US versus Intl. value tilt: Does it make a difference?

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Robert T
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US versus Intl. value tilt: Does it make a difference?

Post by Robert T » Sun Apr 29, 2007 8:42 pm

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I have recently looked at the first quarter US SmB (size premium) and HmL (value premium) numbers as these are now available on Ken French’s website. Return through end March: US Rm-Rf (equity premium) =0.18, US SmB= 0.71, US HmL= –0.36; while DFA Intl. Large = 4.38 and DFA Intl. Value = 5.03 - so the US value premium was slightly negative and it seems the Intl value premium was positive for the first quarter. In reflecting on this short-term outcome it brought me back to the common suggestion – that if you want a value tilt just take it with your US allocation.

Does it make a difference where you take your value tilt?

Here is the analysis I did to try to answer this question - it may be useful for others. The analysis obviously assumes a decision to value tilt has already been taken.

The analysis uses the US Benchmark Factor data and International Index Portfolio data from Ken French’s website for the period 1975-2006.

1. Correlations: US-HmL and Intl-HmL had about the same correlation coefficient as between US-market and Intl. market and the average correlation of Intl-HmL with US Mkt, US HmL and Intl Mkt, and average correlation of US-HmL with Intl Mkt, US HmL, and US Mkt were both low.

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Correlation Matrix

             US Mkt     US HmL     Intl. Mkt     Intl HmL
US Mkt         1.00			
US HmL        -0.32      1.00		
Intl. Mkt      0.49     -0.21         1.00	
Intl. HmL     -0.25      0.45         0.01         1.00
2. Intl and US factor return differences: Interestingly the annualized return for Intl. HmL from 1975-2006 was larger than US HmL (6.7 vs. 4.1 percent from 1975-2006). This was larger than the difference between Intl market and US market returns (13.9 vs. 13.1 percent respectively). Will this value premium difference persist – time will tell – but sine 1975 an international value tilt would have yielded higher returns than the equivalent (equal value loading) US tilt.

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Annualized Return Comparison: 1975-2006

                       US-Mkt	US-HmL   Intl. Mkt	Intl. HmL
Average return          15.1      5.3       14.9        7.1		
Annualized return       13.9      4.1       13.1        6.7 
Standard deviation      15.8 	 15.1       20.8        9.8 
3. Portfolio return differences of US versus Intl. factor tilts. I tested three portfolios (i) P1: an equity portfolio with an equal US and Intl market and value tilt (more specifically a 50:50 US:Intl allocation with a 0.4 value loading for both the US and Intl. allocations); (ii) P2: a portfolio with the same average value loading of 0.4 but with a 0.6 value loading in the US allocation and 0.2 value loading in the Intl. allocation; and (iii) P3: a portfolio where all the value exposure is take on the US side which means a US value loading of 0.8 which will maintain the average overall portfolio loading of 0.4 (i.e. 0.5*0.8+0.5*0.0=0.4).

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1975-2006
                   AR	    SD    Sharpe     Growth of $1 [since 1975]
P1(0.4:0.4)      16.5	  15.3     0.746            132	
P2(0.6:0.2)      16.3	  15.2     0.740            126    
P3(0.8:0.0)      16.1	  15.2     0.727            120    

P4(0.0:0.0)      13.9     15.9     0.562             63	

Figures in parentheses are value loadings for the US and Intl allocation respectively.
AR = Annualized return
SD = Standard deviation
Sharpe = Sharpe ratio
The results suggest that since 1975– taking a value tilt equally in US and Intl markets yielded higher returns than if it was only taken on the US side. The results seem to suggest that – if possible – try to have an even value tilt across US and Intl markets. To add perspective I added a portfolio (P4) with no value tilt (just a 50:50 US:Intl. market split). This had a 2006 portfolio value half the size of the value tilted portfolio from an equal size starting point in 1975. The message seems to be that sine 1975– tilting to value mattered a whole lot more than how this was achieved across US and Intl. markets. Nevertheless the latter was still important.

4. Tracking Error: One implication is tracking error relative with some benchmarks. For example a portfolio with the same average value loading as the illustrative DFA balanced strategies but with most of its value loading on the US portion (unlike the DFA ‘balanced’ approach) will often have significantly different annual returns (tracking error). To illustrate how large this could be I compared the return difference between P1 and P2 (P1-P2). Here are the two largest positive and negative tracking error years.

