Index monkeys beat market cap weighting

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Index monkeys beat market cap weighting

Postby Browser » Fri Apr 05, 2013 10:39 am

Another study that shows indexes based on practically anything except market cap have produced better returns. Arnott recently showed the same thing. It might be luck or maybe not. IMO, market cap is flawed and the lower expense of maintaining a market cap index doesn't compensate for it's underperformance. Shouldn't we be benchmarking against a monkey index instead of a market cap index?
Researchers have found that equity indices constructed randomly by 'monkeys' would produce higher risk-adjusted returns than an equivalent market capitalisation-weighted index over the last 40 years and that they could be a result of luck rather than design.

The findings come from a recent study by Cass Business School (CBS), which was based on monthly US share data from 1968 to 2011. The authors of the study found that a variety of alternative index weighting schemes all delivered superior returns to the market cap approach.

http://www.indexuniverse.com/sections/features/16411-index-monkeys-beat-cap-weighting.html
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Re: Index monkeys beat market cap weighting

Postby pauliec84 » Fri Apr 05, 2013 10:47 am

#1) Historically and probably going forward. Small cap beats large cap. So by moving away from a market-cap weighting you are increasing you loading on the small cap stocks, and thus increase expected returns. So the finding is not a surprise.

#2) Trading Costs. A Market-cap weighted system involves no trading costs except for additions/subtractions from the index (which is just IPOs if you are doing the total market). Conversely any system that is not market weighting invovles constant trading to maintain whatever the arbitrary weight is. So what I didn't see in your article, was does the abnormal risk-adjusted returns persist once we account for trading costs.

#3) Theory. Financial Theory says that market weighted portfolio is the efficient, so by over/under weighting stocks outside of market weight you are playing an active game, betting you know better than the market it; which you are welcome to do, but has not been something there is much evidence that people can do successfully.

#4) If you want more exposure to small stocks. I would bet a penny on it being more efficient to hold a combination of a market-weighted total stock market fund and a market-weighted small-cap fund, rather than an equal-weighted total-stock market fund, given the trading cost issues.
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Re: Index monkeys beat market cap weighting

Postby grayfox » Fri Apr 05, 2013 10:54 am

The study included an experiment that saw a computer randomly pick and weight each of the 1,000 stocks in the sample. The process was then repeated 10 million times over each of the 43 years. Clare describes this as "effectively simulating the stock-picking abilities of a monkey".

"The results of this experiment showed that many of the monkey fund managers would have generated a superior performance than was produced by some of the alternative indexing techniques. However, perhaps most shockingly, we found that nearly every one of the 10 million monkey fund managers beat the performance of the market cap-weighted index," said Clare.


So it says that random-weighting had better risk-adjusted returns than market-cap weighting. Higher risk-adjusted return means higher Sharpe ratio.

In theory, the highest highest Sharpe ratio is the tangency portfolio. And I think according to some theory, the tangency portfolio is the market portfolio? But this sounds like nearly every portfolio was more efficient than the market portfolio. So the market portfolio, rather than being the most efficient, was actually one of the least efficient.

Theory -> Market portfolio is the most efficient of all portfolio
Practice -> Market portfolio is one of the least efficient of all portfolios

In theory there is no difference between theory and practice. In practice there is.
--Yogi Berr

Where is the actual paper? I'd like to see what they actually did and what results they got.
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Re: Index monkeys beat market cap weighting

Postby Blues » Fri Apr 05, 2013 10:58 am

"In theory, there is no difference between theory and practice. But, in practice, there is." - Jan L. A. van de Snepscheut


https://en.wikiquote.org/wiki/Jan_L._A._van_de_Snepscheut
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Re: Index monkeys beat market cap weighting

Postby CyberBob » Fri Apr 05, 2013 10:58 am

Yeah, but market-cap weighting isn't just another method of constructing an index. It represents the makeup of the actual market and how how the market actually exists.
So, the actual market isn't efficient now?

