Quant View -- Investing by the Numbers -- Archives: September '11 Work in Progress

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September 2011
Theory vs. Reality
Are the Benefits of Asset Allocation Oversold?
“In theory, there is no difference between theory and practice; In practice, there is.”
-- Chuck Reid

 

OMETIMES INVESTORS OUT THINK themselves. A prime example is asset allocation. For the past two decades, a misinterpretation of a seminal study has led many to believe that asset allocation explains over 90% of investment return when in reality, the study showed it explained over 90% of the variation in investment return. As a result of this misunderstanding, investors often focus on maintaining their portfolio's specific asset allocation. In many instances, this requires them to constantly readjust the mix to keep within their desired boundaries.
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.

It seems to make sense given that portfolio return stems from three sources: (1) asset allocation, (2) specific investment holdings, and (3) market timing. Individual assets tend to trade in tandem with their overall market sector, diminishing the importance of specific holding selection. Market timing rarely pays off, particularly for smaller investors, so a steady asset allocation across all market conditions would seem to be the most logical approach. This, of course, only leaves the asset allocation as the investor's primary decision.

But how much impact does asset allocation really have on a well-constructed portfolio? Certainly it doesn't explain that 90% of return, but is its effect really all that significant?

Quantitative Portfolio 6 provides an excellent case study. When it was introduced in May of 2004, it came with a primer on asset allocation. This was necessary because P6 was created as a trading model, so it only made sense to compare it to a buy-and-hold as well as a static asset allocation approach. To do this, we not only created the active dynamic allocation model (P6) but also a buy-and-hold benchmark and one balanced back to the initial static allocation. Now that they've all been around for over seven and half years, we can draw some conclusions about the benefits of the different forms of asset allocation we've been comparing.

 

The Three Alternatives -- The Details
Portfolio 6 is a quantitative model with potential investments in the U.S. and abroad, equity and fixed income. It's based on exchange traded funds (ETFs) representing only five asset classes: (1) U.S. Intermediate Term Government Fixed Income, (2) U.S. Aggregate Bonds, (3) U.S. Large Cap Stocks, (4) U.S. Small Cap Stocks, and (5) Foreign Developed Country Stocks (for more information, see the sidebar at right or click here). The model is reoptimized/balanced every quarter and there are no limits on the number of holdings it must utilize or the degree of change from quarter to quarter. This is an example of dynamic asset allocation.

Because it's a blend of not only stock but bond indexes, a simple, single class index like the S&P 500 or Aggregate Bond Index wouldn't be an appropriate benchmark. That's why we created two blended benchmarks distinguished by -- you guessed it -- their asset allocation policy. The first was a straight-forward "buy and hold" approach. This benchmark started out with P6's initial allocation (25% bonds, 48% large cap stocks, 21% small cap stocks, and 6% foreign stocks) and would never be rebalanced, just like a typical buy-and-hold investor would do. (P6's initial allocation was based on historical performance from the period 1979-2003.)

The second benchmark uses static asset allocation. As the various asset classes diverge through daily trading, it's rebalanced back to the original mix when at least least one asset class strays more than 5% from its initial allocation. This rebalancing rule limits the number of trades by not requiring any action if the change in allocation is not significant. It should also distinguish this benchmark from its buy-and-hold counterpart which is never rebalanced. Archive Index

Static asset allocation is typically advocated by financial planners as well as endowments or foundations with investment policy statements. It works best in a generally trendless market because its rebalancing forces the investor to take profits form the appreciated assets and purchase those which have underperformed. It won't work so well in a trending market but dynamic asset allocation (as is used in P6) will. Instead of periodically reducing the allocation to the trending asset, it allows the investor to actually increase its allocation. This is the most aggressive form of asset allocation because it amounts to "market timing" which many doubt can be done successfully over the long term. That's why many investors simply throw up their hands and stick with the buy-and-hold approach which is something of a middle ground. While it allows them to enjoy all the benefits of a trending market, it also subjects them to increased losses when the market reverses.

From January 2004 through June 2011 the markets experienced a number of different trends. The initial years showed strong growth until 2007 when the credit crisis erupted. Stocks fell sharply in 2008 but showed steady improvement through the remainder of the period. Interestingly, emerging market and commodity investments performed the best across all years, yet these classes were not represented in the model portfolio or either of its benchmarks.

