Testing Forward Looking Asset Allocation

Quantitative Asset Allocation

Many investors seem to be in the process of losing faith in asset allocation. In September and October of 2008, it seems that all asset classes have moved together—straight down. The positive benefits of asset allocation rely upon certain asset classes having low correlations with one another—when one dives, others don’t. While correlations tend to go up during fairly short periods of panic selling in crashes, the value of managing a portfolio using asset allocation has been consistently demonstrated. In this article, we present a useful data point in this regard.

In an article in April 2008, I [Considine] combined Quantext’s research with research from a range of institutional sources to suggest that effective diversification (determined by asset allocation) could add 2% to 2.5% per year in return to a generic portfolio made up of a mix of domestic equity indices and a bond index. In this article, we are able to expand upon this theme using out-of-sample testing of Quantext’s portfolio planning model over 9+ years. We have also tried to level the playing field by benchmarking against a far more diverse benchmark portfolio. The results suggest that a quantitative approach using forward-looking asset allocation adds considerable value.

Benchmarking Portfolio Performance

It is well known that most equity mutual funds under-perform the S&P 500. In fact, the severity of this effect is somewhat masked by survivorship bias—the fact that shuttered mutual funds simply disappear. For these reasons, the S&P 500 is often used as a performance benchmark. This may have been somewhat justified in the decades when U.S. equities dominated all other asset classes, but there are surely better benchmarks now. Even if one were to decide that the S&P 500 is a decent benchmark for U.S. equity funds, it is important to establish a benchmark for a well-diversified portfolio: the total portfolio benchmark.

What would a solid benchmark for total portfolio performance look like? A viable benchmark would include domestic and foreign stocks, a variety of durations of bonds, commodities and real estate. The relative allocations would be a bit tricky because you don’t want to allocate based on a single historical period. Further, you will want to choose different benchmarks based on some measure of risk—such as the allocation to bonds.

To provide a reasonable benchmark, we started with a group of Vanguard funds that have been around for a while and built a generic portfolio with 40% bonds by having equal allocations to each of the list below:

The one non-Vanguard component is an allocation to the Dow Jones AIG Commodity Index (which is available as an ETF: DJP). Most of this portfolio can be exactly replicated using ETFs. We could substitute IVV for the S&P 500, ICF and RWR for VGSIX, EFA for VEURX, and EEM for VEIEX. We used Vanguard funds because they have more historical data (they have been around longer) and are, therefore, better suited to an historical analysis. The funds listed here are not an optimal set---but this portfolio is a considerably harder-to-hit benchmark than the S&P 500. The other potential substitutions would not be exact, but the purpose of this analysis is to examine whether quantitative portfolio models add value.

Strategic Asset Allocation

One of the most often cited issues in portfolio management is the importance of rebalancing. Rebalancing is perhaps the most basic form of strategic asset allocation (other than buy-and-hold). Let’s start by comparing an annual rebalancing strategy to a simple buy-and-hold, starting with the equal weight portfolio among the components listed above. The re-balancing is performed once at the end of each 12-month period, and takes the portfolio back to equal weights. We will be looking at the period from July of 1999 through August of 2008 using end-of-day adjusted closing prices, inclusive of dividends. This was the longest period for which we have all of these funds available, allowing for three years of lead time (prior to July of 1999). We will be using this lead time to drive some forward looking models in a later section.

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Several points are immediately apparent. First, the equally-weighted buy-and-hold portfolio diversified among these funds has done quite well over the 9.2 years of this study, with an average annual return of 10.6% and a standard deviation of 9.3%. Annual rebalancing of this portfolio decreases both risk and return—a phenomenon that has been documented in a range of studies. Simple calendar rebalancing reduces risk, but it also reduces return. Both the buy-and-hold and annually rebalanced portfolios have done well over this period, despite the fact that the cumulative gain in the S&P 500 over this entire period is 8%--i.e. less than 1% per year.