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Re: Index monkeys beat market cap weighting

Postby grayfox » Fri Apr 05, 2013 11:00 am

Was it Yogi Berra or Jan L. A. van de Snepscheut?
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Re: Index monkeys beat market cap weighting

Postby rkhusky » Fri Apr 05, 2013 11:02 am

This article contains links to the papers.

http://www.cass.city.ac.uk/news-and-eve ... ap-indices
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Re: Index monkeys beat market cap weighting

Postby Blues » Fri Apr 05, 2013 11:05 am

grayfox wrote:Was it Yogi Berra or Jan L. A. van de Snepscheut?


"In theory, there is no difference between theory and practice. But, in practice, there is."

Van de Snepscheut cited in Doug Rosenberg and Kendall Scott (2001) Applying Use Case Driven Object Modeling With UML. p.1
This quote has also been attributed to Yogi Berra, to Chuck Reid, and to Karl Marx (1818 - 1883)

I always suspected Yogi was a "leftist"! :oops:

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Re: Index monkeys beat market cap weighting

Postby grayfox » Fri Apr 05, 2013 11:16 am

Paper 1
Paper 2

Thanks for those links. It looks like those papers have a whole lot more than the headline that monkeys beat cap-weighting. The monkeys don't even show up until section 7.1 See Figure 5. The distribution of monkeys' terminal wealth values (1,000 picks), starting with $100.

(Figure 5 here)

Monkey distribution is bell-shaped, eyeballing the mean at about $9000, with a spread of about $7000 to $11,000 (+/- 3 SD's)
Market-cap weighted had terminal wealth of under $5000
Equal-weighted, about $9000
Inverse-volatility weighted, about $10,500

Figure 6 The distribution of monkeys' Sharpe ratios really shows how inefficient the market cap portfolio is

(Figure 6 here)

Monkey's Sharpe Ratio distribution is also bell shaped, mean around 0.385 and spread of 0.35 to 0.42
Market-cap weighted had Sharpe ratio of under 0.32
Equal-weighted, about same as monkey mean
Inverse-volatility weighted, about 0.45

Very interesting paper and results.
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Re: Index monkeys beat market cap weighting

Postby Rick Ferri » Fri Apr 05, 2013 11:21 am

Any Monkey can Beat the Market

Rick Ferri

PS. Grayfox is correct. The paper is about equal weighting versus cap weighting. Also about not rebalancing growth and value portfolios to achieve higher returns in both. The monkey question has to do with 100 monkey picks in an equal weighted portfolio versus a cap weighted index. Result - monkeys win due to the small cap premium in the market.
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Re: Index monkeys beat market cap weighting

Postby Blues » Fri Apr 05, 2013 11:30 am

Rick Ferri wrote:The monkey question has to do with 100 monkey picks in an equal weighted portfolio versus a cap weighted index. Result - monkeys win due to the small cap premium in the market.


Image

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Re: Index monkeys beat market cap weighting

Postby Browser » Fri Apr 05, 2013 3:09 pm

Another take is that "tilting" works because it moves away from cap weighting -- not because of any mystical "small cap premium" that is thereby enhanced. Tilting is just an inefficient closet technique to mitigate the drag of cap weighting on returns.
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Re: Index monkeys beat market cap weighting

Postby Rick Ferri » Fri Apr 05, 2013 3:17 pm

There is no "drag of cap weighting on returns." Cap weighting is a measure of market value. It's a economic yardstick. It is not an inefficient methodology.

Are their better investment strategies? Perhaps, but that's a different question. Cap weighting is efficient for what it was designed to do.

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Market-cap weighted indexes or all others?

Postby Taylor Larimore » Fri Apr 05, 2013 3:34 pm

Another study that shows indexes based on practically anything except market cap have produced better returns. Arnott recently showed the same thing. It might be luck or maybe not. IMO, market cap is flawed and the lower expense of maintaining a market cap index doesn't compensate for it's underperformance. Shouldn't we be benchmarking against a monkey index instead of a market cap index?


Browser:
The referenced study was partially paid for by a private advisory firm. Its conclusions should be suspect. There may be better indexes than an index that holds stocks in exact proportion to their market value. However, Morningstar did a 18 year comparison of Vanguard cap-weighted index funds and DFA small-value weighted funds and John Rekenthaler, Morningstar Research Director, wrote this (underline mine):
Buy the Market? Or Slice & Dice?
This leads neatly to the Question of the Week, posed by Alex Frakt. Alex, known to you Vanguard Diehards as "lowwall" (what’s that all about?) asks me to adjudicate the Vanguard versus DFA debate. As he puts it, "The former group holds that anything other than owning the market by capitalization weight is just making a bunch of sector bets. The latter says that anything other than equally weighted sectors is making one sector bet: large growth. What do you think?"