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Annual return difference

            P1-P2
1999	      4.3
2003         2.0
1976        -2.1
2001        -2.0
To get back to the question: It may make a difference where you take your value tilt – but the difference may be relatively small.

Bottom line message (at least to me): (i) try to get an even value tilt across US and Intl. markets; (ii) if this is not possible – you may lose (the past loss was 0.4 percent annualized in the extreme case), but the difference is relatively small relative to value tilting itself (2.2 percent annualized for lowest return in above example [p4-p3]); (iii) recognize that there will be annual tracking error of portfolios with the same average factor loading but with different allocations to value across US and international markets.

Robert
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Last edited by Robert T on Mon Apr 30, 2007 5:01 pm, edited 1 time in total.

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Post by lswswein » Mon Apr 30, 2007 12:15 am

Hi Robert
That's an interesting analysis. The fact that the difference is only 5% between the P1(0.4:0.4) & P2(0.6:0.2) and the increase in ER going from US Value vs Intl Value might mean that the difference is negligible.

Would it be possible for you to do a similar study for Small? Because Intl Small is so difficult to get access to (High ER too), in my portfolio I get all my Small in US. I wonder how much the difference would be.

thanks
-h

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Post by BrianTH » Mon Apr 30, 2007 6:58 am

As someone who thinks there are real risks associated with SV investing which are likely associated with human capital and consumption issues, I also tend to think those risks are likely lower for an investor investing outside his own country, since his human capital and consumption risks will likely be mostly closely associated with stocks in his own country. So, as long as SV stocks are paying a premium largely because their domestic investors need it to compensate for the associated human capital and consumption risks, foreign investors can piggyback on that premium and actually get something of a "free lunch" to the extent they face less such risks than those domestic investors.

Obviously, that "free lunch" would diminish to the extent that domestic investors became dominated by foreign investors, which is happening with increasingly global capital market. But you would still likely do better concentrating your SV investing outside your home country as long as there is any overall domestic bias in stock investing at all, which will likely persist both for behavioral reasons and because of currency risk. So, all else being equal, I personally think it would be a good idea to do one's SV investing in foreign stocks if at all possible, and for US investors in particular that could be a big issue (since the US makes up so much of the world's stock markets).

Unfortunately, for many of us (including me), this may not be possible due to limited investment options.

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Intl SmB

Post by Robert T » Mon Apr 30, 2007 4:27 pm

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h,

The expense ratio differences are not too large – by my estimate about 0.05 percent per year between P1 and P2 and 0.07 percent between P1 and P3. There maybe other costs (transaction costs, etc) but from expense ratios alone P1 seems to still come out marginally ahead (0.1 percent annualized over P2 [perhaps negligible?] and 0.3 percent annualized over P3). There are obviously no guarantees that this relative performance will repeat.

FWIW: My current value loading targets are 0.6 for US; 0.3 for Non-US Developed; 0.0 for EM to give an average portfolio value loading target of 0.4. As other intl. options become available I may consider shifting to a more even US:Non-US split.

Unfortunately there is no Intl SmB on Ken French’s website so its difficult to do a similar analysis for small cap exposure. While its possible to generate a ‘SmB’ type series from the MSCI website, the relevant data don’t extend back to 1975. However if you look at the returns in the attached link ( http://www.dfaus.com/philosophy/dimensions/ ) international small seems to have back-tested fairly well so I would expect some benefit from both a US and Intl small cap tilt over the period used for the ‘value tilt’ analysis - 1975-2006. There will no doubt be periods of underperformance – see the third graph in the attached link ( http://www.efficientfrontier.com/ef/702/3FM-10.htm ) which should be expected going forward.

Brian,

I agree that consumption and human capital risks should be considered in overall allocation decisions (including where to value tilt) – but other factors sometimes dominate as you indicate (e.g. available options, tracking error risk, personal preference etc).

On human capital risk, the article on "The International Diversification Puzzle is Worse Than You Think" by Baxter and Jermann - American Economic Review, March 1997 is an interesting read. The researh suggested that as the correlation of return to labor and return to capital in the US was high (0.99 correlation coefficient over 1960-1993), a truly diversified portfolio (accounting for ‘average’ human capital risk) would be short US equity and long non-US equity. More specifically ‘a diversified’ equity portfolio for the average US investor which takes account of human capital risk was considered to be -12% US and 112% Non-US. Perhaps this approach is for the purists but from a personal perspective (and deviations from average), I am comfortable with my 50:50 US:Non-US allocation and with my current higher value tilt in my US allocation given the available options.

