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

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May 2011
Return Is Not A Bad Word
A Shameless Returns-Based Analysis of P3 and P4
“Advice is judged by results, not by intentions.”
-- Cicero (106 BC - 43 BC)

 

TODAY'S WORLD, IT'S CONSIDERED crass to base investment decisions on return. Advisors admonish investors to forego, “chasing return.” They warn return numbers alone are insufficient to truly analyze an asset or strategy. Instead, one must consider not only the outcome of an investment decision but what led to it. Risk and external market conditions are just as important, if not more so, than return.

All of this is true when making an objective review of performance. On the other hand, there’s no need to deny what we all know, whether we acknowledge it or not, to be true: The ultimate determinant of holding and selling, if not buying, an investment is its return. While investors may also consider risk, market conditions, Modern Portfolio Theory, or whatever else, if an investment fails to perform acceptably over a limited period of time, it will be sold for that reason alone. Archive Index

Even more importantly, there’s nothing wrong with this line of thinking. You can’t deposit a good Sharpe Ratio at the bank. No merchant will honor a low standard deviation. Historical alpha won’t put food on your table or send your kid to college. Only real return will do that so there’s no need to feel guilty about seeking it. Isn’t this why investors invest in the first place? If it’s not, it probably should be.

Over the years we’ve evaluated our model portfolios in a number of ways. Just take a look at the prior Work in Progress topics and you’ll see what we mean. Return is essentially the one thing that hasn’t had an explicit focus. The time has come.

 

What to Look For
Quantitative models P3 and P4 were both launched eleven years ago on July 1, 2000. They both have the S&P 500 as their benchmark and universe of potential holdings. Because of this, there’s a common measure of performance not only to the benchmark but to one another. Along the way, we’ll also mention risk and risk-adjusted return, but portfolio return will be the major focus here.

Despite their similarities, P3 and P4 differ in two significant ways. P3 seeks the best stocks from the entire S&P 500 with no regard to sector weighting. P4 is required to always market-weight its sectors at each semi-annual rebalancing. This limits P4’s ability to add value to specific stock selection. P3 has more flexibility because it can also boost performance through astute sector 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.

P3 tends to be more of a momentum model not only with its additional equity selection flexibility but also because it’s rebalanced bi-monthly as opposed to P4’s semi-annual reconstitutions. This affords P3 a better opportunity to respond to changing market conditions. In a trending market this won’t make much difference, but in a volatile market it can have quite an impact.

From Chart 1 it’s easy to see that the two portfolios have had a similar cumulative trajectory, yet somewhat different results. Both got off to a quick, albeit short-lived start. Within two months of their inception, a three-year bear market was underway. Both models sold off more than the benchmark index and both spent the majority of the following decade catching back up.

By itself, Chart 1 doesn’t paint a very impressive picture of either P3 or P4. By March 31, 2011, P4 had finally pulled ahead of the S&P 500 by about 5%. That means in roughly eleven years it returned 5% more than the unmanaged benchmark. That’s a gross return and doesn’t include the actual trading costs it would take to actually invest in this portfolio. Although P4’s annual turnover is a relatively low 59%, that’s still about 54 stocks a year (27 buys and 27 sells). With a discount brokerage charging around $10 a trade, this would amount to an annual expense of $540. That’s still a modest amount for an actively managed all-equity portfolio, but over eleven years, this would likely wipe out P4’s slight cumulative advantage over the unmanaged index. One might conclude a passive index fund or ETF would be a comparable – if not better – alternative.

Again, if looking at Chart 1 in isolation, this conclusion would be even less arguable in the case of P3. By the end of March 2011, P3 still trailed the S&P 500 by over 20% -- and that’s even before transaction costs are considered. These returns certainly don’t speak well for either model, especially P4.

Certainly anyone investing in P3 and P4 over the full eleven-year period would be disappointed with the results. In fact, it’s highly likely they would have abandoned either model (or a passive investment in the S&P 500) long before the market turned back up in late-2002. That’s the thing about return-based investing, disappointing results lead to turnover. When it comes right down to it, in practice, most investors have a time horizon of about a year, two at the most. Investments failing to live up to return expectations in that time frame get the heave, regardless of what the other statistics say. As a result, P3 and P4 would have been deemed failures long before March 2011.

 

The Rest of the Story
But this is only part of the story. In 2009 many analysts were referring to the prior ten years as the “lost decade” for domestic equities. Following the declines from the credit crisis in 2008, all of the recovery gains of the previous six years were completely wiped out. Investors who entered the market at the beginning of the decade were back underwater. It didn’t matter if they were in P3,  P4, he S&P 500, or virtually any other domestic passive index investment. Just as the rising tide lifts all boats, the falling equity tide sank all investors.
Chart 1
Cumulative Returns
P3, P4, and S&P 500
July 2000 - March 2010
Graph -- P3, P4, and S&P 500, July 2000 - March 2011
Data Source: Ibbotson Associates/Quantview
After a slow start, P3 and P4 have been steadily picking up ground on the benchmark, S&P 500. In fact, by March 31, 2011, P3 had pulled ahead. higher than the index.

Although the model portfolios and the index itself struggled from July 2000 through March 2011, the fact is, few investors did well over the period. Nevertheless, many were invested for other sub-periods. Some came back in 2002 when the market turned. Some left in 2008 when it again reversed. Many returned in 2010 following the two-year run-up (chasing return?). These, too, are legitimate periods and worthy of evaluation.