Vanguard, in a landslide. Don’t get me wrong; I like and respect DFA. The company has always represented the best aspects of professional financial advice: a portfolio orientation, tax sensitivity, affordable costs, and ethical standards. Consequently, it attracts many of the best financial advisors in the business--including Frank Armstrong and Bill Bernstein, among others. Nevertheless, DFA’s position is illogical. Effectively, DFA believes that when allocating among investment styles, one should ignore the market’s judgments, but that when making stock-by-stock decisions, one should strictly obey them. Curious.

At heart, DFA is by and for engineers. The company collected a ton of data, analyzed it extensively, and came up with an indexing scheme that it views as being better and more-sophisticated than "naïve" indexers like Vanguard. All this analysis is predicated on the premise that the future will mimic the past and, therefore, that the initial inputs are correct. I dispute the premise, and therefore, I dispute the results. More to the point, so has the market. In its 18 years of existence, DFA’s small-value tilt has harmed it more than helped. You’d have made a lot more money following Vanguard’s cap-weighted approach.

Best wishes.
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Re: Index monkeys beat market cap weighting

Postby EDN » Fri Apr 05, 2013 4:22 pm

Cap weighting isn't inefficient, it just leads to a portfolio holding bigger and more economically healthy stocks, so in effect a cap weighted portfolio with no size or price restriction (TSM or S&P 500 or Russell 1000) is a large cap portfolio with a growth bias.

Cap weighting is an efficient way to implement a portfolio, as it is naturally rebalanced. Even value or small portfolios that are cap weighted are more efficient than the alternative (say, equal or fundamentally weighted) from an implementation standpoint: less turnover, less trading, less exposure to negative momentum, etc.

Ideally, if you are going to assemble a non-cap weighted portfolio to achieve specific tilts to small or value, you are still going to want to stay as close to cap weight as possible while being able to achieve the small and value exposure. For example, instead of randomly equal weighting, you will want to underweight LG by 10%, LB by 5%, while increasing mid cap by 10% and and small cap and value by 5% relative to their market proportions, or whatever the right %s are. This preserves most of the cap weigting benefits while increase expected returns and exposure to unique risks.

You just have to call it like it is. Cap weighted portfolios = LC. Anything non cap weighted =/= large cap. These monkey portfolios wouldn't fare well against, say, a market cap weighted mid cap portfolio (assuming it has similar size orientation).

Eric

PS -- Rekenthaler's article has been completely discredited, it was published at the peak of the tech bubble and has been a noose around his neck ever since. He himself has a signficant conflict of interest as he is director of research for a subscription based mutual fund rating service. Since 2000, growth of $10,000:

1YR Bonds = $14,782
VTSMX = $14,846
DFSVX = $40,135
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Re: Index monkeys beat market cap weighting

Postby grayfox » Fri Apr 05, 2013 5:02 pm

If these results in the paper are indeed correct, I find them quite shocking. Basically it says that if you have 10 million randomly-weighted portfolios, ~99.9% of them have both higher returns (Fig. 5) and higher Sharpe Ratios (Fig. 6) than the market portfolio. In other words, they are more Markowitz efficient.

Now I would expect dispersion of the Sharpe ratios of 10 million random portfolios. And I would have expected that some would be better and some worse than the market portfolio. But I would have thought that the market would be about the mean of 10 million random portfolios. Not 3+ standard deviations below the mean. That's the part I find shocking.

Implications :arrow: an active stock fund could pick a random weighting and there is a near certainty that they will beat Vanguard Total Stock Market VTSMX.

But then why don't 99.9% of active funds beat VTSMX :?: They must be doing something wrong if they can't beat the monkeys. Or are they skimming off the profits.
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Re: Index monkeys beat market cap weighting

Postby Rick Ferri » Fri Apr 05, 2013 5:06 pm

The past 12 year has been a very unusual period for small and value stocks. The premiums over the total market were historically high. I don't think we'll see those premiums again for quite some time. Much of the premium since 2000 can be attributed to large cap growth stocks become so widely overvalued in the tech bubble and then crashing back down to Earth over the next few years.

