New spin on the Fundamental Law of Active Management finds US mutual funds were “a victim of their own success”

The Fundamental Law of Active Management posits that the success (i.e. Information Ratio) of an active manager depends on three things:  their “information coefficient” (ability to forecast security prices), the number of opportunities in their universe of securities, and their “transfer coefficient” (their flexibility in pursuing those opportunities).  In our January 2007 post on the topic, we observed that:

“The information coefficient is just the correlation between the manager’s forecasts and what actually transpires. It’s 1.0 if the manager has a crystal ball and is named “the Amazing Kreskin” and it’s 0.0 if the manager is a chimpanzee taking target practice.”

What we didn’t mention was our skepticism that you could ever really measure the manager’s forecasts for each stock – especially for a fundamental bottom-up manager who probably doesn’t even have a price target (or time frame) for their picks.  If only there was a way to restate the Fundamental Law that didn’t require such detailed (and theoretical) information.

Now there just might be.  In an article published in the Fall 2010 Journal of Portfolio Management, Edouard Senechal of asset manager Singer Partners lays out a framework that “requires no assumption regarding the manager’s asset returns expectations or investment process.”  (Article is also available here on the Singer website.)

Senechal calls his version the “Empirical” Law of Active Management.  After walking through its derivation, he promptly applies it to the US mutual fund Industry.  You know it spells trouble when US mutual funds are put under any sort of microscope.  More on that later; first, here’s the rationale…

As they say, diversification is a “free lunch.”  By simply combining two assets with imperfect correlations, you’ll get a volatility that is lower than the simple weighted average of the two assets’ volatilities.  Since the return on your two-asset portfolio would be the weighted average of the returns of each asset, you’ll likely to end up with a higher risk/return ratio on your “diversified portfolio” than you would by holding one asset or the other.

Because of this, a manager shouldn’t get credit for this free lunch (and, by extension, you shouldn’t pay then to have it delivered it to you).  Senechal calls the free lunch the “Diversification Factor” (“DI”) and defines it as the ratio of the position-weighted volatility of the portfolio to the portfolio’s actual active risk.  If all the positions were perfectly correlated, there would be no free lunch and the DI would equal 1.0.

If you re-arrange this equation to solve for the portfolio’s actual active risk, you get:

Since the Information Ratio is calculated like this…

…you can combine the two formulas and get this:

So basically, the manager’s IR is equivalent to what Senechal calls the “skill” factor times the free lunch:

He’s points out that this is essentially the same as the Fundamental Law, which also describes IR as a factor of skill (“IC”) and diversification (the number of discrete investment opportunities available to the manager, n).  But – and this is the critical difference – by integrating the weight average of volatilities into the Skill Factor, the Skill Factor embeds information about the portfolio concentration and size of the manager’s opportunity set.

As Senechal explains, the Empirical Law is also much more practical when measuring the skill of fundamental managers because it disregards the exact size of the manager’s opportunity set…

“[F]undamental managers cannot cleanly separate transfer coefficient and breadth. The concept of TC makes sense for quantitative managers using models that provide expected returns on wide ranges of securities irrespective of whether they can be implemented or not. On the other hand, given the cost of bottom-up research, fundamental analysts focus on trades that can be implemented. In an investment firm that runs long only portfolios, one rarely sees analysts spending much time on overvalued assets. This makes the distinction between transfer coefficient and diversification less meaningful for fundamental managers.”

He borrows the “Information Triangle” from pioneers of the Fundamental Law (Richard Clarke, Harindra de Silva and Stephen Thorely) to compare the two Laws:

US Mutual Funds

Okay then:  How do US mutual funds stack up in the “Skill” Department?

Senechal acknowledges recent studies showing that higher levels of active management leads to out-performance (including Cremers’ & Petajisto’s “Active Share” measure – see related post).  However, he says that these metrics don’t capture “the impact of concentration in positions’ volatilities and correlations among positions.”

First, he finds that diversification has gone way up over the years (see chart below):

Over the years, US mutual funds have become more diversified.  This means that more of their returns were from the free lunch, not skill (“SK”).  Meanwhile alpha (based on factor model benchmark appropriate for each fund) has been shrinking.  These trends combine to paint a pretty abysmal picture of US mutual funds.

He proposes two theories to explain this “decline in skill.”  First, mutual funds have grown from 3% to nearly half of US equity markets.  They are simply becoming the market, and so this is likely a major contributor.  But the second, non-exclusive possibility is more damning.  As Senechal writes:

“The second explanation for this phenomenon is that the quality of U.S. Equity mutual funds has declined. The industry would have responded to the increase in demand for mutual funds that took place during the 80’s and 90’s by creating sub-par products…there is a large incentive for unskilled managers to flood the market and distribute low cost investment strategies that add no value while charging active management fees. This incentive is even greater when demand expands and new customers with less financial acumen enter the market. Under such circumstances, unskilled managers, or “closet indexers”, will want to take the minimum level of risk that allows them to charge active management fees.”

Now, an increase in demand is usually met by higher prices.  That’s the way more industries work, especially those with somewhat inelastic supply.  But with a virtually infinitely elastic supply, Senechal contends that the asset management industry took advantage of increasing demand in the 1990’s to increase supply at the cost of quality – leading to a market full of highly diversified closet indexers.  The US mutual fund industry, as he says, “was a victim of its own success.”

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