my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by nisiprius »

burritoLover wrote: Thu Jun 08, 2023 8:56 am The definition of tilts on this forum is weird. On the one hand, apparently whatever bond allocation (not market cap weight) and whatever bond assortment you have (not at market-cap weights either) are NOT tilts, even though, obviously, if they are not market-cap weighted, they are tilts. And apparently 100% US bonds is not a tilt even though you are excluding the rest of the world's bonds. Same with stocks - a 100% US total stock allocation is not a tilt either. Apparently the definition of maximally diversified here is simply holding 100% US total stock - nothing else in your portfolio matters as long as you have some bonds no matter what they are and no matter what their allocation is.
This is defensible, because even casual experimentation with PortfolioVisualizer backtests will reveal that changes in the composition of the bond part of the portfolio make very little difference in the portfolio as a whole, much less than changes in stock composition. In any portfolio with a meaningful stock allocation, the risk behavior of the stocks really dominates the portfolio.

Decisions such as US-only or total global are much more consequential on the stock side than the bond side.

Thus: using four Vanguard index funds--Total [US} stock market, total international stocks, total [US] bond market, total international bonds--we construct three portfolios, all 60/40 stocks/bonds.
  • Below, the blue line is our starting point, US only.
  • The red line shows the effect of globalizing stocks only, 50/50 between US and international. (It's the one on the bottom.)
  • The yellow line shows the effect of globalizing bonds only, 50/50 between US and international. (Hard to see because it's so close to the blue line).
Source

Image

Please let me emphasize: the point is not that international stocks happened to underperform over this particular time period, no, that is truly not my point.

My point is that in a "typical" whole portfolio, tinkering with the stock holdings made a big difference, while tinkering with the bond holdings made only a little difference.

If you try some experiments, with realistic stock and bond choice you might actually think about making, I think you'll find that this holds generally.

Bond flavor differences, as represented e.g. by the Morningstar style boxes--stand-ins for the rarely-mentioned Fama-French bond factors--only look big if you are exploring 100%-bond portfolios. Once you add stocks to the picture, their importance recedes.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by km91 »

nisiprius wrote: Thu Jun 08, 2023 8:15 am The big question is whether the "market portfolio," the actual stock market itself and everything in it, and the cap-weighted total stock market indexes that mirror it, represent maximum diversification, or whether you can argue that it is "not diversified" (because there's "too much" money invested in the mega-cap stocks--circularity IMHO because it is just saying the stocks with more money invested in them have more money invested in them), and that it is possible to achieve more diversification by tinkering with the weighting scheme--small-cap value tilts, fundamental indexing, "smart beta."
Is there any reason to expect the market portfolio to produce the most diversified portfolio? The top 10 constituents of VTI account for 25% of it's market cap, the top 10 constituents of IXUS account for less than 10% of it's market cap. Market cap weighting produces portfolios with very different characteristics depending on what you choose as the 'market' portfolio. If US TSM is the optimally diversified portfolio does this suggest that IXUS is sub optimal? They have completely different sector exposures, valuation exposures, and top component concentrations, surely they both can't be optimally diversified in absolute terms
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Beensabu »

Northern Flicker wrote: Thu Jun 08, 2023 12:35 am
Beensabu wrote: Wed Jun 07, 2023 9:37 pm You know... sometimes I wonder if all you really need is a couple mega umbrella corps in each sector.
If you pose that as a question, the answer would be no. For one thing, not all sectors even have megacaps. But it would be too few stocks in number to diversify away idiosyncratic risk.
How many stocks do you need to effectively reduce unsystematic risk? I thought it was at least 20.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by nisiprius »

km91 wrote: Thu Jun 08, 2023 9:27 am...Is there any reason to expect the market portfolio to produce the most diversified portfolio? ...
Once again, it's a useless question if you are not willing to explicitly give a definition and a numeric measuring stick for "diversification" and, ideally, a description of the specific benefits it achieves. That is, what does diversification optimize other than diversification itself?

Yes, there is a good reason to expect the market portfolio to have a higher Sharpe ratio than any other set of portfolio weights. It's a theorem in financial economics, and it's what Jeremy Siegel was referring to in the passage I quoted above. The reasons depend on typical "spherical cow" assumptions, but the assumptions aren't totally crazy. If you don't believe the assumptions, then they don't apply. And if you don't accept the Sharpe ratio as meaningful, then it is irrelevant. But, yes, there is A reason.

The other side of the coin is that if market cap weighting is so bad, it ought to be possible to beat it easily, consistently, and by a lot. The track record for products that do that is not impressive at all. As I noted, we don't seem to hear much about fundamental indexing or smart beta these days. RSP, the S&P 500 equal weighted index is an often-cited red herring, and gets attention because of having had higher return than cap-weighted, but it is clearly riskier and if you take risk into account it is inferior.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by nisiprius »

Beensabu wrote: Thu Jun 08, 2023 9:35 am How many stocks do you need to effectively reduce unsystematic risk? I thought it was at least 20.
The 15-Stock Diversification Myth
One of the most dangerous investment chestnuts is the idea that you can successfully diversify your portfolio with a relatively small number of stocks, the magic number usually being about 15.
...
[data and research findings]
...
So, yes, Virginia, you can eliminate nonsytematic portfolio risk, as defined by Modern Portfolio Theory, with a relatively few stocks. It's just that nonsystematic risk is only a small part of the puzzle. Fifteen stocks is not enough. Thirty is not enough. Even 200 is not enough. The only way to truly minimize the risks of stock ownership is by owning the whole market.
That's old and it's just a blog posting, but in particular an actual recent-ish paper by Bessembinder confirms it. The average return of the stock market is attributable to a very small number of "superstocks," and if you only hold fifteen or twenty stocks you have too good a chance of missing all of them. There's vicious positive skew, and in order to average things out you need a much bigger sample than you would need if there weren't.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by burritoLover »

nisiprius wrote: Thu Jun 08, 2023 9:19 am
burritoLover wrote: Thu Jun 08, 2023 8:56 am The definition of tilts on this forum is weird. On the one hand, apparently whatever bond allocation (not market cap weight) and whatever bond assortment you have (not at market-cap weights either) are NOT tilts, even though, obviously, if they are not market-cap weighted, they are tilts. And apparently 100% US bonds is not a tilt even though you are excluding the rest of the world's bonds. Same with stocks - a 100% US total stock allocation is not a tilt either. Apparently the definition of maximally diversified here is simply holding 100% US total stock - nothing else in your portfolio matters as long as you have some bonds no matter what they are and no matter what their allocation is.
This is defensible, because even casual experimentation with PortfolioVisualizer backtests will reveal that changes in the composition of the bond part of the portfolio make very little difference in the portfolio as a whole, much less than changes in stock composition. In any portfolio with a meaningful stock allocation, the risk behavior of the stocks really dominates the portfolio.

