Since 1992 Vanguard has had a total stock market index fund "designed to provide investors with exposure to the entire U.S. equity market, including small-, mid-, and large-cap growth and value." The expense ratio is 0.04. Why do you need to look any further with regard to investing in the U.S. stock market? Burton Malkiel's "A Random Walk Down Wall Street" is in its 13th edition. If you haven't read it, you should.
I have two questions about the proof, which both have to do with the construction of portfolio B. And yes, "I don't understand".
1. When constructing portfolio B, there is the "not dominated by the combination of other risky securities" caveat about including a security. A broad market index might in fact include stocks that are dominated by combinations of other stocks, no? How does that fit into the picture?
2. The discussion about constructing portfolio B does not say anything about the relative weights (amounts) of the securities that go into portfolio B. Just saying that B ends up being a "broad market index" seems to pre-suppose that we do weighting by market cap and that gives the optimal result, but that part is really not obvious to me.
(1) The theoretically optimal portfolio B is not necessarily the same as an existing index fund. But for practical purposes, they are close.
(2) The theoretically optimal portfolio B would have weights based on the statistical properties of the stocks, not based on market cap. But again, for practical purposes, the difference seems unimportant.
I guess I'm just having trouble understanding why existing index funds are close enough for practical purposes to the optimal portfolio B. Is there some theoretical reason it should be? Some sort of assumptions about companies being uncorrelated in some ways? Something else?
My stock market investing strategy is built a round the concept that “I don’t understand”. Hence, I basically only own total market index funds, and maybe a handful of individual stocks of places where I am/have been employed at. I use the “smart people that I tend to trust on other things who seem to know what they’re talking about say that it makes sense to own index funds”-heuristic. So far, it’s worked out ok.
These kinds of discussions always raise the question: why don't I buy index funds? The answer ends up being one of three options:
1. I'm an idiot.
2. My 'larger portfolio' includes things outside of stocks.
3. The so-called index funds aren't actually index funds.
Number 2 is pretty relevant - basically, I can hedge against my career, my housing, and so on, by choosing stocks that wouldn't fit similarly in someone else's portfolio. In this case, the 'narrow index' might actually help with such an approach.
The above discussion by Arnold touches on (3) - and the fact that managers mess with the index continuously and charge various fees makes me suspicious that it isn't at all the thing it claims to be.
Of course, those managers might just point to (1).
One related thing I don't feel I understand is whether the observations of the small cap and value anomalies are robust enough to make a small cap or value stock index superior to a total market index in mean expected value.
"I have to say that I am not sure that these days the S&P 500 is close to the theoretical market index."
A typical 401k will allow the following:
SP500
Mid-cap fund
Small cap fund
Cash Fund
Bond Funds (quality and duration varies in different 401ks)
Sometimes a "real resource" fund
Some kind of international stock fund
Some target date mix of the above
The expense fees on these can also vary. SP500 is often the cheapest. Depending on the quality of the 401k fees can either be about as decent or get really high on some of the alternative funds. My Dad's old retirement fund had incredibly shitty management fees.
I take it that you would add mid and small cap funds to the SP500, and maybe a bond fund (if a decent option is available).
I will note that having a mix of cap index funds myself the small and middle often swing quite wildly. And I believe the Russell 2000 has underperformed the SP500. Feels weird to have more risk and get less money.
If we think we live in a gangster state of regulatory capture, shouldn't the big companies keep dominating the small companies?
I agree regulation favors the bigger companies and skews returns towards them. Adding insult to injury, small cap returns are further reduced by the best companies leaving to join mid and large cap funds so small cap doesn't get much of the total return.
This discussion seems anchored in the portfolio construction developments of the 1960s. Work continues! One approach relevant to some of the comments here are asset allocation models that assume that the model parameters (esp. covariances) are estimates (i.e., draws from a distribution) and not known with certainty. This approach was expounded in the 1990s by Richard Michaud (among others) and summarized in his short, dense book: Efficient Asset Management (available on Amazon). A notable result of this quantification of "epistemic humility" about market returns is that his frontiers (which are traditional frontiers averaged over many sample parameter draws) turn DOWN for high (average) levels of portfolio risk. That is, even optimized high risk portfolios may have a lower expected return than lower risk portfolios (because their covariances are estimated with less certainty). [Googling suggests that this approach has been commercialized and may be used by family offices.]
