## Investor behavior and fund returns: a paradox?

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Topic Author
mdrileynyc
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### Investor behavior and fund returns: a paradox?

It's often said that fund investors under-perform the fund by substantial percentages (2% or more) by poor market timing. Is this due entirely to trading costs and fees? Because if you ignore trading costs and fees, the average return of an investor weighted by his starting balance I believe equals the average return of a fund weighted by its starting balance. It's simple arithmetic; I'll post the equations in a followup. So:

1) if it's not all trading costs and fees, then what have I missed?
2) if it is all trading costs and fees, then it's not so much poor timing as useless timing on average, yes?
Last edited by mdrileynyc on Mon Jan 02, 2012 4:34 pm, edited 6 times in total.

livesoft
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### Re: Investor behavior and index funds: a paradox?

Or it is fees on index funds. My spouse has an S&P500 index fund available in her 401(k), but the sponsor tacks on a hefty surcharge to use it with an expense ratio of about 2% when all is said and done. There are many such 401(k) plans out there.

Or just use an advisor that charges 1.5% to 2% and puts one in index funds. Not unheard of.
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Topic Author
mdrileynyc
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### Re: Investor behavior and index funds: a paradox?

Here's the claim. Let B[i,f] be the starting balance of the ith investor in the fth fund and let B'[i,f] be the ending balance after some period - say a year. Then:

Fund f's return: R[f] = (Sum_i B'[i,f]) / (Sum_i B[i,f])

Investor i's return: R = (Sum_f B'[i,f] / (Sum_f B[i,f])

But:

Sum_f R[f] (Sum_i B[i,f]) / (Sum_i,f' B[i,f']) =
Sum_i R (Sum_f B[i,f]) / (Sum_i',f B[i',f])

Topic Author
mdrileynyc
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### Re: Investor behavior and index funds: a paradox?

Livesoft - thanks for the reply. The expense ratio should affect the fund's performance as well as the individual's. I edited the OP to say the fund's return rather than the index's return. The advisor cost I'd include in 'trading fees'; I edited adding 'and fees' to be clearer. Sorry to make your reply less understandable if they don't read this .

SpecialK22
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### Re: Investor behavior and index funds: a paradox?

I believe investor market timing comes into play as well. For example, someone who sells TSM in early 2009 and goes to cash only to return to TSM in mid 2011. Despite being an investor in TSM they would have underperformed the index substantially over the same period. Even indexers, especially non-bogleheads, are subject to emotionally driven investing: Panicking during decline or recession and irrational exuberance during a bull market.

Topic Author
mdrileynyc
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### Re: Investor behavior and fund returns: a paradox?

Specialk22 - Well 'cash', say a money market, is a fund too and is already included in the claim, yes? So I don't see how that can be it.

nisiprius
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### Re: Investor behavior and index funds: a paradox?

I think what you're missing is that investors enter and exit the fund, and not necessarily all at the same time... and that--I'm not sure of this, but I think--the stated returns of a fund are the hypothetical return that would have been experienced by an investor who stayed in the fund.

These explanations of how investors earn a different amount than the fund are always based on the fund's asset inflow and outflow.

For example, suppose that a fund has 200 million shares priced at \$50 each, for a total of \$10 billion in assets in January, 2008, and that it is owned by a 100,000 investors each of which has exactly 2,000 shares of the fund, for a total of \$100,000 each.

Suppose that the fund's price halves, to \$25 a share in March, 2009. Suppose that 90,000 of the fund's shareholders all sell the fund at that time, for a total of \$4.5 billion. They have collectively lost \$4.5 billion total, a 50% loss for each of them.

There remain 10,000 investors, holding a total of 20 million shares, each worth \$25.

Now suppose the fund climbs back up again to \$55 a share in January, 2010. Each of the remaining investors now hold shares worth 10% more then they began. Since anyone who held the fund over that 2-year period would have earned 10%, I believe the reported returns for that 2-year period would be 10%.

