Financial journalist Jason Zweig once asked Harry Markowitz how he manages his investment portfolio. "My intention," he explained, "was to minimize my future regret. So I split my contributions 50/50 between bonds and equities."

Why would the founding father of modern finance choose a naïve strategy of equal weighting over his own theory for designing portfolios? Markowitz won a Nobel prize for his quantitative framework that identifies the optimal portfolio-the one that maximizes expected return for a given level of risk. Perhaps his choice of portfolio strategy has something to do with the fact that his analytic brainchild is highly sensitive to the accuracy of the required forecasts of returns, volatility and correlations.

No wonder that the true efficient portfolio is the stuff of dreams. Mere mortals have trouble estimating the parameters that lead to optimization because the future is forever murky. What looks like an efficient portfolio on the computer screen has a habit of delivering sub-optimal results in practice.

Markowitz's plug for equal weighting suggests that he's well aware of the practical limitations that bedevil his famous theory. That's no slur on his achievements, which are rightly extolled as the seminal development in lifting finance out of the dark ages. The fundamental advice in his seminal 1952 paper (and the more elaborate book-length treatment that followed in 1959) is still correct: Every investor should seek the ideal asset mix. The debate is over the details for pursuing that goal.

Modern software packages and various enhancements to Markowitz's original framework can help smooth the rough edges. But the inherent dangers of forecasting aren't so easily engineered away. In search of guidance, investors have long turned to asset-pricing models of one kind or another. The standard choice is the capital asset-pricing model (CAPM), in part because of its simplicity. CAPM reduces the complexities of finding Markowitz's optimal portfolio to a simple idea: Buy the market. According to the one-factor CAPM, the efficient strategy is the value-weighted portfolio of all the securities in the targeted asset class (or all the asset classes for a broad asset allocation strategy).

Investing is certainly easier in a CAPM world, although a rising tide of critical research warns that the model's attributes are oversold. The growing awareness of CAPM's flaws has inspired a search for better models. From the arbitrage pricing theory of the 1970s to the Fama-French three-factor model in the 1990s to the 21st century's fundamentally weighted indexing, academics and investment strategists are keen on developing new theories that bring portfolio management closer to a Markowitzian ideal.

But how much progress should we expect from building better asset-pricing mousetraps? All models are approximations of reality, which means that all models are imperfect. Just as Tolstoy observed that every unhappy family is unhappy in its own way, each asset-pricing model suffers its own unique set of glitches. The snags may not be fatal, but they can cause trouble at times. Perhaps that explains Markowitz's soft spot for equal weighting, which is the quintessential model-free investment strategy. The fact that equal weighting holds its own against most, if not all, allegedly superior strategies suggests we should at least consider why naïve portfolio design can be smart. This naïve portfolio structure may not move us to use it for managing money, but its neutrality makes it a worthy benchmark for evaluating its various competitors.

**
An Ancient Pedigree
**

Equal weighting is the world's original portfolio advice. The Babylonian Talmud of the fourth century recommends dividing wealth into thirds: land, business and liquid assets. Financial strategy has come a long way since then, but maybe not as far as we think.

A naïve strategy of holding equal portions of assets is surprisingly competitive if not superior, according to a number of studies in recent years. Academics are (re)discovering the power of forgoing models in favor of a simple diversification plan that's notable for its lack of assumptions about how markets work. Formally, this is known as the rule of 1/n, a reference to the fractional weight devoted to each investment based on n securities or asset classes.

The closest that the 1/n strategy comes to predicting is its implicit assumption that the future is unknowable. The rational response in that case is hedging one's bets in the extreme by avoiding bias in the capital allocation. This can be a critical advantage because it eliminates what's widely cited as the main challenge in pursuing optimization: overfitting the data, as statisticians say.

Trouble arises when one crunches historical data in search of relationships that are expected to prevail in the future. Searching for patterns in the past can be helpful, but the data's always burdened with an error term-random, unpredictable noise. That's why historical analysis should be supplemented with forward-looking estimates. But this is hardly a cure-all for uncertainty.

As a result, forcing a model to dispense a forecast can lead to highly unstable predictions if the expectations are less than perfect. Small, unexpected changes in market activity can lead to big surprises. This isn't a problem for the 1/n rule. There's no risk of model failure because there's no model to begin with. Accordingly, the hazards of overfitting the data and misjudging the future are nil with equal weighting.