Chart 2 shows a number of periods ending March 31, 2011, including the one starting July 1, 2000. The results put P3 and P4 in much better light.

P4 obviously made up ground on the S&P 500 following the steep declines of 2001 – 2002. As a result, it outperformed the benchmark from 2002’s trough through March 31. The ten-year numbers capture most of this recovery. Now, even considering transaction costs, P4 is a much more viable alternative.

Over the shorter periods, it also holds its own or exceeds the index. This could be a positive reflection of the changes made in July 2003 and January 2010 . The former changed the model’s rebalancing frequency from annual to semi-annual and the latter changed the underlying algorithm based on newer market data. Or maybe the improved comparisons were the result of a rising market. Regardless, P4’s performance relative to the S&P 500 has improved significantly over the more recent periods.

More importantly, not only has relative performance to the index improved absolute performance – what you take to the bank – has as well. Again this may be a function the improved equity environment or a model which performs better in an up market, but the bottom line is, it doesn’t matter. When all you’re concerned with is return, it’s hardly arguable that P4’s returns have improved in real terms over the past eleven years.
Chart 2
P3, P4, and S&P 500 Performance Periods
July 1, 2000 - March 310, 2011
Graph -- P3, P4, and S&P 500, Performance Periods, July 1, 2000 - March 30, 2011
Data Source: Ibbotson Associates/Quantview
P3 and P4 don't look so good since inception, but pick any other time period and they seem a lot better. Better that than the alternative.

P3 is more of a mixed review. As noted above, it still hadn’t caught up to the benchmark index as of March 31, 2011. Nevertheless, it, too, has seen its results pick up – particularly in the most recent time periods.

As you've probably already noticed, Chart 2 also includes results from Morningstar's Large Cap Blend category. We've includes this so you can get some perspective of how well our model portfolios have done in comparison. Yes, the cumulative period is sad, especially for P3. but then pick any other period -- that's right any other period -- and the story is different. Even when the Large Cap Blend category was up over 14.5% in 2010 our models were 5.5% - 11.5% better. How's that for five-star performance?

In fact, five stars is probably what our portfolios would have given that Morningstar's ratings don't go back as far as those first few months when our models had such a bad stumble. With so much emphasis placed on the past five years, they'd be in great shape. (By the way, the comparisons on Chart 2 actually favor the mutual fund category average because that's a total return, not simply a price return measure as we've been using for our models and the S&P 500.)

 

Beat with Beta
Those of you who are still uncomfortable talking about good old pure return, are probably wondering about risk. Sure, P3 and P4 have been impressive in the past ten (of eleven) years, but how much more risk did they take on to achieve it?

Risk is certainly the other side of return given that they're directly related. Typically when two assets are in the same class and one noticeably outperforms the other it's because it's being rewarded for taking on additional risk. This is especially true for homogeneous categories like the Large Cap Blend we're dealing with here. Put another way, when there's a difference in return between assets of a similar nature, it usually stems from a risk differential.
Chart 3
P3, P4, Morningstar Large Cap Blend Category, and S&P 500 Period Statistics
July 1, 2000 - March 310, 2011
Graph -- P3, P4, Morningstar Large Cap Blend Category, and S&P 500, July 1, 2000 - March 30, 2011
Data Source: Ibbotson Associates/Quantview
P3 and P4 have always carried greater market risk than the benchmark. This is reflected in their higher standard deviations and slightly lower Sharpe Ratios. The differences still aren't that significant -- even less so if all you're interested in is return.

Unquestionably, both P3 and P4 have always sported above average betas (~1.25 and 1.10, respectively vs. 1.00 for the S&PO 500). In general terms, this means they carry more than the norm (as defined by the index) of market risk. Higher levels of market risk can assist performance when the market is trending up and hurt when it's going down. You can clearly see the effects for both P3 and P4 in the early months of their existence and the periods subsequent to 2002. But recently, those betas have helped the models make up lost ground. As mentioned earlier, P4 is now ahead of the S&P 500 since inception and P3 has made huge strides to close the gap in the past two years.

As far as overall risk is concerned, P3 and P4 have substantially higher standard deviations than the S&P 500 or Morningstar's Large Cap Blend funds. In regard to the latter, this is what you'd expect given that both models have a growth tilt. In regard to the benchmark, the best way to get a handle on the risk differential is to take a look at risk-adjusted return -- we're focusing on return, remember?

The Sharpe Ratio is a commonly used measure of risk-adjusted return. The calculation is simple: The numerator is the asset's gross return less the return of the 30-Day Treasury Bill. The Treasury Bill represents the risk-free rate, what you could have earned with virtually no risk. The denominator of the Sharpe Ratio is the asset's standard deviation. As you can see by the make-up of the ratio, higher returns and lower risk will yield greater results.

For the entire period July 1, 2000 through March 31, 2011, the S&P 500's Sharpe Ratio was 0.0084. That's more than P3's (0.0050) but less than P4's 0.0238. The fact that they're all positive indicates an investor would have been at least minimally rewarded for the additional risk of any of the alternatives. Nevertheless, none are much more than zero so they're all about the same.

P3 and P4 have come a long way from their poor start. On a returns basis, they've been better than the benchmark index, particularly since the mid-point of the measurement period. Even when risk is factored in, there is no major element recommending a passive approach over P3 and P4's quantitative algorithms. So there, it's been said: Just looking at returns, P3 and P4 look just fine.


 

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