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I am running a simple 4 factor model which includes the factors: Benchmark (Market - FortyConsumerSixtyHealthcare), SMB, HML and MOM.

When I simply apply the regression to the portfolio returns and the benchmark I get a statistically significant result and a fairly strong Beta of 0.4262:

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                                   coef    std err          t      P>|t|      [0.025      0.975]
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Intercept                        0.0192      0.006      2.973      0.004       0.006       0.032
FortyConsumerSixtyHealthcare(BM) 0.4262      0.178      2.398      0.018       0.073       0.779

However when I run the model with the other factors included the significance is lost and the loading is also reduced significantly to 0.1809:

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                                   coef    std err          t      P>|t|      [0.025      0.975]
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Intercept                        0.0233      0.006      3.902      0.000       0.011       0.035
FortyConsumerSixtyHealthcare(BM) 0.1809      0.171      1.060      0.292      -0.158       0.520
SMB                              0.0085      0.003      3.374      0.001       0.003       0.013
HML                             -0.0017      0.002     -0.706      0.482      -0.007       0.003
MOM                             -0.0055      0.002     -2.589      0.011      -0.010      -0.001

The only statistically significant factors now seem to be size and momentum both of which have tiny loadings.

I am not sure why the loading on the benchmark has changed so significantly by adding other factors and why it is now not statistically significant, surely this would lead someone to think that the portfolio is market neutral when in fact it has a beta 0.4262?

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A lot has been written on the Fama-French and Carhart factors -- including that SMB may help proxy for the market index being too narrowly-defined. Here you may also be facing that problem. Why else might your coefficient estimates have changed so much? Perhaps HML, SMB, or MOM is multicollinear with your benchmark index.

However, your benchmark index is likely a problem: it is even more narrow than the S&P 500 and has a strong industry bias. I would try using a different benchmark to see how that affects your results.

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  • $\begingroup$ Thank you this is really helpful! The fund is mainly invested in consumer and healthcare in-fact they are run as separate sleeves and combined under one fund so I thought a blended index would be better as a benchmark. How does one usually run the Carhart model for example on sector specific portfolios? $\endgroup$
    – Simon Nicholls
    Aug 8, 2020 at 8:13
  • $\begingroup$ I would keep the SMB, HML, and MOM factors all the same as their usual definition, use the S&P 500 or S&P 500 and Russell 2000 as indices, and maybe add XLV and (XLP or XLY) as additional indices. Maybe. $\endgroup$
    – kurtosis
    Aug 8, 2020 at 8:25
  • $\begingroup$ Thank you for your help, I’m still a little confused about how a factor can become statistically insignificant after adding a factor, the other way round I can understand if it became significant but I can’t quite picture insignificant. Does this mean that the regression with just the benchmark above where it is significant we can’t rely on these results? $\endgroup$
    – Simon Nicholls
    Aug 10, 2020 at 8:56
  • $\begingroup$ A factor (say, factor A) can become insignificant after adding another factor (say, factor B) if B is highly correlated with A but has less noise. Also possible is that on their own, A or B are significant but they are correlated so that together they share the explanatory power leaving neither significant -- even though their combination as a single variable would be significant. Regarding your benchmark, it is possible that adding other factors might make the benchmark insignificant -- meaning the added factors better explained returns than the benchmark. $\endgroup$
    – kurtosis
    Aug 10, 2020 at 9:02
  • $\begingroup$ Thanks Kurtosis! I just have one more question around this and it’s about the coefficients for the significant factors being SO low, I understand that the factors may better explain returns and indeed the r squared value goes from 5% with just the benchmark to 25% with the factors but the significant factor coefficients are 0.0085 and -0.0055 surely this shows barely any relationship at all yet the r squared is much higher? $\endgroup$
    – Simon Nicholls
    Aug 10, 2020 at 15:54

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