Decisions such as US-only or total global are much more consequential on the stock side than the bond side.

Thus: using four Vanguard index funds--Total [US} stock market, total international stocks, total [US] bond market, total international bonds--we construct three portfolios, all 60/40 stocks/bonds.
  • Below, the blue line is our starting point, US only.
  • The red line shows the effect of globalizing stocks only, 50/50 between US and international. (It's the one on the bottom.)
  • The yellow line shows the effect of globalizing bonds only, 50/50 between US and international. (Hard to see because it's so close to the blue line).
Source

Image

Please let me emphasize: the point is not that international stocks happened to underperform over this particular time period, no, that is truly not my point.

My point is that in a "typical" whole portfolio, tinkering with the stock holdings made a big difference, while tinkering with the bond holdings made only a little difference.

If you try some experiments, with realistic stock and bond choice you might actually think about making, I think you'll find that this holds generally.

Bond flavor differences, as represented e.g. by the Morningstar style boxes--stand-ins for the rarely-mentioned Fama-French bond factors--only look big if you are exploring 100%-bond portfolios. Once you add stocks to the picture, their importance recedes.
Well, let's compare a 50/50 portfolio of US stocks and bonds. Our base portfolio is 50 TSM / 50 short-term treasuries. In one portfolio, we add a hefty 50% tilt to small-caps on the equities side (from the OP's original question) and in the other portfolio we instead add a 50% tilt to long-term treasuries. In this case, no one would really call any of the bond changes "tilts" but the 50% equities tilt to small caps - there'd be blood raining down from the skies on Bogleheads. And we only compared bonds with no credit risk here, so only one "flavor" of bonds changing here.

Since Jan 1978 (PV earliest data for LTT):

Code: Select all

Portfolio	Initial Balance	Final Balance	CAGR	Stdev	Best Year	Worst Year	Max. Drawdown	Sharpe Ratio	Sortino Ratio	Market Correlation
50 TSM / 50 STT	        $10,000	$455,342 	8.77% 	8.03%	23.95%	-15.18%	-23.89% 	0.56	0.83	0.98
25 TSM,  25 SC / 50 STT	$10,000	$495,097 	8.97% 	8.75%	25.16%	-14.94%	-24.78% 	0.54	0.79	0.96
50 TSM / 25 STT, 25 LTT	$10,000	$584,173 	9.37% 	8.70%	28.44%	-18.37%	-22.05% 	0.59	0.88	0.92
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by rkhusky »

km91 wrote: Thu Jun 08, 2023 9:27 am
nisiprius wrote: Thu Jun 08, 2023 8:15 am The big question is whether the "market portfolio," the actual stock market itself and everything in it, and the cap-weighted total stock market indexes that mirror it, represent maximum diversification, or whether you can argue that it is "not diversified" (because there's "too much" money invested in the mega-cap stocks--circularity IMHO because it is just saying the stocks with more money invested in them have more money invested in them), and that it is possible to achieve more diversification by tinkering with the weighting scheme--small-cap value tilts, fundamental indexing, "smart beta."
Is there any reason to expect the market portfolio to produce the most diversified portfolio? The top 10 constituents of VTI account for 25% of it's market cap, the top 10 constituents of IXUS account for less than 10% of it's market cap. Market cap weighting produces portfolios with very different characteristics depending on what you choose as the 'market' portfolio. If US TSM is the optimally diversified portfolio does this suggest that IXUS is sub optimal? They have completely different sector exposures, valuation exposures, and top component concentrations, surely they both can't be optimally diversified in absolute terms
VTI and IXUS represent different markets. VTI is near-optimal (not sure anything could be said to be optimal, except in hindsight) for the US market. And IXUS for international markets. VT is near-optimal for the global market.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by alluringreality »

nisiprius wrote: Thu Jun 08, 2023 9:38 am The other side of the coin is that if market cap weighting is so bad, it ought to be possible to beat it easily, consistently, and by a lot. The track record for products that do that is not impressive at all. As I noted, we don't seem to hear much about fundamental indexing or smart beta these days. RSP, the S&P 500 equal weighted index is an often-cited red herring, and gets attention because of having had higher return than cap-weighted, but it is clearly riskier and if you take risk into account it is inferior.
I'm not sure easy and consistent outperformance is necessarily the reason for tilts. I'm also not following significance for the top of the market outperforming over the last decade in relation to future unknowns. On a basis of what Frank Knight might label "a priori", and considering that historical stock returns seem to exhibit skew and bubbles at times, might doubling the weight of one or more individual companies represent possible future risk to some extent? It's debatable if Apple and Microsoft might double in weight again in the future, but if that was to happen, then US Total Stock Market funds may not meet the reasoning used to define diversified for the 1940 act. Essentially I'm not sure that past data is necessarily an ideal way select holdings in relation to some future unknowns.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by km91 »

nisiprius wrote: Thu Jun 08, 2023 9:38 am
km91 wrote: Thu Jun 08, 2023 9:27 am...Is there any reason to expect the market portfolio to produce the most diversified portfolio? ...
Once again, it's a useless question if you are not willing to explicitly give a definition and a numeric measuring stick for "diversification" and, ideally, a description of the specific benefits it achieves. That is, what does diversification optimize other than diversification itself?

Yes, there is a good reason to expect the market portfolio to have a higher Sharpe ratio than any other set of portfolio weights. It's a theorem in financial economics, and it's what Jeremy Siegel was referring to in the passage I quoted above. The reasons depend on typical "spherical cow" assumptions, but the assumptions aren't totally crazy. If you don't believe the assumptions, then they don't apply. And if you don't accept the Sharpe ratio as meaningful, then it is irrelevant. But, yes, there is A reason.

The other side of the coin is that if market cap weighting is so bad, it ought to be possible to beat it easily, consistently, and by a lot. The track record for products that do that is not impressive at all. As I noted, we don't seem to hear much about fundamental indexing or smart beta these days. RSP, the S&P 500 equal weighted index is an often-cited red herring, and gets attention because of having had higher return than cap-weighted, but it is clearly riskier and if you take risk into account it is inferior.
Sure, I'll define diversification as broad exposure across market capitalizations, valuations, geography, number of holdings, sectors, and top 10 components. You can challenge whether these are valid criteria to evaluate diversification, I think there's strong theory and intuition to suspect they're mostly right. I don't think we need an absolute numerical threshold for any of these characteristics, we just need to compare portfolios on this basis. VOO, VTI, VT, and IXUS are all market cap weighted market portfolios yet all produce different exposures to these characteristics. So which is optimally diversified? I'm wary of using Sharpe as a measure of diversification. The only risk it considers is volatility. Tesla and Nvidia blow TSM out of the water based on Sharpe, but we know these single stock portfolios are incredibly risky, clearly more risky than Sharpe implies. I don't think anyone is seriously claiming market cap weight is bad, but it should be apparent that a US TSM investor has concentration to many of the above characteristics compared to a global investor. Different total market portfolios do contain different degrees of diversification and some may be preferred to others. Arguably the entire point of diversification is to protect against risks that have never shown up in the back test or historical data
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by km91 »

