Well, if you remember the Three-Factor Model, that would be accounting for

any small or large tilt in portfolio composition or any value or

growth tilt in the composition of the portfolio holdings.

So on the Three-Factor Model, in index funds of small stocks should have an alpha

of zero when we're looking at gross returns, same for the value index fund.

It should have an alpha of zero as well when looking at the gross returns.

Now the net returns should have an alpha that's slightly negative reflecting

that when we look at the benchmark in a CAPM or Three-Factor Model,

we're looking at a benchmark of an index fund with zero expenses.

So in the real world, these index funds are going to have some expense.

It might be as low as 5 basis points for the S&P 500 on an annual basis, but

there'll be some expense.

So, this expense charged by the fund would be reflected in a negative

alpha in the Three-Factor Model.

So kind of bottom line, gross returns in this example.

The alpha will be zero in each case.

Net returns after expenses, slightly, slightly negative.

Let's get to a study here that's looking at

the average performance of actively managed mutual funds.

What should be a key bullet point you should take away of knowledge of how

do these actively managed equity funds perform?

Fama and French, this isn't the first time you've heard that pair of names.

They did a 2010 study where they look at the performance

US actively-managed equity funds from 1984 to 2006.

They evaluate the performance of all the actively-managed mutual funds on both

an equal-weighted and value-weighted basis.

So in an equal-weighted basis, it means we just take the average return,

regardless of how much money is invested in the fund.

On evaluated basis, we're going to give more weight to the returns of funds that

have a lot of assets under management and

less weight to those that have a limited amount of investment in that.

So, how are they going to evaluate the performance of these funds?

They're going to use several different risk return models.

First, start out with classic CAPM.

Not surprisingly, given it's Fama and French.

We have to use a Fama and French model, the Three-Factor Model where

we'll control for size and value affects, then the Four-Factor Model

where we look at size and value and we also control for any momentum effects

when we want to measure the rest adjusted performance of the fund.

So in this study, we're going to Fama and French analyze performance

both on a net basis after annual fees that investors have to pay and

on a gross basis before annual fees and

they're looking at these returns on an annualized basis and percentage points.

They're running regressions using monthly data.

But when they calculate the alpha, they'll gross that up, so

it'll be easy to interpret in an annual basis.

In the tables I'm about to show you, coefficient estimates from the model,

the betas and the alpha.

They're reported in one row with the t-statistics

of those estimates in the row right beneath it.

So remember, the quick stats review in module one, the t-statistic of

at least two indicates statistical significance at a conventional 5% level.

So if you see these t-statistics, look for

t-statistics greater than two in magnitude.

So, let's get and look at their results here and this is very useful for

just giving a broad sense of how do mutual funds do?

Do they deliver value to investors?

And this is very useful to think of should we go the actively managed route or

should we go the index route?

So, what are Fama and French doing here?

We're looking at the excess return of mutual funds and

we'll consider a simple CAPM model.

So, you can see that is in the first row here.

When we're looking at mutual fund returns when we equally weight,

that means every mutual fund has the same weight in the regression.

We just take the average regardless of how much money.

The mutual funds are managed.

The CAPM regression result is in row one.

Also for valuated returns, that means when we're doing this analysis,

when we're looking at the average mutual fund return, those mutual funds that have

more assets under management get more weight in this average than those mutual

funds that don't have much assets under management and under the valuated returns.

The first row here is also the CAPM estimates,

then they do a Three-Factor Model.

Those are the estimates provided in the second row here where we're accounting for

the size tilt and the value tilt in the portfolio, and

we do this for both equally weighted, and value weighted.

And then finally, a Four-Factor Model where now we're also controlling for

any momentum effects in the returns of the portfolio.

That will be subtracted out when measuring the alpha and that's in the final row

here, the third row for the equal weighted analysis and the valuated analysis.

So, let's just focus on the three factor models.

After all, it's a study done by Fama and French here.

So, let's just focus on that.

So, let's look at these regression results.

So here, we have the beta for the market, market's up two.

This is basically one.

So, this beta of one and

this is the t-stat relative to is this statistically different from one.

So this 0.98, it's really not statistically different from one.

This t-stat is less than two in magnitude, the size factor.

So there seems to be, for the average mutual fund,

a little tilt towards small stocks, but not very much.

The value factor here, this coefficient zero.

So, there isn't a tilt value to growth.

Let's focus on the alpha and

these are alphas that a gross stop to reflect an annual basis.

So, what's the net alpha telling us?

It's telling us for the average mutual fund,

it's underperforming its benchmark by 0.9% on an annual basis.

So once you pay the fees, you're actually underperforming

your 0 cost index fund by 0.9% on an annual basis.

In terms of gross returns and that's statistically significant,

this t-stat is greater than two in magnitude.

When you're looking at gross returns, whether the returns that the average

mutual fund before fees, it's 0.36% per year.

So not a big difference, but not statistically different from zero,

this t-stat's less than one.

Let's look at the results when we value weight.

So here, when we do the average, we're going to give a higher weight to mutual

funds that have more assets under management,

less of a weight to mutual funds that have less assets under management.

So we see here, kind of similar pattern.

Kappa and beta of about one,

which you would kind of expect when you add up all these mutual funds together.

They kind of have about the same sensitivity to the market,

as the market does itself.

The beta's about one.

Slight tilt towards small stocks, but very small coefficient here on the size factor.

And then this value factor, it's basically zero.

So, not real a big tilt when you aggregate up across the mutual funds on the size or

value dimension.

Let's look at the alphas.

So once we evaluate, again, we see this strong,

under performance after fees, mutual funds when you evaluate them

under performing their best mark by about 0.8% on an annual basis.

Once you take into account the fees investors have to pay,

statistically significant when we look at what's their gross performance.

So how are mutual fund managers doing,

just in terms of their benchmark before we subtract out any fees.

Well, it's kind of like the individual investors, the alpha's basically zero.

So they're kind of just getting what they should given the rest they're taking,

this is 0.13% per year.

Slightly positive, but basically zero.

So what's kind of the bottom line we see here,

let's just focus on the value weighted averages here.

Regardless of whether you use the CAPM, you use the Three-Factor Model or

you use a Four-Factor Model.

You see mutual fund industry actively managed stock funds underperforming

their benchmark once you take into account the fees you pay by about one

percentage point per year.

So you can aggregate up one percentage point less return per year,

it can be nontrivial difference in wealth.

So you may want to then ask the question well, okay, so after fees, these actively

managed mutual funds on average seem not to do that well for the investor.

They'd maybe be better off just investing in an index fund with an expense ratio of

five basis points per year.

How do the mutual fund managers do though,

just looking at their absolutely performance, their gross performance?

Do they have good information?

Are they at least earning a positive alpha before fees?

When you look at the aggregate mutual fund industry,

that doesn't seem to be the case.

You look across the CAPM, the alpha is slightly negative.

Three-Factor Model is slightly positive.

Four-Factor Model is slightly negative.

All of these are not statistically different from zero.

So you don't see when you look at aggregate mutual fund industry,

you don't see any positive alpha being generated from their investments.

So, it doesn't mean that an individual mutual fund isn't earning

a positive alpha.

And if they are, then you have to think is that due to skill or luck?

But when you look at the actively managed mutual fund industry as a whole,

two clear pictures.

One, no outperformance when you're looking at gross returns.

And two, negative alpha once you subtract out the fees which is

relevant to you as an investor.