Do factors explain the benefit of int’l diversification?

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Northern Flicker
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Do factors explain the benefit of int’l diversification?

Post by Northern Flicker » Thu Oct 24, 2019 7:14 pm

Here’s a comparison of factor loadings of a US index fund and developed markets index fund relative to a cap weighted universe of all developed markets (including US):

https://www.portfoliovisualizer.com/fac ... e&total1=0

Note the complementary factor exposures. I did not include emerging markets equity because portfoliovisualizer does not offer the global market as the universe against which to regress. Nonetheless, VTMGX has 81% of the market cap of a total int’l index fund.

Holding portfolios for US and non-US that tilt to the same factors may defeat some of the diversification benefit.
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columbia
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Re: Do factors explain the benefit of int’l diversification?

Post by columbia » Thu Oct 24, 2019 7:30 pm

Alternate theory about ex-US:

1. Far lower exposure to tech
2. Myriad of countries with investing protections inferior to US
3. Inability for US investors to get 100% foreign tax credit
4. The dollar is king and there’s no end in sight for that

There’s more, probably.

rkhusky
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Re: Do factors explain the benefit of int’l diversification?

Post by rkhusky » Thu Oct 24, 2019 8:57 pm

The p-value on many of the TSM numbers is quite high. Not sure if the global market is a good model for US returns. (also shows in the R2 value)

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Re: Do factors explain the benefit of int’l diversification?

Post by whodidntante » Sat Oct 26, 2019 1:51 am

columbia wrote:
Thu Oct 24, 2019 7:30 pm

4. The dollar is king and there’s no end in sight for that
I've noticed that markets like to disappoint people. You've just single-handedly doomed the USD. I hope you're happy. :happy

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Re: Do factors explain the benefit of int’l diversification?

Post by Uncorrelated » Sat Oct 26, 2019 5:03 am

You are using the factor analysis the wrong way. The international factor set should be used to test a portfolio of international stocks, but you are testing a portfolio consisting of only US stocks and a different portfolio of only developed ex-US stocks. By definition the factor exposure of the sum of those two funds sum to zero.

International exposure does not diversify across factors, but reduces idiosyncratic risk.

Anyway, as you can see in the rolling regression, the factor exposure is not stable and I would not pay attention to these numbers.

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Re: Do factors explain the benefit of int’l diversification?

Post by nisiprius » Sat Oct 26, 2019 5:05 am

"Time Period Dec 2000 - Aug 2019"

You are asking "do factors explain the benefit of international diversification" over a time period during which there was no benefit from international diversification.

Source

Portfolio 1 (blue)
VTSAX Vanguard Total Stock Mkt Idx Adm 100.00%

Portfolio 2 (red)
VTSAX Vanguard Total Stock Mkt Idx Adm 50.00%
VTMGX Vanguard Developed Markets Index Admiral 50.00%

Over the time period you chose, using the international stock fund you chose, an international exposure of 50% of stocks would have lowered return (CAGR) -1.35%. Despite the "diversification," volatility as measured by standard deviation was not decreased. And the two measures of risk-adjusted return, the Sharpe and Sortino ratios, were both reduced.

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Re: Do factors explain the benefit of int’l diversification?

Post by Northern Flicker » Sat Oct 26, 2019 3:24 pm

You are using the factor analysis the wrong way. The international factor set should be used to test a portfolio of international stocks, but you are testing a portfolio consisting of only US stocks and a different portfolio of only developed ex-US stocks.
No, the universe I used is all developed stocks, including US, and US and non-US are the subsets of that universe being regressed.
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Re: Do factors explain the benefit of int’l diversification?

Post by Uncorrelated » Sat Oct 26, 2019 4:34 pm

Northern Flicker wrote:
Sat Oct 26, 2019 3:24 pm
You are using the factor analysis the wrong way. The international factor set should be used to test a portfolio of international stocks, but you are testing a portfolio consisting of only US stocks and a different portfolio of only developed ex-US stocks.
No, the universe I used is all developed stocks, including US, and US and non-US are the subsets of that universe being regressed.
You need to regress the entire universe. Not a subset of that universe. Unless that subset specifically promises consistent factor exposure (such as a factor ETF's) you are not going to get reliable forward-looking results.

