Does market cap weighted indexing logically follow from EMH?

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selters
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Does market cap weighted indexing logically follow from EMH?

Post by selters »

If the efficient market hypothesis (EMH) is right, is market cap weighted index investing the only logical way to invest? I'm asking because market cap weighted indexing is usually recommended as the way to invest around here.

I'm not doubting market capitalization weighting, but do we use it BECAUSE of what the EMH says, or do we use for another reason?

Despite that historical evidence tells me otherwise, my gut feeling can't help thinking that it doesn't make sense to hold ten times as much in a 500 billon dollar company as in a 50 billion dollar company, and one hundred times as much as in a 5 billion dollar company. Is costs the only reason why market capitalization weighting works so well, or is it something else?

I've read that all stock market gains in the last 30 years or so have come from 30% of the stocks. That means that 70% of all public stocks have resulted in losses, so if you were using equal weighting with yearly rebalancing, you would be rebalancing into losers and out of winners every year. Is that one of the reasons (apart from costs) why market capitalization weighting works?
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baw703916
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Re: Does market cap weighted indexing logically follow from

Post by baw703916 »

If there's a single "market" then assuming the market is efficient at allocating capital, the market portfolio (the total market cap of all investible assets) is on the efficient frontier. For an individual investor, holding everything according to their market cap weights replicates the market portfolio, so it should also be on the efficient frontier.

Where this breaks down is that there isn't a single market. In particular for fixed income, market weights are determined by how much debt various issuers are willing to take on. Nor is it appropriate risk-wise for every investor's portfolio to have the same ratio of debt:equity as the financial markets overall. Furthermore tax costs depend on whether an equity has a REIT structure and where it is domiciled. Also, while the market is pretty efficient, it can't be perfectly so on theoretical grounds (for it to be efficient, somebody has to be able to make money via arbitrage).
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Day9
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Re: Does market cap weighted indexing logically follow from

Post by Day9 »

This paper might be relevant:

Three Proofs that TSM is efficient
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rapporteur
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Re: Does market cap weighted indexing logically follow from

Post by rapporteur »

You need to compare and contrast the implications of the EMH versus the CAPM - they are not coextensive.

The EMH is, at heart, a statement about the impact of extremely rapid dissemination of publicly available **information** on securities investment markets (and is sometimes extended to other markets). In a nutshell, it says that, at any given moment the prices of one security, a portfolio of securities, or all securities reflects all (publicly) available information.

Simplistically, ignoring subtleties of strong, semi-strong, and weak versions, it basically says that the price of a/all securities very rapidly adjusts to reflect (at the margin) the expectations of everyone who is willing to put his money where his mouth is, given that each market participant has (in principle, whether directly, indirectly, or implicitly) access to the publicly available information. Note that the expectations do not have to be correct or even very rational, only that markets reflect dollar-weighted expectations - we can still have bubbles and crashes.

The CAPM is broader. By a number of arguments it arrives at the conclusion that the market portfolio MUST not only be priced to clear the market, but is also right on the efficient frontier (in the Markowitz sense). Further, the market portfolio must occur exactly at the 'tangency point' of the 'leverage line' (for risk-free borrowing) where it touches the efficient frontier. It is a beautiful theory, a tour de force of analysis and logic, the understanding of which will bring tears to your eyes contemplating it. (I am reminded of Feynman's devastating observation about beautiful theories - but finance lacks the mental rigour of physics, I guess.) In short, there is, sadly, a fly in the ointment: the CAPM theory is manifestly wrong (or, more charitably, a very coarse approximation to reality).

The CAPM says that (having diversified away idiosyncratic risks of individual stocks) the return of any particular portfolio needs only one explanatory parameter with respect to its expected return versus that of the market as a whole: its beta. The only small problem is that it's demonstrably untrue! (and has been known to be untrue since only shortly after the model was first enunciated). Formally, in many/most empirical tests of the theory, the 'Security Price Line' (SPL) is not only NOT coincident/parallel to the upsloping market portfolio/riskless-borrowing tangency line, the SPL is often horizontal or even downward sloping for long periods. Beta is not a particularly good explanatory parameter for expected return - it definitely is not even close to explaining the whole catastrophe (as Zorba might say).

