It is difficult to imagine a more challenging investment environment than the one now confronting us. The world economy is mired in an epic recession. The credit markets are dysfunctional. The rule of law is under attack from Congress. And market pundits offer a bewildering array of advice spoken with a sense of confidence that can be born only of ignorance. What are wealth managers to do?

We should not try to be heroic and search for the asset class or strategy that will yield the best return, nor should we panic and allocate all of our savings to gold. Rather, we should embrace two fundamental tenets of prudent investing: diversify and eliminate unnecessary costs.

Diversify
The only problem with diversification is that it’s never been tried — at least not properly. Most investors look to their domestic equity market as the main engine of growth for their portfolio, and they search for other assets to diversify this exposure. But the typical investor considers only average correlations when measuring an asset’s diversification benefits, and average correlations tend to be very misleading. For example, when both U.S. and non-U.S. equities produce returns greater than one standard deviation above their mean, their correlation equals –17 percent, and when both markets produce returns more than one standard deviation below their mean, their correlation rises to +76 percent.¹ This pattern is the opposite of what we need. The assets chosen to complement a portfolio’s main engine of growth should diversify this asset when it performs poorly and move in tandem with it when it performs well. Reliance on average correlations is akin to owning clothes suitable only for the year’s average temperature rather than the extremes that prevail in January and July.

We can condition correlations on a variety of factors, including threshold returns, inflation, interest rates, and even measures of market turbulence. This latter factor is particularly pertinent given the current environment.

A turbulent period is defined as one in which the returns across a set of assets behave in an uncharacteristic fashion. One or more of the assets’ returns, for example, may be unusually high or low, or two assets that are highly positively correlated may move in the opposite direction. This measure of turbulence tends to be more robust than measures that focus only on volatility, such as the VIX Index, because in addition to volatility, it captures strange interactions among a wider set of assets. Consider, for example, the following scatter plot of hypothetical stock and bond returns.

Each plot represents the returns of stocks and bonds for a particular period, such as a day or a month. The center of the ellipse represents the average of the joint returns of stocks and bonds. The shaded ellipse represents return combinations associated with quiet periods because the observations are not particularly unusual. The observations outside the shaded ellipse are statistically unusual and, therefore, likely to characterize turbulent periods. Notice that some returns just outside the narrow part of the ellipse are closer to the ellipse’s center than some returns within the ellipse at either end. This illustrates the notion that some periods qualify as outliers not because one of the returns was unusually high or low but, instead, because the returns moved in the opposite direction during that period despite the fact that the assets are positively correlated, as evidenced by the positive slope of the scatter plot.

If we add a third asset, we need to add a third dimension to the graph and use an ellipsoid to distinguish quiet periods from turbulent periods. We are unable to graph the separation of quiet regimes from turbulent regimes beyond three assets, but mathematically, we can apply this methodology to as many assets as we like. We end up with a score for each period indicating its level of unusualness that takes into account the size of the returns as well as how they interact with one another.² The chart below shows that this statistically derived measure of turbulence captures well-known turbulent events throughout history.

We can use this information to control risk more efficiently and to structure portfolios that are more resilient to turbulent markets. For example, we can stress test our portfolio by estimating exposure to loss based on volatilities and correlations that prevailed during the turbulent subperiods rather than based on values averaged over all market conditions, resulting in a portfolio more suitable to our risk tolerance.

We can also blend the volatilities and correlations from turbulent regimes with those from nonturbulent regimes in accordance with our expectation of the relative likelihood of turbulence and quiescence, thereby producing portfolios that should perform better in turbulent periods than ones derived from average volatilities and correlations.

