Demand is high for quant models that manage asset allocation. Investors need to understand the limits of quant models, and this involves some geeky math. Bottom line: Quant will never replace human decision making.

During the last week, quant models for tactical asset allocation (TAA) have crossed my desk not once but twice: One email cited this article from the *Journal of Portfolio Management*, and an SA reader asked me about the Cambria Global Tactical ETF (NYSEARCA:GTAA) (pdf here). I have also seen lots of interest in the market for quant TAA in ETFs, mutual funds, and in quant services for investment advisors.

**Bubbles**

Despite the surge of interest, I must respectfully disagree with using a pure quant model for TAA. Most of the ones I have seen are based on trend following, so they are continually chasing performance. This contributes to bubbles.

Generally speaking, quant models are very good at telling us what worked over the last 20 years. But they tell us very little about what will happen in the years ahead. That's because most quant models are based on backtesting, which tend to overfit the data. For example, these portfolios invariably recommend an allocation to gold simply because it has performed well in the past. This overfitting is mere extrapolation of the past, and it results in nonsense portfolios.

In addition, mean-variance optimization results in large estimation errors, which was identified as a problem quite some time ago. (This old article offers a great summary). In a nutshell, an optimized portfolio tends to concentrate assets in a manner that also concentrates risk, so the portfolio manager must introduce constraints. The very idea of constraints, however, takes us away from quant and towards human judgment. This reveals the limits of pure quant.

**Bootstrapping**

One way of avoiding this overfitting of past data is to use longer testing periods, and Monte Carlo simulations. This is a way of "bootstrapping" results, and creating many samples and simulations from a limited set of historic data.

The problem with bootstrapping is that market returns cannot be disconnected from their historical context. Bonds have beaten stocks for the 30-year period ending in 2011. This happened for a reason, and we need to understand this reason. Monte Carlo simulations treat each year as unrelated to the prior year (so there is no serial correlation), and each year is disconnected from its historic context.

Here's a simple example: Backtesting now suggests that my mom should own long-term U.S. government bonds. I think that this is stupid. My mom is a conservative retiree, and Treasurys are in a bubble. Therefore, I recommend a mix of corporate bonds and dividend stocks for my mom, since I believe this portfolio has a better risk/return profile. (Details of my mom's portfolio are here.)

**Cloning Soros**

In addition, asset allocation today is radically different than it was ten years ago. "Stocks/Bonds/Cash" used to suffice, but now everyone is a global macro investor, a la George Soros. Or, better yet, we are all macro traders, thanks to a quant system. Many of these systems are based on price momentum, and contribute to market bubbles. So they are not only naïve, but dangerously naïve.

**The Human Element**

Personally, I would rather rely on human assumptions by a human being. My associate, Ed Stavetski of PCM Partners, is a good example, since he can tell me what he owns and why he owns it. If I cannot do that for a client, then shame on me. I am not going to tell the client "Sorry, the model failed. No retirement for you."

Alternatively, an investor could rely on a professional TAA fund run by human beings. This includes two of the largest tactical funds: Ivy Asset Strategy C (WASCX) and Pimco All Asset Inst'l (PAAIX). Both funds have returned between 5% and 6% over the last five years, and both are run with specific assumptions about the outlook for capital markets. These funds are complex; I wrote about their limitations here.

Unfortunately, there is no way of getting around the fact that decisions by human being are ultimately responsible for investment performance. Granted, investors may clamor for models, and for wizardly TAA portfolios. But most investors are better off doing their asset allocation the old fashioned way: low-cost funds, broad diversification, and periodic rebalancing. In academic circles, this is called the 1/N portfolio.

**The Value of Quant**

Let me say that I *do* appreciate the insights of backtesting, and mean-variance optimization using Markowitz 2.0. Paul Kaplan of Morningstar is a humble innovator in this vein, and he just published the *Frontiers of Modern Asset Allocation*. As he noted, quant methods sharpen our focus, and force us to state our assumptions about future returns and future correlations. This is a tremendously useful exercise, and it should be our focus. We need to spend our time evaluating our assumptions, not endlessly tweaking our quant models.

**For Math Geeks**

My final tirade about quant models is described in "Models Behaving Badly": Mathematics can only *describe* reality; mathematics does not *create* reality. Wall Street's obsession with mathematics has pushed these models into applications that are far beyond their capacity, and this contributes to bubbles and crashes.

For math geeks, this is described by Gödel's incompleteness theorum. This shows that will always be statements that are undecideable in any formal mathematical system. Thus, no mathematical model can be a complete description of reality, *even in principle*. This should make any quant humble, and it has implications for all types of quant models, especially those that drive tactical asset allocation.

Another way of saying it is this: The *choice* of any particular model returns us to the human element, so there is no way to turn the art of investing into a mathematical science. To me, the search for a perfect quant system for TAA is a fool's errand: It's a search for a square circle.

I may sound dogmatic, but I'm always looking for ways my ideas may be wrong or incomplete. Intellectual humility is a good thing. So I welcome comments from readers to point out the mistakes and limitations of my thinking.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.