"Three Proofs That TSM Is Efficient"

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
Post Reply
User avatar
Topic Author
Taylor Larimore
Advisory Board
Posts: 29946
Joined: Tue Feb 27, 2007 8:09 pm
Location: Miami FL

"Three Proofs That TSM Is Efficient"

Post by Taylor Larimore »

Bogleheads:

John Norstad, a retired mathematician at Northwestern University, did a very important study about the most "efficient" (highest return with the least risk) U.S. stock portfolio. You can read it here:

Three-Proofs That TSM Is Efficient

Best wishes.
Taylor
Jack Bogle's Words of Wisdom: "My preferred index fund happens to be the total stock market which includes large, medium, and small stocks."
"Simplicity is the master key to financial success." -- Jack Bogle
Whakamole
Posts: 1193
Joined: Wed Jan 13, 2016 9:59 pm

Re: "Three Proofs That TSM Is Efficient"

Post by Whakamole »

We give three proofs that, under three different assumptions, TSM is efficient, in the sense that no other US stock portfolio can be more efficient than TSM (have lower risk and higher expected return).
I thought Fama said that the outperformance he observed was due to added risk.
pdavi21
Posts: 1296
Joined: Sat Jan 30, 2016 4:04 pm

Re: "Three Proofs That TSM Is Efficient"

Post by pdavi21 »

"1. The Efficient Market Hypothesis.
2. The Capital Asset Pricing Model.
3. The Fama-French Three Factor Pricing Model

If any one of these assumptions is true, TSM must be efficient. If any other US
stock portfolio has a higher expected return than TSM with lower risk, we must
reject all three of the assumptions."

I wonder why he didn't try to go backwards and prove that 1,2,3 are false because the total stock market is not efficient.
"We spend a great deal of time studying history, which, let's face it, is mostly the history of stupidity." -Stephen Hawking
jsprag
Posts: 201
Joined: Sun Nov 26, 2017 11:25 am

Re: "Three Proofs That TSM Is Efficient"

Post by jsprag »

Taylor Larimore wrote: Mon Jul 29, 2019 12:50 pm Bogleheads:

John Norstad, a retired mathematician at Northwestern University, did a very important study about the most "efficient" (highest return with the least risk) U.S. stock portfolio. You can read it here:

Three-Proofs That TSM Is Efficient

Best wishes.
Taylor
All three "proofs" could be extended to show that a cap-weighted total world portfolio is more efficient. Raise your hand if you recommend holding international stocks in their global market weights.
longinvest
Posts: 4428
Joined: Sat Aug 11, 2012 8:44 am

Re: "Three Proofs That TSM Is Efficient"

Post by longinvest »

"Whether markets are more efficient or less efficient, costs matter" -- Jack Bogle
:wink:
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW
pdavi21
Posts: 1296
Joined: Sat Jan 30, 2016 4:04 pm

Re: "Three Proofs That TSM Is Efficient"

Post by pdavi21 »

jsprag wrote: Mon Jul 29, 2019 3:17 pm
Taylor Larimore wrote: Mon Jul 29, 2019 12:50 pm Bogleheads:

John Norstad, a retired mathematician at Northwestern University, did a very important study about the most "efficient" (highest return with the least risk) U.S. stock portfolio. You can read it here:

Three-Proofs That TSM Is Efficient

Best wishes.
Taylor
All three "proofs" could be extended to show that a cap-weighted total world portfolio is more efficient. Raise your hand if you recommend holding international stocks in their global market weights.
+1

If the average investor raises less than 1.0 hands, does that mean the global market weight portfolio isn't efficient?
"We spend a great deal of time studying history, which, let's face it, is mostly the history of stupidity." -Stephen Hawking
longinvest
Posts: 4428
Joined: Sat Aug 11, 2012 8:44 am

Re: "Three Proofs That TSM Is Efficient"

Post by longinvest »

jsprag wrote: Mon Jul 29, 2019 3:17 pm All three "proofs" could be extended to show that a cap-weighted total world portfolio is more efficient. Raise your hand if you recommend holding international stocks in their global market weights.
Some Bogleheads often suggest to invest into Vanguard's LifeStrategy Moderate Growth Fund (VSMGX) which approximates the market portfolio at a low cost, except for a relatively fixed 60/40 allocation (close enough to market weights) and a moderate home bias justified by some inefficiencies in international investing.

Other Bogleheads effectively suggest to invest into the world's stocks and bonds portfolio, possibly using only two ETFs: total world stocks (VT) and total world bonds (BNDW). See this thread.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW
User avatar
vineviz
Posts: 7813
Joined: Tue May 15, 2018 1:55 pm

Re: "Three Proofs That TSM Is Efficient"

Post by vineviz »

Taylor Larimore wrote: Mon Jul 29, 2019 12:50 pm Bogleheads:

John Norstad, a retired mathematician at Northwestern University, did a very important study about the most "efficient" (highest return with the least risk) U.S. stock portfolio. You can read it here:

Three-Proofs That TSM Is Efficient
Man, that attempt by Norstad goes completely off the rails in the first sentence of the abstract.
Many people do not understand why the cap-weighted total US stock market (TSM) plays such a central role in financial economics.
The "cap-weighted total US stock market" plays no central role in financial economics. The "market portfolio" in theoretical financial economics is a global portfolio of all risky tradable financial assets. It includes junk bonds, emerging markets stocks, derivatives, etc.