Going Further

As many (if not most) readers are aware, the development of portfolio theory is generally regarded as one of the greatest financial innovations on the 20th century. The idea behind portfolio theory is that investors should combine available investments so as to maximize return at a given risk level. This process exploits correlations between available asset classes. If you make a chart showing the highest available return at each risk level, you have created what is called the efficient frontier. The funds that we combined in the original portfolio already exploit diversification (simply by virtue of combining asset classes that have historically exhibited fairly low correlation), but there is no reason to assume that this portfolio is optimal.

The challenge of ‘optimizing’ a portfolio by calculating the efficient frontier is that you need to have estimates for the expected returns and standard deviations of all available asset classes, as well as the correlations between them. Where do you get such data? A simple minded approach to this problem is simply to use historical data. This leads to poor results, in general, if you manage a real portfolio simply by looking backwards in this manner. William Bernstein performed an experiment in which he created asset allocations based on trailing data in which he optimized historical returns with a risk constraint over a series of time periods. In other words, he calculated the efficient frontier using historical data and then allocated a model portfolio so that it was on the efficient frontier. He found that a portfolio managed in this way generated a substantially lower return than a simple static allocation with annual rebalancing, in which the portfolio was spread between the major asset classes ('The Intelligent Asset Allocator', P. 70). The under-performance occurs because asset allocation using historical data simply tends to over-weight the portfolio to the assets that have performed well in that specific period. This tends not to work well going forward (e.g. out-of-sample).

If allocating based on history fails, what do we do? Surely we can do something smarter than just spreading our portfolios across the major asset classes using an arbitrary rule (like equal weights). This is where forward-looking models come in. Forward-looking portfolio models combine historical data with analytical models to produce projections for each asset class that compensate for recent out-performance or under-performance. Forward-looking models are well-established as an analysis framework and, somewhat remarkably, the results from a range of institutional-grade models agree on how much benefit can be derived from a portfolio that is properly designed using forward-looking analysis. In earlier studies, we compared QPP’s projected returns for a range of portfolios over extended out-of-sample periods to estimates from trailing returns and found that QPP’s projections were consistently more accurate than using trailing returns as an estimator of future performance . In this analysis, we are going a step further by optimizing a portfolio based on QPP’s projections and looking at subsequent portfolio performance over 12-month periods.

The original motivation for this analysis using Vanguard funds was to see if Quantext Portfolio Planner (QPP), a forward-looking model, could provide asset allocations that would beat a naive equally weighted allocation (called the 1/N model because 1/Nth of the portfolio goes into each of N funds) on an absolute and risk-adjusted basis on a series of out-of-sample tests. How do we do this? We start with three years of data to initialize QPP, and then run EXCEL’s optimizer to maximize QPP’s projected portfolio return, while constraining projected portfolio risk to be at or below an annualized standard deviation of 10% (this is about the same risk level as a generic 60/40 portfolio). We then look at how this optimized portfolio performs over the next 12 months. At the end of twelve months, we run QPP again to generate portfolio outlooks and optimize again using trailing three years of data, etc. We performed this process over the 9.2 year period—nine portfolio updates.

We have the earlier naïve buy-and-hold and annually rebalanced equal-weight portfolios as benchmarks. To provide an additional point of reference, we performed the portfolio optimization just using the trailing three years of data (similar to Bernstein’s study)—and updated once annually. We expect, based on Bernstein and others, that the historical optimization will yield poor results. The table below summarizes our results:

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Building a portfolio by optimizing on historical data leads to bad results—as expected. This approach has the lowest returns and the highest risk (measured by volatility) of the four strategies. A simple risk-adjusted return metric, the ratio of annual return to standard deviation (Return/SD) shows this quite clearly. Second place honors in terms of returns go to buy-and-hold with equal weights (10.6% per year in average return). That said, the annual rebalancing back to equal weights provides risk management benefits, so the Return/SD ratio is higher with annual rebalancing.

Building an optimized portfolio using QPP’s projections provides the highest returns—adding 1.8% per year over the buy-and-hold strategy, with no additional risk. The reader should understand that this test analysis was entirely automated and shows results that are fully out-of-sample with all default settings in QPP.

