to outperform the buy-and hold strategy in four of the five-year periods.

You can clearly see this from Chart 2. Here we've divided the 25 years up into 5-year periods. In three of the five, the rebalanced mix leads the buy-and-hold strategy, and the fourth is basically a push. In the fifth, however, it trails badly.

That's no surprise since stocks were running from January 1994 through December 1998. Every time the static mix rebalanced, it sold high-performing stocks for low-performing bonds. In this case, rebalancing caused it to fall behind.

Even so, looking back at Chart 1, you'll notice the static mix didn't fall behind its counterpart until the late-1990s. In essence, it took that long for the latter to overcome the lead established in the earlier periods. Rebalancing helped then, and again when stocks stumbled in the early part of this decade.

Although it's hard to tell from Chart 1, rebalancing must have occurred in each of the 5-year periods or else the returns would not have differed to such an extent in each period. Not only did rebalancing occur, it really made a difference. This is exactly what Modern Portfolio Theory predicts.

Also as predicted, the static mix is more efficient than buy-and-hold. This is illustrated on Chart 3 which plots the benchmarks as well as their constituent indexes in risk/return space. Here both have roughly the same return but the static mix has less risk. As a result, its risk-adjusted return is higher.

So in the past, these two approaches have had textbook results. Asset allocation actually prevailed over simple buy-and-hold. But what about now?
Chart 3
BENCHMARKS AND INDEXES, RISK AND RETURN
January 1979 - December 2003
Graph -- Buy-and-Hold, Static Benchmark, and Major Indexes, Risk and Return Scatterplot, January 1979 - December 2003
Source: Ibbotson Associates
Over the 25 years ending December 2003, the static and buy-and-hold mixes had roughly the same return, yet the former had a lower standard deviation. In other words, the static benchmark had better risk-adjusted return, just as Modern Portfolio Theory would predict.

 

Recent Past
It's not been five years since the launch of Portfolio 6 and the two benchmarks. Instead, it's only been a little over two. As of March 2006, however, the static mix hasn't moved far enough away from its initial target to be rebalanced -- yet.

That's not to say the buy-and-hold mix hasn't begun to stray. As you'd expect, that started in its first few months.

As you probably recall, stocks reawakened in 2003 with small caps taking the lead. The Russell 2000 was up 17% in 2004 and just over 3% in 2005. Bonds, on the other hand, have been flat to slightly down, victims of the Fed's tightening policy.

By December 2005, bonds had fallen from the initial 25% to 21% of P6's benchmark mix. Had they fallen just one percent more, the first rebalancing would have occurred and the two benchmarks would have started 2006 moving independently Archive Index

Instead, small stocks faltered briefly as the year got underway, allowing the bond position to move back to 22%. By mid-February, however, fears of rising inflation and a prolonged monetary tightening again sent them back down to 21%.

Even if bonds continue to decline as a percentage of the benchmark, no rebalancing will occur until P6 is reoptimized. This will occur in the first few weeks of the second quarter. If markets continue their current trend, the benchmarks could easily diverge in April.

It's not an issue of if the two benchmarks will separate, it's simply a question of when. Chart 2 clearly illustrates how differently the mixes behaved in the past. There's no reason to believe they won't -- and in fact there's every reason to believe they will -- act in the same manner over the next 25 years.


 

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