Carr and Wu approximated the variance swap rate with a combination of options and measured the variance risk premium as its difference from the realized variance observed afterward. Consider a hypothetical example in which the variance swap rate is 400 (20% in volatility terms) and realized variance is 256 (16%). The difference is 256 − 400 = −144. When the difference is negative, the seller of variance receives more than the buyer pays.
In that paper, using data from January 1996 to February 2003, the average for the S&P 500 index and others was strongly negative. This is the direction of a past average, however. In individual periods realized variance can exceed the implied level, and the seller can lose.