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Yet More Shocking Findings About Active Management

Updated: May 18, 2022

From Seneca Investment Managers' public marketing material. Seneca is now part of Momentum Global Investment Management.

Most of you will have heard of ‘active share’, the simple measure of the ‘active-ness’ of an actively managed fund popularised in 2009 by Yale’s Martijn Cremers and Antti Petajisto. However, you may not have heard of 'active share' (sic), another measure of ‘active-ness’ that has been around since 2005.

"The implication of this is that ‘multi-asset’ may be an area where active management works well"

This was the brainchild of the State University of New York’s Ross Miller, as presented in his paper The True Cost of Active Management by Mutual Funds. Sadly, Miller’s ‘active share’ did not appear to get as much attention as that of the Yale chaps.

Not, that is, until now.

To recap, the active-ness of a fund is not about activity (turnover). It is about how different a fund is in comparison with its benchmark or passive equivalent. Knowing this helps one gauge whether one is paying for genuine active management or (overpaying) for passive in disguise.

There are a few ways you can do this for a particular fund.

The simplest way would be to eyeball the investment performance to see how much it deviates from its benchmark from period to period (months or weeks, say). This is fine, but it does not provide you with a quantitative measure of ‘active-ness’ and thus the scope to compare funds with each other.

Or, you could do something similar, but do it systematically. How? By looking at the tracking error of the fund’s returns in relation to its benchmark index. However, although tracking error is a quantitative measure of ‘active-ness’, and thus can be used to compare funds, it is simplistic and thus limited in meaning.

A third way would be to use the Yale chaps’ ‘active share’. This is indeed an interesting and useful yardstick, but it does require one to know all the holdings of the fund and their weights, as well as the holdings - and their weights - of the benchmark index. These may not, in many cases, be readily available. Furthermore, this version of active share only calculates ‘active-ness’ at one point in time, which may not be representative.

One unique attribute of ‘Yale active share’ is that it distinguishes between funds that have high tracking error but low stock concentration (what Cremers and Petajisto term ‘Factor Bet’ funds – funds with highly active sector positions but low stock level concentration within sectors) and those that have high tracking error and high stock level concentration (what they call ‘Concentrated Stock Pickers’). The latter is where they find the great performers, with ‘Factor Bet’ funds on average doing OK before fees but nothing net of fees.

However, it is somewhat limited in that it neither tells you what you are effectively paying for the active service, nor what the active service is generating in terms of investment performance (alpha).

For this, please welcome Ross Miller.

Miller’s key insight is that any fund can be thought of as the combination of an active part (the active share) and a passive part and that these parts, though not ‘observable’ as such, can be objectively calculated as portions that add to 100%. Once this has been done, one can isolate what one is paying for the active part (the active expense ratio) as well as the value added one is receiving in relation to the active part (active alpha) by attributing typical passive fees (e.g. 0.1%) as well as the (zero) passive alpha to the passive part, then seeing what’s left.

Having calculated the active alpha and the active expense ratio one can divide one by the other to get what is arguably the key metric for all active funds, namely the cost of one unit of alpha.

So, how does Miller divide funds into their constituent parts?

First, he notes that if one can discern a passive part of an active fund, it should be the part that is 100% correlated with the benchmark index. Similarly, the active part should have zero correlation. Aggregating the two would then give you something that had the same overall correlation features as those of the fund itself (defining active management in conceptual terms as ‘that which bears no relation to the index’ is, I think, Miller’s key and brilliant intuition).

Second, to derive the numerical proportions, he applies some clever maths using only the correlation coefficient, R. (For more detail, take a look at The True Cost of Active Management by Mutual Funds. You can see in Table 1 of the paper that the full sample to which Miller applies his analysis comprises 4,752 US mutual funds whose average active share is calculated to be 22.1%. Although this might sound low, and it is, it is still a fairly meaningless number. What really matter are the active expense ratios and the active alphas.)

Now, it is important to understand that the active and passive parts are not ‘observable’ – in other words they are not sub-portfolios with their own holdings and weightings. Rather, they are conceptual, albeit measurable, components. Imagine mixing 40% yellow paint (representing passive) and 60% blue paint (active). One cannot separate the two but what one can do is calculate the proportions by assessing the precise shade of the resulting green.