Furthermore, even thusly defined the "market portfolio" is just one of the efficient portfolios.

And worse, all the proofs that TSM is an efficient portfolio (even if those proofs were sound) would only get you to the point at which the TSM was efficient in aggregate. Many more assumptions (most of which are unsupportable, by the way) are necessary for the TSM to be an efficient portfolio for any individual investor.

It seems to me that Nortstad built a cursory knowledge of financial economics, but not quite enough to get him through the topic without making mistakes that are catastrophic to the argument that it seems he wanted to advance.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
longinvest
Posts: 4428
Joined: Sat Aug 11, 2012 8:44 am

Re: "Three Proofs That TSM Is Efficient"

Post by longinvest »

Dear Vineviz,
vineviz wrote: Mon Jul 29, 2019 3:37 pm The "market portfolio" in theoretical financial economics is a global portfolio of all risky tradable financial assets. It includes junk bonds, emerging markets stocks, derivatives, etc.
In practical terms, one aims to invest into broad total markets.

John Norstad chose the US total stock market for his proof. This is fine.

In various contexts it's appropriate to choose a total market. Here are the words of Prof. William Sharpe, Nobel laureate, when defining passive and active management:

The Arithmetic of Active Management
If "active" and "passive" management styles are defined in sensible ways, it must be the case that
  1. before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar and
  2. after costs, the return on the average actively managed dollar will be less than the return on the average passively managed dollar
These assertions will hold for any time period. Moreover, they depend only on the laws of addition, subtraction, multiplication and division. Nothing else is required.

Of course, certain definitions of the key terms are necessary. First a market must be selected -- the stocks in the S&P 500, for example, or a set of "small" stocks. Then each investor who holds securities from the market must be classified as either active or passive.
  • A passive investor always holds every security from the market, with each represented in the same manner as in the market. Thus if security X represents 3 per cent of the value of the securities in the market, a passive investor's portfolio will have 3 per cent of its value invested in X. Equivalently, a passive manager will hold the same percentage of the total outstanding amount of each security in the market.
  • An active investor is one who is not passive. His or her portfolio will differ from that of the passive managers at some or all times. Because active managers usually act on perceptions of mispricing, and because such misperceptions change relatively frequently, such managers tend to trade fairly frequently -- hence the term "active."
Second, in The Market Portfolio, Prof. William Sharpe (again) suggests to use the world's stocks and bonds portfolio, float-adjusted, as a proxy for the theoretical "Market Portfolio":
In a simple world, the market portfolio would include every publicly traded security, with each held in proportion to the total amount outstanding. An investor could hold his or her version of the market portfolio by purchasing x% of the outstanding shares of every traded stock and x% of the outstanding number of bonds for every traded bond, where x is the ratio of his or her invested wealth to the total value of the amounts invested by everyone.
[...]
There are of course other types of investments. Some, such as traded options, have net values of zero, with one public investor on one side of an agreement and another on the other. Others, such as stocks of private corporations, are not liquid and thus not particularly suitable for a portfolio that may need to be liquidated on relatively short notice.
[...]
it seems sensible to consider a portfolio of publicly traded bonds and stocks as a surrogate for the market portfolio of investment theory.
[...]
Our goal is to select investment vehicles and appropriate amounts to be invested in each sector to obtain a good approximation for the World Bond/Stock Portfolio, (hence: WBS).
[...]
we follow the advice given in mid-2015 on the Vanguard web site:
In fact, the right balance of four of our broadest index funds could give you a complete portfolio, with full exposure to U.S. and international stock and bond markets.

Get details on:
  • Vanguard Total Bond Market Index Fund
  • Vanguard Total International Bond Index Fund
  • Vanguard Total Stock Market Index Fund
  • Vanguard Total International Stock Index Fund
[...]
Index providers increasingly have tried to represent the returns on publicly available securities by focusing on “free float”, that is, omitting from their calculations holdings not “freely available” for purchase by outside investors.
[...]
One might ask why non-U.S. Bond exposures should be hedged but not non-U.S. Stock exposures. A partial justification would be the much greater uncertainty about the value of stock positions a month hence, making currency hedges based on the estimated value a month hence of the securities currently held far less than perfect. Happily, despite providing this additional feature, the expense ratio for VTABX is considerably lower than the costs for NonU.S. bond funds that do not employ currency hedging.


Promoters of active investing often attack total-market index investing by claiming that one cannot be a "real" total-market index investor unless one invests into an illusive impossible to hold "total assets and derivatives of the universe" portfolio. That's false.

It's perfectly fine to select a broad market or a set of broad markets to invest into using index funds and still be a total-market indexer. There's no need for perfection.
Last edited by longinvest on Mon Jul 29, 2019 4:16 pm, edited 1 time in total.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW
schooner
Posts: 388
Joined: Sun Jun 09, 2019 8:27 am

Re: "Three Proofs That TSM Is Efficient"

Post by schooner »

vineviz wrote: Mon Jul 29, 2019 3:37 pm
Taylor Larimore wrote: Mon Jul 29, 2019 12:50 pm Bogleheads:

John Norstad, a retired mathematician at Northwestern University, did a very important study about the most "efficient" (highest return with the least risk) U.S. stock portfolio. You can read it here:

Three-Proofs That TSM Is Efficient
Man, that attempt by Norstad goes completely off the rails in the first sentence of the abstract.
Many people do not understand why the cap-weighted total US stock market (TSM) plays such a central role in financial economics.
The "cap-weighted total US stock market" plays no central role in financial economics. The "market portfolio" in theoretical financial economics is a global portfolio of all risky tradable financial assets. It includes junk bonds, emerging markets stocks, derivatives, etc.