Eliminate Unnecessary Costs
Inefficient diversification imposes an indirect cost on our portfolio because for our chosen level of risk, we accept a portfolio with a lower expected return than we could otherwise achieve. But most investors incur unnecessary direct costs as well in the form of management fees, transaction costs, and taxes. By far, the most effective way for reducing these costs is to invest passively. For example, a typical U.S. equity mutual fund charges 1.25 percent of assets under management to private investors compared with about 10 bps for an equity index fund. In addition to charging higher fees, active equity managers trade much more frequently than index funds. Active managers continually seek to replace stocks believed to be overvalued with those perceived to be undervalued. Index funds, instead, trade only when the index is reconstituted. The typical actively managed U.S. equity mutual fund experiences about 95 percent turnover annually compared with about 4 percent for an index fund. This additional turnover increases the expense of active management in two ways: by increasing trading costs and by increasing capital gains taxes. Hedge funds suffer even greater costs. The typical hedge fund charges a management fee equal to 2 percent of assets under management and a performance fee equal to 20 percent of profits. Moreover, hedge funds typically experience far greater turnover than mutual funds. Based on the investment assumptions shown below, we use Monte Carlo simulation to estimate expenses, net return, and future wealth for these alternative investment approaches.³

We start with a base case in which the mutual fund and hedge fund managers have no skill. This assumption may not necessarily be the most plausible one, but it highlights the hurdle active managers face. As shown below, the index fund produces a net return of 7.28 percent, compared with 4.70 percent for the mutual fund and 2.38 percent for the hedge fund. Notice that the hedge fund collects a performance fee, even though its average alpha equals zero. This occurs because, even though alpha averaged over 10 years equals zero, in some years, the hedge fund adds value and collects a fee, but it does not reimburse the investor in those years when alpha is negative.⁴

The index fund more than doubles wealth in 10 years, while the mutual fund grows wealth by less than 60 percent and the hedge fund by less than 30 percent over the same period. In fact, it would take more than 15 years for the mutual fund to double wealth, and the hedge fund would require more than 30 years.

Laurent Barras, Olivier Scaillet, and Russ Wermer (BSW) have provided evidence that most active managers generate an alpha about equal to their fees.⁵ If we assume, therefore, that the mutual fund generates an alpha of 1.25 percent and the hedge fund produces a 2.00 percent alpha, the index fund still outperforms the mutual fund by 1.81 percent per year and the hedge fund by 3.93 percent after we account for taxes. In order to generate as much wealth net of all expenses 10 years hence as the index fund does, the typical mutual fund requires an alpha of more than 4.00 percent, and the typical hedge fund must outperform by more than 10.00 percent!⁶

How likely are we to identify — in advance — active managers who will generate sufficient outperformance to overcome their costs? BSW showed that only 0.6 percent of managers produce alpha as a consequence of skill. Most of the alphas that show up in mutual fund performance data reflect luck as opposed to skill. BSW examined the returns of 2,076 U.S. mutual funds. They took into account the following fact: In a universe in which alpha does not exist but noise does, some fraction of observed alphas will nonetheless appear to be significantly positive. If, for example, we require 95 percent confidence to declare an outcome a true positive alpha, even in a universe without any true alphas, 5 percent of the observed alphas will appear as true positive alphas. After reducing the total fraction of observed positive alphas by the fraction that was really caused by luck, BSW found that from 1989 to 2006, the fraction of skilled managers (active returns exceed costs) declined from 14.4 percent to 0.6 percent. BSW attributed this shift to an increase in unskilled managers who nonetheless charged high fees.

BSW, however, understated the challenge of finding managers who can cover their costs because they considered costs to include administrative fees, management fees, and transaction costs, but not taxes. If we include taxes in the calculation of alpha, it is much less likely than even 0.6 percent that any fund could generate alpha.

Conclusion
Rather than try to divine the unknowable, wealth managers should focus on practices that are almost certain to improve their clients’ financial health:

1. Estimate expected returns, volatilities, and correlations net of taxes and use these values to construct after-tax efficient portfolios from a broad range of assets.
2. Separate historical returns into quiet and turbulent regimes and use these subsamples to measure the diversification properties of assets.
3. Invest passively to eliminate unnecessary management fees, transaction costs, and taxes.

Mark Kritzman, CFA is president and CEO of Windham Capital Management. For more discussion, see Mark Kritzman, 2009. Managing Assets in Turbulent Markets, CFA Institute Conference Proceedings Quarterly, v.26, n.1, 53-61.