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Re: Index monkeys beat market cap weighting

Postby EDN » Fri Apr 05, 2013 5:26 pm

grayfox wrote:If these results in the paper are indeed correct, I find them quite shocking. Basically it says that if you have 10 million randomly-weighted portfolios, ~99.9% of them have both higher returns (Fig. 5) and higher Sharpe Ratios (Fig. 6) than the market portfolio. In other words, they are more Markowitz efficient.

Now I would expect dispersion of the Sharpe ratios of 10 million random portfolios. And I would have expected that some would be better and some worse than the market portfolio. But I would have thought that the market would be about the mean of 10 million random portfolios. Not 3+ standard deviations below the mean. That's the part I find shocking.

Implications :arrow: an active stock fund could pick a random weighting and there is a near certainty that they will beat Vanguard Total Stock Market VTSMX.

But then why don't 99.9% of active funds beat VTSMX :?: They must be doing something wrong if they can't beat the monkeys. Or are they skimming off the profits.


Why?

Stop and ask yourself what the Total Stock Index is. Don't just settle for "its total" or "its everything", really think about it.

It is a collection of stocks that is extremely concentrated in the largest most successful companies with the lowest costs of capital and lowest expected return. So literally any other portfolio that is weighted differently cannot put the same amount of emphasis on these big, low returning stocks. Arnott did a study one time and found that the realized return over a subsequent 10 year period for the top 10 companies in the market (after they reach that plateau) was something like "S&P 500 minus 3% per year".

Now, if we go through an anomalous stretch like the late 1990s, and the size and value premiums are negative (and the safest, lowest cost of capital companies produce the highest returns), then you won't find this to be the case. But as we saw with the turn of the century, just as soon as Morningstar "research directors" stick their foot in mouth, the market reverts to the norm.

VTSMX beats probably 75% of large cap funds. Compare it to mid or small, you come up with a very different #. All large cap funds hold most of these same big successful companies as VTSMX does in slightly different %s, so VTSMX wins on fees and 0% cash holdings. Beyond that, there's no magic. It also beats the majority of all funds, but only because there are far more LC funds than mid and small.

Eric

PS --- We have not had an "unusual" period for small and value since 2000. In the US, through 2012, the size premium has been 4.3% and 5.8% for value. These aren't even 1SD away from their mean over all 13 year periods historically (they've averaged 2.3% and 4.0% per year). Actually, that's exactly what you'd expect (slightly higher size/value than average) during a period where TSM has underperformed t-bills, and there has been 0% equity premiums.

From 1965-1981, for example, another painfully long stretch of 0% real returns on TSM, the size premium was +6.2% and value was +4.9%.

That's why we diversify, and why you hold enough size/value to actually make it count. You cannot just rely on a handful of LG type companies to always produce acceptable returns.
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Re: Index monkeys beat market cap weighting

Postby grayfox » Fri Apr 05, 2013 6:40 pm

Yes, it turns out from Fig 5 that the the Equal-Weighted Index is closest to the return of the monkeys' random weightings.

If you look in the appendices of the paper, there are some are 8-charts for each of the 9 weightings. It shows how each is tilted to various factors relative to market cap index. Equal-weight is about -48% in the top decile by size.

They wrote (page 21)
Overall, our results indicate that the performance differences between Market-cap index and the alternative indices is a function of a bias towards small cap stocks and to a less degree with high book-to-market values.
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Re: Index monkeys beat market cap weighting

Postby protagonist » Fri Apr 05, 2013 6:56 pm

Blues wrote:
grayfox wrote:Was it Yogi Berra or Jan L. A. van de Snepscheut?


"In theory, there is no difference between theory and practice. But, in practice, there is."