Furthermore, even thusly defined the "market portfolio" is just one of the efficient portfolios.

And worse, all the proofs that TSM is an efficient portfolio (even if those proofs were sound) would only get you to the point at which the TSM was efficient in aggregate. Many more assumptions (most of which are unsupportable, by the way) are necessary for the TSM to be an efficient portfolio for any individual investor.

It seems to me that Nortstad built a cursory knowledge of financial economics, but not quite enough to get him through the topic without making mistakes that are catastrophic to the argument that it seems he wanted to advance.
I don't know about that. Some guy named Bill Sharpe talks about a market-cap weighted portfolio a lot:

https://web.stanford.edu/~wfsharpe/art/ ... active.htm

For someone who knows so much about the market, you really spend a lot of time on this forum. If you're really crushing it in the market, why do you care at all about us lowly plebs and our vanilla index funds?

Also, it's ironic that your signature line is a quote by Peter Lynch. Not only did his replacement at Magellan coin the phrase "closet index" but his marquee fund has been languishing for years. Investors would have been better off...drum roll please...just buying an SP500 index fund
User avatar
vineviz
Posts: 7813
Joined: Tue May 15, 2018 1:55 pm

Re: "Three Proofs That TSM Is Efficient"

Post by vineviz »

longinvest wrote: Mon Jul 29, 2019 3:59 pm Promoters of active investing often attack total-market index investing by claiming that one cannot be a "real" total-market index investor unless one invests into an illusive impossible to hold "total assets and derivatives of the universe" portfolio. That's false.
I want to be clear that I neither promote active investing nor do I have any intent to attack total stock market indexing as an investment strategy.

Total stock market indexing is a totally reasonable approach, one with which I have no quibbles.

On the other hand, some claims about TSM investing reach beyond the actual merits of the approach and onto ground that is neither theoretically nor empirically defensible.

Jack Bogle was a great advocate for financial literacy, and my personal view is that we owe it to him to make note of investing claims that are not supported by theory or evidence.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
glorat
Posts: 678
Joined: Thu Apr 18, 2019 2:17 am

Re: "Three Proofs That TSM Is Efficient"

Post by glorat »

jsprag wrote: Mon Jul 29, 2019 3:17 pm All three "proofs" could be extended to show that a cap-weighted total world portfolio is more efficient. Raise your hand if you recommend holding international stocks in their global market weights.
I'll bite!
Disclaimer: I'm a non-US investor so my equities actually really are all in buying cap-weighted total world (VWRD)

The US investors have the benefits of the most efficient capital markets - low domestic costs, global reserve currency of choice, cheapest brokerage costs, no withholding taxes. In boglehead terms, you save a lot of costs just keeping your investments in your home country and saving costs is good.

To invest abroad, you might have higher brokerage fees, currency risk for foreign domestic based companies - the latter risk which is probably not a compensated risk. If I were US, I'd be so happy with your <0.1% costs of having so much.

As a non-US investor, I pay 0.25% to Vanguard to get total world coverage, plus the 15% dividend withholding taxes on US stocks. My market access is not as cost efficient.

I think if costs and currency risks were out, then the original argument wins. In reality, I think the non-US markets aren't as efficient as the US markets
jsprag
Posts: 201
Joined: Sun Nov 26, 2017 11:25 am

Re: "Three Proofs That TSM Is Efficient"

Post by jsprag »

longinvest wrote: Mon Jul 29, 2019 3:33 pm
jsprag wrote: Mon Jul 29, 2019 3:17 pm All three "proofs" could be extended to show that a cap-weighted total world portfolio is more efficient. Raise your hand if you recommend holding international stocks in their global market weights.
Some Bogleheads often suggest to invest into Vanguard's LifeStrategy Moderate Growth Fund (VSMGX) which approximates the market portfolio at a low cost, except for a relatively fixed 60/40 allocation (close enough to market weights) and a moderate home bias justified by some inefficiencies in international investing.

Other Bogleheads effectively suggest to invest into the world's stocks and bonds portfolio, possibly using only two ETFs: total world stocks (VT) and total world bonds (BNDW). See this thread.
Perhaps my point wasn't clear. It wasn't about how one could create a global cap-weighted portfolio -- that information is readily available -- but whether one should do so. I contend that if you believe U.S. TSM index is the "best" way to hold U.S. stocks based on this article, you should also believe that total a world index is the "best" way to invest internationally.1

The generalized principle presented by Norstat is that within a given market no other portfolio can be more efficient2 (lower risk and higher return) than the cap-weighted portfolio. If we accept this is (theoretically) true for the U.S. market then we must also accept that it is (theoretically) true for the global market.

Any derivative arguments that advocate for a U.S. TSM fund as the "single best way" to invest in U.S. stocks must acknowledge that a total world index is the "single best way" to invest in global equities.

1"best" is my choice of word to reflect what a reader might reasonably take away from the article or the OP; it is not used in either.