And if beta does not explain return expectations the conclusion that the market portfolio is on the efficient frontier and so your portfolio should mirror its composition loses much of its theoretical cogency. It MAY be true (or at least 'pretty good' ) but we're back to using either no theory or a damaged one to justify our portfolio selections. What to do? What to do?

What to do? Brutally and unfairly summarizing the last 50 years of financial research: Add more parameters! Not just simple market beta, but size, value, momentum, profitability, and on and on (often with varying, even conflicting, definitions for those parameters). And with little or no pretence that these are true 'state variables' that capture the underlying mechanics - nope, mostly just statistical analysis buttressed by a plausible story of why a given parameter might reflect some 'risk' - or instead perhaps some 'behavioral pattern'. And we can then debate how persistent these other parameter returns are, whether they can be arbitraged away, and on and on. Tremendous intellectual effort and much complicated math and data mining to justify what amounts to ad-hoc-ery of the first order. We know very little.

But, excuse my hubris in presuming to summarize. Instead get the story (with a lot less cynicism and bitterness) from the masters who have been there from the outset: Fama & French.
The Capital Asset Pricing Model: Theory and Evidence
http://papers.ssrn.com/sol3/papers.cfm? ... _id=440920

Download the pdf and read the whole thing, not just the summary - it's well worth the effort.

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lee1026
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Re: Does market cap weighted indexing logically follow from

Post by lee1026 »

The CAPM is not stronger than the EMH - if the EMH is true, then the CAPM is true. It does not have to work in reverse.

Assume the EMH. Lets say that the market portfolio is not the optimal one. Therefore the rational investor would tilt away from the market portfolio toward the optimal portfolio. But since all investments are in the market portfolio, that means that there must be other people who are tilting away from the optimal portfolio. The people who are tilting from the optimal portfolio are clearly idiots. EMH says that there are idiots.
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SimpleGift
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Re: Does market cap weighted indexing logically follow from

Post by SimpleGift »

selters wrote:Despite that historical evidence tells me otherwise, my gut feeling can't help thinking that it doesn't make sense to hold ten times as much in a 500 billon dollar company as in a 50 billion dollar company, and one hundred times as much as in a 5 billion dollar company.
The beauty of market capitalization-weighted indexes is that they automatically reflect the consensus investor estimates of each company's relative value at every moment in time. Market price is a powerful mechanism to establish and change views about a company's future performance. As a result, relevant information is continuously incorporated into stock prices through investor trading, which is then reflected in market capitalization. And the passive investor reaps the benefits of all this efficiency!

You might find this Vanguard white paper instructive: A Review of Alternative Approaches to Equity Indexing.
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Re: Does market cap weighted indexing logically follow from

Post by stlutz »

my gut feeling can't help thinking that it doesn't make sense to hold ten times as much in a 500 billon dollar company as in a 50 billion dollar company, and one hundred times as much as in a 5 billion dollar company
I'll pass on the EMH and CAPM discussions since I don't really subscribe to either, but cap. weighting is logical. Take your 500 billion dollar company. Suppose it splits up into 2 companies, as happens periodically. Now you have two 250 billion dollar companies. Should you buy more of both of these simply because yesterday they were one company but today they are two?

How much less would you want to own of a restaurant chain operating in 10 cities versus 10 individual restaurants operating in the same cities? Absent any other information, it seems you would want to own the same percentage of each restaurant, which means that your investment in the chain would equal the 10 other restaurants combined.

Deviating from cap weighting makes sense if you have better actionable information than other market participants, but cap weighting is always the most obvious and sensible place to start.
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Re: Does market cap weighted indexing logically follow from

Post by rapporteur »

Assume the EMH. Lets say that the market portfolio is not the optimal one.
So many ways to refute this - which one to choose?