Van de Snepscheut cited in Doug Rosenberg and Kendall Scott (2001) Applying Use Case Driven Object Modeling With UML. p.1
This quote has also been attributed to Yogi Berra, to Chuck Reid, and to Karl Marx (1818 - 1883)

I always suspected Yogi was a "leftist"! :oops:

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Great quote. Too bad. I have always rooted for Yogi. But here is an interesting tidbit, from Wikipedia: "In the early morning hours of February 23, 1994, van de Snepscheut attacked his sleeping wife, Terre, with an axe. He then set their house on fire, and died as it burned around him. Terre and their three children escaped their burning home.[2] "
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John Rekenthaler

Postby Taylor Larimore » Fri Apr 05, 2013 7:01 pm

Rekenthaler's article has been completely discredited, it was published at the peak of the tech bubble and has been a noose around his neck ever since. He himself has a signficant conflict of interest as he is director of research for a subscription based mutual fund rating service.


Just as soon as Morningstar "research directors" stick their foot in mouth, the market reverts to the norm.

EDN:

This is Mr. Rekenthaler's bio:
John Rekenthaler, CFA is vice president of research for Morningstar. In this role, he oversees Morningstar’s research methodologies and is involved in a variety of new development efforts. His recent projects in 2009 include the launches of the Morningstar Target-Date Fund Series Rating and Research Reports and the Morningstar Global Fund Investor Experience Survey. The former project consists of comprehensive reports on 20 of the largest U.S. target-date fund series, while the latter is a one-of-a-kind study that examines how mutual fund investors are treated in 16 countries across Europe, Asia, and North America.

Rekenthaler previously served as president of Morningstar Associates, LLC, a registered investment advisor and wholly owned subsidiary of Morningstar, Inc. During his tenure, Rekenthaler led the company’s retirement advice business, building it from a start-up operation to one of the largest independent advice and guidance providers in the retirement industry.

Rekenthaler joined Morningstar in 1988 and has served in several capacities. Prior to his position at Morningstar Associates, he was the firm’s director of research, where he helped to develop Morningstar’s quantitative methodologies, such as the Morningstar Rating™ for funds, the Morningstar Style Box™, and industry sector classifications. He also served as editor of Morningstar Mutual Funds™ and Morningstar FundInvestor™.

Rekenthaler holds a bachelor's degree in English from the University of Pennsylvania and a master's degree in business administration with high honors from the University of Chicago Graduate School of Business. He holds the Chartered Financial Analyst (CFA) designation, and he is a member of the Investment Analysts Society of Chicago.

It is not necessary to disparage those with whom we disagree.

Thank you and best wishes.
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Re: John Rekenthaler

Postby EDN » Fri Apr 05, 2013 7:11 pm

Taylor Larimore wrote:
Rekenthaler's article has been completely discredited, it was published at the peak of the tech bubble and has been a noose around his neck ever since. He himself has a signficant conflict of interest as he is director of research for a subscription based mutual fund rating service.


Just as soon as Morningstar "research directors" stick their foot in mouth, the market reverts to the norm.

EDN:

This is Mr. Rekenthaler's bio:
John Rekenthaler, CFA is vice president of research for Morningstar. In this role, he oversees Morningstar’s research methodologies and is involved in a variety of new development efforts. His recent projects in 2009 include the launches of the Morningstar Target-Date Fund Series Rating and Research Reports and the Morningstar Global Fund Investor Experience Survey. The former project consists of comprehensive reports on 20 of the largest U.S. target-date fund series, while the latter is a one-of-a-kind study that examines how mutual fund investors are treated in 16 countries across Europe, Asia, and North America.

Rekenthaler previously served as president of Morningstar Associates, LLC, a registered investment advisor and wholly owned subsidiary of Morningstar, Inc. During his tenure, Rekenthaler led the company’s retirement advice business, building it from a start-up operation to one of the largest independent advice and guidance providers in the retirement industry.

Rekenthaler joined Morningstar in 1988 and has served in several capacities. Prior to his position at Morningstar Associates, he was the firm’s director of research, where he helped to develop Morningstar’s quantitative methodologies, such as the Morningstar Rating™ for funds, the Morningstar Style Box™, and industry sector classifications. He also served as editor of Morningstar Mutual Funds™ and Morningstar FundInvestor™.

Rekenthaler holds a bachelor's degree in English from the University of Pennsylvania and a master's degree in business administration with high honors from the University of Chicago Graduate School of Business. He holds the Chartered Financial Analyst (CFA) designation, and he is a member of the Investment Analysts Society of Chicago.

It is not necessary to disparage those with whom we disagree.