2Of course, this doesn't guarantee that the TSM portfolio is uniquely efficient. Other portfolios (as demonstrated by Markowitz) could be equally efficient by moving along the risk-return frontier.
longinvest
Posts: 4428
Joined: Sat Aug 11, 2012 8:44 am

Re: "Three Proofs That TSM Is Efficient"

Post by longinvest »

jsprag wrote: Tue Jul 30, 2019 12:47 pm
longinvest wrote: Mon Jul 29, 2019 3:33 pm
jsprag wrote: Mon Jul 29, 2019 3:17 pm All three "proofs" could be extended to show that a cap-weighted total world portfolio is more efficient. Raise your hand if you recommend holding international stocks in their global market weights.
Some Bogleheads often suggest to invest into Vanguard's LifeStrategy Moderate Growth Fund (VSMGX) which approximates the market portfolio at a low cost, except for a relatively fixed 60/40 allocation (close enough to market weights) and a moderate home bias justified by some inefficiencies in international investing.

Other Bogleheads effectively suggest to invest into the world's stocks and bonds portfolio, possibly using only two ETFs: total world stocks (VT) and total world bonds (BNDW). See this thread.
Perhaps my point wasn't clear. It wasn't about how one could create a global cap-weighted portfolio -- that information is readily available -- but whether one should do so. I contend that if you believe U.S. TSM index is the "best" way to hold U.S. stocks based on this article, you should also believe that total a world index is the "best" way to invest internationally.1

The generalized principle presented by Norstat is that within a given market no other portfolio can be more efficient2 (lower risk and higher return) than the cap-weighted portfolio. If we accept this is (theoretically) true for the U.S. market then we must also accept that it is (theoretically) true for the global market.

Any derivative arguments that advocate for a U.S. TSM fund as the "single best way" to invest in U.S. stocks must acknowledge that a total world index is the "single best way" to invest in global equities.

1"best" is my choice of word to reflect what a reader might reasonably take away from the article or the OP; it is not used in either.

2Of course, this doesn't guarantee that the TSM portfolio is uniquely efficient. Other portfolios (as demonstrated by Markowitz) could be equally efficient by moving along the risk-return frontier.
Jsprag,

International investing is less efficient than domestic investing for most investors around the world. A security (stock or bond) doesn't carry the same returns for two investors, a domestic one and a foreign one.

As a consequence, one could easily question the validity of a naive generalization of the "most efficient" argument to the global stocks and bonds portfolio. This doesn't mean that this portfolio isn't efficient, but it would be quite reasonable for most investors to adopt a moderate home bias when investing into a global portfolio, as the Vanguard LifeStrategy Moderate Growth Fund (VSMGX) does.

I invite you to read the following series of posts from the "If riskier than US, why doesn't international outperform?" thread where I illustrated and tried to quantify in details some inefficiencies in international investing: Note that the hidden costs and inefficiencies of international investing have significantly decreased over the last decades. The lower they get, the less home bias is justified.

I think that we both agree that a good starting point, for building a portfolio, is the global stocks and bonds portfolio. I think that some moderate home bias is justified.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW
User avatar
willthrill81
Posts: 20845
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

Re: "Three Proofs That TSM Is Efficient"

Post by willthrill81 »

vineviz wrote: Mon Jul 29, 2019 4:18 pm
longinvest wrote: Mon Jul 29, 2019 3:59 pm Promoters of active investing often attack total-market index investing by claiming that one cannot be a "real" total-market index investor unless one invests into an illusive impossible to hold "total assets and derivatives of the universe" portfolio. That's false.
I want to be clear that I neither promote active investing nor do I have any intent to attack total stock market indexing as an investment strategy.

Total stock market indexing is a totally reasonable approach, one with which I have no quibbles.

On the other hand, some claims about TSM investing reach beyond the actual merits of the approach and onto ground that is neither theoretically nor empirically defensible.
I entirely agree. TSM does seem to be efficient, but it is far from the only efficient means of owning stock, and it is highly debatable whether it is the most efficient.

Many of the claims made on the forum regarding TSM simply baffle me (e.g. "TSM is exposed to all factors," "owning anything but TSM is an active bet," etc.).
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings
jsprag
Posts: 201
Joined: Sun Nov 26, 2017 11:25 am

Re: "Three Proofs That TSM Is Efficient"

Post by jsprag »

Taylor Larimore wrote: Mon Jul 29, 2019 12:50 pm Bogleheads:

John Norstad, a retired mathematician at Northwestern University, did a very important study about the most "efficient" (highest return with the least risk) U.S. stock portfolio.
I overlooked a subtlety on my first reading of your post. We should be clear that Norstad did not say TSM was the most efficient, nor did he state that it offered the "highest risk with the least return".

What Norstad claimed was that no other portfolio could be more efficient by simultaneously offering both less risk and more return.

Other portfolios could be equally efficient by offering either less risk + less return, or more risk + more return. TSM is guaranteed to be efficient, but not guaranteed to be uniquely so. It is only one point on the efficient frontier, not a provably optimal sweet spot in the investing universe.

