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Diminishing tails effect of more factor tilt
Robert T 06-17-2007, 5:08 PM | Post #2401289 | 
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Larry,

Following your earlier posts I had a look at whether factor tilts have had a linear effect on reducing the dispersion of returns. The results seem to indicate that the small and value tilt effect on reducing weight in the tails has not been linear and has historically diminished as factors loadings increase beyond a certain point (not sure where the exact point has been) but the following example is illustrative:


1927-2006
                                  P1        P2       P3
Beta loading                    1.00      0.68     0.53
Value loading                             0.40     0.80   
Size loading                              0.20     0.40 

Annualized return              11.38     11.38    11.38 
Standard deviation             21.01     16.56    15.47 
Top one year                   57.88     50.98    49.05
Top five years (average)       50.66     42.51    41.38
Bottom one year               -47.10    -36.20   -31.16
Bottom five years (average)   -30.90    -22.63   -19.35

Source: Derived from the Fama-French US Benchmark factors


P1 is a US Market portfolio. Lets call this the 'total market' approach.

P2 has an equity:fixed income split of 68:32 with a size and value loading of 0.2 and 0.4 respectively. Lets call this a 'Balanced' approach (as its not too far off the factor loadings of the DFA sample Balanced Strategy).

P3 has double the size and value loadings of P2 and an equity:fixed income split of 53:47. Lets call this a 'Small Value" approach as the size and value factor loadings seem to correspond fairly closely to the index tracked by the Vanguard Small Value fund.

All portfolios had the same annualized return of 11.38 percent from 1927-2006.

The standard deviation of the small value approach [p3] and the balanced approach were 26 and 21 percent lower than the total market approach (21.01 vs. 15.47, and 21.01 vs16.56) for the same annualized return (i.e. same return but with less weight in the tails). So the balanced approach [P2], with half the value and size loadings of the small value approach [P3], still picked up about 80 percent of the small value [P3] effect on reducing the standard deviation of returns.

A similar result is found if we look at the best an worst years. The small value approach [P3] gave up on average 18 percent of the return in the best years but reduced losses by 37 per

Originally posted in thread: 59269
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