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Re: Do factors explain the benefit of int’l diversification?

Post by nedsaid » Sat Oct 26, 2019 6:40 pm

columbia wrote:
Thu Oct 24, 2019 7:30 pm
Alternate theory about ex-US:

1. Far lower exposure to tech
2. Myriad of countries with investing protections inferior to US
3. Inability for US investors to get 100% foreign tax credit
4. The dollar is king and there’s no end in sight for that

There’s more, probably.
The original poster asked a perfectly good question but I think the diversification benefit has more to do with industry sectors than factors, hence point number one above. Developed Market stocks are cheaper than US Stocks but I am skeptical there would be enough for there to be a Value factor. You might also get a bit of a corruption premium for Emerging Markets stocks. Another diversification benefit would be currencies.
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Re: Do factors explain the benefit of int’l diversification?

Post by columbia » Sat Oct 26, 2019 6:55 pm

nedsaid wrote:
Sat Oct 26, 2019 6:40 pm
columbia wrote:
Thu Oct 24, 2019 7:30 pm
Alternate theory about ex-US:

1. Far lower exposure to tech
2. Myriad of countries with investing protections inferior to US
3. Inability for US investors to get 100% foreign tax credit
4. The dollar is king and there’s no end in sight for that

There’s more, probably.
The original poster asked a perfectly good question but I think the diversification benefit has more to do with industry sectors than factors, hence point number one above. Developed Market stocks are cheaper than US Stocks but I am skeptical there would be enough for there to be a Value factor. You might also get a bit of a corruption premium for Emerging Markets stocks. Another diversification benefit would be currencies.
ie: Trying to isolate and back test supposed beneficial factors doesn’t mean much, when there are significant structural differences.

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Re: Do factors explain the benefit of int’l diversification?

Post by Call_Me_Op » Sun Oct 27, 2019 7:41 am

columbia wrote:
Thu Oct 24, 2019 7:30 pm
Alternate theory about ex-US:

1. Far lower exposure to tech
2. Myriad of countries with investing protections inferior to US
3. Inability for US investors to get 100% foreign tax credit
4. The dollar is king and there’s no end in sight for that
All of which are widely known and presumably baked-into current stock prices.
Best regards, -Op | | "In the middle of difficulty lies opportunity." Einstein

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Re: Do factors explain the benefit of int’l diversification?

Post by nedsaid » Sun Oct 27, 2019 11:23 am

columbia wrote:
Sat Oct 26, 2019 6:55 pm
nedsaid wrote:
Sat Oct 26, 2019 6:40 pm
columbia wrote:
Thu Oct 24, 2019 7:30 pm
Alternate theory about ex-US:

1. Far lower exposure to tech
2. Myriad of countries with investing protections inferior to US
3. Inability for US investors to get 100% foreign tax credit
4. The dollar is king and there’s no end in sight for that

There’s more, probably.
The original poster asked a perfectly good question but I think the diversification benefit has more to do with industry sectors than factors, hence point number one above. Developed Market stocks are cheaper than US Stocks but I am skeptical there would be enough for there to be a Value factor. You might also get a bit of a corruption premium for Emerging Markets stocks. Another diversification benefit would be currencies.
ie: Trying to isolate and back test supposed beneficial factors doesn’t mean much, when there are significant structural differences.
Factors are at work in International Stocks too but nothing unique compared to US Stocks save for a possible corruption premium with Emerging Markets. International Stocks are cheaper than US Stocks but there are rational reasons for this.
A fool and his money are good for business.

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Northern Flicker
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Re: Do factors explain the benefit of int’l diversification?