There is another point that is well-worth noting. The optimizer used QPP’s projections to constrain total portfolio risk (annualized standard deviation in return) to at or below 10%. In the outcome portfolios, the actual observed standard deviation in returns is 9.3%---quite close to the constraint. This means that the model is creating portfolios with volatility levels that are close to the desired level. In other words, QPP’s projections of portfolio volatility are pretty good.

Discussion

As with all tests of analytical models, no single test is conclusive. Any analytical test must be considered as part of a validation process. The period in question here is only nine (and a bit) individual years of analysis. We chose this short period because we wanted to use real funds where possible. We see these results as one important validation of Quantext Portfolio Planner’s projections. By using the model with all default settings and allowing an optimizer to select the allocations without any human intervention, we are really testing the boundaries of the model in a new way. Further, the benchmark against which we are comparing is high—a considerable amount of the available diversification benefit is captured already.

This out-of-sample analysis of QPP over nine annual re-analyses leads to a performance advantage of 1.8% per year over a naïve diversification (1/N) using a range of funds. What does this mean? Within the context of all of the extensive testing that we have performed on QPP, these results reinforce that forward projections of portfolio risk and return can add considerable value. In a year when the S&P 500 is down 30% or so, this may not be a huge consolation. Over time, an increase in average return of this magnitude is enormous. These results demonstrate the value of a quantitative approach to Strategic Asset Allocation (SAA). There are a range of strategies for Tactical Asset Allocation (TAA) that might be layered on top of SAA, of course, that can enhance portfolio performance. I have discussed some of these in the context of QPP. We are not saying that SAA is the whole story---but it is a crucial part of getting portfolio management right.

Fellow QPP user, Pete Manhardt, collaborated on this study and article. He integrated QPP with commercial back-testing simulation software. Pete can be reached at the QPP Forum, by email: [e-mail] or via Linked-In.

Comments

[SmartETF:]

Can we finally kill Modern Portfolio Theory? How much pain does one need? If it worked why are all of your accounts so decimated? Why is Meriwether on the verge of another Long-Term Capital explosion and where are your 10% annualized returns?

Flaw #1: MPT relies on normal distribution which by defaults ignores risk outside of 3 standard deviations (sigma 1=68.3%, sigma 2=95.4%, sigma 3=99.7%), or .15% for each tail. So what are the odds of a 5 sigma event? It’s one in 7000 years. So tell me why have we had a half dozen 5 sigma events or more this year? The use of normal distribution is simply wrong. Changing to a log-based distribution called a ‘stable distribution’ exposes the tails to better see risk.

Flaw #2: MPT uses linear correlation. This static approach illustrates the average relationship of 2 assets over time. This is crazy because as Geoff Considene accurately points out the relationships change (becoming more correlated) as volatility increases. The old adage is the only thing that goes up in down markets is correlation. So why not use a dynamic correlation model that adjusts for volatility. It exists and it’s called a ‘copula dependency model’.

Flaw 3: MPT is based on long-term averages. If in 2000 you used 40 years of history to model equities returns you would expect returns of 10%. Using 15 years you would return 15%, using 3 years you would model 30%. So the key in most models is know how much data to use and how best to weight the data. The author here is weighting new data as being more valuable; which is actually true. The danger in doing this however is during cycle changes (like 2000) and it disregards historical patterns. So exponentially weighting may be better than mean-variance but EWMA’s have its main flaw is its inability to appreciate historical data (patterns like a 60’s or 70’s market) because it works like a present value model that heavily discounts old data.

Using a physics concept called GARCH takes the historical data and examines its recent clustering effect; think Doppler radar instead of MVO’s Farmer’s almanac approach. The GARCH concept won its inventors the Nobel Prize in Economics in 2003, a bit more recent than the MPT concept developed 50 years ago.

Flaw #4: Rebalancing more than once a year is considered inefficient to the MPT user; which is true. That is because new data is meaningless. Adding a month of new data into a data set of 40 years is like throwing a bucket of water into a pond; meaningless. This is why asset allocators always hold fast to their 60/40 mix range. If you could value newer data as more valuable you would rebalance more often to capitalize on the change in market conditions (risk & return). This is why the QPP model is trumping MVO/MPT because it rebalances more than the buy & hold and it ostensible values newer information as more valuable.