None of this would mean much if equal weighting delivered disappointing investment results. In fact, the opposite seems to be true. The 1/n rule's advantages are widely known (it's been a formal subject of inquiry in financial economics since at least the 1970s) and its charms are increasingly topical these days. For example, a recent study finds that a strategy equally weighting a U.S. stock portfolio is competitive with more than a dozen forms of optimization. "None is consistently better than the 1/n rule" when ranked on Sharpe ratios and other performance metrics, according to "Optimal Versus Naive Diversification: How Inefficient is the 1/n Portfolio Strategy?" in the May 2009 issue of *The Review of Financial Studies*.

According to another study, "The 1/n Pension Investment Puzzle" which appeared in the July 2004 *North American Actuarial Journal*: "The 1/n portfolio is consistent with the Markowitz efficient portfolios, given a limited set of information."

Richard Michaud of New Frontier Advisors agrees. "An equally weighted portfolio may often be substantially closer to true [mean-variance] optimality than an optimized portfolio," he writes in the 2008 edition of his book *Efficient Asset Management*. A September 2011 paper from the EDHEC-Risk Institute ("Improved Beta? A Comparison of Index-Weighting Schemes") arrives at a similar conclusion by comparing several alternatively weighted indices targeting U.S. and global equity markets.

**Managing Expectations**

Equal weighting is hardly perfect, but its agnostic outlook certainly distinguishes it from everything else. Even the "passive" worldview of CAPM, which informs most of the world's index funds, has an assumption: market values are optimal. The 1/n portfolio rejects this and every other theory of how markets price assets.

The question is whether the absence of theoretical guidance gives equal weighting a competitive advantage. In search of an answer, or at least some perspective, let's recognize that 1/n investing isn't immune to disappointing results. The degree of headwind for equal weighting can be estimated with three factors:

1. The degree of uncertainty

2. The total of n assets available for investing

3. The size of the learning sample (the depth and span of the historical database)

"Typically, the larger the uncertainty and the number of assets and the smaller the learning sample, the greater the advantage of the heuristic," advises Gerd Gigerenzer, a psychologist and director of the Harding Center for Risk Literacy in Berlin, in his book *Rationality for Mortals: How People Cope with Uncertainty.*

There's no shortage of uncertainty in economics, and the menu of possibilities with individual securities and funds isn't hurting either. The glut of choices is one reason for narrowing the list of potential investments to mutual funds and ETFs and focusing on asset allocation. But that's only a partial solution. Even if we limit our universe to ten funds, we should only expect the 1/n strategy to underperform if we can analyze 500 years of historical data, according to the authors of the "Optimal Versus Naive Diversification" study. That's about five times longer than what's considered reliable stock market history for the U.S. The historical database is even shorter for most foreign markets and non-equity asset classes.

The lesson is clear: Equal weighting's prospects improve when forecasting is difficult, when there are lots of investment choices and when the historical learning sample is limited. That more or less describes the profile of the capital markets.

**Real Results**

Equal weighting looks good on paper and it performs handsomely in practice, too.

Perhaps the leading example is the Rydex S&P Equal Weight ETF (RSP). With nearly nine years of history, the fund offers a real-world test of the 1/n rule against identical index products that differ only in the weighting of securities. RSP compares favorably to its cap-weighted counterpart, the SPDR S&P 500 ETF (SPY), for instance (see Figure 1).

Equally weighted funds are still a rare breed, but the niche is growing. Rydex SGI recently launched several ETFs that track MSCI equal-weighted benchmarks targeting various slices of U.S., foreign and global equity markets. This past March also witnessed the arrival of an equal-weighted asset allocation mutual fund: the 7Twelve Balanced Fund (SEVNX). The strategy applies the 1/n rule to seven asset classes (via 12 "subcategories") across foreign and domestic stocks, bonds, REITs, commodities and cash by holding single-asset class ETFs and mutual funds.