rkhusky wrote: Thu Jun 08, 2023 10:08 am
km91 wrote: Thu Jun 08, 2023 9:27 am
nisiprius wrote: Thu Jun 08, 2023 8:15 am The big question is whether the "market portfolio," the actual stock market itself and everything in it, and the cap-weighted total stock market indexes that mirror it, represent maximum diversification, or whether you can argue that it is "not diversified" (because there's "too much" money invested in the mega-cap stocks--circularity IMHO because it is just saying the stocks with more money invested in them have more money invested in them), and that it is possible to achieve more diversification by tinkering with the weighting scheme--small-cap value tilts, fundamental indexing, "smart beta."
Is there any reason to expect the market portfolio to produce the most diversified portfolio? The top 10 constituents of VTI account for 25% of it's market cap, the top 10 constituents of IXUS account for less than 10% of it's market cap. Market cap weighting produces portfolios with very different characteristics depending on what you choose as the 'market' portfolio. If US TSM is the optimally diversified portfolio does this suggest that IXUS is sub optimal? They have completely different sector exposures, valuation exposures, and top component concentrations, surely they both can't be optimally diversified in absolute terms
VTI and IXUS represent different markets. VTI is near-optimal (not sure anything could be said to be optimal, except in hindsight) for the US market. And IXUS for international markets. VT is near-optimal for the global market.
But which represents the optimal diversified portfolio for an investor to hold?
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Beensabu »

km91 wrote: Thu Jun 08, 2023 11:11 am But which represents the optimal diversified portfolio for an investor to hold?
If cap weighted total market is optimal diversification, then it's clearly VT.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Northern Flicker »

CloseEnough wrote: Thu Jun 08, 2023 6:35 am To add diversification you need to add investments or assets that are in a different asset class than the stock market. Fixed income is a different asset class, adds diversification to a total equity market fund. but is still tied to the market. Best diversification would be a non-financial market investment or asset.
There are two types of diversification.

1. Diversification across asset classes. This is accomplished when establishing an asset allocation.

2. Diversification within an asset class. This is accomplished when selecting funds to implement an asset class.

How well a fixed income subclass diversifies equity risk is not driven by whether it is traded in the market but by the properties of the fixed income subclass.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Northern Flicker »

Beensabu wrote: Thu Jun 08, 2023 12:37 pm
km91 wrote: Thu Jun 08, 2023 11:11 am But which represents the optimal diversified portfolio for an investor to hold?
If cap weighted total market is optimal diversification, then it's clearly VT.
Not really. VT holds multiple asset classes. If you consider that an asset allocation has to be done at market weight, then you would have to peg equities at 40% of assets, or whatever the weighting is.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by CloseEnough »

Northern Flicker wrote: Thu Jun 08, 2023 12:58 pm
CloseEnough wrote: Thu Jun 08, 2023 6:35 am To add diversification you need to add investments or assets that are in a different asset class than the stock market. Fixed income is a different asset class, adds diversification to a total equity market fund. but is still tied to the market. Best diversification would be a non-financial market investment or asset.
There are two types of diversification.

1. Diversification across asset classes. This is accomplished when establishing an asset allocation.

2. Diversification within an asset class. This is accomplished when selecting funds to implement an asset class.

How well a fixed income subclass diversifies equity risk is not driven by whether it is traded in the market but by the properties of the fixed income subclass.
Yes, I get your point. I was obviously focused on number 1, read the OP too fast, as the question was focused, I guess, on number 2. In my defense ( :happy ), I was not alone.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by km91 »

Beensabu wrote: Thu Jun 08, 2023 12:37 pm
km91 wrote: Thu Jun 08, 2023 11:11 am But which represents the optimal diversified portfolio for an investor to hold?
If cap weighted total market is optimal diversification, then it's clearly VT.
I agree, and this necessarily implies that US TSM is not optimally diversified based on market cap alone. VTI has 25% of it's market cap in it's top 10 holdings vs 15% for VT. 85% in the top 500 holdings vs 65%, and PE of 20 vs 16. A US-only investor would need to tilt value and size to get a similar portfolio composition to VT, if VT truly represents the optimized level of diversification
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by abc132 »

For a typical portfolio with outcomes dictated by stock growth or loss, the definition of diversification should be owning other assets that provide preservation or growth when the existing assets deliver their risk instead of their expected return.

1) What other things do when your existing portfolio delivers it's expected returns is of small importance.

This is where the factor argument is weakest ... They backtested what happened when stocks delivered and then claimed diversification was things that move different than the market when the market delivered. We really don't need diversification in this case. We need things that backtest well when the market does not deliver returns over an extended period of time.

2) What other things do when stocks do not deliver is of very big importance.

Using this idea, bonds are always going to be your best diversifier to a portfolio with stock risk.

...

Having more steady results is a nice feature but makes little difference if the stock portion of a portfolio does not deliver. If you have enough portfolio that you don't need stock to deliver then you don't need steady returns. You are already diversified enough.

For stocks Ex-Us is going to be your best diversifier. It doesn't matter what international has done when US stocks delivered. What matters is what happens if US stocks do not deliver. Having some international gives you a chance at success if you need stock returns and the US does not deliver. Diversify if you desire this feature.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Beensabu »

Northern Flicker wrote: Thu Jun 08, 2023 1:01 pm
Beensabu wrote: Thu Jun 08, 2023 12:37 pm
km91 wrote: Thu Jun 08, 2023 11:11 am But which represents the optimal diversified portfolio for an investor to hold?
If cap weighted total market is optimal diversification, then it's clearly VT.
Not really. VT holds multiple asset classes. If you consider that an asset allocation has to be done at market weight, then you would have to peg equities at 40% of assets, or whatever the weighting is.
Sure, for the entire global stock and bond market. I was just referring to the three stock market options that were listed: VTI, IXUS, and VT.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by rkhusky »

km91 wrote: Thu Jun 08, 2023 11:11 am
rkhusky wrote: Thu Jun 08, 2023 10:08 am
km91 wrote: Thu Jun 08, 2023 9:27 am
nisiprius wrote: Thu Jun 08, 2023 8:15 am The big question is whether the "market portfolio," the actual stock market itself and everything in it, and the cap-weighted total stock market indexes that mirror it, represent maximum diversification, or whether you can argue that it is "not diversified" (because there's "too much" money invested in the mega-cap stocks--circularity IMHO because it is just saying the stocks with more money invested in them have more money invested in them), and that it is possible to achieve more diversification by tinkering with the weighting scheme--small-cap value tilts, fundamental indexing, "smart beta."
Is there any reason to expect the market portfolio to produce the most diversified portfolio? The top 10 constituents of VTI account for 25% of it's market cap, the top 10 constituents of IXUS account for less than 10% of it's market cap. Market cap weighting produces portfolios with very different characteristics depending on what you choose as the 'market' portfolio. If US TSM is the optimally diversified portfolio does this suggest that IXUS is sub optimal? They have completely different sector exposures, valuation exposures, and top component concentrations, surely they both can't be optimally diversified in absolute terms
VTI and IXUS represent different markets. VTI is near-optimal (not sure anything could be said to be optimal, except in hindsight) for the US market. And IXUS for international markets. VT is near-optimal for the global market.
But which represents the optimal diversified portfolio for an investor to hold?
Are you restricting your portfolio to just stocks? If so, what stocks? US, Global, above a certain size? If not, what other investments are in your portfolio? Bonds, micro-lending, reinsurance, real estate, timber, precious metals, commodities?