OK, I've decided on today's tack. Let's look at the phrase 'optimal one' . And in looking at it, I'm going to pass over the alluring but meretricious 'optimal' and instead look at the homely prosaic 'one'. You see, there is no 'one' - there are instead 'many'! And this 'many' aspect remains true no matter how fully and quickly information diffuses.

At the most obvious trivial level, let's say you are in the 50% tax bracket while I am at 0%. Do you really still maintain we should hold the same portfolio and that, in each our cases, it should be total market portfolio? Even if we are both exemplars of rationality?

Ah, but you may reply that I 'polluted' the purity of the EMH/CAPM analysis by bringing up extraneous matters such as taxation. Yes, I confess, I let reality intrude.

And are different levels of risk aversion a manifestation of galloping irrationality? Because different levels of risk aversion definitely DO exist and definitely DO result in different portfolios, NOT just different positions on the the riskless borrowing tangent line which touches the efficient frontier at the 'market portfolio' (not least of all because borrowing at the riskless rate is an utter fiction inaccessible to most of us).

And while we're at it, let us note that the CAPM, when in full feather, is not just about investible securities such as stocks, or even stocks and bonds, and not solely USian stocks and bonds, but includes ALL capital, including such elusive aspects as real estate, private capital, and human capital. (CAPM advocates usually pass over such aspects with their fingers in their ears while humming loudly - that they are experimentally, procedurally, mathematically, and statistically rather intractable to data gathering and analysis is NOT sufficient warrant to ignore them!)

Even at the stocks and bonds level, our patriarch Bogle's recommendation to only invest 20% in foreign securities flies in the face of the CAPM. Would he not have us hold the *global* market portfolio? Burn the apostate heresiarch! :happy Alternatively, if markets really are segmented how fine is the granularity? ...is it only between countries or also within them? So much for the supposed single optimal market portfolio!

As for the EPH, in its generally simplified form, it effectively assumes that public information is disseminated instantly - no market player gets an exploitable advantage (As the old joke goes, "'Don't pick up that $20 bill - if it were genuine somebody else would already have picked it up.") Again, not true. We instead have what in IT is called a 'race condition' . Yes, modern communication diffuses information very quickly - but the same technologies make it even faster to trade on early access to the diffusing but not yet fully diffused information. Or have you not noted the ultrafast trading phenomenon?

But rather than pile up further examples, I'll instead appeal to authority. In the paper I cited Fama & French who, while not quite admitting CAPM is fatally broken, acknowledged its many flaws.

But you say, and I quote:
...if the EMH is true, then the CAPM is true. It does not have to work in reverse.
You may be right about it not having not having to work in reverse: If the CAPM is true perhaps the EMH may nonetheless be false.
But applying elementary logic to your contingent assertion (i.e., if the EMH is true, then the CAPM is true) this implies that if the CAPM is NOT true then the EPH must NECESSARILY be false (i.e., (p --> q) --> (~q --> ~p) ). And the CAPM is generally conceded, even by F&F, to come very close to being 'not true'!

In short, be careful about your logic statements lest modus tollens get you. :happy

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lee1026
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Re: Does market cap weighted indexing logically follow from

Post by lee1026 »