The bottom line is MVO models just don’t work except in long up-trending markets, but you’ll never outperform. Mandelbrot, Sharpe and several of the other inventors of MPT/CAPM express their issues about their creation and yet these words go unheeded because it is in the text books and accreditation programs. Mandelbrot recommends Extreme Value Theory (EVT), a dynamic approach to asset allocation. Using EVT for the past four years you would have had nearly twice the returns of the basic 60/40 mix in the up years and been down only half that amount this year. That is serious alpha. So let’s bury MPT/CAPM and these mean-variance models and take a scientific approach to investing.

2008 Oct 23 01:36 PM

[Geoff Consi...:]

SmartETF:

As always, we have a post from somone with no public analysis making extravagant claims. If you are credible, you need to show some meaningful analysis aside from diatribes attacking other peoples' articles. Please--give us some links to evidence that your approach works. Even Mandelbrot says that his approach is not ready for application. In all your posts, you make tremendous claims, but where is the evidence? You have provided none. Your comments do not address mine--they are just your standard diatribe.

2008 Oct 23 02:18 PM

[Geoff Consi...:]

To SmartETF:

It has been suggested to me that you are a representative of the firm Smart Portfolios LLC. Please confirm or deny this. Further, if you are, despite your fantastic claims, I note that the mutual fund based on your models is not performing especially well (ASENX) given that it is 60% fixed income. If you are not from this firm, I apologize for the mixup. If you are touting the models from this firm, theb track record of ASENX will speak for itself and perhaps confirm your claims in some way.

2008 Oct 23 03:28 PM

[SmartETF:]

I was trying to support your claims, not tarnish. I was not attacking but rather educating; I wish you could see it in its true light. I don’t print my results because I don’t want to come across as self-promoting. What Mandelbrot wrote 4 years ago was already in use and has been improved upon. If you want proof that Extreme Value Theory works check out my fund Aston Smart Portfolios Allocation Fund 'ASENX'.

The TIAA-CREF overlay account since inception (9 funds: June 2006 – Sept 2008) on their family of funds are up 5.98% with a std. dev. (SD) of 8.85% compared to an index (35% S&P 500, 35% EAFE, 30% Lehman Agg) of 0.01% and SD of 9.91%. The S&P 500 returned -1.73% with SD of 12.55% and the NASDAQ returned –0.95 with SD of 16.79%.

The Pacific Life overlay account for VUL (includes all insurance costs and loads from June 2005 to Sept 2008) delivered 6.76% vs. 1.11% for the S&P 500, 1.2% for Nasdaq, and 2.61% for the same index. The risk (measured in SD) for the same were PacLife account 5.44%, S&P 500 5.05%, Nasdaq 6.39%, and index 4.61%.

If you want to see the numerous SMA accounts we manage I'd be happy to show them to you but I doubt you would change from the QPP punch you’re drinking. If you want proof that ‘Expected Shortfall’ is far superior to standard deviation and Value-at-Risk I can prove that all day long. If you want proof that GARCH is superior to mean-variance that too is a no brainer. If you really think linear correlation is superior to copula dependency then god help you and your clients. I have always commented that your model is better that the typical MPT/MVO model; I still do. The only times I’ve been defensive with you is when you try to defend your models against newer methodologies that you obviously have no desire to learn or embrace.

Last year I warned investment professionals at many of the major investment conferences where I spoke (Schwab, FPA, CFA, NAAIM, etc) that the market was set for a major decline; but they hung onto the sinking MPT ship. I’m in the business as an advocate for investors and I’m obviously passionate about educating advisors about the new models to help them help their clients; why else would I share all this info without listing the firms which use our models? What is your motivation? If you want to go toe-to-toe bring it on. Personally, I’d rather work together to increase the awareness of better models to help investors and improve the reputation of our industry. Your call. But as long as you write about asset allocation in public forums I have the right to enlighten advisors and protect investors.