By theory alone, one might have expected P6's dynamic approach would have had the advantage in the upward trending years. In addition, because the trend lasted so long, the buy-and-hold approach would be expected to outperform the static benchmark as long as 2008's declines weren't so severe as to wipe out the prior years' advantage. This is the order we expected to see in the returns.

 

Several Surprises
Some of the results went exactly had expected. For example, the order of the cumulative returns (see Chart 1, below) were right in line with predictions. P6's active allocation allowed it to definitively take the lead over the benchmarks in late 2007 as stocks declined toward their lowest point. This was because P6 increased fixed income holdings and shifted out of U.S. stocks. When stocks rallied, it moved back into stocks, focusing most heavily on foreign holdings. This allowed it to take advantage of changing market conditions.
Chart 1
CUMULATIVE PRICE RETURNS
Growth of $1
January 1, 2000- June 30, 2011
Graph -- P6, Static, and Buy-and-Hold Benchmarks, Cumulative Price Returns, January 1, 2000- June 30, 2011
Data Source: Ibbotson Associates and Quantview
P6 moved ahead of its benchmarks in late 2007 and has maintained the lead ever since. The "benchmarks" were actually one benchmark until they finally parted ways in April 2004. Since then, the static benchmark has only required rebalancing three other times.

Earlier in the period, P6 struggled with it's benchmarks. Although stocks were experienced a mild uptrend, P6 was dramatically overweighing -- particularly foreign stocks -- over fixed income alternatives. The other benchmarks were holding their own as their investment mix was remaining relatively steady.

And that steady asset mix is responsible for the first surprise: The static and buy and hold benchmarks were one in the same. This occurred because the static benchmark never required rebalancing until April 2006, two and quarter years after inception. It was only at that point that one of its asset classes (Aggregate Bonds) strayed more than 5% from its initial level. Few would have expected that, especially with so few holdings in the portfolio.

Things haven't changed all that much since then, either. The static benchmark has only had to be rebalanced three more times in the last five years. That covers the credit crisis, the strong equity rally in its aftermath, this year's sharp decline, and bond yields at historic lows. Again, this was not expected.

The fact that so little rebalancing was required also helps explain not only why the two benchmarks tracked so closely, but why their returns didn't differ significantly from P6's. Over the entire period, the annual arithmetic returns differed by less than 0.7%, geometric by less than 0.9%. Over the entire measurement period, P6 gained about 4.5% more than the static benchmark, and 8.5% more than the buy and hold.

At first it might seem like the similarity of returns -- at least between P6 and the two benchmarks -- is also surprising, but actually it shouldn't be. To see why, consider Chart 2 which simply adds the cumulative returns of the constituent asset classes to Chart 1. (In addition, it also includes returns for Morningstar's Moderate Allocation Category, which is defined as 60% equity, 40% bonds and cash.) Small domestic stocks and foreign stocks outperformed P6, but domestic large cap stocks, and bonds trailed. Even with these additional series, returns are closely grouped. That's the result of the volatility over the period.
Chart 2
CUMULATIVE PRICE RETURNS
Growth of $1
January 1, 2000- June 30, 2011
Graph -- P6 and Various Market Benchmarks, Cumulative Price Returns, January 1, 2000- June 30, 2011
Data Source: Ibbotson Associates and Quantview
Stocks did better than P6, bonds did worse. Interestingly, Morningstar's Moderate Allocation Category Average also outperformed the model.

The blended mixes fall between the best and worst performing asset classes. That's what would be expected from blended allocations. No surprise here. That is, of course, unless you consider the fact P6 was bested by the average Moderate Allocation fund. If nothing else, that's a little discouraging.

 

Then There's Risk
Of course it's possible those Moderate Allocation funds assumed more risk so would be expected to have higher returns. Chart 3, the risk and return scatter plot for the period, covers this. As it turns out, the average Moderate Allocation fund (inside blue oval on Chart 3)actually carried slightly less Standard Deviation than P6 (13.3 vs. 13.4, respectively). When this is coupled with the fund's higher return, the average Moderate Allocation fund also has a slightly higher Sharpe Ratio (0.1362 vs. 0.1016).