Good article. If one resolves, for example, to maintain 18-22% cash, balance equity index funds, buying more equity only if/when cash exceeds 22%, one would do very well over the long haul. And sell equity if/when cash drops below 18%.
I will admit this theory does feel kind of clunky to me. I'm going to try to put my dissonance into words, but please feel free to correct any misconceptions I might have.
Is an index fund really fundamentally different from the stock of an individual company? If we take a hypothetical company with a highly diversified set of financial interests, something like a super-Amazon; and a highly specialized stock market, perhaps within a country whose economy is dominated by mineral export, couldn't the positions be reversed?
I ask mostly because it doesn't feel like we're really setting aside personal knowledge when choosing to invest. Rising valuations across an index relies on the knowledge that money will flow into it from somewhere. A zero or negative sum market would function pretty differently.
I assume you are entirely correct in saying that a leveraged position on an S&P 500 index fund would be preferable to a narrow gamble on an individual stock within that market, but is the same true for the Nikkei and stocks within its market? Or the Nikkei vs an individual company within a US stock market that has traditionally performed very consistently?
Follow up on Q2, please: Why do you say that on average you will underperform the market? It seems that by definition, the average investor ties the market? Some beat and some trail, tending towards the market average over longer time periods?
Also, is it not possible that the market always prices in the sum total of the EMOTION of all market participants, in addition to the knowledge of all market participants? When Bryan Caplan fearfully sells all of his equities in March 2020, EMH would require that Caplan's sale is adding to the information content of the market. But is it not actually an emotional response with no additional informational content?
You have always seemed to believe in complex human behavior, as opposed to homo economicus. Why would human foibles of fear, greed, and desire to conform to the herd not apply to investing?
Thanks for trying to help me understand your concepts!
Yup. Though an important followon question would be: what if everyone realized they should just be in an index fund and not trading individual stocks, how well are those individual stocks priced? I hadn't researched the issue. If everyone were trading individual stocks it seems like a range of information is coming to bear on pricing the stock, some good and some bad. When most people move to index funds, it seems individual stocks might be more likely to be traded by outliers in either direction: those who truly are experts and the clueless who think they know something, but don't, who should be in index funds. If the experts all think "sell": who buys, will it lead to a price crash more easily? Will that lead to more volatility when the truly knowledgeable push in one direction more heavily than in the market with people with a range of information?
Question 1: If you buy options, which have an expected return of less than zero, does that not reduce your expected future returns on that portfolio?
Question 2: you assert that "if you truly know something about a stock that other people don’t know, then you can earn an extraordinary return by betting on that stock". Why would that not apply to PUBLIC information that I don't "truly know", but upon which I place higher predictive value than other investors do?
Question 3: Are you simply assuming away the possibility that some individual stocks can have higher "expected future returns" than others for any given level of expected variance in those expected future returns?
Question 4: How is the variance of expected future returns measured? Is it based upon past volatility of a stock? And if so, doesn't that contradict even the soft form of EMH, which says future movements of a stock's price can't be predicted from past movements?
Q1 The assumption is that the person is a gambler. I am just pointing out that gambling by buying an option on an index has more upside than gambling by buying one stock.
Q2 Of course, the market has to be inefficient for you to be able to make money on public information. Even if the market is efficient, you can always bet on your own point of view. It's just that on average you will underperform the market.
Q3 Not at assuming that at all.
Q4 In principle, variances and covariances are expected going forward. Perhaps based on past data, perhaps not. Not really known. But even knowing variance and covariance does not enable you to predict the price.
It seems to me that your notion of variance is an oversimplification, in a way that matters here.
The point of diversifying is to avoid "putting all your eggs in one basket," that is, putting all or most of your investment capital in the same or similar investments such that one event could cause most of it to substantially lose value. To avoid this I don't just want investments with a high or low variance in an absolute sense. I want them to have a low correlation with each other, on the downside especially.
You are correct that covariance is what matters. A stock with high variance but low covariance with other stocks in portfolio B is a better candidate to be added to portfolio B than a stock with the opposite characteristics
Since 1992 Vanguard has had a total stock market index fund "designed to provide investors with exposure to the entire U.S. equity market, including small-, mid-, and large-cap growth and value." The expense ratio is 0.04. Why do you need to look any further with regard to investing in the U.S. stock market? Burton Malkiel's "A Random Walk Down Wall Street" is in its 13th edition. If you haven't read it, you should.