At the most obvious trivial level, let's say you are in the 50% tax bracket while I am at 0%. Do you really still maintain we should hold the same portfolio and that, in each our cases, it should be total market portfolio? Even if we are both exemplars of rationality?
In theory (and obviously not in practice), there would swaps agreements that allow for everyone to the exposed to the same risks while the tax advantaged payments go to the most tax advantaged accounts. E.g. Municipal bond futures. People who have high tax brackets would buy the bonds and short the futures to hedge it, and people with low taxes would buy the bond futures. The CME actually tried something like in the past under this theory, and it wasn't terribly popular. But then again, this is more of an example of EMH not being absolutely and totally true then anything else.
And are different levels of risk aversion a manifestation of galloping irrationality? Because different levels of risk aversion definitely DO exist and definitely DO result in different portfolios, NOT just different positions on the the riskless borrowing tangent line which touches the efficient frontier at the 'market portfolio' (not least of all because borrowing at the riskless rate is an utter fiction inaccessible to most of us).
Different levels of risk aversion is accounted for by different leverage ratios. Borrowing at a riskless rate is actually surprisingly easy - futures is reasonably easy to get access to, and the rates are reasonably close to LIBOR/FFR rates, depending on whether we are talking about stock or bond futures.
ALL capital, including such elusive aspects as real estate, private capital, and human capital.
The market isn't perfectly efficient, especially when it comes to human capital?
Even at the stocks and bonds level, our patriarch Bogle's recommendation to only invest 20% in foreign securities flies in the face of the CAPM. Would he not have us hold the *global* market portfolio? Burn the apostate heresiarch! :happy Alternatively, if markets really are segmented how fine is the granularity? ...is it only between countries or also within them? So much for the supposed single optimal market portfolio!
I don't think Bogle ever believed in the CAPM; he certainly didn't suggest leverage as the main way of controlling risk.
But rather than pile up further examples, I'll instead appeal to authority. In the paper I cited Fama & French who, while not quite admitting CAPM is fatally broken, acknowledged its many flaws.
Fama-French also implied that the stock markets is not even remotely efficient. I only claim that EMH implies CAPM. If you are going to reject EMH, then you probably shouldn't be too surprised if you also find reasons to reject the CAPM.
But applying elementary logic to your contingent assertion (i.e., if the EMH is true, then the CAPM is true) this implies that if the CAPM is NOT true then the EPH must NECESSARILY be false (i.e., (p --> q) --> (~q --> ~p) ). And the CAPM is generally conceded, even by F&F, to come very close to being 'not true'!
Correct. If the correct conclusion to the low vol puzzle is that the CAPM does not hold, then it follows that the EMH is not true. At a minimum, the ideal stock portfolio would be a combination of the total stock fund and a market neutral fund strategy of long low beta, short high beta. The fact that no such market neutral fund exists suggest that people are leaving cash on the table.
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Re: Does market cap weighted indexing logically follow from

Post by jaab »

Lee, there is a difference between the market portfolio beeing (multi factor) efficient - or not - and beeing CAPM efficient - or not. CAPM is just a very simpe model with strong assumptions.

I agree however that only a small part of market participants can "tilt" in the same direction (e.g. SV + MOM/QUAL). If Arnott, Asness, Ilmanen, Lussier, Bridgeway, DFA, Larry, Graham & Doddsville, LovVol guys and the like find enough followers, their returns will dimish or may even turn into long term underperformance. Doesn't really matter then if said investors believe the market is multi factor efficient and they are taking more (equity) risk for higher returns. Or if they think it's inefficient (to a degree) and others make mistakes/are constraint by regulations or similar. The "risk people" are vulnerable to floods of money from (large institutional) investors who simply don't buy the risk story.
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Re: Does market cap weighted indexing logically follow from

Post by Rodc »

Day9 wrote:This paper might be relevant:

Three Proofs that TSM is efficient
This makes some common mistakes.

First, US TSM is very clear far from being the market portfolio. Bonds are not risk free and are commonly and cheaply available. The bond market is enormous. The US market share is order of magnitude half the world market (current somewhat less than half I believe, but it varies). So US TSM is order of magnitude 1/4 of the easily invested in market portfolio if we only think about little investors. Little investor are not really the main market drivers. Big players can and do invest in real estate, natural resources, derivatives and who knows what. So in the full market portfolio where the things in the paper apply, US TSM is a tiny slice. Might as well argue that small caps must be "optimal".

CAPM an F-F are just simple models - not without their uses to be sure. But saying well if CAPM is true then X is true does not actually make X true.

That said, the nature of how systems and things like minimum variance problems often work out, it is likely any well diversified portfolio is pretty likely in the long run to have returns that reflect the level of risk taken. Just as different types of bonds have different types of risk, and thus there is some element of luck involved especially on short time scales as to which will provide the best risk adjusted return, so to to different types of company stocks have different types of risk, and thus there is some element of luck involved especially on short time scales.