It's a nuanced but significant distinction, easily magnified when we look for what we want to see.
jsprag
Posts: 201
Joined: Sun Nov 26, 2017 11:25 am

Re: "Three Proofs That TSM Is Efficient"

Post by jsprag »

longinvest wrote: Tue Jul 30, 2019 1:11 pm International investing is less efficient than domestic investing for most investors around the world.
Hmmm... I'm not sure I agree as you've written it, and here's why:

Let's stipulate that a security is less efficient than an alternative if it carries greater risk to produce the same return (we could, without changing anything that follows, alternatively define it as lower return for same risk).

Further, let's stipulate that each dollar should be invested in the most efficient option available (why WOULDN'T we do that??)

When I invest my first dollar, I can choose to invest domestically or internationally. Assuming your statement is true, no rational investor would allocate that dollar to a less efficient (international) security and accept the same return available domestically while bearing higher risk.

Repeat for your second dollar, and each additional dollar after that. When complete--if you've acted consistent with a belief that international is less efficient than domestic--then you'll have a 100% domestic and 0% international allocation. This dominates any alternative.

I think we can agree that it's more complex than that. It isn't that domestic is always more efficient than international, it's that a portfolio of domestic and international securities creates efficient risk/return combinations that aren't available with either one alone, and one of those combinations might be right for you.
longinvest wrote: Tue Jul 30, 2019 1:11 pm I think that we both agree that a good starting point, for building a portfolio, is the global stocks and bonds portfolio. I think that some moderate home bias is justified.
I agree with the first, and take no exception to the second :wink:
longinvest
Posts: 4428
Joined: Sat Aug 11, 2012 8:44 am

Re: "Three Proofs That TSM Is Efficient"

Post by longinvest »

jsprag wrote: Tue Jul 30, 2019 2:38 pm
longinvest wrote: Tue Jul 30, 2019 1:11 pm International investing is less efficient than domestic investing for most investors around the world.
Hmmm... I'm not sure I agree as you've written it, and here's why:

Let's stipulate that a security is less efficient than an alternative if it carries greater risk to produce the same return (we could, without changing anything that follows, alternatively define it as lower return for same risk).

Further, let's stipulate that each dollar should be invested in the most efficient option available (why WOULDN'T we do that??)

When I invest my first dollar, I can choose to invest domestically or internationally. Assuming your statement is true, no rational investor would allocate that dollar to a less efficient (international) security and accept the same return available domestically while bearing higher risk.

Repeat for your second dollar, and each additional dollar after that. When complete--if you've acted consistent with a belief that international is less efficient than domestic--then you'll have a 100% domestic and 0% international allocation. This dominates any alternative.

I think we can agree that it's more complex than that. It isn't that domestic is always more efficient than international, it's that a portfolio of domestic and international securities creates efficient risk/return combinations that aren't available with either one alone, and one of those combinations might be right for you.
Effectively, we agree that it's more complex. I wasn't advocating for 100% domestic and you're right that my statement, as written, would imply that.
jsprag wrote: Tue Jul 30, 2019 2:38 pm
longinvest wrote: Tue Jul 30, 2019 1:11 pm I think that we both agree that a good starting point, for building a portfolio, is the global stocks and bonds portfolio. I think that some moderate home bias is justified.
I agree with the first, and take no exception to the second :wink:
:sharebeer
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW
User avatar
willthrill81
Posts: 20845
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

Re: "Three Proofs That TSM Is Efficient"

Post by willthrill81 »

jsprag wrote: Tue Jul 30, 2019 1:56 pmWhat Norstad claimed was that no other portfolio could be more efficient by simultaneously offering both less risk and more return.
The theory might support such a claim, but I'm not sure that the empirical data do.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings
User avatar
vineviz
Posts: 7813
Joined: Tue May 15, 2018 1:55 pm

Re: "Three Proofs That TSM Is Efficient"

Post by vineviz »

willthrill81 wrote: Tue Jul 30, 2019 3:44 pm
jsprag wrote: Tue Jul 30, 2019 1:56 pmWhat Norstad claimed was that no other portfolio could be more efficient by simultaneously offering both less risk and more return.
The theory might support such a claim, but I'm not sure that the empirical data do.
Most research I've seen suggest that aiming for a mean-variance portfolio is one of the least effective ways of getting one: optimizing for diversification, minimum variance, risk parity, or inverse volatility ALL are generally more likely to produce portfolios with higher ex-post Sharpe ratios than actually optimizing for mean-variance efficiency.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
User avatar
grabiner
Advisory Board
Posts: 27928
Joined: Tue Feb 20, 2007 11:58 pm
Location: Columbia, MD

Re: "Three Proofs That TSM Is Efficient"

Post by grabiner »

pdavi21 wrote: Mon Jul 29, 2019 3:09 pm "1. The Efficient Market Hypothesis.
2. The Capital Asset Pricing Model.
3. The Fama-French Three Factor Pricing Model

If any one of these assumptions is true, TSM must be efficient. If any other US
stock portfolio has a higher expected return than TSM with lower risk, we must
reject all three of the assumptions."
The third theorem is incorrect because the definition of "lower risk" is incorrect. The Fama-French model says that expected return and risk come from exposure to the market, size, and value factors. The paper's definition of "lower risk" is lower or equal exposure to all three factors, with lower exposure to one factor. But that is not a proper definition of "lower risk"; it is quite possible for a portfolio with lower exposure to the market factor but higher exposure to the value factor to have a lower standard deviation and higher returns. (This is the same argument as US versus international, which the paper excludes by limiting the argument to US portfolios; a portfolio of 70% US stock and 30% foreign stock might well have lower risk than a portfolio of 100% US stock.)
Wiki David Grabiner
larryswedroe
Posts: 16022
Joined: Thu Feb 22, 2007 8:28 am
Location: St Louis MO