And how do you define optimal? And diversified?
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Northern Flicker »

km91 wrote: Thu Jun 08, 2023 1:19 pm
Beensabu wrote: Thu Jun 08, 2023 12:37 pm
km91 wrote: Thu Jun 08, 2023 11:11 am But which represents the optimal diversified portfolio for an investor to hold?
If cap weighted total market is optimal diversification, then it's clearly VT.
I agree, and this necessarily implies that US TSM is not optimally diversified based on market cap alone. VTI has 25% of it's market cap in it's top 10 holdings vs 15% for VT. 85% in the top 500 holdings vs 65%, and PE of 20 vs 16. A US-only investor would need to tilt value and size to get a similar portfolio composition to VT, if VT truly represents the optimized level of diversification
It does not imply that. PE ratios are not diversification measures.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Gaston »

rkhusky wrote: Wed Jun 07, 2023 2:50 pm And I don’t recall Fama or French predicting that future factor premiums will be positive.
Yes, in their academic work Dr. French and Dr. Fama express their views more cautiously, as all academics should. In their 1992 paper on the 3-factor model, for example, they hint at factor premia by saying that “If our results are more than chance, they have practical implications for portfolio formation and performance evaluation by investors whose primary concern is long-term average returns.”

And in their 2014 paper on the 5-factor model, they merely affirm that “a five-factor model directed at capturing the size, value, profitability, and investment patterns in average stock returns performs better than the three-factor model”.

You will know, however, that Dr. Fama served as a Director with DFA, and it was there that he assisted in the initial design of DFA products targeting factor premia. I’m not sure if he is still active at DFA.

You also are correct that Dr. Fama and Dr. French never said that factor premia can only be positive. Both have said that such premia can be negative for long periods of time. This is one reason, I guess, why Dr. French recommends an MCW portfolio for most investors.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Beensabu »

Northern Flicker wrote: Thu Jun 08, 2023 3:54 pm PE ratios are not diversification measures.
They can be if someone wants valuation diversification. :D
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by DonIce »

freyj6 wrote: Wed Jun 07, 2023 2:00 pm
rkhusky wrote: Wed Jun 07, 2023 1:31 pm
freyj6 wrote: Wed Jun 07, 2023 1:00 pm Imagine AAPL gets bid up to 1000x earnings.
Is that current earnings or future earnings? Perhaps the market foresees several new products in the future that will greatly increase Apple’s earnings. Then a price of 1000x current earnings may not be unreasonable.

Amazon’s P/E is currently 291.
Amazon's P/E looks that way because of how the accounting works. That's why a lot of quants thought it looked so expensive in 2015 before it 10x'd.

Anyway, that's beside the point.

The point I was making is that the S&P's market cap is about 35 trillion. Apple's is about 3 trillion at 30x earnings. If APPL got bid up to 1000x (let's make this simple and assume other stocks stay the same) then AAPL has 100 trillion market cap and the rest of the S&P is 32 trillion. In that case AAPL is 75% of the S&P. Again let's just let this all be simple because complicating it is beside the point.

The point is with AAPL at 75% of the S&P and ~70% of the total US market, you now have huge idiosyncratic, sector, region and factor risk holding the market portfolio.

The same is true for market cap weighting with more "realistic" valuations, it's just less obvious.
If AAPL went up that much, presumably it would be for a reason and not just randomly for no reason. It may be off somewhat but it's unlikely to be as out-of-whack as you suggest in your example. The idea of market cap weighting being a reasonable portfolio solution relies on the hypothesis that the market is reasonably efficient.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by km91 »

Northern Flicker wrote: Thu Jun 08, 2023 3:54 pm
km91 wrote: Thu Jun 08, 2023 1:19 pm
Beensabu wrote: Thu Jun 08, 2023 12:37 pm
km91 wrote: Thu Jun 08, 2023 11:11 am But which represents the optimal diversified portfolio for an investor to hold?
If cap weighted total market is optimal diversification, then it's clearly VT.
I agree, and this necessarily implies that US TSM is not optimally diversified based on market cap alone. VTI has 25% of it's market cap in it's top 10 holdings vs 15% for VT. 85% in the top 500 holdings vs 65%, and PE of 20 vs 16. A US-only investor would need to tilt value and size to get a similar portfolio composition to VT, if VT truly represents the optimized level of diversification
It does not imply that. PE ratios are not diversification measures.
Why not? Investors, including myself, may desire diversification across a broad range of company valuations. The valuation difference between VTI and VT implies that US stocks in aggregate fall above the global average and that a US only investor has a concentration to higher than global average valuations. It's not unreasonable to assume that high valuations represent a risk and prefer to diversify it
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by km91 »

rkhusky wrote: Thu Jun 08, 2023 3:50 pm
km91 wrote: Thu Jun 08, 2023 11:11 am
rkhusky wrote: Thu Jun 08, 2023 10:08 am
km91 wrote: Thu Jun 08, 2023 9:27 am
nisiprius wrote: Thu Jun 08, 2023 8:15 am The big question is whether the "market portfolio," the actual stock market itself and everything in it, and the cap-weighted total stock market indexes that mirror it, represent maximum diversification, or whether you can argue that it is "not diversified" (because there's "too much" money invested in the mega-cap stocks--circularity IMHO because it is just saying the stocks with more money invested in them have more money invested in them), and that it is possible to achieve more diversification by tinkering with the weighting scheme--small-cap value tilts, fundamental indexing, "smart beta."
Is there any reason to expect the market portfolio to produce the most diversified portfolio? The top 10 constituents of VTI account for 25% of it's market cap, the top 10 constituents of IXUS account for less than 10% of it's market cap. Market cap weighting produces portfolios with very different characteristics depending on what you choose as the 'market' portfolio. If US TSM is the optimally diversified portfolio does this suggest that IXUS is sub optimal? They have completely different sector exposures, valuation exposures, and top component concentrations, surely they both can't be optimally diversified in absolute terms
VTI and IXUS represent different markets. VTI is near-optimal (not sure anything could be said to be optimal, except in hindsight) for the US market. And IXUS for international markets. VT is near-optimal for the global market.
But which represents the optimal diversified portfolio for an investor to hold?
Are you restricting your portfolio to just stocks? If so, what stocks? US, Global, above a certain size? If not, what other investments are in your portfolio? Bonds, micro-lending, reinsurance, real estate, timber, precious metals, commodities?

