In https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true, it states that

3M VIX/SPX realized Beta calculation:

  • Use a blend of 1st, 2nd and 3 month VIX futures to calculate VIX 3M RVOL
  • Use level change instead of log return for VIX futures RVOL calculation
  • Use log returns for SPX 3M RVOL calculation
  • 3M VIX/SPX realized Beta = VIX 3M RVOL (based on level change)/SPX 3M IVOL (based on log return)

1) I dont see how the 1st and 2 month futures can be used to calculate 3M realised volatility?

2) Why use level change instead of log return?

3) Why use log returns to SPX though?

4) Why has we not times the numerator by VIX futures in my other question (linked)?

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