John Bogle, regarded as the Father of the Index Fund (where the fund manager invests in stocks or bonds or whatever, according to some index - like the S&P 500 or TSE 60) said, in his book Common Sense on Mutual Funds:

Only 33 of the 200 growth and value funds that survived the 15 year period (1983-1998) outpaced the Wilshire 5000 index during this period; the remaining 167 fell short."

Finally, a recent New York Times article said:

"Over 10 and 15 years, the Vanguard 500 has beaten the average actively managed fund by more than 2 percentage points a year."

Also, check out Active or Passive investing.

Even Sharpe says - and demonstrates with simple arithmetic - that (before costs) the total return of all investors (active and passive) is necessarily the same as the total market, and since the returns of the passive investors equal that of the market, the average of active investors must equal the market as well.

>So, that means ...
Pay attention. I'm not finished.
If the average returns of active and passive investors are the same, and active investors pay more for their trading (an "actively managed" mutual fund would have a higher MER = Management Expense Ratio), then after costs, the average active investor has a lower return.

>So, investing in an Index Fund, like the Vanguard 500, is better, eh?
No, I'm not saying that. I'm saying "don't be an average active investor" or, if you invest in mutual funds, don't invest in an "average" fund.

>And you can pick these funds which will, in future, be better than average, eh?
Of course. Can't you?

Seriously, I don't know why the Average return of actively managed funds is relevant to the argument. Shouldn't one be interested in the average return of the investor who invests in managed funds (as opposed to those who invest in passive, Index Funds)?

>But isn't the MER less for a passive fund? I mean, the manager doesn't have to spend much time determining which companies to invest in. She just picks the companies in some Index and ...
True, but does that prove that actively managed funds are worse?

>But you've already said - and so did Bogle and the NY Times and Sharpe - that the average actively managed fund is worse ...
Careful. Sharpe talked about the average actively managed dollar ... not the average active fund. It's certainly possible to have every actively managed fund beat the market and every active do-it-yourself investor do worser so that ...

>So that their average equals the market, eh?
Exactly.

Besides, I'm interested in the returns for the average investor, not the average fund.
Consider this.

There are three funds which comprise the universe of Mutual Funds on Planet X: A, B & C.
A & B are actively managed.
C is a passive Index fund.
The annualized returns are
A: 10%
B: 15%
C: 13%
The "average" return of the active funds is (A+B)/2 = 12.5%
Conclusion?
Passive beats Active.

Now I tell you that there are 1000 active-investors on Planet X and 999 of those 1000 active-investors invest in fund B.
(There's just one poor chap who invests in A.)
Further, the remaining investors of Planet X invest in C.

>I assume that "active-investors" means those who invest in actively managed funds.
Yes. Pay attention.
The "average" return of the active-investors is (1 x 10% + 999 x 15%)/1000 = 14.995%, compared to 13% for the "passive-investors".
Conclusion?
Active beats Passive.

Now I tell you that those 999 (of the 1000 active-investors) - they each invested $1.00 where the poor guy who invested in Fund A invested $1001, making a total of $999+$1001 = $2000.
The "average" return of the active-dollars invested is
(Total Dollar Gain)/(Total Dollars invested) = (10% x $1001 + 999 x 15% x $1)/$2000 = 12.498%, compared to 13% for the "passive-investors".
Conclusion?
Passive beats Active.

>And that proves ... what?
Only that it makes little sense to consider the performance of the average active-fund. Surely one should consider the performance of the active-investors. If, for example, a hundred new actively-managed funds were to appear on Plant X ... each with a single investor and a fund manager incapable of rational thought ... then the "average" performance of the active-funds could very well go down.

>And that proves ... what?
That we shouldn't consider the "Average" active-fund, but rather ...

>... the "Average" active-investor, right?
Right! To get a feeling for what the average investor gets, I suspect it's more reasonable to consider just the huge funds which have a jillion investors ... and ignore the tiny funds who may screw up that "average".
For example, the average 10-year returns for the S&P500 and two of the largest U.S. mutual funds are:

S&P 500: 14.32%   this is the average, not the annualized return
Vanguard 500 Index Fund: 14.37%   passive, eh?
Fidelity Growth & Income Fund: 14.88%   an actively managed fund

>Don't you have any pictures? A picture is worth a thousand ... Okay, here's a picture: The Vanguard Wellington Fund is old - since 1928 or 1929, I think - and is actively managed. >It's an equity fund, I presume. Well, equities and bonds. >And you're comparing to the S&P500? That's like apples and oranges and ... Yes, yes. Give me time. I'll get the data and demonstrate, one way or t'other, that Active beats Passive or Passive beats Active ... but based upon a rational comparison scheme. None of this Average mutual fund comparison or Most funds fail to beat the index. >I can hardly wait.