And how do you define optimal? And diversified?
OP seemed to be asking in the context of equities only so I guess my question was really "which represents the optimal diversified equity portfolio for an investor to hold?"

For equities I would define diversification as broad exposure across market capitalizations, valuations, geography, business cycles, number of holdings, sectors, and top 10 components

For a total portfolio I would define diversification as broad exposure to known risk premiums: equity, value, quality, momentum, credit, term, trend, as well as risk free assets

As for "optimal", maybe it's like "obscenity" I know it when I see it
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Northern Flicker »

Beensabu wrote: Thu Jun 08, 2023 3:59 pm
Northern Flicker wrote: Thu Jun 08, 2023 3:54 pm PE ratios are not diversification measures.
They can be if someone wants valuation diversification. :D
Within a given market PE can be used to identify value stocks, and a value tilt can be viewed as a factor diversification. PE is not a diversification measure across markets, and allocating by absolute values of PE is market timing, not diversification. Value factor measures are relative, not absolute.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by km91 »

Northern Flicker wrote: Thu Jun 08, 2023 6:04 pm PE is not a diversification measure across markets...
Right, it is a characteristic metric of stocks that an investor might desire to have diversified exposure to. Presumably an investor doesn't want concentrated exposure to the upper end of the range or lower end of the range. All cap world index has a PE of 16 which suggest that some markets, like the US, are more concentrated in the higher end of the range than the global market as a whole. Even if an investor doesn't accept the expected return story of value, a US only investor might find some benefit of a value tilt if they are dead set against adding some ex US into the mix
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Northern Flicker »

That usage would reduce asset diversification across PE's by narrowing the range of PE's held. It might increase factor diversification if it led to a value tilt.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by bertilak »

Another way to look at things is to think about "success" in investing. I would define that as a measure of how well you did compared to the total investments in the market. "Total market" does NOT mean all companies that offer stock but "total" means all the money that is invested in these companies.

For your investments to do better than all that invested money you MUST invest in something OTHER than (a percentage subset of) that money. The same could be said for doing worse. If you tilt away from TSM you will do ether better or worse than TSM. I think that is a form of RISK. Thus, tilting adds risk. Is it compensated risk?
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by km91 »

Northern Flicker wrote: Thu Jun 08, 2023 8:37 pm That usage would reduce asset diversification across PE's by narrowing the range of PE's held. It might increase factor diversification if it led to a value tilt.
If the weighted average PE, ie the dollar weighted center of the distribution, of VTI is 20, and an investor adds a fund like VTV with a PE of 16 so that the weighted average PE of the portfolio is now below 20, the distribution of invested dollars across PE's has widened. If I measure the average height of a basketball team to be 6'6 and the average height of a group of school children as 5', combining the two groups broadens the range of heights in the sample.

If an investor looks at VTI with a PE of 20 and all cap world index with a PE of 16, they might come to the conclusion that VTI is weighted towards higher valuations than the global market as a whole, and this may present a risk. The obvious action would be to just add international stocks, but some investors seem to view this as a no go. Alternatively they could add a fund like VTV to get a US only portfolio that more closely matches the characteristics of a globally diversified portfolio. This is a reasonable form of asset diversification that does not require one to believe in the value premium, they are simply trying to match the characteristics of the global portfolio in a US only portfolio
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by Northern Flicker »

There is no logical reason that a US portfolio that matches the PE of the global market portfolio is more diversified than the US market portfolio. A simple counterexample to such a claim would be to have a portfolio with 2 stocks, one with PE less than that of the global market portfolio one with a PE higher. Then hold the two in the proportion that matches the PE of the global market portfolio. I think we agree that a portfolio of two stocks is less diversified than the market portfolio.

That two such stocks must exist currently follows from the premise that the US market portfolio currently has a higher PE than the global market portfolio, while some portfolio of US stocks matches that of the global portfolio.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by rkhusky »

km91 wrote: Thu Jun 08, 2023 4:27 pm As for "optimal", maybe it's like "obscenity" I know it when I see it
So, you are the judge of optimal?
A more democratic and objective algorithm for finding the optimal portfolio would using market-based techniques. Therefore VT is a representation of the optimal global portfolio and VTI is a representation of the optimal US portfolio.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by dbr »

rkhusky wrote: Sat Jun 10, 2023 6:56 am
km91 wrote: Thu Jun 08, 2023 4:27 pm As for "optimal", maybe it's like "obscenity" I know it when I see it
So, you are the judge of optimal?
A more democratic and objective algorithm for finding the optimal portfolio would using market-based techniques. Therefore VT is a representation of the optimal global portfolio and VTI is a representation of the optimal US portfolio.
And what is it that has been optimized in the optimal portfolio? By optimized one usually imagines some desirable property that is at a maximum compared to some kind of variation from the optimum or an undesirable property that is at a minimum compared to some kind of variation from the optimum. What is it that is being varied?

Example: When blending a portfolio of total stock and total bond the properties of diversification ratio and Sharpe ratio tend to reach a maximum at about 20/80 ratio of stocks to bonds. That is also the point of risk parity and pretty much the point of tangency on an efficient frontier plot, at least roughly with variation in different time periods. This example offers specific measures of what is being optimized and with respect to variation of what.

I am much less clear on the concept of what has been optimized when one adds either or both a small cap fund or a value fund to a total stock market portfolio. One can track what Fama French factor loadings result. It is clear that Fama and French created a model in which they find that loading on their small and value factors predicts a higher expected return relative to the market at zero small and value loading. Was something optimized in adding those tilts. Between 2004 and now addition of VBR at 40% to VTI produces small and value loadings of .22 and .19 and reduces the Sharpe ratio from .55 to .49, produces a diversification ratio of 1.02, effectively nothing, and produces a CAGR of 8.53% vs 9.06% for TSM. We know, of course, that small cap loading has not materialized as an increased return in that time period, the infamous result of trying to do this.
Last edited by dbr on Sat Jun 10, 2023 7:45 am, edited 1 time in total.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by rkhusky »

dbr wrote: Sat Jun 10, 2023 7:20 am
rkhusky wrote: Sat Jun 10, 2023 6:56 am
km91 wrote: Thu Jun 08, 2023 4:27 pm As for "optimal", maybe it's like "obscenity" I know it when I see it
So, you are the judge of optimal?
A more democratic and objective algorithm for finding the optimal portfolio would using market-based techniques. Therefore VT is a representation of the optimal global portfolio and VTI is a representation of the optimal US portfolio.
And what is it that has been optimized in the optimal portfolio?
Perceived future return as a function of perceived risk.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by dbr »

rkhusky wrote: Sat Jun 10, 2023 7:26 am
dbr wrote: Sat Jun 10, 2023 7:20 am
rkhusky wrote: Sat Jun 10, 2023 6:56 am
km91 wrote: Thu Jun 08, 2023 4:27 pm As for "optimal", maybe it's like "obscenity" I know it when I see it
So, you are the judge of optimal?
A more democratic and objective algorithm for finding the optimal portfolio would using market-based techniques. Therefore VT is a representation of the optimal global portfolio and VTI is a representation of the optimal US portfolio.
And what is it that has been optimized in the optimal portfolio?
Perceived future return as a function of perceived risk.
Thanks and sorry for my slow posting. I added more comments above. So if return is increased vs risk a measure in which we would see that would be Sharpe ratio.