0.04 percent (per year), you mean?
I have two questions about the proof, which both have to do with the construction of portfolio B. And yes, "I don't understand".
1. When constructing portfolio B, there is the "not dominated by the combination of other risky securities" caveat about including a security. A broad market index might in fact include stocks that are dominated by combinations of other stocks, no? How does that fit into the picture?
2. The discussion about constructing portfolio B does not say anything about the relative weights (amounts) of the securities that go into portfolio B. Just saying that B ends up being a "broad market index" seems to pre-suppose that we do weighting by market cap and that gives the optimal result, but that part is really not obvious to me.
(1) The theoretically optimal portfolio B is not necessarily the same as an existing index fund. But for practical purposes, they are close.
(2) The theoretically optimal portfolio B would have weights based on the statistical properties of the stocks, not based on market cap. But again, for practical purposes, the difference seems unimportant.
I guess I'm just having trouble understanding why existing index funds are close enough for practical purposes to the optimal portfolio B. Is there some theoretical reason it should be? Some sort of assumptions about companies being uncorrelated in some ways? Something else?
the intuition is that the marginal effects of changing the weights while meaningful, will not materially change the mean variance significantly
My stock market investing strategy is built a round the concept that “I don’t understand”. Hence, I basically only own total market index funds, and maybe a handful of individual stocks of places where I am/have been employed at. I use the “smart people that I tend to trust on other things who seem to know what they’re talking about say that it makes sense to own index funds”-heuristic. So far, it’s worked out ok.
These kinds of discussions always raise the question: why don't I buy index funds? The answer ends up being one of three options:
1. I'm an idiot.
2. My 'larger portfolio' includes things outside of stocks.
3. The so-called index funds aren't actually index funds.
Number 2 is pretty relevant - basically, I can hedge against my career, my housing, and so on, by choosing stocks that wouldn't fit similarly in someone else's portfolio. In this case, the 'narrow index' might actually help with such an approach.
The above discussion by Arnold touches on (3) - and the fact that managers mess with the index continuously and charge various fees makes me suspicious that it isn't at all the thing it claims to be.
Of course, those managers might just point to (1).
Utter Rubbish
One related thing I don't feel I understand is whether the observations of the small cap and value anomalies are robust enough to make a small cap or value stock index superior to a total market index in mean expected value.
If you are going to explain this, you might do well to start with the distinction between expected value and variance itself in a more concrete way.
And how the concept of time factors into it.
"I have to say that I am not sure that these days the S&P 500 is close to the theoretical market index."
A typical 401k will allow the following:
SP500
Mid-cap fund
Small cap fund
Cash Fund
Bond Funds (quality and duration varies in different 401ks)
Sometimes a "real resource" fund
Some kind of international stock fund
Some target date mix of the above
The expense fees on these can also vary. SP500 is often the cheapest. Depending on the quality of the 401k fees can either be about as decent or get really high on some of the alternative funds. My Dad's old retirement fund had incredibly shitty management fees.
I take it that you would add mid and small cap funds to the SP500, and maybe a bond fund (if a decent option is available).
I will note that having a mix of cap index funds myself the small and middle often swing quite wildly. And I believe the Russell 2000 has underperformed the SP500. Feels weird to have more risk and get less money.
If we think we live in a gangster state of regulatory capture, shouldn't the big companies keep dominating the small companies?
I agree regulation favors the bigger companies and skews returns towards them. Adding insult to injury, small cap returns are further reduced by the best companies leaving to join mid and large cap funds so small cap doesn't get much of the total return.
This discussion seems anchored in the portfolio construction developments of the 1960s. Work continues! One approach relevant to some of the comments here are asset allocation models that assume that the model parameters (esp. covariances) are estimates (i.e., draws from a distribution) and not known with certainty. This approach was expounded in the 1990s by Richard Michaud (among others) and summarized in his short, dense book: Efficient Asset Management (available on Amazon). A notable result of this quantification of "epistemic humility" about market returns is that his frontiers (which are traditional frontiers averaged over many sample parameter draws) turn DOWN for high (average) levels of portfolio risk. That is, even optimized high risk portfolios may have a lower expected return than lower risk portfolios (because their covariances are estimated with less certainty). [Googling suggests that this approach has been commercialized and may be used by family offices.]