SEVNX's history is too short to say much about performance, but we can examine a 1/n asset allocation with a simple back test for the 20 years through this past September. Let's build three paper portfolios, each with six slices of the major asset classes represented by conventionally weighted benchmarks with the start date of September 1991. The first strategy is labeled "Global": an unmanaged allocation that starts with 60% stocks (an equal mix of U.S. and foreign), 30% bonds (evenly split between domestic and foreign) plus 5% in REITs and 5% in commodities. The second portfolio is identical except that it's rebalanced to the original 60/30/5/5 mix at the end of each year (we'll call this the "Global-R" strategy). The third portfolio (the "Global-EW" strategy) is initially allocated with an equal mix across the six markets and rebalanced to equal weight every December 31.

Equal weighting wins the performance race (see Chart 1). The Global-EW portfolio posts a 7.7% annualized total return, comfortably above the 7.2% for the rebalanced 60/30/5/5 strategy (Global-R) and the 6.7% for its unrebalanced sibling. Even better, the equal-weighted strategy's higher performance came with a bit less volatility and therefore a stronger risk-adjusted score (Sharpe ratio) against its two competitors.

Note that rebalancing is a critical (and necessary) aspect for the 1/n strategy. Even if we knew the secret for building a truly optimal portfolio, it would require periodic rebalancing to keep it from turning into a market-value-weighted strategy, i.e., a CAPM strategy. Of course, if you believe that a CAPM portfolio is optimal, you wouldn't need to rebalance. Instead, you could simply buy a market-cap-weighted index fund in the first place.

If you have doubts about CAPM, the focus inevitably turns to rebalancing. After diversifying across asset classes, rebalancing is the critical risk management tool for portfolio design and management. But rebalancing back to what?

**
Practical Matters
**

The common denominator for most strategies is the expectation that they will deliver an edge over a CAPM-inspired market-value-weighted portfolio, which automatically and continuously rebalances itself. The mechanism for delivering this edge is tightly bound up with the act of rebalancing. But if we're unsure of which model works best, a reasonable response to uncertainty is rebalancing to equal weights.

Can we do better? The answer depends on our confidence in an asset pricing model. We can also turn the question around and wonder if the drawbacks of the 1/n rule should inspire us to look for greener pastures elsewhere. If the known defects of equal weighting outweigh the skepticism that inevitably lingers over a model's assumptions, the case for something other than a 1/n game plan may be reasonable after all.

For example, higher volatility with 1/n is a possibility, particularly for equal weighting within a single asset class. (As our back test suggests, however, that risk can be mitigated in a multi-asset context.) Equal weighting, by virtue of diversifying into everything, also ensures that you'll own more of the securities (or asset classes) that are currently unpopular with the crowd. In addition, maintaining an equal mix with regular rebalancing raises expenses and trading costs, unlike less-demanding strategies. The 1/n portfolio also suffers higher tracking error against benchmarks targeting more familiar weighting systems (or asset allocations), such as the popular 60/40 stock/bond standard or a CAPM yardstick. Depending on the target pool of assets, equal weighting can also lead to unwelcome concentration in certain types of securities or asset classes. And if we factor in the particular circumstances of any one investor-risk tolerance, investment horizon-the one-size-fits-all concept of equal weighting looks even less appealing.

Steve McCarthy, a CFP at McCarthy Asset Management in Redwood Shores, Calif., says the rebalancing aspect of equal weighting is compelling. He sees it as a tool for exploiting the bias toward mean reversion in market returns. "By equal weighting, you're adding to areas that have underperformed." So why not equal weight asset allocations for clients? McCarthy says he can add more value by taking a more proactive approach to managing the asset allocation.

Jeff Troutner of Equius Partners doesn't reject equal weighting per se, but the 1/n rule's silence on the subject of risk bothers him. "When you equal weight [an equity fund], by definition you're overweighting small-cap and value stocks," he says. As a result, the equal-weighted strategy may have a higher expected return, but there's a risk explanation for that. He argues that any edge with 1/n can be traced to the lessons in the three-factor Fama-French model. "A model-free investment strategy is like a sailboat without a rudder."

Most advisors, money managers and investment strategists agree. Yet the power of equal weighting can't be denied. One might wonder if there's room for compromise, a midway point between 1/n and traditional portfolio designs. Actually, if you look below the surface of several new weighting strategies, you'll find portfolio rules that move closer to equal weighting without formally embracing the idea. Why not go all the way? The standard response from the finance industry is a familiar refrain-namely, a belief in the existence of a better model.

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