Re: "Three Proofs That TSM Is Efficient"

Post by larryswedroe »

First, it is called the efficient markets hypothesis, meaning it's a theory. If it was TRUE then it would be a law like we have in physics.
Second, we know it is false, despite the link to the paper as there are many well known anomalies that show that it relatively easy to outperform TSM by simply screening out all the lottery stocks which have awful returns, and no need to short.
So if there is a proof of EMH being true it is demonstrably false.
Larry
User avatar
willthrill81
Posts: 20845
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

Re: "Three Proofs That TSM Is Efficient"

Post by willthrill81 »

vineviz wrote: Tue Jul 30, 2019 4:10 pm
willthrill81 wrote: Tue Jul 30, 2019 3:44 pm
jsprag wrote: Tue Jul 30, 2019 1:56 pmWhat Norstad claimed was that no other portfolio could be more efficient by simultaneously offering both less risk and more return.
The theory might support such a claim, but I'm not sure that the empirical data do.
Most research I've seen suggest that aiming for a mean-variance portfolio is one of the least effective ways of getting one: optimizing for diversification, minimum variance, risk parity, or inverse volatility ALL are generally more likely to produce portfolios with higher ex-post Sharpe ratios than actually optimizing for mean-variance efficiency.
The humble and meager research that I have done supports that as well.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings
User avatar
abuss368
Posts: 21537
Joined: Mon Aug 03, 2009 2:33 pm
Location: Where the water is warm, the drinks are cold, and I don't know the names of the players!
Contact:

Re: "Three Proofs That TSM Is Efficient"

Post by abuss368 »

Thanks Taylor!
John C. Bogle: “Simplicity is the master key to financial success."
User avatar
Forester
Posts: 1551
Joined: Sat Jan 19, 2019 2:50 pm
Location: UK

Re: "Three Proofs That TSM Is Efficient"

Post by Forester »

TSM seems pointless vs the S&P 500. Could the S&P be termed "total market"(?) Do people own the 3,000 smaller companies because it feels good?
User avatar
JoMoney
Posts: 9766
Joined: Tue Jul 23, 2013 5:31 am

Re: "Three Proofs That TSM Is Efficient"

Post by JoMoney »

Forester wrote: Wed Jul 31, 2019 5:52 am TSM seems pointless vs the S&P 500. Could the S&P be termed "total market"(?) Do people own the 3,000 smaller companies because it feels good?
It is what it is, and the S&P 500 is not "total" (neither are other market indexes, they are just closer to "total")... but it is probably the most widely reported on benchmark for the U.S. market.

Among the rationale for holding smaller companies is the belief that smaller stocks (although riskier) have higher returns, but if held in a portfolio at the right proportions it can generate higher "risk adjusted returns" as the small-stock returns may not be correlated and the lack of correlation can make the combined portfolio of the riskier small-stocks mixed with the larger stocks less volatile than the small stocks alone, but with the incremental higher returns small stocks are believed to have.
The same portfolio theories and "market efficiency" arguments that drive people to TSM make the argument for tilters to "TILT" even further to riskier stocks. Personally, I don't believe the market is truly "efficient" in the way that some theorize. I don't believe there's anything intrinsic to small stocks that would give them higher returns other than some compensation by a few to make up for the increased failure in most (there are periods where it's happened, but there are plenty of periods where they haven't). Since the founding of DFA's DFSCX fund (after the academic "discovery" of the small-cap effect) to present, the returns have been the same as Vanguard's 500 index (but you likely would have paid some adviser a fee to manage a portfolio of DFA funds along the way).
MStar Chart
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham
User avatar
willthrill81
Posts: 20845
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

Re: "Three Proofs That TSM Is Efficient"

Post by willthrill81 »

Forester wrote: Wed Jul 31, 2019 5:52 am TSM seems pointless vs the S&P 500. Could the S&P be termed "total market"(?) Do people own the 3,000 smaller companies because it feels good?
Since 1972, the annualized returns of the S&P 500 and TSM have varied from each other by a grand total of six basis points (i.e. .06%). Their standard deviations were only .31% different. Their maximum drawdowns were within .08% of each other.

For all practical purposes, I'd call those equivalent.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings
longinvest
Posts: 4428
Joined: Sat Aug 11, 2012 8:44 am

Re: "Three Proofs That TSM Is Efficient"

Post by longinvest »

According to the CRSP methodology, US Micro-cap stocks represent the smallest 2% of the capitalization of the total US stock market, and US Small-cap stocks represent the next 13%. Approximately 1/3 of each category is classified as value stocks. As a consequence, Small-cap Value stocks represent 5% or less of the capitalization of the total US stock market. It's a small portion of the US stock market.