Good article. If one resolves, for example, to maintain 18-22% cash, balance equity index funds, buying more equity only if/when cash exceeds 22%, one would do very well over the long haul. And sell equity if/when cash drops below 18%.
Does the mathematical proof of the portfolio separation theorem depend on the investor being allowed to go long/short? Does this version?
I will admit this theory does feel kind of clunky to me. I'm going to try to put my dissonance into words, but please feel free to correct any misconceptions I might have.
Is an index fund really fundamentally different from the stock of an individual company? If we take a hypothetical company with a highly diversified set of financial interests, something like a super-Amazon; and a highly specialized stock market, perhaps within a country whose economy is dominated by mineral export, couldn't the positions be reversed?
I ask mostly because it doesn't feel like we're really setting aside personal knowledge when choosing to invest. Rising valuations across an index relies on the knowledge that money will flow into it from somewhere. A zero or negative sum market would function pretty differently.
I assume you are entirely correct in saying that a leveraged position on an S&P 500 index fund would be preferable to a narrow gamble on an individual stock within that market, but is the same true for the Nikkei and stocks within its market? Or the Nikkei vs an individual company within a US stock market that has traditionally performed very consistently?
Follow up on Q2, please: Why do you say that on average you will underperform the market? It seems that by definition, the average investor ties the market? Some beat and some trail, tending towards the market average over longer time periods?
Also, is it not possible that the market always prices in the sum total of the EMOTION of all market participants, in addition to the knowledge of all market participants? When Bryan Caplan fearfully sells all of his equities in March 2020, EMH would require that Caplan's sale is adding to the information content of the market. But is it not actually an emotional response with no additional informational content?
You have always seemed to believe in complex human behavior, as opposed to homo economicus. Why would human foibles of fear, greed, and desire to conform to the herd not apply to investing?
Thanks for trying to help me understand your concepts!
Yup. Though an important followon question would be: what if everyone realized they should just be in an index fund and not trading individual stocks, how well are those individual stocks priced? I hadn't researched the issue. If everyone were trading individual stocks it seems like a range of information is coming to bear on pricing the stock, some good and some bad. When most people move to index funds, it seems individual stocks might be more likely to be traded by outliers in either direction: those who truly are experts and the clueless who think they know something, but don't, who should be in index funds. If the experts all think "sell": who buys, will it lead to a price crash more easily? Will that lead to more volatility when the truly knowledgeable push in one direction more heavily than in the market with people with a range of information?
Question 1: If you buy options, which have an expected return of less than zero, does that not reduce your expected future returns on that portfolio?
Question 2: you assert that "if you truly know something about a stock that other people don’t know, then you can earn an extraordinary return by betting on that stock". Why would that not apply to PUBLIC information that I don't "truly know", but upon which I place higher predictive value than other investors do?
Question 3: Are you simply assuming away the possibility that some individual stocks can have higher "expected future returns" than others for any given level of expected variance in those expected future returns?
Question 4: How is the variance of expected future returns measured? Is it based upon past volatility of a stock? And if so, doesn't that contradict even the soft form of EMH, which says future movements of a stock's price can't be predicted from past movements?
Q1 The assumption is that the person is a gambler. I am just pointing out that gambling by buying an option on an index has more upside than gambling by buying one stock.
Q2 Of course, the market has to be inefficient for you to be able to make money on public information. Even if the market is efficient, you can always bet on your own point of view. It's just that on average you will underperform the market.
Q3 Not at assuming that at all.
Q4 In principle, variances and covariances are expected going forward. Perhaps based on past data, perhaps not. Not really known. But even knowing variance and covariance does not enable you to predict the price.
It seems to me that your notion of variance is an oversimplification, in a way that matters here.
The point of diversifying is to avoid "putting all your eggs in one basket," that is, putting all or most of your investment capital in the same or similar investments such that one event could cause most of it to substantially lose value. To avoid this I don't just want investments with a high or low variance in an absolute sense. I want them to have a low correlation with each other, on the downside especially.
You are correct that covariance is what matters. A stock with high variance but low covariance with other stocks in portfolio B is a better candidate to be added to portfolio B than a stock with the opposite characteristics