Of course if the measure is for a perceived future then we have to wait until the future is past to see what happens.

Regarding the OP here, does that mean that an expected maximization of Sharpe ratio would be the definition of diversification in this case. If so do we have an estimate of what function the perceived future Sharpe ratio would be of the inputs, namely the small and value loadings? Isn't it the case that this problem is optimized when the small and value loadings are maximized, meaning, I guess, when one holds only some kind of pure long-short small and value portfolio. Otherwise in practice it would mean to hold 100% VBR or maybe some other fund which is a more pure SCV realization. Remember in an optimization problem sometimes the optimum is at the endpoints.

I would just like to see people be specific regarding what they are defining and how they measure it from the raw data of investment behavior on the market over time. I assume you mean by risk in your comment above specifically the standard deviation of investment returns in some time periods.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by alluringreality »

dbr wrote: Sat Jun 10, 2023 7:53 am Isn't it the case that this problem is optimized when the small and value loadings are maximized, meaning, I guess, when one holds only some kind of pure long-short small and value portfolio. Otherwise in practice it would mean to hold 100% VBR or maybe some other fund which is a more pure SCV realization. Remember in an optimization problem sometimes the optimum is at the endpoints.
Tilt may also suggest an incomplete move away from the market. The intent might fall more along the lines of the Treynor–Black model. Essentially someone could buy a market based portfolio for one bet and another portfolio for another bet. I'm not intending to formalize this, just to clarify plausible intent from people spreading bets.
https://en.wikipedia.org/wiki/Treynor%E ... lack_model
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by rkhusky »

dbr wrote: Sat Jun 10, 2023 7:53 am
rkhusky wrote: Sat Jun 10, 2023 7:26 am
dbr wrote: Sat Jun 10, 2023 7:20 am
rkhusky wrote: Sat Jun 10, 2023 6:56 am
km91 wrote: Thu Jun 08, 2023 4:27 pm As for "optimal", maybe it's like "obscenity" I know it when I see it
So, you are the judge of optimal?
A more democratic and objective algorithm for finding the optimal portfolio would using market-based techniques. Therefore VT is a representation of the optimal global portfolio and VTI is a representation of the optimal US portfolio.
And what is it that has been optimized in the optimal portfolio?
Perceived future return as a function of perceived risk.
Thanks and sorry for my slow posting. I added more comments above. So if return is increased vs risk a measure in which we would see that would be Sharpe ratio.

Of course if the measure is for a perceived future then we have to wait until the future is past to see what happens.

Regarding the OP here, does that mean that an expected maximization of Sharpe ratio would be the definition of diversification in this case. If so do we have an estimate of what function the perceived future Sharpe ratio would be of the inputs, namely the small and value loadings? Isn't it the case that this problem is optimized when the small and value loadings are maximized, meaning, I guess, when one holds only some kind of pure long-short small and value portfolio. Otherwise in practice it would mean to hold 100% VBR or maybe some other fund which is a more pure SCV realization. Remember in an optimization problem sometimes the optimum is at the endpoints.

I would just like to see people be specific regarding what they are defining and how they measure it from the raw data of investment behavior on the market over time. I assume you mean by risk in your comment above specifically the standard deviation of investment returns in some time periods.
The market assesses the risk and return of each stock individually. I don’t think that investors in individual stocks generally use Sharpe ratio or standard deviation or size or simple value metrics.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by rkhusky »

dbr wrote: Sat Jun 10, 2023 7:20 am One can track what Fama French factor loadings result. It is clear that Fama and French created a model in which they find that loading on their small and value factors predicts a higher expected return relative to the market at zero small and value loading.
The FF model does not predict that value and size premiums will be positive. Hence, a portfolio with positive size and value loadings could overperform or underperform the market. The FF model does not predict higher expected return for a small value portfolio.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by dbr »

rkhusky wrote: Sat Jun 10, 2023 9:53 am
dbr wrote: Sat Jun 10, 2023 7:20 am One can track what Fama French factor loadings result. It is clear that Fama and French created a model in which they find that loading on their small and value factors predicts a higher expected return relative to the market at zero small and value loading.
The FF model does not predict that value and size premiums will be positive. Hence, a portfolio with positive size and value loadings could overperform or underperform the market. The FF model does not predict higher expected return for a small value portfolio.
Yes, I often forget that. Maybe a lot of other people forget that as well. A better statement is that they have a model that explains expected return as a function of small and value loadings given the premia for those, positive or negative, in the data considered.

Getting to Traynor and Black, I got far enough in their paper to understand that their concept of what is being optimized is that one seeks minimum variability at fixed return. This would be pretty standard in the sense that one objective of an investor is to reduce risk without reducing return. It is pretty important that if one wants to talk about optimizing things that one be clear what it is that is to be optimized. Their exact words are:
"We take as our objective minimizing [sigma-p^2] while holding [u-p] fixed."

To be honest I have no dog in this fight other than trying to read things and understand what people are trying to talk about.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by km91 »

Northern Flicker wrote: Sat Jun 10, 2023 1:38 am There is no logical reason that a US portfolio that matches the PE of the global market portfolio is more diversified than the US market portfolio. A simple counterexample to such a claim would be to have a portfolio with 2 stocks, one with PE less than that of the global market portfolio one with a PE higher. Then hold the two in the proportion that matches the PE of the global market portfolio. I think we agree that a portfolio of two stocks is less diversified than the market portfolio.

That two such stocks must exist currently follows from the premise that the US market portfolio currently has a higher PE than the global market portfolio, while some portfolio of US stocks matches that of the global portfolio.
Yes we agree, however that's not the claim I was making. My above example used VTI and VTV, the portfolio contains all 4000 US companies held by the total market index. Here is the distribution of $10000 invested in IVV and a 50/50 combo of IVV + ILCV. The combination portfolio has a flatter and wider distribution of invested dollars across PE ratios. Visually at least, it has a broader dollar exposure across the range of PE, which my be a desirable feature in a portfolio. If an investor believes that US is overweight higher valuations relative to the US long term average and relative to the global market portfolio, there are good reasons to want to flatten and shift the distribution to the left. It is a form of diversification to consider, especially for a US only investor.

