Which value index (fund) has been the most style consistent?

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Robert T
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Which value index (fund) has been the most style consistent?

Post by Robert T » Wed Oct 24, 2007 11:57 am

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It's often assumed that some value funds (e.g. from DFA) are more style consistent than other funds (e.g. those tracking the S&P, MSCI and Russell indexes).

I have tried to test whether this has been the case (using backtested index data). The methodology used was as follows:
  • 1) Estimate the factor loadings of several value indexes (funds) over the period July 1995 to April 2007 (presented in this earlier post).
    2) Calculate the monthly returns (R-Rf) implied by the factor loadings estimated over this period (as factor loads multiplied by the respective annual Mkt-Rf, SmB, HmL returns).
    3) Calculate rolling 36 month correlations between the historical annual index (fund) returns (less the risk free rate) and those implied by the factor loads (calculated in 2).
Correlations equal to 1 for any of the 36 month sub-periods (107 in total) implies that the index (fund) returns were exactly correlated to the returns implied by the factor loadings i.e. the return characteristics (or style) of the sub-period were exactly consistent with the return characteristics (or style) of the full period. The further correlations are from 1 the greater the style drift in the sub-period.

The results below are listed from most style consistent to the least style consistent (as defined above) for a set of mid-cap indexes (tickers for funds currently tracking these are also listed) and for a set of small-cap indexes (including the DFA small value fund).

All the indexes were fairly style consistent. The DFA small value fund was the ‘most style consistent’. The Russell indexes also did fairly well. The least consistent was the S&P 600 pure value index. The S&P 600 value index came out slightly ahead of the MSCI small value index (the reverse was true for mid-cap value). One caveat - the numbers just tell us about correlations and not the absolute return differences with the FF factor load equivalent.

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Results for 36 month rolling correlations (107 in all) between 'actual' returns and 
those implied by estimated factor loadings over July 1995 - April 2007 
			
			
                                                  Correlations
	                                    Average   Highest  Lowest    SD
MID-CAP VALUE
Russell Mid Cap Value [IWS]               0.96    0.97    0.90    0.017 
MSCI US Mid Cap Value [VOE]               0.95    0.97    0.89    0.019    
S&P 400 Value [IJJ]                       0.94    0.96    0.88    0.022 

SMALL-CAP VALUE
DFA Small Value                           0.98    0.99    0.94    0.011 
Russell 2000 Value [IWN]                  0.96    0.98    0.89    0.017 
S&P 600 Value [IJS]                       0.95    0.98    0.89    0.020
MSCI US Small Value [VBR]                 0.94    0.97    0.87    0.026 
S&P 600 Pure Value [RZV]                  0.92    0.97    0.80    0.039  


Source of primary data: MSCI, S&P, Russell websites and M* Principia
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Just one approach to try to answer the question.

Robert

Edit - after redoing the analysis the table and text above were changed to reflect the new results. Apologies for previous errors.
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Last edited by Robert T on Wed Oct 24, 2007 6:23 pm, edited 3 times in total.

SmallHi
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Post by SmallHi » Wed Oct 24, 2007 1:22 pm

Interesting, Robert.

I wonder how much of that has to do with the fact that the S&P Indexes have much less of an orientation to value than Russell, MSCI, or DFA?

(To match a 50% 400 Value, 50% 600 Value portfolio since 1995, you would need 8% DFA Large Cap, 32% DFA Large Value, 20% DFA Small Cap, and 40% DFA Small Value -- or only 70% Value, and 30% Blend)...so I figured we would stick with the deepest value indexes (and the Pure Value style adjusted performance is so bad I don't see much use it including it)

I looked at the standard deviation of quarterly HmL sensitivities (average HmL during all Jan - March's; April - May's...) relative to total HmL sensitivities over the entire period (1995-2007) to get an idea for how HmL exposure drifts over time.

I found that Russell had the lowest quarterly standard deviation of HmL sensitivity (6.6), while MSCI had the highest (14.2). DFA was closer to Russell than MSCI (8.5).

I would imagine the most drift comes not from the style indexes themselves, but the drift on a portfolio level if you incorporate Large Cap, Small Cap as well as Mid Value and Small Value. In a year like this, you may have started off 0.2/0.4....but with the strong underperformance of value, you could very easily be closer to 0.15/0.30 today (just guessing here) if you weren't adding enough new $ to keep the portfolio in line.

SH

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Post by lazyday » Wed Oct 24, 2007 1:38 pm

Robert,

FYI, you may already know this, but S&P changed value index methodology toward the end of your timeframe. Used to be BARRA, just based on P/B, but is now multifactor, including antigrowth--penalizing value companies from inclusion if they grow fast.

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Post by SmallHi » Wed Oct 24, 2007 1:50 pm

If I know Robert, he has certainly included only the current data series (as that is all that is relevant to investors today).

I did the same...fyi

SH

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Post by larryswedroe » Wed Oct 24, 2007 3:11 pm

Keep in mind that indices that reconstitute once a year get more growthy every day. Until the reconstitute
That is significant advantage for DFA which looks at value stocks ranking basically every day.

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Post by Robert T » Wed Oct 24, 2007 6:07 pm

SH,

Thanks for the analysis. See repost above (after correcting error). The numbers are fairly similar - DFA sv comes out slightly ahead.

Lazyday,

The 'new' S&P citigroup indices were used in the analysis. The old Barra benchmark had higher value loadings and as an investor in fund I changed my allocation when the benchmark changed in 2005 to ensure I still maintained my portfolio factor loading target (IMO it was a signficant enough shift in the value loading to make the change).

Larry,

Thanks and agree - but it seems hard to quantify the impact of different reconstitution approaches on returns.