Robert
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Re: Intl SmB

Post by BrianTH » Mon Apr 30, 2007 5:20 pm

Robert T wrote:On human capital risk, the article on "The International Diversification Puzzle is Worse Than You Think" by Baxter and Jermann - American Economic Review, March 1997 is an interesting read. The researh suggested that as the correlation of return to labor and return to capital in the US was high (0.99 correlation coefficient over 1960-1993), a truly diversified portfolio (accounting for ‘average’ human capital risk) would be short US equity and long non-US equity. More specifically ‘a diversified’ equity portfolio for the average US investor which takes account of human capital risk was considered to be -12% US and 112% Non-US. Perhaps this approach is for the purists but from a personal perspective (and deviations from average), I am comfortable with my 50:50 US:Non-US allocation and with my current higher value tilt in my US allocation given the available options.

Robert
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Thanks for the cite--I'll check it out.

I also find the result unsurprising. And perhaps as practical barriers to investing internationally continue to come down, and perhaps as tracking error takes on a different meaning, we will see more and more people in the US heading that way. Indeed, I gather we already are.

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Post by SmallHi » Mon Apr 30, 2007 5:25 pm

The real benefit of taking your size and value risks globally instead of in one particular country is, regardless of time period, the globally tilted allocation seems more likely to be as close to optimal as possible vs. regional tilting.

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....................P1.....P2.....P3
US Value...........25%.....50%.....0%
US Small...........25%.....50%.....0%
Int'l Value........25%......0%....50%
Int'l Small........25%......0%....50%

1975-1997
Return............20.2%...19.1%..19.9%
RISK..............16.0....18.0...18.5
REBAL BONUS........0.8%....0.1%...0.1%

1997-2007
Return............12.8%...12.7%..12.3%
Risk..............23.9....24.7...26.3
REBAL BONUS........0.6%....0.5%...0.2%
In this example taken from the sister site, you can see that regardless of period (one where US tilt was superior, the other where Int'l tilt was superior), the global tilt maintained superiority over both in each subperiod.

Thought that would be an interesting addition to the conversation.

SmallHI

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Post by BrianTH » Mon Apr 30, 2007 5:36 pm

SmallHi,

I haven't read the paper yet, but I think it is important to note your study doesn't account for human capital, which apparently is precisely what pushed the optimal portfolio toward actually shorting the US. In other words, P3 might easily beat P1 once you account for human capital. And if it is true that SV stocks are even more highly correlated with human capital risks, then you might end up concluding you should short US stocks even more if you are SV tilting.

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Post by SmallHi » Mon Apr 30, 2007 5:59 pm

Brian,

Realistically, I doubt anyone is going to short domestic stocks to achieve the proper human capital adjusted portfolio, but I do get your point.

Your comment, along with the #s above, just support the need to target the 3F risks in as many regions of the world as possible....The historical #s are only one aspect to this argument.

Robert's 50% Int'l allocation seems reasonable to me.

HI

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Human capital and consumption risk

Post by Robert T » Mon Apr 30, 2007 7:54 pm

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SmallHi,

Thanks for the addition – interesting.

Brian,

My modest view of human capital risk is I think its implications are specific to each individual/family. The American Economic Review article while interesting gives some ‘average’ estimates for human capital risk and portfolio diversification. But individuals typically have a job in a particular industry rather than in an industry reflecting the characteristics of the weighted aggregate of the companies in the Wilshire 5000 (as an example). Many work in non-public traded companies, etc..

Let’s assume that the return to labor in a particular industry has a high correlation with the performance of the industry. What we observe is the correlation coefficients of the aggregate US market portfolio with 49 US industry groups of the market portfolio vary from 0.06 to 0.91 (from 1975-2006). Following the above assumption – this suggests a wide variation of the correlation of returns to labor (human capital risk) and US market performance (I would also expect a wide variation in US industry correlation with a US value tilted equity allocation). So holding a US allocation is still partially diversifying US human capital risk. Just as owning non-Enron US stocks was to Enron employees. In some cases, the industry correlations between the US market and Intl market portfolios are not dramatically different (given the correlations in the first post the industry correlations between value tilted US and Intl market may also be similar in some cases).

In addition, consumption risk (incl. US inflation risk) plays a role – particularly for retirees, for paying for US college etc. – all of which seem to suggest the need for a greater US allocation.