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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by burritoLover »

rkhusky wrote: Sat Jun 10, 2023 9:53 am
dbr wrote: Sat Jun 10, 2023 7:20 am One can track what Fama French factor loadings result. It is clear that Fama and French created a model in which they find that loading on their small and value factors predicts a higher expected return relative to the market at zero small and value loading.
The FF model does not predict that value and size premiums will be positive. Hence, a portfolio with positive size and value loadings could overperform or underperform the market. The FF model does not predict higher expected return for a small value portfolio.
It does depending on your definition of "predict". It's a pricing model that one could use to determine the expected return of a diversified portfolio. So, generally speaking, a small-value portfolio would have a higher expected return than a market portfolio based on the model. Of course, your realized return could be different over some future period, but that is also the case with the equity risk premium alone (the market portfolio) which can underperform the risk-free rate over long periods.

That all said, the factor models are not reality and they might not work as well going forward - either because the model(s) are inherently flawed and/or the premiums are arbitraged away in some way (something factorheads here underestimate as a possibility).
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by secondopinion »

burritoLover wrote: Sun Jun 11, 2023 6:39 am
rkhusky wrote: Sat Jun 10, 2023 9:53 am
dbr wrote: Sat Jun 10, 2023 7:20 am One can track what Fama French factor loadings result. It is clear that Fama and French created a model in which they find that loading on their small and value factors predicts a higher expected return relative to the market at zero small and value loading.
The FF model does not predict that value and size premiums will be positive. Hence, a portfolio with positive size and value loadings could overperform or underperform the market. The FF model does not predict higher expected return for a small value portfolio.
It does depending on your definition of "predict". It's a pricing model that one could use to determine the expected return of a diversified portfolio. So, generally speaking, a small-value portfolio would have a higher expected return than a market portfolio based on the model. Of course, your realized return could be different over some future period, but that is also the case with the equity risk premium alone (the market portfolio) which can underperform the risk-free rate over long periods.

That all said, the factor models are not reality and they might not work as well going forward - either because the model(s) are inherently flawed and/or the premiums are arbitraged away in some way (something factorheads here underestimate as a possibility).
There may be the possibility that there is no premium but there is still a meaningful reason to tilt for macroeconomic risk management. That is, it can still explain some of the variance of returns in a predictable manner but not in a manner that one can obtain alpha.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by burritoLover »

secondopinion wrote: Mon Jun 12, 2023 6:47 pm
burritoLover wrote: Sun Jun 11, 2023 6:39 am
rkhusky wrote: Sat Jun 10, 2023 9:53 am
dbr wrote: Sat Jun 10, 2023 7:20 am One can track what Fama French factor loadings result. It is clear that Fama and French created a model in which they find that loading on their small and value factors predicts a higher expected return relative to the market at zero small and value loading.
The FF model does not predict that value and size premiums will be positive. Hence, a portfolio with positive size and value loadings could overperform or underperform the market. The FF model does not predict higher expected return for a small value portfolio.
It does depending on your definition of "predict". It's a pricing model that one could use to determine the expected return of a diversified portfolio. So, generally speaking, a small-value portfolio would have a higher expected return than a market portfolio based on the model. Of course, your realized return could be different over some future period, but that is also the case with the equity risk premium alone (the market portfolio) which can underperform the risk-free rate over long periods.

That all said, the factor models are not reality and they might not work as well going forward - either because the model(s) are inherently flawed and/or the premiums are arbitraged away in some way (something factorheads here underestimate as a possibility).
There may be the possibility that there is no premium but there is still a meaningful reason to tilt for macroeconomic risk management. That is, it can still explain some of the variance of returns in a predictable manner but not in a manner that one can obtain alpha.
The model doesn't describe alpha though - not sure if that is what you meant. These premiums are decidedly non-alpha and what can't be described by the model, would be either unknown factors or alpha in a diversified portfolio.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by rkhusky »

burritoLover wrote: Sun Jun 11, 2023 6:39 am. So, generally speaking, a small-value portfolio would have a higher expected return than a market portfolio based on the model.
What the FF model can tell you is: if the expected return of value is greater than growth and the expected return of small is greater than big, then the expected return of a small value portfolio will be greater than the market. The expected values of value, growth, small and big are determined outside the FF model, ie they are inputs to the model.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by gtrplayer »

alluringreality wrote: Wed Jun 07, 2023 10:13 am
retiredjg wrote: Wed Jun 07, 2023 9:57 am As you hint...it all depends on how one defines "diversify". To me, the total market is by definition most diversified.
My personal generalization is that the market portfolio amounts to systematic risk. Various sources suggest systematic risk cannot be mitigated through diversification. If someone chooses to define diversification as attempting to limit specific or unsystematic risk, I'm thinking the market portfolio does not necessarily address that intent. There is a recent thread that gets into some of this definitional consideration, but this older thread probably discusses additional touchpoints around diversifiable risk.
viewtopic.php?t=251043
As you say, it depends on how you define diversification. I’ve always defined it as having multiple stocks/bonds and limiting concentration in a certain area. If own a share of Apple, I’m not diversified at all. If I own Apple and Berkshire, I’m a little diversified. If I own every publicly traded stock, I’m very diversified. If I add total bond, I’m even more diversified. This doesn’t maximize returns, but it guarantees the average.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by burritoLover »

rkhusky wrote: Tue Jun 13, 2023 11:21 am
burritoLover wrote: Sun Jun 11, 2023 6:39 am. So, generally speaking, a small-value portfolio would have a higher expected return than a market portfolio based on the model.
What the FF model can tell you is: if the expected return of value is greater than growth and the expected return of small is greater than big, then the expected return of a small value portfolio will be greater than the market. The expected values of value, growth, small and big are determined outside the FF model, ie they are inputs to the model.
No, that isn't what that means - I would suggest you do some more reading.
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by rkhusky »

burritoLover wrote: Tue Jun 13, 2023 12:18 pm
rkhusky wrote: Tue Jun 13, 2023 11:21 am
burritoLover wrote: Sun Jun 11, 2023 6:39 am. So, generally speaking, a small-value portfolio would have a higher expected return than a market portfolio based on the model.
What the FF model can tell you is: if the expected return of value is greater than growth and the expected return of small is greater than big, then the expected return of a small value portfolio will be greater than the market. The expected values of value, growth, small and big are determined outside the FF model, ie they are inputs to the model.
No, that isn't what that means - I would suggest you do some more reading.
That’s exactly what it means. One uses realized values for the factor premiums and the portfolio returns to determine the factor loadings for the portfolio through least squares minimization. One can then calculate expected values for the portfolio returns by using the computed factor loadings and expected values for the factor premiums.