2008 Oct 23 04:25 PM

[SmartETF:]

Ah yes, you've found me, congratulations. Yes we are at 40% fixed income but a week ago we were 78% in SHY (1-3 year treasuries) and have been heavily invested in short term treasuries all year. Note: this is only an asset allocation model which rebalanced monthly. Our models are still very skeptical and it still prefers to be partially short, but I’ve over-ridden the model because the current valuations are worthy of extending our equity position. Also of note, we are not 60% equities but have a 3.5% in commodities, 7% in real estate, and 36.5% in S-T treasuries and cash. The model recommends 60.5% S-T treasuries and cash, 7% RE, 3.5% Commodities, and 29% equities with a 5% short position.

Out TIAA-CREF accounts are only 2% equities while the Paclife funds I mentioned earlier hold 14% in equities. If you would like to continue this bout I suggest we take it offline because it is counter to my goal of educating and is totally unproductive. Signing off -

2008 Oct 23 04:49 PM

[Geoff Consi...:]

SmartETF:

As far as I can see, ASENX does nothing special--the holdings show it has 60% or so in bonds and a bit of cash. Compare it to STLBX which is a target date fund with about 60% in bonds and cash and they track perfectly:

finance.yahoo.com/q/bc...

Please tell me/us what is special about this? Is this proof of a superior model?

2008 Oct 23 04:52 PM

[SmartETF:]

Your right, our SMA accounts have demonstrated substantially higher returns with a lot less risk; nothing special there. Meanwhile, you're looking at the allocation on one specific day in one specific fund. Brillient -

2008 Oct 23 05:09 PM

[Geoff Consi...:]

SmartETF:

When I ask for evidence, what I am interested in is some kind of documented record. You said

"If you want proof that Extreme Value Theory works check out my fund Aston Smart Portfolios Allocation Fund 'ASENX'. "


You suggested ASENX as evidence of your better approach and it has not out-performed a generic benchmark so far--it tracks perfectly in fact with a target date fund with the same FI allocation (STLBX). But ASENX has like 400% annual turnover which means that you would need to dramatically out-perform if this were a taxable account, too.Your mutual fund using your approach certainly counts--and we can keep an eye on that.

Just saying that your method is superior or mentioning things like GARCH or EVT does not provide any concrete support---its just jargon until you demonstrate something. This is where publications are really useful--you can publish examples from your models on a forum like SA and then see how they have done. You could also have an objective / standard model that other people can test--as I have discussed in my article here.

2008 Oct 23 05:27 PM

[Flav:]

Geoff: How would shorting stocks affect the analysis? Considering than when you short, you profit when the stock goes down, it would have a negative correlation with the other portfolio assets, and therefore, coud short-sale improve the risk/return profile of the portfolio?

Thanks in advance

2008 Oct 24 10:05 AM

[Geoff Consi...:]

Flav:

Allowing the model to short would be a good addition to the analysis--perhaps a follow up. Frankly, this study is a starting point for more. Validation is a long-term process and there are so many ways to stress test. Pete Manhardt, my co-author who did the analysis, has created a platform for doing a wide variety of interesting studies.

Geoff

2008 Oct 24 11:34 AM

[Flav:]

Geoff: Again, thank you very much for your quick response. I’ve been reading past articles from yours, and i have a few questions (i must apologise first, they aren't fully related to this article):
Does QPP estimate covariances, so that you can optimize using Excel's solver in order to build the model portfolio? If that's the case, you can compute the correlation coefficients between stocks (or assets)?

If you entered QPP the time series of, for example, the SPY, using the last year and a half data, did the tail risk signal this kind of drop?

Thanks in advance

2008 Nov 01 06:14 PM

[Indexor:]

Geoff:

He's b-a-a-a-a-c-c-c-k-k-k.

I must say, Smart ETF's comments are extremely interesting. If you two have taken this private, as he suggested, we'll all miss out on a tremendous education. Could you provide us with a Cliff's Notes version?

2008 Nov 26 12:36 AM