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.