Post by Northern Flicker » Sun Oct 27, 2019 9:51 pm

You need to regress the entire universe. Not a subset of that universe. Unless that subset specifically promises consistent factor exposure (such as a factor ETF's) you are not going to get reliable forward-looking results.
What you can regress has zero to do with what the subset being analyzed promises or doesn’t promise. A factor model is a linear model of factors to try to explain the performance of a stock relative to a market universe in which it lives. A single stock belonging to that universe or a portfolio (subset) of stocks also can be regressed to the universe. As long as all of the stocks in the portfolio belong to the universe, the factor model allows the portfolio to be regressed to the universe.
Index fund investor since 1987.

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Re: Do factors explain the benefit of int’l diversification?

Post by 305pelusa » Sun Oct 27, 2019 10:10 pm

Northern Flicker wrote:
Thu Oct 24, 2019 7:14 pm
Here’s a comparison of factor loadings of a US index fund and developed markets index fund relative to a cap weighted universe of all developed markets (including US):

https://www.portfoliovisualizer.com/fac ... e&total1=0

Note the complementary factor exposures. I did not include emerging markets equity because portfoliovisualizer does not offer the global market as the universe against which to regress. Nonetheless, VTMGX has 81% of the market cap of a total int’l index fund.

Holding portfolios for US and non-US that tilt to the same factors may defeat some of the diversification benefit.
Correct me if I'm wrong but this is like regressing the S&P 500 Growth and S&P 500 Value (using USA as regression universe), then noticing that they have different factor loadings that "complement" each other, summing to zero, and concluding that "factors explain the benefit of value diversification".

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Re: Do factors explain the benefit of int’l diversification?

Post by Northern Flicker » Mon Oct 28, 2019 1:55 pm

Yes it is like that, except there was no a priori reason to assume they were complementary. Both could show no tilts and still “sum to zero”.

In the case of regressing value and growth components of some universe and finding that they complement each other with respect to the value factor, it would be circular because value and growth were defined in the first place by having positive and negative loadings on the value factor. The complementary regression would be just verifying that the value and growth portfolios being regressed had been defined properly in the first place.

But there was no reason to assume a priori that either US stocks or non-US developed market stocks as a whole had any particular tilts with respect to the universe of developed markets. These are both broadly diversified portfolios. Consider the value factor. Both could have just as easily been neutral with zero loadings or more polarized with large magnitude loadings of opposite signs. Either way they would still “sum to zero” for the whole market.

I am not trying to claim this is a definitive explanation of diversification benefits of non-US equities. There are different currency exposures, non-identical markets, different industry sector weightings, different central bank policies, etc.

But I thought the different factor weightings were interesting. I think many investors who use tilted portfolios just looking at factor weightings of a US portfolio components within the US universe and non-US components within the non-US universe. Looking at the whole portfolio in comparison to the whole universe gives a more universal multi-factor view of the portfolio.

For instance, a factor proponent might note that if US stocks tilt some to quality and non-US DM stocks tilt some to value, then the recent US over-performance might be explained by it being a period where quality was rewarded and value was not.

It could be that tilting US to quality and non-US to value or tilting US to value and non-US to quality produces better diversification.

A proponent of just holding a US-only market index fund or US and non-US index funds with a low US exposure, say in the 0-20% range, may in fact be implementing a quality factor tilt, which may align with their qualitative justification for the allocation.
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Re: Do factors explain the benefit of int’l diversification?

Post by 305pelusa » Mon Oct 28, 2019 2:17 pm

Northern Flicker wrote:
Mon Oct 28, 2019 1:55 pm
Yes it is like that, except there was no a priori reason to assume they were complementary. Both could show no tilts and still “sum to zero”.

In the case of regressing value and growth components of some universe and finding that they complement each other with respect to the value factor, it would be circular because value and growth were defined in the first place by having positive and negative loadings on the value factor. The complementary regression would be just verifying that the value and growth portfolios being regressed had been defined properly in the first place.

But there was no reason to assume a priori that either US stocks or non-US developed market stocks as a whole had any particular tilts with respect to the universe of developed markets. These are both broadly diversified portfolios. Consider the value factor. Both could have just as easily been neutral with zero loadings or more polarized with large magnitude loadings of opposite signs. Either way they would still “sum to zero” for the whole market.