But only 10% of the investors in the fund actually earned 10%. The other 90% lost 50%. So the average investor in the fund lost 44%, even though "the fund earned 10%."

Nevertheless, I tend to agree with you. I have read these numbers about the average investor often enough to believe they must be factually true, but they can't mean what people say they mean--I am not willing to believe that the average investor is systematically and reliably wrong in judging market movements.
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peter71
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### Re: Investor behavior and fund returns: a paradox?

yessiree83
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### Re: Investor behavior and index funds: a paradox?

mdrileynyc wrote:Here's the claim. Let B[i,f] be the starting balance of the ith investor in the fth fund and let B'[i,f] be the ending balance after some period - say a year. Then:

Fund f's return: R[f] = (Sum_i B'[i,f]) / (Sum_i B[i,f])

Investor i's return: R = (Sum_f B'[i,f] / (Sum_f B[i,f])

But:

Sum_f R[f] (Sum_i B[i,f]) / (Sum_i,f' B[i,f']) =
Sum_i R (Sum_f B[i,f]) / (Sum_i',f B[i',f])

The "return of the fund" is not the percentage of total assets gained or lost by the fund...the "return of the fund" is the hypothetical return of an investor which never sells and it is completely independent of the amount of assets under management (ie Sum_i B[i,f] or Sum_i B'[i,f]).

So the equation for R[f] should be
R[f] = B'[j,f]/B[j,f] for a single investor j who holds the fund throughout the entire period.
This is only the same as your equation if all the fund's investors hold throughout the entire period, but they don't which is why they receive what you calculated instead of the "return of the fund".

larryswedroe
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### Re: Investor behavior and fund returns: a paradox?

To be clear
The return of the fund assumes single investment at start of period and 100% reinvestment of dividends. This is a time weighted return, not a dollar weighted return which of course can be entirely different.
What typically happens is investors buy YESTERDAY's hot performing fund, which did great with very small assets. Like Bill Miller or Julian Robertson (Tiger 21 hedge fund). Both had spectacular returns when assets were small, cash flowed in and at the peak they had terrible returns. Investors obviously earned far lower returns on dollar weighted basis then returns reported by the funds themselves
Peter Lynch once reported that he did study on Magellan for period he ran it and found that while fund made money average investor actually lost (wish I had that citation).
Best
Larry

Topic Author
mdrileynyc
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### Re: Investor behavior and fund returns: a paradox?

yessiree83, larry - good catch. thanks. I was wondering who was getting all that money and the answer is (on average) nobody - things add up.

Still seems paradoxical to me though since the 'hypothetical' buy-and-hold investor appears to be effectively getting 2% over either side of the last equality above.
But that I believe is just the 'market' return - i.e. for the 'fund' of all the funds. But if I buy-and-hold the market I should get the market return not an excess return. Confused .

yessiree83
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### Re: Investor behavior and fund returns: a paradox?

mdrileynyc wrote:yessiree83, larry - good catch. thanks. I was wondering who was getting all that money and the answer is (on average) nobody - things add up.

Still seems paradoxical to me though since the 'hypothetical' buy-and-hold investor appears to be effectively getting 2% over either side of the last equality above.
But that I believe is just the 'market' return - i.e. for the 'fund' of all the funds. But if I buy-and-hold the market I should get the market return not an excess return. Confused .
Not sure if this is what's confusing you, but the fund of all mutual funds is not the same as the market because stocks are also owned by many entities other than mutual funds.

Topic Author
mdrileynyc
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### Re: Investor behavior and fund returns: a paradox?

yessiree - well each stock held by individuals could be considered a fund with one component but then a different result might happen.

Ignoring trading costs and fees, my intuition is the return for all mutual fund investors, where trading I'd think cancels as people move between funds, should mimic the market return with 'market' suitably defined. But if the return seen by mutual fund investors matches the market return then you should be able to get excess returns with a buy-and-hold strategy of holding funds however they were weighted to give that >2% (if not just trading costs)! That seems fishy.