Calculations of the active expense ratios and the active alpha involve similar maths, but in addition to R require two further independent variables: the typical fees of the equivalent passive fund (one that seeks to track the index that the fund uses as its benchmark) and the expense ratio of the fund itself.

One other interesting aspect of Miller’s analysis is that it allows the direct comparison of mutual funds with hedge funds. One can compare the active expense ratio of a mutual fund with the actual fee (management plus performance) of a hedge fund that is producing the same level of alpha. This does however assume that hedge funds produce only alpha (no beta) which as we all now know is not quite true.

As for the results of Miller’s analysis, many of them were astonishing. Below is one extract pertaining to Fidelity’s Magellan Fund, which had previously been managed by the great high conviction stock picker Peter Lynch (the below appears to indicate that things changed dramatically under one of his successors).

In other words, the fund had such a high correlation with the benchmark index that its active share was very low. Thus the not unheard of overall alpha of -2.67% became a shamefully high -27.45% active alpha when calculated in relation to the small active portion.

Another of Miller’s interesting observations is that the difference between the average overall alphas of funds with the ten lowest and ten highest active expense ratios can be explained almost entirely by the difference in overall expense ratios (more on this later).

I now come to what you may all have been waiting for: an analysis of UK funds.

We at Seneca are multi-asset managers, so it seemed only right to consider a multi-asset fund sector, specifically one that contained one of our funds. The tables at the bottom of this post set out the results of Miller’s framework as applied to the IA Mixed Investment 20-60% Shares sector (investment performance was assessed over the last five years, with 102 funds measurable over this period).

I have used the same passive equivalent for all funds, namely the Vanguard LifeStrategy 40% Shares Fund. Since some may argue that this is not the benchmark they seek to beat, I have also provided volatility-adjusted returns. It can be seen that all funds at the bottom of the list score poorly on this measure, so use of the Vanguard fund appears justified.

I have only named the best ten funds, though I would be happy to provide my full Excel spreadsheet upon request.

It is encouraging that although only 23 of the 102 funds generate active alpha equivalent to three times the active fees (i.e. at least two thirds of gross active alpha goes to the customer), the vast majority (71 funds) produce positive alpha net of fees. The implication of this is that ‘multi-asset’ may be an area where active management works pretty well (as opposed to ‘single-asset’ where evidence clearly indicates the opposite).

I would surmise that the reason for this is that markets are more predictable than individual stocks. Take the government bond market, for example. If the real yield of the five-year linker is -2%, you know that the real five-year return will be -2% annualised. You also know that the real return of the five-year “nominal” will on average be pretty close to -2% annualised (breakeven inflation rates are generally a reasonably good predictor of actual future inflation). Furthermore, if the real yield of the ten-year linker is -2%, the subsequent five-year real return is likely to be pretty close to -2% annualised. And so forth. (See

There are similar findings with equity markets1 in relation to starting period dividend yields. If starting yields are above average, subsequent returns tend to be above average (the opposite holds when yields are below average).

Back to Miller and the 20-60% Shares sector.

In relation to the Vanguard fund, the average fund’s beta is a low 79.7%, meaning that funds are on average taking less market risk. All else being equal, this naturally allows alphas to be higher.

Perhaps the most interesting chart that can be derived from the numbers in the above table is the one below, which compares net overall alphas with OCFs (Ongoing Charges Figure). The correlation (R-squared) is very low, which means that factors other than OCFs mostly explain alphas. Where OCFs do provide some explanation, it is that the higher the OCF, the higher the alpha (note the upward sloping best fit line). In other words, funds with lower OCFs do not necessarily produce better returns for investors. In fact, returns tend to be worse. Perhaps the FCA might like to give Prof. Miller a call.

Published in Investment Letter, September 2017

The views expressed in this communication are those of Peter Elston at the time of writing and are subject to change without notice. They do not constitute investment advice and whilst all reasonable efforts have been used to ensure the accuracy of the information contained in this communication, the reliability, completeness or accuracy of the content cannot be guaranteed. This communication provides information for professional use only and should not be relied upon by retail investors as the sole basis for investment.

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