A lesson in "new math" shows another way to measure cost in mutual funds.

    A while back, a division of Germany's Volkswagen AG took over famed Italian sports car maker Lamborghini, fending off rumors that plodding VW guts would soon be dropped into sleek Lambo bodies. To date, nobody's yet discovered a Beetle hiding under the hood of their quarter-million-dollar Diablo.
    Investors and advisors, however, would do well to double-check the innards of their mutual fund portfolios to make sure they're not paying high-performance prices for putt-putt results. This warning comes on the heels of the publication of a paper by State University of New York finance professor Ross Miller. In his paper, Miller proposes a simple calculus to slice mutual fund performance-and costs-into active and passive components to better gauge a manager's value.
    Miller's work is premised on the institutional notion that the unbundling of beta and alpha sources serves to reduce costs and enhance performance.  

The Mutual Fund Package
    Most advisors know that mutual funds are primarily suppliers of beta, or generalized market risk. Morningstar attests to this by pegging the beta (taken as the degree of volatility relative to the S&P 500 Index, or SPX) of the large-cap mutual fund category at .95, or 95%. That's obviously a lot of market exposure.
    Mutual fund investors live in the constant hope that portfolio managers will deliver positive alpha into the bargain. Alpha, of course, represents the "excess return" earned by a manager's security selection and timing acumen. Alpha can, of course, be either positive or negative, depending upon a manager's skill. According to Morningstar, alpha isn't easily snagged from the large-cap market. The three-year alpha of the category was last clocked at -.18 (that's negative 0.18 %). Thus, the "average" fund annually earned six basis points less than the return predicted by its beta.

Unbundling The Package
    Institutional investors have a distinct advantage over their retail cousins in their ability to shop for alpha and beta through different outlets; they're not obliged to buy them bundled. Beta can be acquired cheaply through index funds or derivatives such as swaps or futures, depending upon an institution's taste for leverage, while alpha can be ported from any number of sources. Among the most frequently tapped supplies of alpha are hedge funds.
    Most hedge funds attempt to provide uncorrelated, or beta-free, alpha. Some hedge fund styles naturally filter out stock market exposure better than others. For example the wide net cast by the CSFB/Tremont Hedge Fund Index-a 1,000-portfolio benchmark of various styles-captures a .26 beta, while the fixed-income arbitrage subsector, made up of two dozen narrowly focused funds, snags a barely perceptible .01 beta coefficient.

The Cost Of Alpha
    In addition to their reputation as alpha dynamos, hedge funds are notorious for their high costs. Management fees-often running 2% or more-along with incentive fees of 20% can nick investors' returns. Incentive fees are collected against new net profits earned over an accounting period.
    A hedge fund represents the "less is more" concept. Like the premium charged for the nonfat version of popular foodstuffs, hedge fund expenses reflect the "costs" of stripping away the beta "fat" so that pure alpha can be delivered.
    According to recent Morningstar data, domestic large-cap mutual funds levy an average 1.21% annual expense charge to cover overhead and manager's fees. On the surface, these expenses appear modest compared with hedge fund costs. But are they really?
    Let's play with some numbers to find out. Say we're considering the purchase of a hypothetical no-load, large-cap fund-the Got Bucks Portfolio (GTBUX)-carrying a 1.10 % annual expense ratio. For that price, the fund delivers both alpha and beta. To make a fair comparison with a hedge fund that only delivers alpha, we'll need to do a little math.

Carving Out Alpha And Beta
    First, we need to dissect the GTBUX portfolio into its "active" and "passive" components. The passive portion represents the part that delivers beta and thus could conceivably be replaced by a low-cost index fund. The active portion represents the mechanism that contributes uncorrelated alpha.
    Say Morningstar gives GTBUX an r2 correlation of .93. From this, we know that 93% of GTBUX's variance is explained by the movements of its SPX benchmark. A retail S&P 500 index fund can be held for an expense ratio of only ten basis points, so the rest of the GTBUX's expenses-100 basis points-can be reasonably attributed to active management.
    Spreading that cost over the actively managed segment ought to tell us what we're paying for stock picking. The r2 statistic implies that ex-SPX management accounts for just 7% of the portfolio's variance. That said, a crude reckoning of the portfolio's active management costs appears to be an alarming 14.3 %.
    This back-of-the-envelope approach, while simple, grossly overestimates the actual cost. Why? Because r2 is denominated in terms of statistical variance. We can't spend or trade variance. To come up with a realistic, and usable, value, we need to reduce the portfolio's active and passive weight into dollars.