So, while I reject this paper as particularly valid for TSM and no other small slice of the market portfolio, I think TSM is a fine fund.

But this rests as much as anything on low cost and high diversity vs magical market properties.
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Re: Does market cap weighted indexing logically follow from

Post by tadamsmar »

lee1026 wrote:The CAPM is not stronger than the EMH - if the EMH is true, then the CAPM is true. It does not have to work in reverse.
I thought it was the other way around. The EMH can be true when the CAPM is false. Fama showed that CAPM was not the only pricing model that was consistent with the EMH.
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Re: Does market cap weighted indexing logically follow from

Post by pkcrafter »

selters wrote:If the efficient market hypothesis (EMH) is right, is market cap weighted index investing the only logical way to invest? I'm asking because market cap weighted indexing is usually recommended as the way to invest around here.

I'm not doubting market capitalization weighting, but do we use it BECAUSE of what the EMH says, or do we use for another reason?

Market cap weighting is the profile of where investors have put their money. The rationale for using an index fund that tracks the market does not require any knowledge of the EMH or CAPM. The merits of indexing are the elimination of most of the fees and the elimination of problems actively managed funds can run into that hurt performance. The result is increased efficiency of using your invested money. Data backs this up as it shows that simply indexing the market profile outperforms about 80% of all actively managed funds over a period of 20 years.

Despite that historical evidence tells me otherwise, my gut feeling can't help thinking that it doesn't make sense to hold ten times as much in a 500 billon dollar company as in a 50 billion dollar company, and one hundred times as much as in a 5 billion dollar company. Is costs the only reason why market capitalization weighting works so well, or is it
something else?

A company that is 10 times larger than another company gets 10x more of your dollar than the smaller company, so that means the two companies get an equal share of the dollar based on their worth. Investing the dollar that way buys the investor the same percentage in each company. Keep in mind that this just mirrors where active investors put their money. If you gave each company an equal percentage of your dollar you would in essence be buying 10 more of the smaller company and you would not be buying the market profile.

I've read that all stock market gains in the last 30 years or so have come from 30% of the stocks. That means that 70% of all public stocks have resulted in losses, so if you were using equal weighting with yearly rebalancing, you would be rebalancing into losers and out of winners every year. Is that one of the reasons (apart from costs) why market capitalization weighting works?

I had not heard that before, but there certainly is turnover in the market--companies do not last forever. I looked at the S&P500 going back to 1992 and the average annual turnover rate was about 4.5%. There is a large failure rate in micro and small companies so that may be where the figure come from.

Paul
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Re: Does market cap weighted indexing logically follow from

Post by lee1026 »

Lee, there is a difference between the market portfolio beeing (multi factor) efficient - or not - and beeing CAPM efficient - or not. CAPM is just a very simpe model with strong assumptions.

I agree however that only a small part of market participants can "tilt" in the same direction (e.g. SV + MOM/QUAL). If Arnott, Asness, Ilmanen, Lussier, Bridgeway, DFA, Larry, Graham & Doddsville, LovVol guys and the like find enough followers, their returns will dimish or may even turn into long term underperformance. Doesn't really matter then if said investors believe the market is multi factor efficient and they are taking more (equity) risk for higher returns. Or if they think it's inefficient (to a degree) and others make mistakes/are constraint by regulations or similar. The "risk people" are vulnerable to floods of money from (large institutional) investors who simply don't buy the risk story.
Well, value is more risky than TSM, so it is not inherently silly that it might get better returns. Problem is, growth is also more risky than TSM. Growth and value can't both outperform TSM, so one side of the tilt is being stupid, which goes against EMH.
That said, the nature of how systems and things like minimum variance problems often work out, it is likely any well diversified portfolio is pretty likely in the long run to have returns that reflect the level of risk taken.
No. A highly diversified portfolio of shorting stocks, bonds, and commodities is still fairly risky and diversified, and is unlikely to work out.
I thought it was the other way around. The EMH can be true when the CAPM is false. Fama showed that CAPM was not the only pricing model that was consistent with the EMH.
I haven't heard this one before, source?
jaab
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Re: Does market cap weighted indexing logically follow from