OTOH, if that is wrong, it's because money moves out of funds and into something individual stocks? Then isn't there excess return to be had by holding stocks (or other assets) as some function of how they differ from their mutual fund holdings?

Something doesn't add up for me.

-m

Topic Author
mdrileynyc
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### Re: Investor behavior and fund returns: a paradox?

In fact, more generally, if you tell me a losing investment strategy (ignoring costs/fees) relative to the market then shouldn't I be able to do the converse and have a winning strategy relative to the market? So shouldn't we be just as suspicious of claimed losing systems as winning ones?

If we pin down exactly what is claimed to be a losing strategy wrt individual fund ownership, we should be able to construct some strategy with excess returns from it. Fishy.

Ignoring costs/fees is important here. If costs/fees are the answer, all makes sense and I can give you lots of losing strategies!

GregLee
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### Re: Investor behavior and fund returns: a paradox?

mdrileynyc wrote:In fact, more generally, if you tell me a losing investment strategy (ignoring costs/fees) relative to the market then shouldn't I be able to do the converse and have a winning strategy relative to the market?
Sure. It's straightforward. You lose if you buy only after prices have just risen and sell only after prices have just fallen. If you choose randomly when to buy and sell, you break even with the market. You win if you buy only after prices have just fallen and sell only after prices have just risen. (But don't try to tell a Boglehead this.)
Greg, retired 8/10.

stlutz
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### Re: Investor behavior and fund returns: a paradox?

The "stock market" is not an entity of fixed size. When the market goes up, there is incentive for new companies to be formed and for existing private companies to go public. When the market goes down, companies also tend to be going bankrupt etc .and new companies are not being formed. In the late 90s there was a big surge in the number of publicly traded companies. Since the .com bust, the number has steadily gone down.

If the market was a static entity where the number of shares was unchanged, then yes, the average return of investors = the market return. Since the market is not static, the return of investors < market return. The "missing money" goes to the people who/work at the new companies and also their customers

For example, Amazon.com survived the 90s only because investors were willing to pour a ton of money into a company that at the time was losing money on every transaction.

yessiree83
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### Re: Investor behavior and fund returns: a paradox?

mdrileynyc wrote:In fact, more generally, if you tell me a losing investment strategy (ignoring costs/fees) relative to the market then shouldn't I be able to do the converse and have a winning strategy relative to the market? So shouldn't we be just as suspicious of claimed losing systems as winning ones?

If we pin down exactly what is claimed to be a losing strategy wrt individual fund ownership, we should be able to construct some strategy with excess returns from it. Fishy.

Ignoring costs/fees is important here. If costs/fees are the answer, all makes sense and I can give you lots of losing strategies!
One of the interesting things about active mutual funds is that they can allow people to invest in a strategy without being able to know what it is until later (after SEC disclosures are published). So although we can say the strategy is losing, that doesn't necessarily mean we can pin down precisely what the strategy is.

I have considered that it may be possible to find arbitrage opportunities by timing mutual fund purchases because there is information embedded in mutual fund pricing which is not and cannot be known by the stock market. Specifically, before SEC disclosures are published:
-Even though stock traders may factor in all public information about a given stock, one thing they can't know is who is on which side of each trade (ie someone lost money on this trade, but was it Peter Lynch or Joe Sixpack?).
-Conversely mutual fund investors don't know anything about the specific stocks their mutual fund is investing in, but they know exactly who is doing the investing (ie Peter Lynch lost money on a trade yesterday, but what was the trade?).
-So the two sets of information are complementary and, if the prices of the stocks purchased by the mutual funds already reflects the public information, by trading mutual funds it may be possible also to extract the benefit of nonpublic information (ie the private knowledge of each mutual fund manager) without actually knowing the information.

What are your thoughts on this? I haven't bothered because most mutual funds have anti frequent trading policies and don't really stick to a constant investment universe...besides, I'm retired.
On the other hand, hedge funds have also been known to invest in mutual funds...so perhaps they're already doing it at the expense of the average active fund investor?