Thank you and best wishes.
Taylor


Taylor,

I did not disparage the individual, I merely pointed out how incorrect his opinion was, updated the evidence as your post did not make it clear that the period you mention ended almost 15 years ago and could be misleading to some, and pointed out his professional conflicts of interest. Similar conflicts to the ones you referenced in your post.

Sorry you misunderstood my comments.

Best wishes,

Eric
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Conflicts of interest.

Postby Taylor Larimore » Fri Apr 05, 2013 7:27 pm

Eric:
Sorry you misunderstood my comments.

I understand your comments about "professional conflicts of interest."

Best wishes.
Taylor
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Re: Index monkeys beat market cap weighting

Postby connya » Fri Apr 05, 2013 7:49 pm

Taylor, the fact that this comparison was done at the top of a spike of large cap overperformance makes it hard for me to accept Rekenthaler's claim that the market disputes the premise of the small value cap premium. Although it may have been true at that very specific time it does sounds kind of misleading today.
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Re: Conflicts of interest.

Postby EDN » Fri Apr 05, 2013 7:50 pm

Taylor Larimore wrote:Eric:
Sorry you misunderstood my comments.

I understand your comments about "professional conflicts of interest."

Best wishes.
Taylor


Yes,

The degree to which Renkathaler's conclusion turned out to be faulty (not to mention his misunderstanding of how the FF 3F model came to be and it's application) is nothing short of alarming, really highlighting the dangers of following conflicted advice from subscription based, actively managed fund rating services.

Eric
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Re: Index monkeys beat market cap weighting

Postby stlutz » Fri Apr 05, 2013 10:50 pm

Folks, we should remember that market-cap weighting will always be beat by a good percentage of possible strategies. Market-cap weighted indexing is simply after the average return, and only beats the market because of low costs.

Something (especially when it comes from a theoretical backtest) is always going to do better than market cap weighting. Index investors need to be prepared for this because it is reality.

As has been discussed, this paper really just rehashed old concepts (small/value/low. vol.)

When it comes to backtested strategies that worked in the past, one can take three approaches:

1) The backtested results are pretty much sure to repeat because of some reason (investor mistakes are predictable, risk etc.)
2) Markets are random; what worked in the past has about a 50% chance of working in the future.
3) Markets mean revert. What worked in the past is less likely to work in the future.

Regardless of which of these three is the best description of reality, cap. weighting will always deliver on its promise of beating the dollar-weighted return of investors as a whole.
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Re: Index monkeys beat market cap weighting

Postby Call_Me_Op » Sat Apr 06, 2013 8:16 am

I would expect a random selection of stocks from an index to outperform the cap=weighted index simply because the random selection will be tilted toward smaller-caps.
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Re: Index monkeys beat market cap weighting

Postby hafius500 » Sat Apr 06, 2013 2:13 pm

Call_Me_Op wrote:I would expect a random selection of stocks from an index to outperform the cap=weighted index simply because the random selection will be tilted toward smaller-caps.


These Morningstar articles conclude that sector differences or differences in real interest rates explain the relative returns of large, mid and small stocks in the USA and Europe.
Did the monkeys beat the European markets when large stocks outperformed mid and small stocks?
If so, how can the size effect explain the outperformance of the monkeys?

Mid-caps: Under-Researched and Under-Represented?
Are mid-caps really under-researched and do they offer superior returns?, Morningstar, Gordon Rose, 23 November, 2011

As mentioned previously, the problem with most of the existing research on mid caps is that it is very often US-focused. As we will see, the US findings are not universally relevant, as the European example shows.
Image


As we can see in the table, US mid caps have indeed offered better absolute and risk adjusted returns compared to small and large caps over the past two decades. In Europe, large caps would have been the preferred investment choice based on a risk adjusted return over the same span...