Post by jaab »

lee1026 wrote:I haven't heard this one before, source?
Just put something like joint hypothesis problem efficient market hypothesis into Google. "EMH implies CAPM" is not true. The CAPM is only one of many asset pricing models that have been proposed over the decades. Also note that there are several variants/extensions of the CAPM itself. A good read about the CAPM and it's idea of priced risk factors ("bad returns in bad times") is an interview with Sharpe from 1998: Revisiting The Capital Asset Pricing Model -> http://web.stanford.edu/~wfsharpe/art/djam/djam.htm
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Re: Does market cap weighted indexing logically follow from

Post by ogd »

I don't think EMH logically leads to market cap weighted indexing, but it clears the way for it.

Leaving the CAPM and factor worlds to the academically inclined, what EMH tells me is that all assets are reasonable buys at the current prices, at least before individual considerations like taxation and currency of interest. So based on that, I am inclined to:
1) avoid turnover, since it's an expense without benefits
2) pay the lowest fees I can find, for the same reasons
3) diversify, since I'm getting a free boost to risk/adjusted returns
Indexing wins on all counts: most other schemes are higher turnover, and managers will refuse to get paid so little for managing thousands of different stocks.

If I didn't think EMH was true for practical purposes (i.e. very hard to beat the market), I'd be perhaps inclined to do something else. So that's what I mean by clearing the way.
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Re: Does market cap weighted indexing logically follow from

Post by Clive »

selters wrote:I've read that all stock market gains in the last 30 years or so have come from 30% of the stocks. That means that 70% of all public stocks have resulted in losses, so if you were using equal weighting with yearly rebalancing, you would be rebalancing into losers and out of winners every year. Is that one of the reasons (apart from costs) why market capitalization weighting works?
The Dow 30 is price weighted, not cap weighted. Compare the long term Dow against the S&P500 and I believe they compare reasonably well.

Gains arise out of the overall averages. Sort any collection of assets by their individual gains and you'll see a left to right tails span that is fractal - applies at both the small and large scales. Typically that span will have the worst case countered by the best case, next worst countered by the next best ... etc. and leave a surplus, more often positive bias.

Comparing for instance the worst 30 year annualised real gains since 1900 for 20 different countries with that of the Dow 30 shorter term gains (losses) and ...

Image

... you can see the similar characteristic. The same would also be seen had the S&P500 been plotted - but that would have had less granularity.

By cap weighting and weighting one or more stocks more heavily than others then you're in effect making a prediction that choice will be more likely to be a right tail holding than a left tail holding. If a stock is 10 times the average weighting and its a left tail holding, then that's like having 10 times as many deep divers that will pull down the whole. Similarly if its a right tail then it pulls up the whole relatively more.

That said, the S&P500 is one of the best choices of mechanical investment IMO. It looks to somewhat equal weight sectors (to some extent). Limits any one stock from being too heavily weighted. It's a large part of the total US market (around 80%) which is around 50% of the total world market (has international exposure/earnings). Is part cap weighted based, part equal weight (most of the smaller companies have similar weightings). Comprises growth and value holdings and momentum stocks, large stocks and smaller stocks.

Contrast that with the MXX (Mexico) where 23% of that index is invested in just a single wireless telecom stock
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Re: Does market cap weighted indexing logically follow from

Post by baw703916 »

The proof that the market portfolio is efficient doesn't apply very well to bonds.

If TIPS are 6% of the U.S. Bond market, does this mean that the efficient frontier portfolio must contain 6% TIPS in its bond allocation?

With bonds, you will either receive payment as agreed upon, or the issuer will default. So the market can't set an arbitrarily high price on say Apple's bonds--you already know the maximum upside.

All bonds aren't equal to all people. For instance, a municipal bond from California is more valuable to someone who lives there than it is to me.

So then if you do own bonds, you have to consider how stock and bond returns correlate to see where the efficient frontier really is. It isn't necessarily the market portfolio for either the equity or the bond portion.
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