Topic Author
mdrileynyc
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### Re: Investor behavior and fund returns: a paradox?

I think it is extremely hard to get excess returns with consistency; unlikely to try myself. Instead I was using this very hard task to suggest creating a consistent losing strategy (ignoring costs) was also very hard - in particular the claimed losing mutual fund investor behavior.

Anyway I just asked all about this here since it seemed paradoxical to me from a market as a whole. Several posters point out extra factors to consider regards 'the market' but not clear to me that they are the main explanation. Thanks anyway.

pkcrafter
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### Re: Investor behavior and fund returns: a paradox?

Here's M*s explanation--

http://www.ifa.com/pdf/InvestorReturns.pdf

Paul
When times are good, investors tend to forget about risk and focus on opportunity. When times are bad, investors tend to forget about opportunity and focus on risk.

Valuethinker
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### Re: Investor behavior and fund returns: a paradox?

mdrileynyc wrote:It's often said that fund investors under-perform the fund by substantial percentages (2% or more) by poor market timing. Is this due entirely to trading costs and fees? Because if you ignore trading costs and fees, the average return of an investor weighted by his starting balance I believe equals the average return of a fund weighted by its starting balance. It's simple arithmetic; I'll post the equations in a followup. So:

1) if it's not all trading costs and fees, then what have I missed?
2) if it is all trading costs and fees, then it's not so much poor timing as useless timing on average, yes?
Fund returns are quoted time weighted.

As an investor, the returns you get are money weighted.

That, in a nutshell, is the difference.

If you hold \$100 in the fund at the start of the period, reinvest all dividends upon receipt, and pay no additional taxes or charges, then the return you should get at the end of the period is the reported return of the fund.

Otherwise, not.

Note all funds underperform the index, which assumes no dealing costs etc. A fund like VG TSM, which does the minimum of buying and selling (only when companies are delisted, taken over, IPO'd etc) except to match cash inflows and outflows from investors, will track the underlying stock market pretty closely.

But redemptions or purchases of fund units by investors impose a cost on *all* fund holders, due to market impact costs and dealing spreads. For this reason, DFA deliberately seeks to reduce client turnover in funds.

Verde
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### Re: Investor behavior and fund returns: a paradox?

The most cited paper on the issue of the performance gap (time weighted - \$ weighted returns) is Ilia D. Dichev of U. of Michigan, "What are stock investors’ actual historical returns? Evidence from dollar-weighted returns" ( http://papers.ssrn.com/sol3/papers.cfm? ... _id=544142 )