Small Caps: Ripe for Further Outperformance?, Morningstar, Gordon Rose, 4 October, 2011|

Looking at the cumulative outperformance (click here), we can see that small caps have outperformed large caps in the U.S. over the last 20 years, whereas small caps in Europe have underperformed large caps.
But why is that? The answer most likely lies in the differences in interest rate environments. The U.S. experienced several periods of negative real interest rates over the last 20 years as the graph above indicates. In contrast, real interest rates remained in positive territory in Europe for most of this period. As negative real interest rates environments are beneficial for small caps, this could help to explain the better performance of small caps relative to large caps in the U.S. Another noticeable difference between the two sides of the Atlantic is the relative weighting of the financial sector...
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Re: Index monkeys beat market cap weighting

Postby grayfox » Sat Apr 06, 2013 2:50 pm

I would encourage people to carefully read the first paper:

An evaluation of alternative equity indices
Part 1: Heuristic and optimised weighting schemes


They compared 8 index construction techniques that set the weights of 1000 stocks against the benchmark, market-cap weighting. The first five index techniques were heuristic

1. Equal weight
2. Diversity weight
3. Inverse volatility
4. Equal risk contribution weights
5. Risk clustering weights

Three index techniques were optimization based

6. Minimum variance weights
7. Maximum diversification weights
8. Risk efficient weights.

The paper describes the exact methods of choosing weights. None of them involved explicitly tilting to small or value stocks. That was more like a side effect of the construction method.

Only after they got the results, did they attempt to analyze and explain the results by decomposing the results by factors compared to the market-cap weighted:

1. Beta
2. Size
3. Book-to-market value
4. Momentum
5. Volatility
6. Downside deviation

Here are a few good summaries

Taken together these results show that a Market-cap index is heavily weighted towards large cap stocks (by design), to the most highly liquid stocks (almost by design), but also to stocks with relatively low return volatility.
...
These results show that the alternative indices are not all uniformly under or overweight market risk, as represented by beta. But we can at least say that the three optimised indices are uniformly overweight low beta stocks or, alternatively, that they are underweight market risk.
...
Overall these results indicate that all of the indices are underweight large cap stocks, and therefore could all be said to have a bias towards small cap stocks. This is particularly true of the Equal Risk Contribution, Inverse Volatility and optimised indices.
...
These results indicate that these alternative indices are generally overweight high book-to- market value stocks relative to the exposure of the Market-cap index.
...
there does not seem to be an obvious momentum bias in the alternative indices where over and underweights are either relatively small, or balanced at either extreme. The clear exception to this narrative however, is the Risk Efficient index which is quite heavily tilted towards low momentum stocks.


Good paper overall. Worth studying.
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Re: Index monkeys beat market cap weighting

Postby pauliec84 » Sat Apr 06, 2013 5:30 pm

I skimmed through the paper so correct me if I am wrong. But the first thing I would do if I wanted to know if one index construction method was better than the other would be to run 4 Factor regression (MKTRF SMB HML UMD) and see what the alphas looked like. Because of the mentioned liquidity issues you would probably also want to include the liquidity factor in there.

This would be the first thing I would test if I were writing a similar paper. That the authors don't do this (they calculate Alpha using the CAPM which I don't think an academic paper has done in 15 years) is somewhat intellectually dishonest.

The joke is that they go to some length to describe how their indices load on the 4 factors, but do not present the alphas from the 4-factor model which is the standard risk adjustment.

I have a good guess why they didn't do this. Because the results are not as headline grabbing when you do... Again, intellectually dishonest. And this still overlooks the trading cost/higher taxes per tunerover issues with implementing a non-market weighted portfolio that would further drag down the Alpha.
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Re: Index monkeys beat market cap weighting

Postby SmartMonkey » Sun Apr 07, 2013 2:26 pm

Thank you all for your interest in our papers, especially those of you who have taken the time to read them. The extent of the press coverage has been somewhat of a surprise and obviously some of the journalists have interpreted the results in their own way.......

The aim of the papers was simply to undertake a thorough analysis of the various "smart beta" indices that seem to have become extremely popular over the past few years. We were initially surprised that all of them beat market cap over such a long period & the question arose as to whether this was due to their extreme smartness or whether any old monkey could do it?
The monkey results were even more of a surprise and we spent many hours checking and re-checking that our methodology for random weighting was correct as we certainly didn't expect them all to beat market cap. The proportion does vary over time which we show in the paper, but we are working in a better way to illustrate this.

"Intellectually Dishonest"?

