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
```

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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
```

*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
```

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
```

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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