The quotes are from the Dichev paper:
The empirical results indicate that aggregate dollar- weighted returns are systematically lower than buy-and hold returns. The annual difference is 1.3 percent for the NYSE/AMEX market over 1926-2002, 5.3 percent for Nasdaq over 1973-2002, and averages 1.5 percent for 19 major stock markets around the world over 1973- 2004.
Transaction costs were not taken into account in this research. So the 1.3 annual difference is in addition to transaction costs paid by investors.
In practical terms, dollar- weighted returns are computed as internal rate of returns (IRRs) from investment projects in which initial market values and contributions from investors (e.g., stock issues) enter with negative signs, and distributions to investors (e.g., dividends, stock repurchases) and final market values enter with positive signs.
To the extent that transactions between investors cause market cap to change, there can be no difference between time and \$ weighted returns. Only to the extent that capital flows between companies and investors can there be such a difference.
These flows include straightforward items like dividends, stock repurchases, and stock issues but could also include more complicated items like contribution and distribution of non-cash assets, exercise of stock options, spin-offs and equity carve-outs, issuing stock in mergers and acquisitions, and listing and delisting of new stocks.
Distributions = MVt-1*(1 + rt) - MVt
where MV is market capitalization (typically calculated as number of shares*stock price) and rt is the total return for that period (including dividends). Positive amounts of Distributions indicate capital flows from the company to investors for that period, and negative amounts indicate flows from investors to the company.3 The intuition behind this calculation is that market value changes result from both real price appreciation and net investor capital flows. Thus, controlling for returns, market value changes identify the capital flows
So if the market drops 50%, and then recovers without there being net flows between companies and investors, the two metrics will be the same. Sure some idiots might sell low and experience a permanent loss, but another investor buys low, in aggregate there is no bad timing cost.
If new stock capital contributions and distributions are “random”, and earn the same average rate of returns as the rest of the stock capital, then there will be no difference between buy-and-hold and dollar-weighted returns. However, buy-and-hold and dollar-weighted returns will differ if there are material correlations between the timing of capital contributions and distributions and past and future stock returns.
So, overall investors can incur a bad timing cost if companies consistently time these new capital contributions and distributions favourably.
These results imply that infusions of stock market capital tend to happen after superior past returns and before subsequent inferior returns; the converse applies for distributions of market capital.
But,
Finally, the findings of this study seem to offer some practical investment implications. One implication is that passive investment strategies are likely to do well because they avoid both transaction costs and the negative effects of timing. Another implication and an area of potential future inquiry is that one might be able to use aggregate timing signals to build superior investment strategies. Taken literally, the evidence in this study implies that a “contrarian” strategy based on taking investment position opposite to that implied by the aggregate market inflows and outflows is likely to be successful.
If the paper’s findings are correct: Companies, have on average, and over long periods of time, been good market timers, all other stock market participants have been bad market timers as a whole.
I am not convinced that the paper’s findings are true, but it offers a good description of how investors can underperform markets.

yessiree83
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### Re: Investor behavior and fund returns: a paradox?

mdrileynyc wrote:I think it is extremely hard to get excess returns with consistency; unlikely to try myself. Instead I was using this very hard task to suggest creating a consistent losing strategy (ignoring costs) was also very hard - in particular the claimed losing mutual fund investor behavior.

Anyway I just asked all about this here since it seemed paradoxical to me from a market as a whole. Several posters point out extra factors to consider regards 'the market' but not clear to me that they are the main explanation. Thanks anyway.
Well how hard is hard? Do you believe the market is weak-form efficient, semi-strong efficient, or strong-form efficient? Most reasonable folks would not claim the market is strong-form efficient because it can clearly be beaten by company insiders who have access to nonpublic information.

So, as you have correctly noted, if there are actors who can consistently beat the market with inside information then there must also be consistent losses on the other side of those trades. However if the losers are investors in mutual funds then public knowledge that they are the losers still would not make it easier for an arbitrager who only has access to public knowledge to get excess returns because he still wouldn't know exactly what these known losers are buying until it's too late to take the other side of their trades.
Verde wrote: If the paper’s findings are correct: Companies, have on average, and over long periods of time, been good market timers, all other stock market participants have been bad market timers as a whole.
I am not convinced that the paper’s findings are true, but it offers a good description of how investors can underperform markets.
Very interesting. So, in a nutshell, the paper's findings are that the timing of distributions like dividends and share buybacks reflects inside information unavailable to public stock market participants. I don't see why you find that suspect...it's just insider trading on behalf of shareholders.

However, I am fascinated by the fact that a "contrarian strategy" (like rebalancing) may essentially trade on this inside information without even knowing it. So if a total stock market "rebalancing bonus" doesn't show up in the future then perhaps we can take that as evidence that the stock market is becoming more strong-form efficient? Fascinating, indeed.

Topic Author
mdrileynyc
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### Re: Investor behavior and fund returns: a paradox?

> yessirre writes: Do you believe the market is weak-form efficient, semi-strong efficient, or strong-form efficient?

I believe it is likely mdrileynyc-efficient - i.e. I can't make any money from assuming otherwise. This is clearly the most important form for me!

Topic Author
mdrileynyc
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### Re: Investor behavior and fund returns: a paradox?

Verde - this paper looks like it exactly addresses my questions. Thanks a lot - just what I wanted it.

-m

Topic Author
mdrileynyc
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