Robert
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Post by Robert T » Wed Oct 24, 2007 7:22 pm

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Another simpler way to address the question may be to look at R^2 and alpha in the Fama-French three factor regressions on each index. i.e.
  • 1. What share of the variability in returns is explained by the three equity risks we are trying to capture (market, value and size in the 3F model)? The closer R^2 is to 1 the more ‘style pure’ the index.

    2. If the returns on the market, value, and size factors are zero are the index returns also zero (i.e. alpha=0)? The closer to zero the more ‘style pure’ the index.
Interestingly if the results are ranked by R^2 they are ordered the same as in the first post. All the alpha coefficients are negative but only ‘statistically significant’ for the Russell 2000 value index (significant enough to lose its place in the order IMO), and is fairly large for the S&P600 pure value index.

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From Fama-French 3F model regressions - July 1995 to April 2007

							                     alpha   t-stat   R^2
MID-CAP VALUE
Russell Mid Cap Value [IWS]              -0.09    -0.83    0.91
MSCI US Mid Cap Value [VOE]              -0.04    -0.30    0.88    
S&P 400 Value [IJJ]                      -0.19    -1.47    0.86     

SMALL-CAP VALUE
DFA Small Value                          -0.13    -1.25    0.95 
Russell 2000 Value [IWN]                 -0.26    -2.40    0.92 
S&P 600 Value [IJS]                      -0.19    -1.49    0.91
MSCI US Small Value [VBR]                -0.18    -1.48    0.88   
S&P 600 Pure Value [RZV]                 -0.30    -1.76    0.84  
Robert
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Style drift

Post by Robert T » Sat Nov 03, 2007 2:16 pm

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Chip’s earlier post on interpreting regressions results raises an important point that IMO needs to be highlighted. I thought it would be useful to do this in the context of style drift – so am posting it here.

In an earlier thread, I posted regression coefficient estimates or factor loadings on selected value funds, but like all OLS regression analysis these are point estimates with non-negligible confidence intervals. And in this context may say something about style drift – the smaller the confidence interval the more ‘style pure’ the fund is expected to be.

The confidence interval of the factor coefficients (factor loadings) are presented in the second table below together with an estimate of expected returns. For the latter, the following assumptions are used.

Expected T-bill returns = 2*
Expected equity premium = 5
Expected value premium = 4
Expected size premium = 2

The current 3-month T-bill yield is about 3.5% (for purposes of this calculation I use 2% to get an expected equity market return of 7% (5+2). Alternative assumptions can be used and plugged in to the equity fund (indexes) expected returns listed below. Please note – expenses have note been deducted from the index expected return.

Few observations (at least my take) – which assumes the 1995-2007 captures the long-term average characteristics of each index and the DFA fund:
  • - For the same level of confidence, the DFA small value fund exposure to risk factors is expected to vary less than the other small value funds, followed by MSCI Small Value and S&P600 value (which are similar), the Russell 2000v, and then the S&P 600 pure value series.

    - For the same level of confidence, this translates into variability of expected return from the low range 11.32 to 12.32 (a 1.32% difference) for the DFA small value fund to 11.50 to 13.71 (a 2.21% difference) for S&P 600 pure value.

    - If we compare the share of the expected return range difference with the point estimate of the expected return we get the following ordering:

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                      (ER[lower]-ER)/ER
DFA small value            -5.5%
MSCI small value           -7.2%
S&P 600 small value        -7.5%
Russell 2000 value         -8.3%
S&P 600 pure value         -8.8%

For interpretation: The DFA small value fund lower bound of the 95% confidence interval is 5.5% of its estimates expected return.
  • The lower bound estimate as a % of expected return (as a proxy for style drift) is lowest for the DFA small value fund and highest for the S&P 600 pure value fund. The orderings is consistent with the FF3F regression R^2 except for MSCI small value.

    - IMO, looking at the regression R^2 and alpha is a quicker and fairly consistent way of determining ‘style purity’. (the higher the R^2 and the closer alpha is to zero, the more ‘style’ pure the fund). [Style purity in this discussion is not which fund have the largest factor loadings but which are likely to have the most consistent exposure to these factors].

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July 1995-April 2007
                                95% Confidence Range                        
                   Coefficient     Upper – Lower      Upper minus Lower
DFA SMALL VALUE
  Beta                 1.08         1.02 –  1.13           0.11
  Size                 0.83         0.77 –  0.88           0.11
  Value                0.73         0.66 –  0.80           0.14
  Expected Return*    11.98        11.32 – 12.63           1.32

MSCI SMALL VALUE
  Beta                 0.99         0.93 –  1.06           0.13
  Size                 0.41         0.35 –  0.48           0.13
  Value                0.80         0.72 –  0.89           0.17
  Expected Return	  11.00        10.21 – 11.80           1.59

S&P600 VALUE
  Beta                 1.01         0.94 –  1.07           0.13
  Size                 0.67         0.60 –  0.74           0.13
  Value                0.63         0.54 –  0.72           0.18
  Expected Return	  10.90        10.09 – 11.72           1.63

RUSSELL 2000 VALUE
  Alpha*              -0.26        -0.48 - -0.05           0.43   
  Beta                 0.97         0.92 –  1.03           0.11
  Size                 0.64         0.58 –  0.70           0.12
  Value                0.79         0.72 –  0.87           0.15
  Expected Return     11.06        10.15 – 11.97           1.83

S&P600 PURE VALUE
  Beta                 1.04         0.95 –  1.13           0.18
  Size                 0.72         0.63 –  0.81           0.18
  Value                0.99         0.87 –  1.11           0.24
  Expected Return	  12.60        11.50 – 13.71           2.21

*alpha was included in the Russell 2000 value expected returns calculation as it was significant. (hope I did it correctly).

Robert
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