>But, the future. Can you tell by looking at past performace? Remember that past performance ...
Yes, yes ... no guarantee. So let's suppose that it's 1995 and we look at, for example, the ABC mutual fund. The average return over the previous five years (1990-1994) is 30.0% whereas the TSE 300 total return is 5.6% so you buy ABC, based upon past performance. Over the next five years ABC has an average return of 13.1% whereas the TSE was sitting at 17.7%.
>So?
So you can't guarantee that past performance will identify the best choice over the next five years.
>So?
Patience. By 2001 ABC had an average return (1995 to 2001) of 14.2% whereas the TSE had 11.9%.
>So?

So, although most investors can't predict the future, I suspect that the past perfomance of an active fund manager can be used to identify those funds which are likely to beat the market. >Most investors can't predict the future? Don't you mean ALL investors? Well ... uh ... some of us can predict the future. Anyway, if we used the average returns over the previous umpteen years - compared to the TSE as the benchmark - we'd like ABC, right? >Do you get a commission for every new ABC client? I don't own any ABC. I just want to investigate ... >Is ABC your only example? A universe of "1" is hardly a convincing ... Okay, okay. Give me a minute ... but, in the meantime, check out Buffett's investments.

>Hey! This last chart says an average return of about 20% for ABC, since 1990, yet you have 17.8% in an earlier chart so ...
Aah, there's a difference between Average and Annualized. That 17.8% is the Annualized return which is always smaller.
(See Average vs Annualized.)

>So? What's your conclusion?
I don't have one ... yet. But give me time and I'll demonstrate that ...

>That Active beats Passive or Passive beats Active, based upon a rational comparison scheme, right?
Well ... that one may be able to identify the actively managed funds which beat the market. For example, if a particular asset allocation beat the market in the past, perhaps we should invest in a fund where the manager uses that particular allocation. The Total Stock Market has no preferences when it comes to asset allocation. It's just there. It doesn't rebalance itself to maintain some prescribed ...

>That's silly. How about a picture?
Here's a particular allocation of Large Cap Growth and Value and Small Cap Growth and Value (with annual rebalancing) which beat the Total Stock Market in every decade from the 1930s to the 1980s:

>I assume the missing asset class is small cap growth.
Yes, but ...

>And the missing decade is the 1990s ... why? Uh ... here it is >Aha! So the market beat your 25+25+0+50 allocation! Yes, but I didn't say this was the best allocation, did I? It's just an example. It doesn't even have bonds. The point is, maybe we can find an allocation which has beaten the market, historically, and then find a manager that abides by that allocation. >Or do the allocation ourselves? Why not? Pick a set of funds which mirror the allocation you've selected. >So, what's the best allocation?

I don't know ... yet, but I suppose it depends upon your genetic configuration.

>So, have you ever recommended something, to a friend or relative or ...? I did suggest an S&P 500 Index Fund to my daughter, but that was so she wouldn't be disappointed in getting a return less than the S&P 500. >Chicken! Well, I'm still looking for a good selection, basing it upon the historical record, past performance, track record yet having a sensible diversification and allocation and ... >While you're looking, remember that past performance doesn't guarantee future ... Yes, yes. Don't bug me. Besides, if we look at particular asset classes then we might conclude that, say, Small Cap Value (SV) has often been the best bet ... >In the past! Yes, in the past. But now suppose we take as our "Market" the collection of all SV stocks. If we take a passive/index approach to generating a Mutual Fund, where the Index is just the SV stocks, then we may be able to beat the larger market, like the S&P 500. In fact, we might consider a collection of stocks which reflect the returns of an entire asset class*. For example, if we select a year at random, from 1950 to 2000, and use the annual returns for that random year, then our portfolio (with various allocations) would look like ... assuming annual rebalancing and annual withdrawals and a Monte Carlo simulation. See? Lots of SV is good. >In the past! Yes.

^* Dimensional Fund Advisors (the "advisors" being some BIG names in investment theory (Eugene Fama, Merton Miller, Myron Scholes, Kenneth French, Roger Ibbotson) uses this strategy.

for Part II

See also Cut & Chop for a spreadsheet which does some of this stuff.

P.S.
Of course, one should beware of comparing long term performances when trying to establish whether investment A beats investment B. Here's an example:

• Annual returns for Mutual Fund XYZ trailed S&P 500 returns by 1%, every year since 1928 ...
  ... except for one year:   1931.
• In 1931 the S&P dropped 43% while our XYZ fund increased by 5%.
• It took until 1996 for the S&P 500 to catch up to XYZ