So I think both human capital and consumption risk are specific to individuals and are important to consider but it’s difficult to make broad generalizations – as some of the articles on the subject try to do (although many of them are fairly interesting).

Robert
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Excuse my dumb question

Post by mutinvestor » Mon Apr 30, 2007 9:14 pm

Pardon a dumb question ... but what is P1, P2 and all the rest? Where can someone find out about this stuff? In plain terms, is there any way you folks can (if you care) educate those of us less learned on these topics to use what you're saying?

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Post by Kenster1 » Mon Apr 30, 2007 9:44 pm

P1, P2 and P3 are just references to the different Portfolios (Portfolio1, Portfolio2, Portfolio3) they're identifying or distinguishing in the example allocations.

HmL
- High minus Low book-to-market value
- Additional return of value stocks (high book/market) over growth stocks (low book/market)
- Market value essentially means market capitalization and Book value is simply considered a firm's accounting value if it were to be liqudated.

SmB
- Small minus Big
- Additional return of Small stocks over Large stocks

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Ah, thanks

Post by mutinvestor » Mon Apr 30, 2007 9:58 pm

Then if I'm reading this correctly, there's still a slight value premium that can be gained internationally? The gains from tilting internationally to value are slight, though, which might be wiped out by higher expenses.
However, assuming I'm reading this correctly (a big assumption) ... then if you stick to Vanguard low-cost funds like Int'l Value, it looks like you can still gain from tilting a little to value on the international side?
On the flip side, it doesn't seem like paying up to buy SSgA's new small cap blend ETF or WisdomTree's small int'l value ETF (both around .60% ER) would be worth it? Wouldn't it seem worth the wait to hold out for Vanguard Int'l Explorer to open ... or a lower-priced ETF to come out?

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Post by BrianTH » Tue May 01, 2007 6:57 am

Robert,

I absolutely agree--human capital and consumption risk are very individualized issues, and my personal feeling is that we have only just begun developing the concepts and tools we need to start analyzing our individual circumstances and incorporating that analysis into our asset allocation decisions. I also agree that many factors push back against US investors underweighting or shorting their US investments.

But I will indulge in one generalization, which is that as I understand it, the weighted average wage provider is actually tilted to SV relative to the stock markets. This is a product of at least two effects: (1) what would be SV companies are less likely to go public, so the existing public SV companies are a better proxy for nonpublic employers; and (2) book value is a better proxy for total wages than market cap (which makes sense). So, I think the baseline assumption should be that the investor's human capital has a SV tilt, which may go a long way toward explaining the Fama-French cross-section of returns.

Again, though, I absolutely agree this is just a starting point for this discussion, and a crude one at that. To do this properly, the investor should try to assess his or her actual individual situation, at least relative to this hypothetical average investor. But again, I will toss in one more generalization which I also suggested above: to the extent the average investor's human capital has a SV tilt, I think that is more relevant to domestic allocation issues than foreign investments. That is why I think we need to be less careful when SV tilting in foreign investments.

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Re: Ah, thanks

Post by BrianTH » Tue May 01, 2007 7:03 am

mutinvestor wrote:Then if I'm reading this correctly, there's still a slight value premium that can be gained internationally? The gains from tilting internationally to value are slight, though, which might be wiped out by higher expenses.
However, assuming I'm reading this correctly (a big assumption) ... then if you stick to Vanguard low-cost funds like Int'l Value, it looks like you can still gain from tilting a little to value on the international side?
On the flip side, it doesn't seem like paying up to buy SSgA's new small cap blend ETF or WisdomTree's small int'l value ETF (both around .60% ER) would be worth it? Wouldn't it seem worth the wait to hold out for Vanguard Int'l Explorer to open ... or a lower-priced ETF to come out?
It is always hard to know whether the SV premiums will justify any particular costs, because that requires predicting their magnitude in advance with a precision we may not have.

But my own two cents is that with Vanguard's products or even WisdomTree's products, the fees are sufficiently low that I think it would make sense for many investors to start SV tilting internationally first, and only start to SV tilt domestically once they have run out of their ability to do this internationally.

With complete discretion over your investments, that might mean, for example, that 100% of your international investments would go into VTRIX and/or DLS before you even contemplate departing from a TSM fund for your US investments. But many people do not have complete discretion over their investments. I, for example, have limited international choices in my biggest accounts (employer plans), so I quickly run out of my ability to use this strategy, and end up with a lot of US SV anyway.