Things are a little different if you focus only on the downside risk. This is our preferred means of evaluation because most investors are only concerned about downside risk and losses in particular. So, based on the Semi-Standard Deviation below 0% (in other words, losses), P6 looks a little better, 8.1% vs. 8.5% for the average Moderate Allocation Fund. This is likely the result of the higher equity level maintained in the funds. At various times during the measurement period, P6 held considerably more than 40% in bonds which helped limit its losses in 2007-2008.

As far as its two benchmarks, both had higher Standard Deviations (12.9% for the static and 13.1% for the buy and hold) as well as higher Semi-Standard Deviations (9.6% and 9.9%, respectively). Again there's no surprise here given their allocations remained relatively fixed with around 75% in stocks. Their Sharpe Ratios were also lower due to that increased risk and lower returns (0.905 and 0.0801, respectively).

Overall, the risk and return for P6 and its benchmarks is in line with expectations. All three were quite similar as illustrated by their tight grouping in the risk/return space of Chart 3. There, the increase in risk and return is almost linear as you move from the relative safety of U.S. bonds to aggressive small cap stocks. Once again, as blends, P6 and its benchmarks would be expected to fall in the middle and that's exactly what they do.
Chart 3
RISK AND RETURN
P6 and Market Benchmarks
January 1, 2000- June 30, 2011
Graph -- P6 and Market Benchmarks, Risk and Return, January 1, 2000- June 30, 2011
Data Source: Ibbotson Associates and Quantview
P6 and its benchmarks were just about where you'd expect them to be in regard to risk and return: Less than stocks, more than bonds.

 

Two Unexpected Results
It's gratifying to see P6 out ahead of its benchmarks and it's equally encouraging to see not only better price return but also lower risk in the process. Ultimately, these results were the purpose in developing the model. Beating the benchmark -- in this case, the benchmarks is always the goal of relative return investing.

From a broader perspective, however, there are two, somewhat less expected things to note. First, one could reasonably classify P6 as a "moderate allocation", and as such, it would be equally reasonable to compare its performance to the average Moderate Allocation fund. In that sense, P6 is a disappointment, at least for its lower return. It's an insult if a quant model can't beat the average fund manager in virtually any category.

Before accepting defeat, it is worthy to note that in this instance P6 and Morningstar's category return are not on equal footing. We only track price return (capital appreciation) for our models which is why you may have noticed all the accompanying charts use benchmarks based on price return -- with the exception of the Moderate Allocation funds. We did not have access to a price return only version of this series so unlike the others, yield -- and compounding yield -- are also included in it. Currently Morningstar reports over 40% of the average fund is invested in bonds and cash instruments. Even with rates as low are they currently are, this still works to increase return. Also, as mentioned earlier, P6 utilized high levels of fixed income in 2007 and 2008, but the beneficial results of that are not reflected in the returns. So although the data here can't prove P6 beat the average Moderate Allocation fund, if nothing else, the difference between the two is overstated by the effects of the funds' yield.

The second point to note regards the impact of the model's and benchmarks' asset allocations. In this case, it might be more accurate to say the lack of impact of the asset allocations. In a world where many advisors' primary claim to adding value is in their asset allocations, these results would tend to suggest that value is minimal. P6's asset allocation was all over the board throughout the measurement period whereas the benchmarks' stayed very close to the initial weightings. Nevertheless, the differences in cumulative return were just above insignificant.

Not only that, the fact that the static allocation only required rebalancing four times over seven and a half years also suggests static asset allocation may be oversold relative to a simply buy and hold approach. Given that so few changes were necessary even when the market was quite volatile also calls into question those managers who rebalance more frequently. Are they doing it because they have no trading rule and are they simply moving back to the original mix regardless of the divergence? Or are they not, and saying they did? Exactly how are they adding value if they sell you an asset allocation model and then rarely (if ever) trade it?

Perhaps these results are simply a function of the market conditions since 2004. Maybe balanced mixes in general required more attention than P6. Perhaps P6 is an outlier in a normal distribution.

Or is it possible that by misinterpreting the importance of asset allocation, investing professionals are overselling its benefits? It's at least something to consider.


 

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