Were you to have asked then we would happily have informed you that none of the alternative weighting schemes has statistically significant alpha using a 3 factor model while 2 of the fundamental indices have statistically significant alpha using a 4 factor model. However this analysis has been done by others already (Chow, Hsu, Kalesnik & Little (2011), “A Survey of Alternative Equity Index Strategies”, Financial Analysts’ Journal) so where is the fun in that?
Also if you base your analysis on the Famma French factors, have you ever asked yourself why?

One of our contributions is to provide a much richer analysis of the various factor tilts of the indices compared to market cap, because we actually knew the weights of each stock each year we did not have to rely on regressions & instead can provide the tilt for each decile which are all illustrated in the appendices.

Another contribution is to test whether the Sharpe ratios are statistically different from market cap using a robust statistical test. Here we found that both Equal Risk Contribution & Inverse Vol weighting as well as two of the fundamental weighting schemes (plus the composite) were in fact statistically (and I suppose economically) different.

Finally there is no reason that the market cap weighted portfolio of 1,000 stocks is efficient, if you think this is a controversial statement, it shouldn't be, Richard Roll pointed it out in 1977 (Roll, Richard (1977), "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory", Journal of Financial Economics) or if you want the short version just google "Roll's critique" & go to Wikipedia.

Now I have to go feed my monkeys..........
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Re: Index monkeys beat market cap weighting

Postby LadyGeek » Sun Apr 07, 2013 3:42 pm

FYI - SmartMonkey's identify has been confirmed.
To some, the glass is half full. To others, the glass is half empty. To an engineer, it's twice the size it needs to be.
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Re: Index monkeys beat market cap weighting

Postby pauliec84 » Sun Apr 07, 2013 4:08 pm

Smartmonkey.

Thanks for the replay. It is much more constructive to discuss a paper with its author.

Per my intellectually dishonest comment, and your subsequent response. "where is the fun in that?":

The fun in that is accurately and honestly present your results. It is fine to not present the tables where you show only 2 of the indices (out of how many? if many than this is just noise) have significant 4 factor alphas; but you don't ever reference the Chow et al result you just told us about. You can't assume the audience of your paper has read the entire bibliography, and frankly the Chow result is huge.

Not including any reference to the Chow result makes me say "WOW this is amazing," with regards to the findings of your paper.

Inclusion of the Chow result makes me say "so what," with regards to the findings of your paper.

This is not something a reader should have to ask to see. The reader should expect the results are not cherry picked to present the strongest argument by the authors, i.e., presenting sharp ratios and CAPM alphas rather than 4-Factor alphas.

Per "Also if you base your analysis on the Fama French factors, have you ever asked yourself why?" I would say per the Roll 1977 CAPM argument and subsequent empirical papers there after the CAPM alpha stinks, and the Fama french + Carhart factor is the best we have.

If you want to dispute the 4-factor model, that is an entire other paper in itself.


If you really feel so strongly against the 4-factor model you have to strongly motivate this in the paper.
Also why not use the DGTW adjusted abnormal returns then (another accepted method of risk adjustment)?

I would turn this question around and say have you ever asked yourself why you didn't us them?

One of our contributions is to provide a much richer analysis of the various factor tilts of the indices compared to market cap, because we actually knew the weights of each stock each year we did not have to rely on regressions & instead can provide the tilt for each decile which are all illustrated in the appendices.
Another contribution is to test whether the Sharpe ratios are statistically different from market cap using a robust statistical test. Here we found that both Equal Risk Contribution & Inverse Vol weighting as well as two of the fundamental weighting schemes (plus the composite) were in fact statistically (and I suppose economically) different.


Thats fine, focus more on these and less on the faux abnormal returns to strengthen paper.

Finally there is no reason that the market cap weighted portfolio of 1,000 stocks is efficient.


There are plenty of reasons that the market cap weighted portfolio of stocks is efficient. They are however contended. To say there is NO reason that the market cap weighted portfolio of stocks is efficient, is to strong. But whatever, I agree with you that in a multi-factor world, portfolios that weight towrds HML, SMB and UMD factors can produce higher sharp ratios. But this is more of an argument that the sharpe ratios are flawed, not that the market cap weighted portfolio is inefficient.

Also as many have said earlier in the discussion thread, from an index-implementation perspective, market-weighted portfolios are much more cost effective to implement as there is less portfolio turnover.
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