See https://www.bogleheads.org/wiki/Fama_an ... ctor_model
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burritoLover
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by burritoLover »

rkhusky wrote: Tue Jun 13, 2023 1:14 pm
burritoLover wrote: Tue Jun 13, 2023 12:18 pm
rkhusky wrote: Tue Jun 13, 2023 11:21 am
burritoLover wrote: Sun Jun 11, 2023 6:39 am. So, generally speaking, a small-value portfolio would have a higher expected return than a market portfolio based on the model.
What the FF model can tell you is: if the expected return of value is greater than growth and the expected return of small is greater than big, then the expected return of a small value portfolio will be greater than the market. The expected values of value, growth, small and big are determined outside the FF model, ie they are inputs to the model.
No, that isn't what that means - I would suggest you do some more reading.
That’s exactly what it means. One uses realized values for the factor premiums and the portfolio returns to determine the factor loadings for the portfolio through least squares minimization. One can then calculate expected values for the portfolio returns by using the computed factor loadings and expected values for the factor premiums.

See https://www.bogleheads.org/wiki/Fama_an ... ctor_model
No, it isn't expected returns that are the inputs - it is actual average returns of a market-risk_free_rate, value-growth, small-big, etc that are inputs to the model - expected future return of the portfolio in question is the output in this scenario we are talking about. I think the point you were trying to make is that factor premiums going forward might be reduced or might go away - I already agreed that is a possibility so I'm not sure what point you are trying to make.
rkhusky
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by rkhusky »

burritoLover wrote: Tue Jun 13, 2023 3:46 pm
rkhusky wrote: Tue Jun 13, 2023 1:14 pm
burritoLover wrote: Tue Jun 13, 2023 12:18 pm
rkhusky wrote: Tue Jun 13, 2023 11:21 am
burritoLover wrote: Sun Jun 11, 2023 6:39 am. So, generally speaking, a small-value portfolio would have a higher expected return than a market portfolio based on the model.
What the FF model can tell you is: if the expected return of value is greater than growth and the expected return of small is greater than big, then the expected return of a small value portfolio will be greater than the market. The expected values of value, growth, small and big are determined outside the FF model, ie they are inputs to the model.
No, that isn't what that means - I would suggest you do some more reading.
That’s exactly what it means. One uses realized values for the factor premiums and the portfolio returns to determine the factor loadings for the portfolio through least squares minimization. One can then calculate expected values for the portfolio returns by using the computed factor loadings and expected values for the factor premiums.

See https://www.bogleheads.org/wiki/Fama_an ... ctor_model
No, it isn't expected returns that are the inputs - it is actual average returns of a market-risk_free_rate, value-growth, small-big, etc that are inputs to the model - expected future return of the portfolio in question is the output in this scenario we are talking about. I think the point you were trying to make is that factor premiums going forward might be reduced or might go away - I already agreed that is a possibility so I'm not sure what point you are trying to make.
If you input the average historical factor premiums, then, if the model is a good fit to the portfolio, the output is the portfolio's average historical return. If you input expected values for the factor premiums, the output is the expected return of the portfolio.
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burritoLover
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Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by burritoLover »

rkhusky wrote: Tue Jun 13, 2023 7:27 pm
burritoLover wrote: Tue Jun 13, 2023 3:46 pm
rkhusky wrote: Tue Jun 13, 2023 1:14 pm
burritoLover wrote: Tue Jun 13, 2023 12:18 pm
rkhusky wrote: Tue Jun 13, 2023 11:21 am

What the FF model can tell you is: if the expected return of value is greater than growth and the expected return of small is greater than big, then the expected return of a small value portfolio will be greater than the market. The expected values of value, growth, small and big are determined outside the FF model, ie they are inputs to the model.
No, that isn't what that means - I would suggest you do some more reading.
That’s exactly what it means. One uses realized values for the factor premiums and the portfolio returns to determine the factor loadings for the portfolio through least squares minimization. One can then calculate expected values for the portfolio returns by using the computed factor loadings and expected values for the factor premiums.

See https://www.bogleheads.org/wiki/Fama_an ... ctor_model
No, it isn't expected returns that are the inputs - it is actual average returns of a market-risk_free_rate, value-growth, small-big, etc that are inputs to the model - expected future return of the portfolio in question is the output in this scenario we are talking about. I think the point you were trying to make is that factor premiums going forward might be reduced or might go away - I already agreed that is a possibility so I'm not sure what point you are trying to make.
If you input the average historical factor premiums, then, if the model is a good fit to the portfolio, the output is the portfolio's average historical return. If you input expected values for the factor premiums, the output is the expected return of the portfolio.
What you are doing is running a regression based on your portfolio's returns and the returns from the factors (market-risk_free, small-big, high b/p - low b/p, etc) over the same period. This will determine the factor loadings for your portfolio. The monthly returns for the factors are published by Dr. French. Neatly, portfolio visualizer has a function to do this for you. So if we take the oldest funds for Vanguard SCV and Vanguard TSM, we get the following factor loadings with the 3-factor model:

Code: Select all

1998-2023
(Vanguard SCV)
Factor	Loading	Std Error	t-stat	p-value
Market (Rm-Rf)	1.00	0.018	56.108	0.000
Size (SMB)	0.51	0.026	19.905	0.000
Value (HML)	0.57	0.023	24.369	0.000

(Vanguard TSM)
Factor	Loading	Std Error	t-stat	p-value
Market (Rm-Rf)	1.00	0.002	474.356	0.000	
Size (SMB)	-0.01	0.003	-2.796	0.000		
Value (HML)	0.02	0.003	6.787	0.000
So, in this case, your long-term expected future return for the small-value portfolio would be higher than that the total market portfolio because you expect both portfolios to earn the same market return but the SCV portfolio is expected to also earn the premium for small and value assuming they are positive going forward - which is the presumption if we decide to target factors. Of course, as we've discussed, models are not reality and risk can show up and premiums may be arbitraged away - blah, blah, blah.
rkhusky
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Joined: Thu Aug 18, 2011 8:09 pm

Re: my understanding is that tilting to small caps adds diversification and tilting to value reduces diversification?

Post by rkhusky »

burritoLover wrote: Wed Jun 14, 2023 6:47 am
So, in this case, your long-term expected future return for the small-value portfolio would be higher than that the total market portfolio because you expect both portfolios to earn the same market return but the SCV portfolio is expected to also earn the premium for small and value assuming they are positive going forward - which is the presumption if we decide to target factors. Of course, as we've discussed, models are not reality and risk can show up and premiums may be arbitraged away - blah, blah, blah.
There is no reason that the future probability distribution, which you use to calculate the expected values, has to match some past historical distribution. One can assume that of course, but it’s not required. And, even if you do make that assumption, you have to also assume the past time period for which to compute the probability distribution. The future probability distribution assumption/choice, and hence expected value assumptions, are not part of the model, but come from external analysis.
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