I am not trying to claim this is a definitive explanation of diversification benefits of non-US equities. There are different currency exposures, non-identical markets, different industry sector weightings, different central bank policies, etc.

But I thought the different factor weightings were interesting. I think many investors who use tilted portfolios just looking at factor weightings of a US portfolio components within the US universe and non-US components within the non-US universe. Looking at the whole portfolio in comparison to the whole universe gives a more universal multi-factor view of the portfolio.

For instance, a factor proponent might note that if US stocks tilt some to quality and non-US DM stocks tilt some to value, then the recent US over-performance might be explained by it being a period where quality was rewarded and value was not.

It could be that tilting US to quality and non-US to value or tilting US to value and non-US to quality produces better diversification.

A proponent of just holding a US-only market index fund or US and non-US index funds with a low US exposure, say in the 0-20% range, may in fact be implementing a quality factor tilt, which may align with their qualitative justification for the allocation.
Ok I'm following. We know Ex-US stocks are smaller and have better P/Es. This formalizes it. You're saying that didn't have to be the case. But it is.

So if US and Ex-US had similar P/Es and size, we'd see each of the holdings with zero loading (or very minimal), and they'd add to zero. In such a case, holding Ex-US with US is not as worthwhile from a factor diversification perspective.

But instead if US and Ex-US had very different factor loadings (which they do), then it becomes ever more useful to hold both. You lose out a lot by not having the complementary Ex-US. Is that a fair way to describe what you've said?

As for the conclusion, my only concern is that I've generally seen factor premia in the context of its own universe (US or Ex-US). Ex: "US size premium was 2% while Ex-US size premium was also 2%" as you might read in, say, Swedroe's book.

So if you want to target a factor load of, say, 0.5 (to capture an overall 1% additional return), you'd need to tilt the US 0.5 in the context of US universe, and Ex-US to 0.5 in the context of Ex-US universe.

If instead you just hold Total Ex-US, you will capture no size premium. Even though if you regressed it to the entire DM universe, it says it has a tilt!

In other words, the factor premium I typically have read is NOT the same or equivalent as the ones you show here.

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Re: Do factors explain the benefit of int’l diversification?

Post by Northern Flicker » Mon Oct 28, 2019 8:09 pm

If you expand the universe, the regressions becomes less reliable because it increases the number of drivers of return (currency exposure as one example). The lower reliability was pointed out by rhusky.

I think one takeaway is that having a value tilt for both US and non-US equities may reduce the diversification benefit of non-US equity.
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Re: Do factors explain the benefit of int’l diversification?

Post by 305pelusa » Mon Oct 28, 2019 9:16 pm

Northern Flicker wrote:
Mon Oct 28, 2019 8:09 pm

I think one takeaway is that having a value tilt for both US and non-US equities may reduce the diversification benefit of non-US equity.
This is the second time you've said this. How do you figure?

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Re: Do factors explain the benefit of int’l diversification?

Post by Northern Flicker » Tue Oct 29, 2019 10:30 pm

Well, first I view this as hypothesis formation not hypothesis confirmation. To respond to a listing of nisiprius, a factor regression is not a performance backtest. You can see factor loadings, but the sample mean or sample variance of excess factor return may not conform the expected value or variance of the excess return of the risk premium.

The regression did not have a very high reliability and it was not a random sample, so I’m certainly not suggesting anyone should change their allocations based on anything in this thread.

If it is true that US equities tend to have a quality tilt relative to all DM equities, and if it is true that non-US DM equities tend to have a value tilt with respect to all DM equities, then if one diversifies internationally, tilting US to value may nullify a source of diversification benefit (quality) and align more closely with drivers of non-US equity returns.

Another view of this is that non-US equities and US value both tend to overperform when US inflation accelerates.

Just some thoughts, not a definitive claim.
Index fund investor since 1987.

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