Active Weight And Expense Ratio
    And here's where Professor Miller's math comes in. The first step is the quantification of GTBUX's active weight. Unfortunately, Morningstar's r2 correlation doesn't offer much precision. Morningstar's ".93" could represent any value between .9245 and .9344. We need the finer-grain detail of three or four decimal places. Owners of Microsoft Office can use the "RSQ" function within Excel to derive a more accurate r2 coefficient from a string of fund and index prices. Just make sure you look for the correlation of periodic returns, not prices. Morningstar uses three years of trailing monthly data for its portfolio statistics.
    Suppose GTBUX's r2 is actually .9320. Plugging this into our arithmetic (see the "New Math" sidebar), we can readily see how much of the GTBUX portfolio weight is given over to active management. As Professor Miller says, "If you can use the memory function of a hand-held calculator, you can derive a fund's active weight." Using our electronic slipstick, it appears that 21% of the portfolio's weight is actively managed.
There's a flip side to this discovery: fully 79% of GTBUX's weight is getting a free ride from the market. Shareholders, however, aren't getting the same price break that index fund investors get for passive management. Instead of paying the commercial value of ten basis points for market tracking, GTBUX shareholders are paying full-boat management fees on the entirety of fund's assets.
    By overlaying the portfolio's 100-basis-point fee premium on its actively managed component (the sidebar walks you through the math), we can come up with the fund's active expense ratio. Thus, we see that investors are paying GTBUX's managers 4.8 %, or more than four times the advertised expense ratio, for alpha-seeking.
    Those hedge fund management fees don't seem so high now, do they?

Active Alpha
    Last, we need to determine how skillful the GTBUX managers are. Perhaps the fund's active expense ratio can be justified by deft stock picking. Suppose Morningstar supplies us an alpha of -1.50 (negative 1.5%) for the GTBUX portfolio. Our new calculus (again, detailed in the sidebar) tells us the fund's active alpha is -6.7 %.
    We now have the common denominator that allows us to compare hedge funds against mutual funds. And by applying just a little more arithmetic, we can also create a tool for comparing mutual funds' alpha efficiency.
    Dividing the active alpha by the active expense ratio yields a benefit-to-cost ratio for GTBUX: a rather dismal -2.14. This should set us out on a search for a more efficient portfolio. A well-performing fund should crank out a positive ratio of 1.00 or higher.
Looking For Alpha Efficiency
    To see how we'd conduct the search, let's start with some of the most widely held funds in the Morningstar universe. Shown in the accompanying table are the characteristics of the ten biggest nonindex retail funds in the large-cap blend category. These funds, amounting to more than $213 billion in assets, are compared against the S&P 500.
    From the figures shown in the table, it's evident that rewards awaited those managers who strayed well away from the SPX benchmark. In fact, judging from Morningstar's "best-fit" analysis, the richest payoffs came from steering portfolios toward growth and international exposures.
    All together, these ten funds earned a not-too-shabby weighted average active alpha of 7.68%. Tellingly, though, the active alpha of the funds hugging SPX averaged -15.66 %.
    This brings us to an important point. Portfolio managers can import beta from a number of sources nowadays. The proliferation of exchange-traded funds, in particular, has made it easier for money runners to pick up core beta cheaply, allowing them to manage their portfolios around the edges for alpha.
    That said, beta isn't always derived from the S&P 500. It might very well come from the Russell 1000 Value Index or any number of tradeable exposures. To accurately gauge the true cost of active management, then, we need to take the measure of portfolios against the best-fitting benchmark.

How Mutual Funds Stack Up
    The important thing to note here, however, is the active expense ratios. These ten funds charged more than 3% on average. Thus, when stock picking is distilled from within a mutual fund, the true cost of active management bubbles to the surface. Excluding the effect of incentive fees, that cost-at least for some of the largest domestic equity mutual funds-seems to be on par, or even higher, than that charged by hedge funds.