“Don't look for the needle in the haystack. Just buy the haystack!” -- Jack Bogle
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW
User avatar
Topic Author
Taylor Larimore
Advisory Board
Posts: 29946
Joined: Tue Feb 27, 2007 8:09 pm
Location: Miami FL

Re: "Three Proofs That TSM Is Efficient"

Post by Taylor Larimore »

willthrill81 wrote:Since 1972, the annualized returns of the S&P 500 and TSM have varied from each other by a grand total of six basis points (i.e. .06%). Their standard deviations were only .31% different. Their maximum drawdowns were within .08% of each other.
willthrill81:

Based on the above, it appears that there is little difference (except additional turnover and potential tax-inefficiencies) by adding small-cap and mid-cap funds to the S&P 500 fund.

Best wishes.
Taylor
Jack Bogle's Words of Wisdom: "We formed the first S&P 500 Index fund in 1975, and then in 1987 pioneered the completion ("Extended Market") index fund, tracking the small- and mid-cap stocks unrepresented in the S&P 500. The idea: To enable investors to make a commitment to the entire stock market, which I consider as the full fruition of the index fund concept. But adjustment of stocks between the two index funds was required as stocks moved in and out of the 500, creating portfolio turnover and potential tax-inefficiencies. So, in 1992 we created the all-in-one Total (U.S.) Stock Market Index Fund."
"Simplicity is the master key to financial success." -- Jack Bogle
User avatar
willthrill81
Posts: 20845
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

Re: "Three Proofs That TSM Is Efficient"

Post by willthrill81 »

Taylor Larimore wrote: Wed Jul 31, 2019 2:35 pm
willthrill81 wrote:Since 1972, the annualized returns of the S&P 500 and TSM have varied from each other by a grand total of six basis points (i.e. .06%). Their standard deviations were only .31% different. Their maximum drawdowns were within .08% of each other.
willthrill81:

Based on the above, it appears that there is little difference (except additional "turnover and potential tax-inefficiencies") by adding small-cap and mid-cap funds to the S&P 500 fund.
In the quantities that mid-cap and small-cap are represented in TSM, yes. But had an investor equally divided their U.S. stock holdings between large-cap, mid-cap, and small-cap, their returns would have been more than 1% higher than either TSM or LC and with only slightly more volatility since 1972.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings
Nowizard
Posts: 3017
Joined: Tue Oct 23, 2007 5:33 pm

Re: "Three Proofs That TSM Is Efficient"

Post by Nowizard »

Not for at least brief moments like today.

Tim
User avatar
Phineas J. Whoopee
Posts: 9675
Joined: Sun Dec 18, 2011 6:18 pm

Re: "Three Proofs That TSM Is Efficient"

Post by Phineas J. Whoopee »

larryswedroe wrote: Tue Jul 30, 2019 8:59 pm First, it is called the efficient markets hypothesis, meaning it's a theory. If it was TRUE then it would be a law like we have in physics.
...
Larry is promulgating an all too common misunderstanding of the meanings of the terms hypothesis, scientific theory, and scientific law. He is entirely incorrect, as a quick perusal of the links will show. He can't complain about my use of scientific theory and scientific law because he himself brings up physics.

I suggest nobody make any financial decisions based upon that misunderstanding, not even if so advised by Larry.

PJW
User avatar
abuss368
Posts: 21537
Joined: Mon Aug 03, 2009 2:33 pm
Location: Where the water is warm, the drinks are cold, and I don't know the names of the players!
Contact:

Re: "Three Proofs That TSM Is Efficient"

Post by abuss368 »

Why search for the needle in the haystack when you can buy the haystack!
John C. Bogle: “Simplicity is the master key to financial success."
lostdog
Posts: 3170
Joined: Thu Feb 04, 2016 2:15 pm

Re: "Three Proofs That TSM Is Efficient"

Post by lostdog »

abuss368 wrote: Wed Jul 31, 2019 11:20 pm Why search for the needle in the haystack when you can buy the haystack!
Haystack has different meaning to some on this board.
User avatar
willthrill81
Posts: 20845
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

Re: "Three Proofs That TSM Is Efficient"

Post by willthrill81 »

lostdog wrote: Thu Aug 01, 2019 8:37 am
abuss368 wrote: Wed Jul 31, 2019 11:20 pm Why search for the needle in the haystack when you can buy the haystack!
Haystack has different meaning to some on this board.
And the data strongly suggest that there are many haystacks, and some haystacks come with greater risk and return than do others.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings
User avatar
abuss368
Posts: 21537
Joined: Mon Aug 03, 2009 2:33 pm
Location: Where the water is warm, the drinks are cold, and I don't know the names of the players!
Contact:

Re: "Three Proofs That TSM Is Efficient"

Post by abuss368 »

lostdog wrote: Thu Aug 01, 2019 8:37 am
abuss368 wrote: Wed Jul 31, 2019 11:20 pm Why search for the needle in the haystack when you can buy the haystack!
Haystack has different meaning to some on this board.
Indeed.
John C. Bogle: “Simplicity is the master key to financial success."
Random Walker
Posts: 4611
Joined: Fri Feb 23, 2007 8:21 pm

Re: "Three Proofs That TSM Is Efficient"

Post by Random Walker »

abuss368 wrote: Thu Aug 01, 2019 8:51 am
lostdog wrote: Thu Aug 01, 2019 8:37 am
abuss368 wrote: Wed Jul 31, 2019 11:20 pm Why search for the needle in the haystack when you can buy the haystack!
Haystack has different meaning to some on this board.
Indeed.
It can range from haystack of stocks in TSM to haystack of factors in a portfolio full of heavy tilts and alternatives.