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Re: Intl SmB

Post by sperry8 » Sun Jan 29, 2017 1:03 am

Robert T wrote:.
h,

The expense ratio differences are not too large – by my estimate about 0.05 percent per year between P1 and P2 and 0.07 percent between P1 and P3. There maybe other costs (transaction costs, etc) but from expense ratios alone P1 seems to still come out marginally ahead (0.1 percent annualized over P2 [perhaps negligible?] and 0.3 percent annualized over P3). There are obviously no guarantees that this relative performance will repeat.

FWIW: My current value loading targets are 0.6 for US; 0.3 for Non-US Developed; 0.0 for EM to give an average portfolio value loading target of 0.4. As other intl. options become available I may consider shifting to a more even US:Non-US split.

Unfortunately there is no Intl SmB on Ken French’s website so its difficult to do a similar analysis for small cap exposure. While its possible to generate a ‘SmB’ type series from the MSCI website, the relevant data don’t extend back to 1975. However if you look at the returns in the attached link ( http://www.dfaus.com/philosophy/dimensions/ ) international small seems to have back-tested fairly well so I would expect some benefit from both a US and Intl small cap tilt over the period used for the ‘value tilt’ analysis - 1975-2006. There will no doubt be periods of underperformance – see the third graph in the attached link ( http://www.efficientfrontier.com/ef/702/3FM-10.htm ) which should be expected going forward.

Brian,

I agree that consumption and human capital risks should be considered in overall allocation decisions (including where to value tilt) – but other factors sometimes dominate as you indicate (e.g. available options, tracking error risk, personal preference etc).

On human capital risk, the article on "The International Diversification Puzzle is Worse Than You Think" by Baxter and Jermann - American Economic Review, March 1997 is an interesting read. The researh suggested that as the correlation of return to labor and return to capital in the US was high (0.99 correlation coefficient over 1960-1993), a truly diversified portfolio (accounting for ‘average’ human capital risk) would be short US equity and long non-US equity. More specifically ‘a diversified’ equity portfolio for the average US investor which takes account of human capital risk was considered to be -12% US and 112% Non-US. Perhaps this approach is for the purists but from a personal perspective (and deviations from average), I am comfortable with my 50:50 US:Non-US allocation and with my current higher value tilt in my US allocation given the available options.

Robert
.
Great analysis. I wonder if you've updated it (since 10 years has passed since the last analysis) and whether French now includes small in his stats as well (providing us for the oppty to analyze that too).
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Re: US versus Intl. value tilt: Does it make a difference?

Post by garlandwhizzer » Sun Jan 29, 2017 1:17 pm

Very interesting post, Robert T, thanks for posting it.

I'll add one point which I got from Larry's recent book. Since its discovery and widespread publication in the financial literature the value premium as well as all of the other described premiums persist but have modestly decreased in magnitude in US markets. The same does not appear to be true for international markets where factor premiums seem to remain more more robust. This implies that US markets may be more efficient now, may use more arbitrage diluting factor excess returns going forward, and may have more professionally managed assets shorting overpriced equity and market pricing errors. Less decay in post-publication factor returns internationally implies that going forward from here (where factors are the rage in financial publications) INTL factor returns may be more robust than US factor returns. I actually believe this to be true, not so much on backtesting which Robert T has done so well, but on expected future returns. INTL equity, especially EM, has substantially underperformed US equity for a long time, producing disparate equity valuations, and in my view this has set the stage for INTL outperformance and especially INTL value going forward. I certainly may be wrong on this, but I believe it sufficiently to tilt heavily to small and to value in both INTL DM and EM. I tilt much more modestly in US where I believe factor premiums will be increasingly difficult to harvest after costs especially in the very closely scrutinized LC space. Granted, my position is not based primarily on backtesting because I believe that backtesting alone does not reflect today's starting point valuation disparity. IMHO backtesting alone may not be a completely reliable guideline to future returns any more than my admittedly less than reliable analysis of the current situation. Clearly there is more risk in INTL as always but I believe that for a pleasant change INTL beta risk and value risk will be rewarded in the future for those who persist through bad times.

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Re: US versus Intl. value tilt: Does it make a difference?

Post by TheGipper » Sun Jan 29, 2017 2:52 pm

Assuming the availability of all mutual funds and ETFs (including DFA without advisor fee).......

Would be interested to survey this crew on the optimal investments to obtain their international small and value tilts.

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