Dave
latebloomer2
Posts: 19
Joined: Thu Jul 12, 2018 3:45 pm

Re: "Three Proofs That TSM Is Efficient"

Post by latebloomer2 »

Haystack has different meaning to some on this board I AGREE
and if you torture the data enough you can come up with whatever
results you desire.
User avatar
abuss368
Posts: 21537
Joined: Mon Aug 03, 2009 2:33 pm
Location: Where the water is warm, the drinks are cold, and I don't know the names of the players!
Contact:

Re: "Three Proofs That TSM Is Efficient"

Post by abuss368 »

latebloomer2 wrote: Thu Aug 01, 2019 9:19 am Haystack has different meaning to some on this board I AGREE
and if you torture the data enough you can come up with whatever
results you desire.
Well said.
John C. Bogle: “Simplicity is the master key to financial success."
jsprag
Posts: 201
Joined: Sun Nov 26, 2017 11:25 am

Re: "Three Proofs That TSM Is Efficient"

Post by jsprag »

abuss368 wrote: Wed Jul 31, 2019 11:20 pm Why search for the needle in the haystack when you can buy the haystack!
Because “buy the haystack” isn’t actionable.

Buy the U.S. cap-weighted equity haystack? The global cap-weighted equity haystack? The global cap-weighted securities (stock + bond) haystack?

Each of these are perfectly reasonable, yet mutually exclusive.
User avatar
abuss368
Posts: 21537
Joined: Mon Aug 03, 2009 2:33 pm
Location: Where the water is warm, the drinks are cold, and I don't know the names of the players!
Contact:

Re: "Three Proofs That TSM Is Efficient"

Post by abuss368 »

jsprag wrote: Thu Aug 01, 2019 1:17 pm
abuss368 wrote: Wed Jul 31, 2019 11:20 pm Why search for the needle in the haystack when you can buy the haystack!
Because “buy the haystack” isn’t actionable.

Buy the U.S. cap-weighted equity haystack? The global cap-weighted equity haystack? The global cap-weighted securities (stock + bond) haystack?

Each of these are perfectly reasonable, yet mutually exclusive.
Agreed.
John C. Bogle: “Simplicity is the master key to financial success."
User avatar
Forester
Posts: 1551
Joined: Sat Jan 19, 2019 2:50 pm
Location: UK

Re: "Three Proofs That TSM Is Efficient"

Post by Forester »

What's better diversified

a) TSM 3,600 stocks

b) 50% DJIA 30 stocks, 50% 30 largest S&P600 SC stocks
User avatar
JoMoney
Posts: 9766
Joined: Tue Jul 23, 2013 5:31 am

Re: "Three Proofs That TSM Is Efficient"

Post by JoMoney »

Forester wrote: Fri Aug 02, 2019 5:27 am What's better diversified

a) TSM 3,600 stocks

b) 50% DJIA 30 stocks, 50% 30 largest S&P600 SC stocks
What is it you expect the "diversification" to achieve? If you're trying to reduce idiosyncratic risk to the point that only the systematic risk of the market remains "A" TSM.
If you're chasing a mean-variance optimized portfolio, and believe "diversification" is justification to add riskier assets to a portfolio, it would be period dependent... over the last decade "A" but over some periods starting around the turn of the century maybe "B"
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham
pdavi21
Posts: 1296
Joined: Sat Jan 30, 2016 4:04 pm

Re: "Three Proofs That TSM Is Efficient"

Post by pdavi21 »

grabiner wrote: Tue Jul 30, 2019 8:34 pm
pdavi21 wrote: Mon Jul 29, 2019 3:09 pm "1. The Efficient Market Hypothesis.
2. The Capital Asset Pricing Model.
3. The Fama-French Three Factor Pricing Model

If any one of these assumptions is true, TSM must be efficient. If any other US
stock portfolio has a higher expected return than TSM with lower risk, we must
reject all three of the assumptions."
The third theorem is incorrect because the definition of "lower risk" is incorrect. The Fama-French model says that expected return and risk come from exposure to the market, size, and value factors. The paper's definition of "lower risk" is lower or equal exposure to all three factors, with lower exposure to one factor. But that is not a proper definition of "lower risk"; it is quite possible for a portfolio with lower exposure to the market factor but higher exposure to the value factor to have a lower standard deviation and higher returns. (This is the same argument as US versus international, which the paper excludes by limiting the argument to US portfolios; a portfolio of 70% US stock and 30% foreign stock might well have lower risk than a portfolio of 100% US stock.)
I don't understand your argument.
1. Standard deviation probably is not the same as risk in FF
2. A portfolio with any combination of the three FF factors is either going to have a higher or lower risk than TSM and a concurrent higher or lower return than the TSM. In the formula risk = expected return, so mathematically any portfolio of stocks will be efficient. The FF formula completely ignores the impact of diversification and exposure to one single risk factor. So with the highest combo of Beta, HML, SMB, the expected return and risk are both huge, (the formula) assuming that diversification between the factors does not reduce risk.
3. US vs INTL is a very clear problem with the paper, but it was written in 2004 and it very clearly stated several times the proof would be in the scope of the total US stock market. You can replace with total world and all theorems would hold.
"We spend a great deal of time studying history, which, let's face it, is mostly the history of stupidity." -Stephen Hawking
Post Reply